for of Recreation Hunting, Fishing

for of Recreation Hunting,  Fishing

The

Demand

for

& Value of

Hunting, Fishing and General

Rural Outdoor

Recreation in

Arizona

Technical

Bulletin

211

Agricultural

Experiment Station

The

University of Arizona

Tucson

The

Demand

for

&

Value of

Hunting, Fishing and General Rural Outdoor Recreation in Arizona

BY

WILLIAM

E.

MARTIN*

**

RUSSELL

L.

GUM

*

**

ARTHUR

H.

SMITH

THE

AGRICULTURAL EXPERIMENT

STATION

UNIVERSITY

OF

ARIZONA

TUCSON, ARIZONA

TECHNICAL BULLETIN

211

4

-M

*

Professor of Agricultural Economics.

** Associate Professor of

Hydrology and

Water Resources.

** Formerly Assistant Professor of Agricultural Economics.

JUNE 1974

ACKNOWLEDGMENTS

The authors owe special thanks to many members of the Arizona Game and Fish Department for their cooperation in connection with this study. Mr.

Robert

A.

Jantzen, Director, Mr.

Thomas Taylor, Federal

Aid Coordinator, and Mr.

John

N.

Carr,

Natural Resources Planner, were especially helpful.

The research reported here was supported by the

Arizona Game and Fish Department under the provisions of the Federal Aid in

Wildlife Restoration

Act,

Project FW

Conversations with Professor David King of the

Department of

Watershed Management at the

University of

Arizona have been helpful throughout the period of this project.

Many thanks to Mrs.

Donna Moore for typing the many manuscript drafts as well as producing the camera ready copy for this bulletin. ii

TABLE

OF

CONTENTS

LIST OF TABLES

LIST OF FIGURES

FOREWORD

Background and Purpose

Summary of Values

ESTIMATING THE VALUE OF OUTDOOR RECREATION

Economic Demand

Conventional Demand Curves

Economic Demand for Recreation

Estimating Demand for

Outdoor Recreation

Economic Value

Consumers' Surplus Value

Nondiscriminating Monopolist Value

VALUES

FOR HUNTING, FISHING AND

GENERAL RURAL OUTDOOR RECREATION

IN

ARIZONA

FOR

1970

Resource Areas

Consumer Surplus Values

Nondiscriminating Monopolist

Values

RESOURCE VALUES

IN

ALTERNATIVE USES

The Value of Surface Area in Alternative Recreation

Uses

A Few Rough Comparisons

APPENDIX

A

-

DETAILS OF THE

ESTIMATION PROCESS

Research Design

The

Questionnaire

Response and Response Bias

Results of the

Statistical Analysis

Evaluating the Resource

APPENDIX

B

-

RELIABILITY

OF THE VALUE

ESTIMATES

APPENDIX

C -

VALUES COMPARED

TO

GROSS EXPENDITURES

REFERENCES

iii

1

1

1

2

2

3

3

4

Page iv vi vi i vii viii

38

38

40

52

54

55

37

37

37

7

9

6

6

31

31

34

LIST OF TABLES

Table

No.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

Prices and Quantities for Statistical Demand (Hypothetical)

Values for Total Quantity of Visits and Added Costs (Hypothetical)

Consumer Surplus Values Generated in

1970, by Activity and Arizona Game and Fish

Department Regions

Nondiscriminating Monopolist Values, by

Activity and Arizona Game and Fish

Department Regions, 1970

Estimates of Resource Values for Use in

Deer Hunting at

Alternative Added

Costs, by Game and

Fish

Regions, 1970

The Value of Deer Hunting in

Arizona at

Alternative Added Costs, 1970

Estimates of Resource Values for

Use in

Big Game Hunting at

Alternative

Added Costs, by Game and Fish Regions, 1970

The Value of Big Game Hunting in

Arizona at Alternative Added Costs, 1970

Estimates of Resource Values for Use in Small Game Hunting at Alternative

Added Costs, by

Game and Fish Regions, 1970

The Value of Small Game Hunting in

Arizona at

Alternative Added Costs, 1970

Estimates of Resource Values for Use in

Waterfowl Hunting at Alternative

Added Costs, by Game and

Fish

Regions, 1970

The Value of Waterfowl Hunting in

Arizona at

Alternative Added Costs, 1970

Estimates of Resource Values for Use in General Hunting at

Alternative

Added Costs, by Game and Fish

Regions, 1970

The Value of General Hunting in

Arizona at

Alternative Added Costs, 1970

Estimates of Resource Values for

Use in

Cold Water Fishing at

Alternative

Added Costs, by Game and Fish Regions, 1970

The Value of Cold

Water Fishing in

Arizona at

Alternative Added

Costs, 1970

Estimates of Resource Values for

Use in

Warm Water Fishing at

Alternative

Added Costs, by Game and Fish

Regions, 1970

The Value of Warm Water Fishing in

Arizona at Alternative Added Costs, 1970

Estimates of Resource Values for

Use in

General Rural Outdoor Recreation at

Alternative Added Costs, by Game and Fish Regions, 1970

The Value of General

Rural

Outdoor Recreation in

Arizona at

Alternative

Added Costs, 1970

Surface Area of Arizona Available for

Rural

Outdoor Recreation Activities, by Region and Activity, 1970

Values of Surface Area Available for Rural Outdoor Recreation in

Arizona, by Region and Activity, 1970

Comparison of Cattle Ranching, Deer Hunting and Other Big Game Hunting Values for a

Section of Land in

Six Different Cattle Producing Areas in

Arizona,

1970 iv

Page

3

4

16

18

18

20

20

21

7

9

11

14

27

30

32

33

21

22

22

24

25

27

35

LIST OF TABLES (coNT'D)

Table

No.

24.

25.

26.

Variables Included in

Each of 14

Equations Fit to the

Data on

Each

Activity in

Each Region

Regression Coefficients, "t"

Values, Number of

Observations and R2's for the

Statistical Demand Equations

Nondiscriminating Monopolist and

Consumer Surplus Values Compared to

Actual

Variable Expenditures, by Activity, Arizona, 1970

Page

39

42

54

I/

LIST OF FIGURES

Figure

No.

1.

Typical Linear Demand Curve (Hypothetical)

2.

3.

4.

5.

6.

7.

8.

Demand Curve for the Total Recreation Experience (Hypothetical)

Demand Curve for the Resource (Hypothetical)

Relationship Between Demand and

Maximum

Total Revenue Generated by the

Optimum

Price

Arizona

Game and Fish Department Regions, 1970

Arizona Game and Fish

Department

Game Management Units, 1970

Map of the Counties of Arizona

Ranching Areas in

Arizona

Page

1

3

4

5

6

6

6

36 vi

FOREWORD

BACKGROUND

AND PURPOSE

In early 1971, the Arizona

Game and Fish Depart- ment authorized a survey of hunting and fishing with- in the state covering the year 1970, having the gen- eral objective of determining the total economic value of benefits assignable to fish and wildlife in

Arizona. Three previous surveys [Armstrong, 1958;

Davis, 1962; and 1967] concentrated on estimating expenditures and participation by hunters and fisher- men, generally following what is termed the "gross expenditure" approach to estimation of the economic value of the activities. of the recreation opportunity which measures the real monetary value that would be lost if the recreation opportunity were not available. The gross expendi- ture figures in themselves do not measure this. They tell us the magnitude of the industry, in one sense, but they do not indicate the value of the losses that would be sustained if the particular recreation op- portunity were to disappear, or the value of the net gain from an increase in a particular recreation opportunity.

The gross expenditure method attempts to measure the value of recreation to the community in terms of the total amount spent on recreation by the partici- pant.1/

This method has been used in the past by many agencies throughout the country, particularly by state resource departments, and by travel depart- ments and tourist promotion agencies. The contention of these departments and agencies has been that the value of a day's recreation must be worth at least the amount of money spent by a person for that pur- pose. Such expenditures have included travel ex- penses; expenses for equipment such as boats, motors, and tackle; and expenses incurred while in the recre- ation area. Estimates of gross recreation expendi- tures still are very popular in many quarters.

Such estimates are easy to understand and are likely to yield large figures, which give the impression of a large and profitable tourist- recreation business. for

In this fourth report, the gross expenditure approach is abandoned. Instead, estimates of con- sumer benefits for hunting, fishing and general rural outdoor recreation that are consistent with current concepts recreation activities are developed. The user benefit method estimation that of an in the is estimation employed of economic demand starts with economic demand curve expressing demand for the whole recreation experience.

Because expenditure data are used in the procedure, the method bears a superficial resemblance to the gross expenditure method. Each approach depends on infor- mation on expenditures by recreationists- -money spent for travel, meals, lodging, equipment, etc.

Since it was necessary to gather the expenditure data, those data are reported in a companion report entitled Participation and Expenditures for Hunting,

Fishing and General Rural Outdoor Recreation in

Arizona, Arizona Agricultural Experiment Station

Research Report

No. 270

[Gum, et al., 1973]. the

Indeed, these values are of some use in indi- cating the amount of money spent on a particular type of outdoor recreation, although it must be recognized that they represent expenditures for many goods and services, some in the year under study but some in previous years.

The figures also have some utility in establishing the income effects of recreation on residents in the area, and therefore in determining the effects of local investments for this purpose.

But they are of little or no consequence for justi- fying public expenditure on recreation, or for deter- mining the worth or benefit of recreation opportuni- ties afforded.

What is needed value added by a is not some gross value but the particular recreation opportunity.

It is the net increase in the value of the resource produced by using the resource for recreation that is crucial; this represents a true net yield that can be compared with what the resource would yield if it were in an alternative use producing other services.

It is the margin above the cost of taking advantage

In the previous three studies, information was developed pertaining to the participation and ex- penditure of only licensed sportsmen in hunting and fishing activities. Yet, it has been recognized that persons other than licensed sportsmen partici- pate and spend monies for hunting and fishing. For example, the wife and young family of a licensed fisherman may accompany him on a fishing trip, and while they may not fish, they are making additional expenditures.

In some sense, they are equal parti- cipants on the trip.

Without their presence, it is possible that the fishing trip may not have been made by the licensed sportsman at all.

Such a com- bination purpose trip is often true for fishing, true to a lesser extent for hunting trips, and is generally true for other types of rural outdoor recreation.

If only the expenditure of licensed sportsmen is recorded, there will be underestimation of the actual expenditures that hunting and fishing trips induce.

1/

This explanation economic value of ences on the economics of gross expenditures versus heavily paraphrases two basic refer- and Clawson and Knetsch

[1966].

Clawson

[1959]

After reviewing the 1970 outdoor recreation data, the authors were convinced that the family is the decision making unit and that the household is the more valid and meaningful recreation unit to analyze than is the licensed sportsman. The decisior to recreate in a particular activity in the lakes, streams, woods and deserts of Arizona is made by individuals within a household setting. The various interests, available time and resources of each vii

household member within the household setting leads to an individual or joint decision, either explicit- ly or implicitly. For example, the decision of a licensed small game hunter to go dove hunting one

Saturday morning, by himself, is still made within the context of the alternatives, time and income available to him and his family.

Another small game hunter may only make the same trip if he can take one or more of the non family members along.

Thus, the emphasis in this report is on the demand for and value of a recreation area and activity to a household.

The decision to study the recreational activi- ties of households rather than licensed sportsmen allowed the possibility of expanding the number of rural outdoor recreational activities which could be researched. Therefore, rather than sampling from a population list made from duplicate fish and game licenses, a more general population list was chosen.

The 1970 Arizona automobile registration list re- duced to a household basis was used under the assum- ption that a family needed a passenger vehicle in order to recreate in the rural outdoors. The tech- nical aspects of how the sample of residents was drawn are described fully in

Appendix

A. almost 1,000 nonresident households in the spring of

1971.

Usable replies were secured from 2,985 resi- dents and 235 nonresidents. Information was obtained on each of five hunting activities, two fishing ac- tivities, and on general rural outdoor recreation in each of the seven 1970 Arizona Game and Fish Depart- ment Regions in the state.

The activities are cold water fishing (trout), warm water fishing

(bass, cat- fish, etc.), deer hunting, other big game hunting

(antelope, bear, bighorn sheep, elk, javalina, tur- key), small game hunting

(squirrel, rabbit, quail, dove), general hunting (predatory animals, i.e., foxes, coyotes, etc.), waterfowl hunting

(ducks and geese), and general rural outdoor recreation.

General rural outdoor recreation includes day picnicking, overnight camping, hiking, swimming, boating, water skiing, birdwatching and snow skiing.

These eight general recreation activities make use of the same land and water resources of the state as do hunting and fishing. They are either complemen- tary, supplementary or competing uses to the re- sources involved with hunting and fishing activities.

The procedure for estimating economic demand functions is not easily adaptable to include demand by nonresidents of the state. Therefore, to the ex- tent that nonresidents participated in hunting, fish- ing and general rural outdoor recreation in

Arizona in 1970, the value of the resources devoted to these activities are underestimated. Expenditures and par ticipation in hunting and fishing activities in

Ari- zona by nonresidents is reported by Gum, et al.,

[1973].

Thus, this bulletin reports estimates of demand for and the value of eight hunting, fishing, and general rural outdoor recreation activities in each of the seven 1970 Regions in Arizona.

The report first outlines the conceptual framework for estima- ting the value of recreation, then presents the es- timates of value for Arizona, and finally puts these values in context by making some comparisons with the values of the same natural resource areas when used in nonrecreational activities. Technical details of the estimation process, including problems of response bias, are reserved for

Appendix

A.

The general method employed in this current study of the demand for and the value of the re- sources areas when used in various recreational ac- tivities is the

Clawson

[1959,

1949]. This method has been modified and improved over time by many researchers. An example of one of the pioneering efforts in the field is the study of the

Oregon Salmon and Steelhead sport fishery by

Brown, Singh and Castle

[1964].

Brown and Nawas

[1972] recently showed how estimates of value could be significantly improved over the traditional ap- proach by using observations on individual recre- ators rather than averaging individual observations within residence zones. This reported research on rural outdoor recreation throughout Arizona gave the opportunity to use a large number of individual ob- servations, as did Brown and Nawas. In addition, by focusing on all types of rural outdoor recreation activities in all regions of the state, it was possi- ble to include the prices of substitute recreation attractions as variables in the estimated demand equations.

To the authors' knowledge, this is the first time that substitute attractions have been in- cluded as an integral part of the demand estimation process.2/

The data were gathered from questionnaires mailed to nearly 15,000 resident households and

SUMMARY OF

VALUES

The total net benefit3/ (consumer surplus value) for the state for all hunting in all regions in 1970 was $34,480,315. Small game hunting was almost half of this total with $15,651,167. Deer and other big game hunting generated most of the balance of value, with general hunting generating $901,749 and water- fowl hunting generating almost

$600,000.

2/

Boyet and Tolley [1966] briefly mention esti- mates of cross elasticities between visits to major national parks, using aggregative secondary data with distances serving as the surrogates for the costs of visiting alternative sites.

3/

The term "total net benefit" is used to de- scribe the consumers' surplus value in order to dis- tinguish these values from "Bross expenditures

".

The benefits are net to the consumer, above their costs of participation. The benefits are not, how- ever, net of production and maintenance costs- which are borne by the producer and not passed on to the consumer as a cost of participation. viii

The total net benefit for fishing was

$64,374,326, almost twice that for hunting.

Warm water fishing generated $34 million while cold water fishing generated $30 million.

The greatest value for cold water fishing is in the White Mountain area of

Region

1.

The greatest warm water value was generated in the larger Central Arizona lakes of

Region

5.

All general rural outdoor recreation activities generated over $144 million in consumer surplus, about 60 percent of the state grand total for all hunting, fishing and other rural outdoor recreation. taken in 1970. The nondiscriminating monopolist values show the maximum total revenue that could have been collected if the optimum entry fee were charged for every participant household -trip. As- sociated with the price of the optimum entry fee and the nondiscriminating monopolistic value is the number of have been taken at that price. The state total for the value of hunting, using the nondiscriminating monopolist pro- cedure, was $13,885,814. The value for fishing was

$30,057,922 while the value for general rural out- door recreation was $91,582,973.

Values were also estimated using the criminating monopolist approach. The nondis- consumer sur- plus approach shows the total net benefit to the consumers generated by a particular activity, as- suming a zero entry fee and the number of trips

When total values were converted to values per square mile of huntable range and values per surface acre of water, it was found that the values to the natural resources when used for recreation purposes were quite comparable to values of the same resource when used for purposes such as cattle ranching or irrigation water. ix

ESTIMATING THE VALUE OF

OUTDOOR RECREATION

That outdoor recreation has "value" is a fact that most people will admit.

It is the size of this

"value" that remains in question.

The problem is that outdoor recreation is not bought and sold in the open market as are most other goods that have

Some people argue that outdoor recreation is of such a high value it is priceless. Until recently, many planners and administrators have shared this view and have been unwilling to include measures of the monetary value of outdoor recreation in the man- agement decisions that affect resource use.

They felt that recreation value defies any type of measure- ment although persons appreciative of outdoor recre- ation felt the value Still others argue that any positive monetary value such as the current recommendations of the

Water Resources

Council's

[1973] rather arbitrary value of

$3.00 to

$9.00 per user day for specialized purposes such as big game hunting is as reasonable as any other value. incur, otherwise they would not be acting rationally in incurring the expense. With a market com- modity, the price that is paid in the market

(along with the cost of time and effort a person spends getting to the market) regulates the amount that a person purchases of a product. Likewise, the money and distance

(time) costs of a recreational activity will determine the amount of vidual recreators, and the received must be people are at willing to participation of indi- satisfaction

(utility) least equal incur. to the cost the

In order to construct demand estimates for out- door recreation that approximate those for priced goods, it is essential that an appropriate money If these costs can be defined, then it is possible to derive statisti- cal demand estimates that are equivalent to market priced commodities. Conventional demand schedules, whether they be theoretical or empirical, relate alternative quantities that would be purchased to alternative market prices at a given point in time.

Concomitant with the confusion and disagreements over both the magnitude and measurability of the value of outdoor recreation there exists a need by those involved in making decisions concerning outdoor recreation development and management for realistic and acceptable measures of outdoor recreation value.

For instance, in a decision as to the desirability of building campground facilities, a monetary measure of the value of the development is often necessary to justify its construction. Certainly any funds used to support outdoor recreation activities could have been spent for other purposes. If the "other purpose" has a value, one needs to know the value of the recre- ational activity in order to make a rational choice in allocating the funds.

The basic principle of demand is that the quan- tity demanded varies inversely with the per unit price. At a high price, a relatively small quantity will be demanded. At a lower price, more of the commodity will be taken.

A typical linear demand curve would look as shown in

Figure

1.

If one accepts Thorndike's dictum "Whatever exists at all, exists in some amount" [Thorndike,

1918], one must believe that the value of outdoor recreation is some definable quantity. The task then becomes one of first setting a theoretical framework for the economic value of outdoor recreation and second, developing and implementing a method to mea- sure that value.

ECONOMIC DEMAND

Conventional Demand Curves

Economic values are measured by what people are willing to give up in order to enjoy possession of a good or service. This explanation of value is con- ceptually the same for an outdoor recreation experi- ence as it is for any other good or service except that most outdoor recreation goods lack a formal market- price. Consumers of any economic goods must receive satisfaction

(utility) that is at least equal to the price that they are willing to

Quantity of

Commodity "A"

FIGURE

1.

TYPICAL LINEAR DEMAND CURVE (HYPOTHETICAL

1

If all other things are held constant, a change in price for commodity

"A" would cause a change in the quantity of commodity

"A" as described by the demand curve in Figure

1.

Changes in the factors other than the price of the commodity in question may cause a complete shift in the demand curve either to the right or left of the current demand curve. A shift to the right of the current position of the demand curve would indicate an increase in demand.

Demand shifters include changes in income, population, the prices of other competing or complementary com- modities, consumer tastes and preferences, and the time and effort involved in purchasing the product. purchase of certain items of a fixed nature such as camping equipment, a recreation vehicle, or other special sporting equipment. These expenditures on items which may be used for more than one trip and in more than one time period, are traditionally called fixed costs.

Once these costs have been incurred, they are not affected by the decision to actually participate in a particular recreation activity. Because they are unaffected by a short participation decision, they, in turn, do not themselves affect the short run decision.

Economic Demand

Recreation demand is simply a modification of conventional consumer demand. The basic notion of the relationship between price and quantity remains unchanged. for

Recreation

The second decision that the individual must face is of a short

Here, within a given period of time, the individual must decide what form of recreation in which he will participate and at what site.

In this case, the important con- siderations are time, travel costs, and any addi-

-site costs that would not have been in- curred had the individual remained at home. The travel costs and any additional expenditures are called variable costs

(the costs affected by the decision to recreate) and are the perti- nent costs for the surrogate price.

For recreation demand, the quantity variable is usually in terms of use.

The use of recreation areas can be measured by such things as visits, trips, or user The concept of the use of a recreation site is only part of what Clawson

[1959, 1966] calls the whole recreation experience. The whole experi- ence includes anticipation and preparation for the trip, travel to the site, the actual on ence, travel back from the site, and recollection of the experience. Clawson maintains that all five phases are present in every major outdoor recreation activity.

It is difficult to separate one part from the others and as statisticians, we measure what people do in terms of the total recreation experience consumed and the costs involved.

The use of price is mating the variable costs as the surrogate analogous to

-run decisions made by a business firm. Economic analysis shows that marginal costs (additional costs) are a function only of the variable costs and that the marginal costs are the decision varia- bles.

The short how much to produce is not affected by the fixed costs. In the same way, only the variable costs are pertinent in esti- short

The major difference between the demand for recreation and ordinary market is that of defining prices. In the conventional type of demand, the by a price of the commodity is established functioning market mechanism wherein the equi- librium price occurs at the point where supply is equated with demand. In contrast, most forms of out- door recreation have no conventional market mechanism.

Alternative quantities of recreation are not offered for sale at alternative prices. Consumer prices are either totally absent or set by administrative fiat.

Estimating Demand for Outdoor Recreation

Estimation of demand for the use of a particu- lar outdoor recreation activity at a particular site or in á particular area proceeds in two steps.

One first must estimate a statistical demand curve for the total recreation experience. Then, the demand curve for the recreation resource itself (for ex- ample, the use of a particular area for hunting deer), is derived by relating posited added costs

(e.g., alternative levels of entrance fees) to the number of visits made to the area for the particular purpose.

Wennergren

[1967], in exploring the early work of

Clawson, examined the problem of pricing outdoor recreation free good. and showed ation developed as a that non although outdoor recre- good, it is not a

There are time and money costs associated with the consumption of recreation which regulate the quantity of outdoor recreation taken. These money costs can be used as surrogate or substitute prices in determining demand functions for outdoor recre- ation with the time costs acting as demand shifters.

A problem arises in determining which costs are to be included as the surrogate price. There are two

-related decisions that a potential recreator must face.

First, there is the long to participate in some form of outdoor recreation. This

A simple example of the procedure, taken from

Clawson and

Knetsch

[1966] is presented below. The data needed in order to derive the demand for the whole recreation experience for this hypothetical example are listed in Table

1.

In this example, the costs from a particular area of residence to the recreation site

(for example, a game region) are assumed to be the same for every visitor from the same area of residence. The number of visits is put on the basis of per 1,000 population from the area of residence. By plotting costs from column

(3) against the corresponding number of visits per thou- sand population in column

(5), a statistical demand

2

TABLE

1.

PRICES AND

QUANTITIES

FOR

STATISTICAL

DEMAND (HYPOTHETICAL)

The resulting demand curve is in terms of added costs and total quantities of visitation.

Cost from

Area of

Number

Population Residence of Visits

Area of of Area of to Recre- Visits per 1,000

Residence Residence ation Site to

Site Population

1

2

3

1,000

4,000

10,000

$1.00

3.00

5.00

500

1,200

1,000

500

300

100

For example, in this study the statistical de- mand curve for the total experience of hunting deer in Region

7 is used to develop a demand curve that describes the alternative quantities of deer hunting trips that would be made to

Region

7 at alternative additional costs at alternative entry fee charges. Of course, access to the region for the activity is now free, and probably always will be, but we wish to know how much households would pay and participate if a fee were charged; that is, if participation in that activity in that region had a market price just as do most other economic goods or services.

2,700

Source: Clawson and Knetsch (1966).

The following example shows this second step.

The total quantity of visits made at the existing costs are 2,700 as shown in Table

1.

By adding in- crements of one dollar to each original cost, the corresponding projected quantity of visits can be determined in the following manner: curve for the total recreation experience can be determined. This curve is shown in Figure

2.

The second step in the analysis is that of de- veloping a demand curve for the resource site itself.

This demand curve is derived from the demand curve for the recreation experience based on the assumption that the resource users would react to changes in costs at the site in the same manner to which they react to costs for the recreation experience as a whole. In developing the demand curve for the re- source, the total projected number of visits is cal- culated at each posited increased interval of cost.

At the

$1 added cost per visit from distance zone

1, the number of visits per 1,000 population is determined from Figure

2 to be

400. In essence, at a cost of

$2 per visit, the number of visits per

1,000 from distance zone

1 is 400.

This figure is then converted to total visits at the $1 added cost in the following manner:

400

1,000

X 1,000 = 400

'

That is, at the $1 added cost, visits

1,000 pop.

X population of the distance zone

= total visits

This same process is repeated for each distance zone.

The total visits for each distance zone at the $1 added cost per visit are summed to establish one point on the demand curve for the resource itself.

This procedure is repeated for different added costs to arrive at a schedule as shown in Table

2.

The points of added cost and total visits as shown in

Figure

3, are points on the demand curve for the resource itself.

This curve shows the alternative number of visits that would be taken at alternative entry prices, if an entry fee were charged. It is this demand curve for the resource that is important in valuing the resource. Estimates of value may be made by two methods as described below.

100 200 300 400 500

600 700

Visits /1,000 Population

ECONOMIC VALUE

FIGURE

2.

DEMAND CURVE FOR

THE

TOTAL RECREATION

EXPERIENCE.

Source:

Clawson and Knetsch (1966).

Consumers' Surplus Value

Simply defined, consumers' surplus measures the surplus satisfaction that a consumer receives from a

3

TABLE

2.

VALUES

FOR

TOTAL QUANTITY OF VISITS AND

ADDED COSTS (HYPOTHETICAL).

Area of

Residence

1

2

3

500

1,200

1,000

0

Number of Visits at Added Cost Per

Visit of

$1.00 $2.00 $3.00 $4.00 $5.00

400

800

0

300 200 100

400

0

0

0

0

0

0

0

0

Total

Visits 2,700 1,200

700 200 100

0

Total

Revenue

Generated

0

$1,200 $1,400 $600 $400

Source: Clawson and

Knetsch (1966).

0

1,000

2,000

,000 commodity above the price that he actually paid for that commodity. The central idea behind consumers' surplus is that the consumer has in his mind a price that he would be willing to pay rather than to go without a certain commodity. The price that the per- son is willing to pay rather than go without must be greater than or equal to the price he actually does pay.

Since price is a measure of satisfaction, the difference in price that the individual is willing to pay and the price that he does pay is a measure of surplus satisfaction.

For example, looking at

Figure

3, it is seen that at least one person would be willing to pay as much as $5 to make a visit.

Other people would visit only if the price was less and finally 2,700 visits would be made if the price were zero. At a zero price, all persons who would have been willing to pay more than zero in order to make the visit would be receiving consumer surplus.

The total consumers' surplus value would be equal to the total area under the demand curve, that is, the sum of the surplus satisfaction generated by each visit.

Total Visits

FIGURE

3.

DEMAND CURVE FOR THE RESOURCE

(HYPOTHETICAL).

Source: Clawson and Knetsch (1966). price that individuals are willing to pay for a land area for use as a cattle ranch, but rarely, if ever, will have an estimate of the consumer surplus gener- ated by such use to compare with the consumer sur- plus generated by use of the Fame land for hunting,

Thus, the consumer surplus value is most useful as a monetary measure of the maximum net value that (for example) of hunting generates in area. For purposes comparison with other uses

'f the resource, it ts more useful to be able to assign a single price that is associated with the value estimate. For this reason, a second method of valuation is also used

Since there is essentially no entry fee for most hunting, fishing and other outdoor recreation acti- vities, the entire area under the demand curve for the site measures the quantity of consumer surplus value.

The consumer surplus value may be interpreted as the total net value of the resource site to the consumers when used for a particular purpose such as

(for example) deer hunting.

A disadvantage of the consumer surplus approach to valuation is that one usually will not have other consumer surplus values for the resource when used in alternative uses, with which to make comparisons. For example, we know the

Nondiscriminating Monopolist

'Value

The nondiscriminating monopolist method for de- termining resource values for outdoor recreation allows introduction of a single price.

This model assumes the existence of a single monopolistic owner of the resource. The rational monopolistic owner would want to charge the price for the resource that would maximize the total revenue from the resource.

He must select one single optimum price for the good since, as a practical matter, he cannot discriminate between consumers relative to the price he charges and charge each the maximum price that that

4

particular consumer would pay. (If he could do so, he could collect all of the consumer surplus.)

Figure

4 shows the relationship between demand

(D) and maximum total revenue

(TR) generated by the op- timum price

(P o

).

Maximum total revenue is the area of the largest rectangle that can be drawn under the demand curve and defines a particular price

(P0

) and associated quantity (Q

).

0

Maximum total revenue that portion of consumers' surplus that could be is extracted by an all powerful monopolist

(e.g.,

The

Arizona

Game and Fish Department) charging a single price. Using this method, the value of the resource is the maximum net revenue that could accrue to an agency by charging a given fee.

Note that we are not suggesting that such a fee be charged. The method is simply a way of obtaining a price and value that can be compared to values of the basic resource in alternative uses.

In the following section, we present estimates of consumer surplus values and nondiscriminating monopolist values for eight rural outdoor recreation activities in the seven

Arizona Game and Fish De- partment Regions in

Arizona.4/ These values are compared to the estimates of gross expenditures ac- tually generated by these activities in 1970 in

Appendix

B.

Q0

Quantity of

Commodity

"A"

4/

The seven regions existent in 1970 have since been consolidated into six regions. Since the data were gathered on the basis of 1970 conditions, however, the 1970 regions are used herein.

FIGURE

4.

RELATIONSHIP BETWEEN DEMAND AND MAXIMUM

TOTAL REVENUE GENERATED

BY THE

OPTIMUM

PRICE.

5

VALUES

FOR

HUNTING,

OUTDOOR

FISHING

AND GENERAL RURAL

RECREATION

IN

ARIZONA

FOR

1970

RESOURCE AREAS

The seven 1970 Arizona Game and Fish Department

Regions are shown in

Figure

5.

Data were originally gathered relative to the smaller Game Management

Units shown in Figure

6.

Demand curves and resource values were estimated only for the Regions, however, since even with observations on 2,985 recreators, data were too sparse to make estimates on the smaller

Units.

Even using the larger Regions, with

7

Regions and

8 activities, 56 statistical demand estimates were required. Region boundaries are not always precisely congruent with the sum of several smaller

Units, therefore, some judgment was necessary in aggregating Unit data into data on Regions.

Figure

7 shows the 14

Arizona counties, also for comparison with the

7

Game and Fish Department

Regions. These

14 counties were used as the areas of residence for purposes of population sampling as explained in detail in

Appendix

A.

Details of the empirical estimation process are also in Appendix

A.

FIGURE

6.

ARIZONA GAME AND FISH DEPARTMENT GAME

MANAGEMENT

UNITS, 1970.

---1--T-- i

I i i i

'

MOHAVE i i

'APACHE i

COCONINO

,

/

(

\

)

ÑG

J

L.

}

A

I

,

JEROM

CAYG

VEVE i I.

,/ti

PRESCÓTT

`/-

YAVAPAI f

!

P}

F.-----1.----\

YW

G

¡ i

YUMA i

I

I

I

I i

\'

SELIGNAN

MARICOPA

GILÁ

BEND

I

PNOENIx

--j

PINAL

-

FLAGSTAFF

GIDBE

!_.I

\ i

I

FLORENCEV

NAVAJO

I

NDLBROOK

GILA FT

'j

I

I-_.

I

I

I

WNlT'

VILLE

RIVER

\

I

R-I

I

APMCNE,-)

_.1{ i GRAHAM

SAFFORO i i

BLUÉi

J w

WI

----1 i

TUCSON i

PIMA

¡BENSON

I

COCHISE

FsANTA

CRUZ

I

\,.ANOGALES

.-.-.-.-I

FIGURE

5.

ARIZONA

GAME AND FISH

DEPARTMENT REGIONS,

1970.

FIGURE

7.

MAP OF THE COUNTIES OF ARIZONA.

6

CONSUMER SURPLUS

VALUES

Estimated values of consumer surplus generated by hunters, fishermen and general rural outdoor recreators are presented in Table

3 for each of the eight activities in each of the seven Game and Fish

Regions. The numbers of household trips made in 1970 that are associated with the consumer surplus value are also shown.

The value for the state for all hunting in all regions was $34,480,315. Small game hunting was al- most half of this total with

$15,651,167.

Deer and other big game hunting generated most of the balance of value, with general hunting generating $901,749 and waterfowl hunting generating almost $600,000. water fishing generated $34 million while cold water fishing generated $30 million.

The greatest value for cold water fishing is in the

White Mountain area of

Region

1.

The greatest warm water value was gen- erated in the larger Central

Arizona lakes of

Region

5.

All general rural outdoor recreation activities generated over $144 million in consumer surplus, about 60 percent of the state grand total for all hunting, fishing and other rural outdoor recreation.

Also shown are the average consumer surplus eight recreation activities.

These values range from a high of $66.54 per general rural outdoor

The total net benefits for fishing was

$64,374,326, almost twice that for hunting.

Warm boating) down to

$6.39 per household for gen- eral hunting.

TABLE

3.

CONSUMER SURPLUS VALUES GENERATED IN 1970,

BY ACTIVITY AND ARIZONA GAME AND FISH

REGION.

TABLE

3.

(CONTINUED)

Activity and

Region

Trips Made in

1970

Deer Hunting

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State Total

24,250

65,871

12,718

7,582

31,959

38,304

32,128

212,812

Other Big Game

Hunting

Region

1

Region

2

Region

3

Region

Region

Region

Region

4

5

6

7

State Total

21,087

24,377

777

545

25,919

22,944

10,571

106,220

Consumer

Surplus

Value

($)

739,460

5,200,161

359,546

453,452

514,352

2,062,223

1,917,056

11,246,250

1,883,041

1,038,362

44,623a

31,299a

2,108,559

717,030

277,353

6,100,267

Average

Consumer

Surplus

Per Trip

($)

52.85

57.43

Activity and

Region

Small Game

Hunting

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State Total

Trips

.,dde in

1970

14,097

29,163

14,156

70,283

264,832

176,962

85,516

655,009

Waterfowl

Hunting

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State Total

4,192

4,648

4,061

17,633

7,725

12,015

8,566

58,840

Consumer

Surplus

Value

($)

103,699

512,806

175,483

1,494,521

6,981,756

4,314,587

2,068,315

15,651,167

51,858

28,217

40,082a

151,941

76,246a

118,588a

113,950

580,882

Average

Consumer

Surplus

Per Trip

($)

23.89

9.87 a

Consumer surplus for this activity in this region computed indirectly as the average value per trip for all other regions for this activity.

Consumer surplus for all activities and regions not footnoted was computed directly from the relevant second function.

Indirect computation was those cases where a reliable statistical demand curve could not be estimated. necessary in

7

NONDISCRIMINATING MONOPOLIST

VALUES

Estimates of the nondiscriminating monopolist values for each region and activity, along with the prices that would create the value are summarized in

Table

4.

These values range from about one fourth to corresponding consumer surplus values. Recall that the consumer surplus values shówed the total net benefit to the consumers generated by the Region when used for a particular activity, assuming a zero entry fee and the number of trips taken in 1970.

These nondiscriminating mo- nopolist values show the maximum total revenue that could have been collected if the optimum entry fee were charged for every household into the

Region for this particular purpose. Associated with the price of the optimum entry fee and the nondis- criminating monopolistic value is the number of household trips that would have been taken at that price. The associated number of trips are shown in the detailed tables that follow.

These monopolist values represent the amount of surplus satisfaction that could be extracted by an all powerful monopolist charging a single price to all consumers.

However, even a monopolist could not extract an amount equal to the total value of consumers' surplus.

To do so, one would have to charge each consumer the maximum price that he would be willing to pay.

Therefore, nondiscriminating monopolist values are lower than consumers' surplus value.

The state total for the nondiscriminating monopolist value for fishing was more than twice the total for hunting, whereas, the consumer surplus value for fishing was somewhat less than twice the hunting value.

The general rural outdoor recreation monopolist value is about 50 percent of the state grand total for all rural outdoor recreation activity including hunting and fishing.

TABLE

4.

NONDISCRIMINATING MONOPOLIST VALUES, BY

ACTIVITY AND ARIZONA GAME AND FISH REGION,

1970.

TABLE

4.

(CONTINUED)

Activity and

Region

Nondiscriminating

Monopolist

Price

($)

Nondiscriminating

Monopolist

Value

($)

Activity and

Region

Nondiscriminating

Monopolist

Price

($)

Nondiscriminating

Monopolist

Value

($)

Deer Hunting,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

35

60

45

60

15

100

120

60

343,934

1,433,769

159,394

171,813

157,037

1,014,809

805,902

3,717,064a

Small Game

Hunting,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

15

45

20

45

50

35

45

35

45,185

215,256

89,846

756,155

3,868,521

2,559,916

1,055,389

7,752,495a

Other Big Game

Hunting,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

70

50

130

40

60

40

479,857

465,367 b b

1,202,048

368,744

108,543

Waterfowl

Hunting,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

25

10

20

20

20

24,005

11,114 b

56,499 b b

47,224

State

2,034,966a

State

127,412a a

The nondiscriminating monopol ist value for the state for a particular activity is less than the sum of the values for each region for that activity (see text, page 14). b

Value could not be estimated because of too few observations to develop the statistical demand function.

The value can be assumed to be relatively small compared to the other regions which are more heavily used for the particular activity.

9

TABLE

3.

(CONTINUED)

CONSUMER SURPLUS VALUES.

Activity and

Region

Trips Made in

1970

General

Hunting

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State Total

7,261

20,962

4,982

13,196

50,951

31,794

11,912

141,058

STATE TOTAL,

ALL

HUNTING 1,173,939

Cold

Water

Fishing

Region

1

Region

2

Region

3

279,050

179,869

38,792

Region

4

Region

5

Region

6

Region

7

1,633

44,003

31,579

28,417

State Total 603,343

Warm Water

Fishing

Region

1

Region

2

20,503

32,959

Region

3

Region

4

Region

5

55,347

83,284

405,535

20,503 Region

6

Region

7

125,138

State Total 743,269

STATE TOTAL,

ALL FISHING

1,346,612

Consumer

Surplus

Value

($)

95,537

49,089

20,826

84,322a

353,634

183,014

115,327

901,749

34,480,315

21,058,930

5,016,989

1,625,167

81,862a

865,388

728,385

867,756

30,244,477

1,279,614

664,687

6,623,530

1,719,646

21,405,617

274,678

2,162,077

34,129,849

64,374,326

Average

Consumer

Surplus

Per Trip

($)

6.39

50.13

45.92

TABLE

3.

(CONTINUED) CONSUMER SURPLUS VALUES.

Activity and Trips Made

Region in

1970

General Rural

Outdoor

Recreation

Region

1

Region

2

224,943

464,093

Region

3

Region

4

Region

5

95,174

103,890

737,094

599,533

Region

6

Region

7

160,106

State Total

2,384,833

STATE GRAND

TOTAL, ALL

ACTIVITIES 4,905,384

Consumer

Surplus

Value

($)

30,765,878

55,856,978

4,885,540

3,807,327

28,493,414

14,907,480

5,665,300

144,381,917

243,236,558

Average

Consumer

Surplus

Per Trip

($)

66.54 a

Consumer surplus for this activity in this region computed indirectly as the average value per trip for all other regions for this activity.

Con- sumer surplus for all activities and regions not footnoted was computed directly from the relevant second

Indirect computation was necessary in those cases where a reliable sta- tistical demand curve could not be estimated.

8

STATE TOTAL,

ALL

HUNTING

Cold

Water

Fishing,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

Warm Water

Fishing,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

STATE TOTAL,

ALL FISHING

TABLE

4.

(

CONT'D) NONDISCRIMINATING MONOPOLIST

VALUES.

Activity and

Region

General

Hunting,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

TABLE

4.

Nondiscriminating

Monopolist

Price

($)

Nondiscriminating

Monopolist

Value

($)

Activity and

Region

20

10

5

15

5

25

5 c

47,466

19,454

7,120 b

117,069

76,529

47,071

253,877a

13,885,814

General Rural

Outdoor Recreation,

Region

1

Region

2

Region

3

Region

4

Region

5

Region

6

Region

7

State

(CONT'D)

NONDISCRIMINATING MONOPOLIST

VALUES.

Nondiscriminating

Monopolist

STATE GRAND TOTAL,

ALL

ACTIVITIES

Price

($)

200

200

100

90

60

30

80

60 c

Nondiscriminating

Monopolist

Value

($)

19,368,992

32,946,847

2,928,689

2,138,720

16,514,449

10,474,190

2,751,233

47,639,237a

91,582,973

120

40

60

110

45

190

25

70

20

25

60

25

35

70

40 c

12,720,613

2,707,965

1,018,815 b

367,038

405,316

563,167

11,225,685a

751,539

411,927

4,719,628

1,065,400

13,499,751

127,397

1,066,849

18,832,237a

30,057,922 aThe nondiscriminating monopolist value for the state for a of the particular activity is less than the sum nondiscriminating monopolist values for each region for that activity (see text, page 14

). bValue could not be cNot applicable. estimated because of too few observations to develop the statistical demand function. The value can be assumed to be relatively small compared to the other regions which are more heavily used for the particular activity.

A better understanding of the contents of sum- mary Table

4 may be obtained by examining the de- tailed data of Tables

5 and

6 which focus only on deer hunting. Table

5 gives, by Region, all the alternative revenues that could have been obtained and the associated numbers of household that would have been made if alternative added costs

(entry fees) had been charged in

1970 above the deer hunter's actual variable costs of participation.

Table

6 sums the data of Table

5 across Regions to obtain the schedule of trips, prices and values for the whole state. Each of the schedules shown in

Tables

5 and

6 are the data from alternative points along the second activity in the given region as section on described in the previous conceptualization of recreation demand.

For example, examine the first section in Table

5 which gives the demand schedule for deer hunting

10

TABLE

5.

ESTIMATES OF RESOURCE VALUES FOR USE IN

DEER

HUNTING AT ALTERNATIVE ADDED COSTS,

BY GAME AND FISH REGIONS, 1970.

TABLE

5.

(CONTINUED)

24,250

20,176

17,484

14,722

13,186

12,083

11,089

9,826

8,420

6,357

5,925

4,063

1,466

220,833

263,724

302,095

332,673

343,934b

336,800

286,103

296,261

243,812

102,654

Activity and

Region

Added Cost

Per Trip

($)

10

15

20

35

40

45

50

Number of

Trips

65,871

60,305

55,955

51,660

47,419

43,234

39,104

35,029

31,959

29,684

Total

Revenue

($) Activity

Added

Cost and

Region

Per Trip

($)

Deer Hunting,

Region

1

0

5

10

15

20

25

30

35a

40

45

50

60

70

Number of

Trips

Total

Revenue

($)

0

100,880

174,845

Deer Hunting,

Region

2 0

5

25

30

60a

70

80

27,665

23,896

20,256

17,080

15,398

13,999

74 O

0

90

100 in Region

1.

In 1970, an estimated 24,250 household trips were made to

Region

1 for the purpose of hunting deer.

A certain amount of variable expense was associated with these trips, but there was no entry fee to the Region, therefore, added costs were zero. Had there been added costs of

$5 per house- hold as an entry fee or simply occurring for any other reason associated with making the trip, it is estimated that only 20,176 household made. If the added cost was in the form of a fee,

$100,880 would have been collected.

110

120

130

140

150

160

170

180

190

12,686

11,437

10,517

9,773

9,103

8,464

7,805

7,328

6,905

1,396,965

1,372,509

1,367,291

1,368,284

1,365,570

1,354,247

1,327,005

1,319,129

1,312,020

200 6,500

1,300,043 the

If higher levels of added cost had occurred, number of trips taken would have been less and 250

350

400

5,142

4,454

1,285,710 trip had occurred, no trips would have been taken.

Had the added cost been in the form of an entry fee total revenues could have been maximized at a price of $35 per trip even though the number of trips taken would have been less than at a lower price.

In this lower price range, demand for deer hunting in

Region

I is termed "inelastic increasing prices bring greater revenues even though less of the com- modity is sold; at prices of more than $35 per house- hold is

"elastic higher prices would cause fewer trips and lower revenues until trips and revenues would finally fall to zero. a

300

439

Nondiscriminating monopolist price for the activity in the region.

4,028

3,856

0

1,110,000

1,000,000

900,000

0 b

Nondiscriminating monopolist value for the activity in the region.

0

301,527

559,553

774,901

948,397

1,080,867

1,173,135

1,226,026

1,278,368

1,335,809

1,383,284

1,433,769b

1,417,987

1,366,413

1,385,870

1,399,959

11

TABLE

5.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

TABLE

5.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Deer Hunting,

Region

3

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45a

50

60

70

Number of

Trips

12,718

10,824

8,953

7,792

6,936

6,182

4,497

4,195

3,895

3,542

2,976

1,581

0

Total

Revenue

($)

The highest total revenue obtainable with its associated price is termed the nondiscriminating monopolist value of the resource and the nondiscrim-

mating

monopolist price, respectively.5/

The remaining sections of

Table

5 give analo- gous information about deer hunting in each of the other six Regions in the state. Note that the esti- mates of total revenue do not necessarily first rise and then fall in a smooth curve.

Rather, revenue may rise, then fall, and then rise and fall again one or more times before finally falling to zero.

For example, in Region

5, revenue rises smoothly to a monopolist value of $157,037 at an added cost of

$15. At an added cost of $20 total revenue falls to

$146,379 but, as price rises farther to $25, total revenue again rises to

$149,116, then falls and rises once more before declining to zero with a price of

$68.

0

54,124

89,535

116,893

138,739

154,557

134,911

146,841

155,824

159,394b

148,814

94,894

0

Activity and

Region

Deer Hunting,

Region

4

Added Cost

Per Trip

($)

0

5

10

70

80

90

100

110

120

130

140

150

160

170

180

190

200

241

15

20

25

30

35

40

45

50

60a

Number of

Trips

Total

Revenue

($) a

Nondiscriminating monopolist price for the activity in the region.

5/ Since estimates are recorded at minimum intervals of $5 of added cost rather than at smaller intervals, the absolute maximum revenue obtainable could be within a one or two dollar interval about the $35 price shown. Intervals shown are

$5 up to an added cost of $50, $10 intervals up to an added cost of $200 and $50 intervals thereafter. b

Nondiscriminating monopolist value for the activity in the region.

0

35,074

65,692

91,755

113,167

129,830

141,822

150,101

159,786

167,235

171,716

171,813b

168,419

167,135

158,807

147,678

139,739

127,098

117,427

110,697

101,348

89,306

74,498

56,498

36,290

15,634

0

7,582

7,014

6,569

6,117

5,658

5,193

4,727

4,288

3,994

3,716

3,434

2,863

2,405

2,089

1,764

1,476

1,270

1,059

903

790

675

558

438

315

191

78

0

12

TABLE

5.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Deer Hunting,

Region

5

Deer Hunting,

Region

6

Added Cost

Per Trip

($)

45

50

60

68

0

5

10

15a

20

25

30

35

40

30

35

40

45

50

60

70

80

90

100a

110

118

0

5

10

15

20

25

Number of

Trips

31,959

21,993

14,658

10,469

7,318

5,964

4,937

4,210

3,438

2,830

2,651

2,319

0

38,304

34,342

31,497

28,801

26,030

23,631

21,813

20,443

19,207

18,067

17,064

15,176

13,913

12,634

10,584

10,148

8,206

0

TABLE

5.

(CONT'D)

RESOURCE VALUES AT

ADDED COSTS.

ALTERNATIVE

Total

Revenue

($)

0

109,968

146,589

157,037b

146,379

149,116

148,114

147,381

137,526

127,359

132,590

139,179

0

0

171,710

314,971

432,024

520,603

590,776

654,413

715,539

768,284

813,057

853,214

910,577

973,945

1,010,753

952,630

1,014,809b

902,746

0

Activity and

Region

Deer Hunting,

Region

7

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45

50

60

70

80

90

100

110

120a

130

140

150

160

161 a

Number of

Trips

32,128

29,231

27,033

24,828

22,797

20,848

18,982

17,200

15,705

14,590

13,666

12,050

10,471

9,284

8,312

7,634

7,036

6,715

6,006

5,260

3,566

241

0

Total

Revenue

($)

0

146,157

270,338

372,431

455,945

521,216

569,487

602,010

628,235

656,561

683,344

723,020

732,989

742,761

748,146

763,470

773,997

805,902b

780,789

736,494

534,939

38,580

0

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

13

TABLE

6.

THE VALUE OF DEER HUNTING

IN

ARIZONA

AT

ALTERNATIVE ADDED COSTS, 1970.

Added

Cost per Trip

($)

Number of

Trips

212,812

183,885

162,149

144,389

129,344

117,135

105,149

95,191

86,618

15,823

13,344

9,263

8,484

7,643

7,096

6,578

5,142

4,454

78,786

73,381

61,948

48,511

41,087

36,058

33,257

29,198

19,211

17,426

4,028

3,856

0

0

5

10

15

20

25

30

140

150

160

170

180

190

200

250

300

350

400

439

90

100

110

120

130

35

40

45

50

60a

70

80

Regions

Included at the

Given

Added Cost

All

All

All

All

All

All

All

All

All

All

All

All

1, 2, 4, 6,

2, 4, 6, 7

2, 4, 6, 7

2, 4, 6, 7

2, 4, 6, 7

2, 4, 7

2, 4, 7

2, 4, 7

2.,

4, 7

2, 4, 7

2, 4

2, 4

2, 4

2, 4

2

2

2

2 none

Total

Revenue

($)

0

919,440

1,621,523

2,165,874

2,586,954

2,928,947

3,154,555

3,331,832

3,464,823

3,545,518

3,669,223

3,717,064b

3,395,994

3,287,062

3,245,453

3,325,916

3,213,447

2,305,509

2,265,507

2,215,475

2,001,857

1,482,133

1,401,503

1,375,979

1,348,310

1,315,677

1,285,710

1,110,000

1,000,000

900,000

0 a

Nondiscriminating monopolist price for deer hunting in the state. b

Nondiscriminating monopolist value for deer hunting in the state.

The explanation is that at certain levels of price, large blocks of households would cease making trips and revenue would fall. Then, for slightly greater price increases, the remaining households are less responsive to price increases and the demand schedule again becomes inelastic. Finally, some of the remaining households drop the activity in the Region and revenues again fa11.6/

A more striking example of this "roller coaster" effect on total revenue is shown for deer hunting in

Region

6.

A nondiscriminating monopolist value of

$1,014,809 with an associated price of $100 per household is marked on Table

5.

Yet, it is seen that an estimate of $1,010,753, essentially the same value, is shown at a price of $80 where more trips are taken.

Where two values are almost iden- tical it is possibly more reasonable to select the value at the lower price as the nondiscriminating monopolist value, since because of errors in esti- mation no value is precisely true, and selection of the value at the lower price is the more "conserva- tive" decision.7/

The estimate for the nondiscriminating monopo- list value for deer hunting for the state, as shown in Table

4 and Table

6, is not simply the sum of the values for individual Regions.

Rather, the state- wide value is determined by horizontally summing the seven regional demand schedules

(as shown in Table

5), at each increment of added cost, to give a sin- gle statewide demand schedule as shown in Table

6.

The maximum value for total revenue on the statewide schedule, $3,717,064 at a price of $60, is the non- discriminating monopolist value for the state. The value for the state is lower than the sum of the nondiscriminating monopolist values for all Regions contained within the state. The reason is that if different "added costs" were charged for each

Region, a larger revenue could be extracted than if only a single price were charged at the state level.

Obviously, a larger total return can be obtained if one discriminated between Regions rather than charge a single price for the whole state.8/

6/

The "roller coaster" shape of the aggregate demand curve is formed by the horizontal summation of the individual curvilinear demand curves.

2/ Choosing the lower value is

"conservative" in terms of guarding against over of resources to recreation.

It may be a

"liberal" choice in terms of other resource uses.

8/ The problem of nonadditivity does not arise with consumer surplus values.

14

All seven Regions are still receiving deer hunting visits at the $60 statewide nondiscriminating monopolist price per household visit

(see

Table

6).

At an added cost of

$70, deer hunters would no longer hunt Regions

3 and

5.

As added costs per trip rise further, trips and total revenues fall until finally at added costs per trip of $250 or more (see Region

4 in

Table

5 and Table

6), only

Region

2 would be hunted. are

Details behind the summary estimates of Table

4 presented in Tables

7 and

8 for other big game hunting, Tables

9 and 10 for small game hunting,

Tables 11 and

12 for waterfowl hunting, Tables 13 and 14 for general hunting, Tables

15 and

16 for cold water fishing, Tables

17 and 18 for warm water fishing, and Tables

19 and 20 for general rural out- door recreation. These tables are all presented at the end of this section without interspersing text.

Interpretation of these tables is analogous to the interpretation of

Table

5 and

6 as explained above.

However, discussion of several discrepancies are in order. in 1970 from relatively great distances at quite high actual variable costs.

Thus, while the estimate at the higher level of added cost is not totally un- reasonable, the estimate at tLe lower level of added cost is it is selected as

"most reasonable" simply because more conservative.

In

Tables

16 and 20, the roller coaster effect shows up in the estimates of value for the whole state, rather than in the value of a

Region as dis- cussed above. In both cases, the maximum value is at a very high added cost, but after visits to most

Regions

(the less favorable areas) would have ceased.

Again, the higher values are conceptually possible but the lower values were selected as

"most reason- able" because all Regions for which estimates are available are represented in the estimates of cold water fishing in Table

16 and all Regions except one remain in the nondiscriminating monopolist estimate for the value of general rural outdoor recreation in

Table

20.

In

Tables

7, 16 and

20, rather extreme examples of the "roller coaster" effect discussed above occur.

In total revenue schedule has been chosen as the "most reasonable" estimate of the nondiscriminating monop- olist value.

In

Table

7, the problem occurs for hunting big game (other than deer) in

Region

1.

Even though the absolute high been rejected as the most reasonable value of the resource, there is a reasonable explanation for the bimodal distribution of values. Region

1 is one of the best areas for big game hunting.

It is very popular. Therefore, relatively heavy participation in hunting is found even at the $70 added cost chosen as the most reasonable level for the nondis- criminating monopolist value.

But, revenue falls very little thereafter as added costs continue to rise and finally revenue rises to the highest point at a

$650 price just before trips fall to zero. It is implied that response to price becomes very in- elastic for the small number of households partici- pating at the higher added costs.

These households would hunt other big game in this Region at almost any price.

In fact, such behavior probably would be true of a small number of households, and a small number of households was found in the sample that took a large number of big game trips to this Region

The discussion thus far has focused on the sin- gle nondiscriminating monopolist value and price for the Region or state. It is obvious, however, that since Tables

5 through

20 are complete demand sched- ules, the tables could have broader usage.

For example, the number of hunting visits to a

Region could be regulated by charging the appropriate fee rather than by the current 1974 approach of issuing permits. An obvious advantage of this approach would be that it would make money for the regulatory agency rather than simply creating administrative costs as does the present system. The size of the fee would depend on the number of hunters desired in the area.

Reading from Table

7, one sees that

21,087 household- to Region

1 for the purpose of hunting other big game in 1970 when no fee was charged. If only 19,631 household- were desired, a higher fee could be charged. Since regulation is usually desired by Management Unit rather than simply by the larger Management Regions, the agency would need to do some experimenting with the size of the fees, charging more in the more desirable units or where fewer visits were desired and charging less in units receiving less hunting pressure. One would not expect that a fee as large as the nondiscriminating monopolist price would ever be charged under such a system.

15

0

5

10

15

20

25

80

90

100

110

120

130

140

150

160

170

180

190

500

550

600

650

668

200

250

300

350

400

450

30

35

40

45

50

60

70a

TABLE

7.

ESTIMATES OF RESOURCE VALUES FOR

USE IN

BIG GAME HUNTING

AT

ALTERNATIVE ADDED

COSTS, BY GAME AND FISH REGIONS, 1970.

Activity and

Region

Big Game

Hunting,

Region

1

Added Cost

Per Trip

($)

Number of

Trips

2,002

1,582

1,337

1,203

1,091

1,019

963

924

901

834

0

8,759

7,791

6,855

5,936

5,120

4,656

4,227

3,805

3,391

3,043

2,841

2,653

2,469

2,288

2,129

21,087

19,631

18,260

16,899

15,550

14,211

12,884

11,567

10,262

9,325

TABLE

7.

(CONTINUED)

Activity and

Region

Added Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

Total

Revenue

($)

474,949

460,863

465,660

464,971

456,651

440,940

426,063

426,282

424,583

419,778

411,982

404,691

0

98,159

182,604

253,498

311,008

355,297

386,530

404,871

410,486

419,630

437,974

467,504

479,857b

400,460

395,584

401,206

421,100

436,713

458,924

481,635

508,696

540,906

542,117c

0

Big Game

Hunting,

Region

2 0

90

100

110

111

35

40

45

50a

60

70

80

5

10

15

20

25

30

24,377

21,016

18,847

16,817

14,936

13,544

12,467

11,633

10,912

10,168

9,307

5,831

5,328

4,682

3,932

3,449

187

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region. c Although this value is the largest total revenue and thus technically the nondiscriminating monopolist value, it has been rejected as unreason- able. The alternate high point at an added cost of

$70 is used. See discussion in the text.

0

105,083

188,478

252,269

298,724

338,610

374,029

407,176

436,495

457,568

465,367b

349,917

373,012

374,560

353,900

344,982

20,665

0

16

TABLE

7.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Added Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

Big Game

Hunting,'

Region

5

45

50

60

70

80

90

100

110

120

130a

140

149

20

25

30

35

40

0

5

10

15

25,919

24,733

23,629

22,570

21,558

20,592

19,672

18,798

17,970

17,188

16,453

15,120

13,848

13,223

12,147

11,757

10,759

9,783

9,246

3,293

0

0

123,669

236,293

338,564

431,173

514,812

590,173

657,947

718,825

773,500

822,663

907,220

969,375

1,057,870

1,093,235

1,175,790

1,183,567

1,174,018

1,202,048b

461,158

0

Big Game

Hunting,

Region

6

0

5

10

15

20

25

30

35

40a

45

50

60

22,944

20,523

18,587

16,641

14,944

12,647

10,620

9,975

9,218

5,970

5,116

0

0

102,615

185,873

249,621

298,881

316,183

318,602

349,133

368,744b

268,687

255,844

0

TABLE

7.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Added Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

Big Game

Hunting,

Region

7

0

5

35

40

45

50

10

15

20

25

30

60a

70

80

85

10,570

8,742

6,626

5,129

4,277

3,632

3,110

2,735

2,510

2,318

2,028

1,809

1,155

857

0

0

43,711

66,262

76,948

85,547

90,818

93,313

95,727

100,416

104,345

101,420

108,543b

80,891

68,575

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

17

TABLE

8.

THE VALUE OF BIG GAME

AT

HUNTING

IN

ARIZONA

ALTERNATIVE ADDED

COSTS,

1970.

TABLE

9.

ESTIMATES OF RESOURCE VALUES FOR

USE

IN

SMALL GAME HUNTING AT

ALTERNATIVE ADDED

COSTS, BY GAME AND FISH REGIONS, 1970.

Added

Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

Regions

Included at the Given

Added Cost

Activity and

Region

Added Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

5

10

15

20

25

30

35

40a

45

50

0

250

300

350

400

450

500

550

600

650

668

110

120

130

140

150

160

170

180

190

200

60

70

80

90

100

104,898

94,645

85,949

78,056

71,265

64,626

58,753

54,708

50,872

44,969

41,663

1,582

1,337

1,203

1,091

1,019

963

924

901

834

0

30,551

27,186

24,698

21,199

19,862

15,173

13,588

12,637

6,336

2,841

2,653

2,469

2,288

2,219

2,002

0

473,237

859,510

1,170,900

1,425,333

1,615,720

1,762,647

1,914,854

2,034,966b

2,023,730

1,981,848

1,833,184

1,903,135

1,975,954

1,907,998

1,986,432

1,669,203

1,630,669

1,642,988

887,221

426,282

424,583

419,778

411,982

404,691

400,460

395,584

401,206

421,100

436,713

458,924

481,635

508,696

540,906

542,117

0

1, 2, 5,

6,

7

1, 2, 5, 6,

7

1, 2, 5, 6,

7

1, 2, 5, 6,

7

1, 2, 5, 6,

7

1, 2, 5, 6,

7

1, 2, 5, 6, 7

1, 2, 5, 6, 7

1, 2, 5, 6,

7

1, 2, 5, 6,

7

1, 2, 5, 6, 7

1, 2, 5, 7

1, 2, 5, 7

1, 2, 5, 7

1, 2, 5

1, 2,

5

1, 2, 5

1, 5

1, 5

1, 5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 none a

Nondiscriminating monopolist price for the state.

Small Game

Hunting,

Region

1

Small Game

Hunting,

Region

2

Small Game

Hunting,

Region

3

0

5

10

15

20

25

30

35

40

45a

50

53

0

5

10

15a

20

22

0

5

10

15

20a

25

28

14,097

5,761

3,771

3,227

480

0

29,163

18,925

13,726

10,943

9,099

7,876

6,816

5,975

5,233

4,783

3,669

0

14,156

8,986

6,808

5,690

4,492

1,055

0

0

28,808

37,716

45,185b

9,601

0

0

94,629

137,265

164,153

181,995

196,901

204,508

209,156

209,323

215,256b

183,464

0

0

44,934

68,080

85,351

89,846b

26,396

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region. b

Nondiscriminating monopolist value for the state.

18

TABLE

9.

(CONT'D) RESOURCE VALUES AT

ALTERNATIVE

ADDED COSTS.

Activity and

Region

Small Game

Hunting,

Region

4

Small Game

Hunting

Region

5

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45

50a

59

0

25

30

35

40

5

10

15

20

45a

50

58

Number of

Trips

70,283

49,170

37,867

31,067

26,455

23,235

20,889

19,087

18,017

16,803

12,447

0

264,832

210,540

171,490

144,807

126,081

112,922

103,089

95,996

88,493

81,589

77,370

0

Total

Revenue

($)

0

1,052,702

1,714,906

2,172,110

2,521,630

2,823,069

3,092,691

3,359,885

3,539,759

3,671,544

3,868,521b

0

0

245,851

378,676

466,011

529,118

580,875

626,696

668,064

720,682

756,155b

622,387

0

TABLE

9.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Small Game

Hunting,

Region

6

Small Game

Hunting,

Region i

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45a

50

60

61

0

5

10

15

20

25

30

35a

40

45

48

Number of

Trips

176,962

141,981

119,238

102,668

91,438

84,178

78,808

73,140

52,233

21,797

0

85,516

64,201

51,579

42,838

36,949

32,582

29,573

27,299

24,809

23,453

18,593

727

0

Total

Revenue

($)

0

709,908

1,192,388

1,540,031

1,828,779

2,104,465

2,364,248

2,559,916b

2,089,358

980,900

0

0

321,009

515,790

642,577

738,986

814,569

887,193

955,474

992,394

1,055,389b

929,693

43,670

0

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

19

TABLE

10.

THE VALUE OF SMALL GAME

HUNTING

IN

ARIZONA

AT

ALTERNATIVE ADDED

COSTS,

1970.

TABLE

11.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

Added

Cost

Per Trip

($)

0

5

35a

40

45

50

60

61

10

15

20

25

30

Number of

Trips

655,009

499,564

404,479

341,240

294,994

261,848

239,175

221,479

188,785

148,425

112,079

727

0

Total

Revenue

($)

0

2,497,841

4,044,821

5,115,418

5,899,955

6,546,275

7,175,336

7,752,495b

7,551,516

6,679,244

5,604,065

43,670

0

Regions

Included at the

Given

Added Cost

All

All

All

All

All

2,3,4,5,6,7

2,4,5,6,7

2,4,5,6,7

2,4,5,6,7

2,4,5,6,7

2,4,5,7

7 none a

Nondiscriminating monopolist price for the state.

Activity and

Region

Waterfowl

Hunting,

Region

2

Added Cost

Per Trip

($)

0

5

10a

15

17

Waterfowl

Hunting,

Region

4

0

5

10

15

20a

25

29 b

Nondiscriminating monopolist value for the state.

Waterfowl

Region

7

TABLE

11.

ESITMATES OF RESOURCE VALUES

FOR USE

IN

WATERFOWL HUNTING

AT ALTERNATIVE ADDED

COSTS, BY GAME AND FISH REGIONS,

1970.

25

30

35

40

43

0

5

10

15

20a

Activity and

Region

Added Cost

Per Trip

($)

Number of

Trips

Total

Revenue

($)

Waterfowl

Hunting,

Region

1

0

5

10

15

20

25a

30

33

4,192

2,520

1,770

1,366

1,184

960

438

0

0

12,601

17,702

20,500

23,689

24,005b

13,165

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region. a

Number of

Trips

4,648

1,791

1,114

361

0

17,633

8,606

4,823

3,241

2,824

1,360

0

8,566

5,507

4,104

2,913

2,361

1,043

822

758

170

0

Total

Revenue

($)

0

8,955

11,144b

5,421

0

0

43,030

48,230

48,615

56,499b

34,005

0

0

27,539

41,046

43,699

47,224b

26,088

24,660

26,547

6,806

0

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist activity in the region. value for the

20

TABLE

12.

THE VALUE OF WATERFOWL HUNTING

IN

ARIZONA

AT

ALTERNATIVE ADDED COSTS, 1970.

TABLE

13.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Added

Cost

Per Trip

($)

30

35

40

43

0

5

10

15

20a

25 a b

Number of

Trips

35,039

18,424

11,811

7,881

6,369

3,363

1,260

758

170

0

Total

Revenue

($)

0

92,125

118,122

118,235

127,412b

84,098

37,825

26,547

6,806

0

Regions

Included at the Given

Added Cost

1, 2,

4,

7

1, 2,

4,

7

1, 2,

4,

7

1, 2, 4,

7

1, 4, 7

1, 4, 7

1, 7

7

7 none

Activity and

Region

General

Hunting,

Region

3

General

Hunting,

Region

5

Nondiscriminating monopolist

Nondiscriminating monopolist price for the state. value for the state.

Added Cost

Per Trip

($)

0

5a

10

11

0

5

10

15a

20

25

27

TABLE

13.

ESTIMATES OF RESOURCE VALUES FOR

USE IN

GENERAL HUNTING AT ALTERNATIVE ADDED

COSTS, BY GAME

AND FISH REGIONS,

1970.

Activity and

Region

General

Hunting,

Region

1

Added Cost

Per

Trip

($)

Number of

Trips

Total

Revenue

($)

General

Hunting,

Region

6

General

Hunting,

Region

7

0

5a

10

13

0

5

10

15

20a

25

30

32

7,261

4,460

3,179

2,660

2,373

1,470

852

0

0

22,302

31,796

39,910

47,466b

36,771

25,560

0

0

5

10

15

20

25a

30

31

General

Hunting,

Region

2 0

5

10a

12

20,96:

2,702

1,945

0

0

13,512

19,454b

0

Number of

Trips

4,982

1,424

349

0

50,951

21,372

10,686

7,804

4,618

1,262

0

31,794

15,305

3,833

0

11,912

5,510

3,742

2,719

2,143

1,882

1,203

0

Total

Revenue

($)

0

7,120

3,491

0

0

106,863

106,860

117,059b

92,371

31,560

0

0

76,529b

38,330

0

0

27,551

37,427

40,791

42,868

47,071b

36,097

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

21

TABLE

14. THE VALUE

OF GENERAL HUNTING

IN

AT

ARIZONA

ALTERNATIVE ADDED COSTS, 1970.

TABLE

15.

ESTIMATES OF RESOURCE VALUES FOR

USE IN

COLD

WATER

FISHING

AT

ALTERNATIVE ADDED

COSTS, BY

GAME AND FISH REGIONS, 1970.

Added

Cost

Per Trip

($)

0

5a

10

15

20

25

30

32 a b

Number of

Trips

127,862

50,773

23,734

13,183

9,134

4,614

2,055

0

Total

Revenue

($)

0

253,877b

237,358

197,770

182,705

115,402

61,657

0

Nondiscriminating monopolist

Regions

Included at the Given

Added Cost

1,2,3,5,6,7

1,2,3,5,6,7

1,2,3,5,6,7

1, 5, 7

1, 5,

7

1, 5, 7

1,

7 none

Activity and

Region

Cold

Water

Fishing,

Region

1

Added

Cost

Per Trip

($) price for the state.

Nondiscriminating monopolist value for the state.

0

70

80

90

100

110

120a

130

140

150

160

30

35

40

45

50

60

5

10

15

20

25

Number of

Trips

279,050

256,001

237,278

219,736

206,123

194,615

183,515

174,943

167,455

160,802

154,477

145,047

132,368

126,271

120,786

115,051

110,156

106,005

91,662

41,850

25,249

0

Total

Revenue

($)

0

1,280,006

2,372,780

3,296,040

4,122,478

4,865,395

5,505,476

6,123,013

6,698,216

7,236,102

7,723,860

8,702,829

9,265,765

10,101,703

10,870,793

11,505,195

12,117,228

12,720,613b

11,916,175

5,859,054

3,787,361

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

22

TABLE

15.

(

CONT'D) RESOURCE VALUES AT

ALTERNATIVE

ADDED COSTS.

TABLE

15.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

Activity and

Region

Cold Water

Fishing,

Region

2

Added Cost

Per

Trip

($)

0

5

10

15

20

25

30

35

40a

45

50

60

64

Cold

Water

Fishing,

Region

3 0

5

10

15

20

25

30

35

40

45

50

60a

70

80

Number of

Trips

179,869

148,885

124,914

107,037

94,648

83,468

75,415

70,393

67,699

41,828

33,010

20,133

0

38,792

32,526

28,722

26,089

23,652

22,170

20,926

19,849

19,039

18,323

17,730

16,980

13,408

0

0

162,634

287,228

391,344

473,048

554,259

627,787

694,729

761,596

824,550

886,524

1,018,815b

938,577

0

Total

Revenue

($)

0

744,427

1,249,147

1,605,561

1,892,961

2,086,717

2,262,452

2,463,789

2,707,965b

1,882,299

1,650,543

1,208,003

0

Activity and

Region

Cold

Water

Fishing,

Region

5

Added Cost

Per Trip

($)

0

35

40

45

50

60

61

5

10

15

20

25a

30

Cold

Water

Fishing,

Region

6 0

5

10

15

20

25

30

35a

40

44

Number of

Trips

44,003

32,688

24,950

20,095

16,969

14,681

9,420

8,609

7,710

6,440

5,147

77

0

31,579

25,412

21,228

18,696

15,897

12,859

12,329

11,580

8,673

0

Total

Revenue

($)

0

163,440

249,501

301,428

339,399

367,038b

282,615

301,326

308,424

289,805

257,377

4,666

0

0

127,061

212,282

280,453

317,955

321,489

369,896

405,316b

346,948

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

23

TABLE

15. (CONT'D) RESOURCE VALUES AT

ALTERNATIVE

ADDED COSTS.

TABLE

16.

THE VALUE OF COLD

WATER

FISHING

IN

ARIZONA

AT

ALTERNATIVE ADDED

COSTS, 1970.

Activity and

Region

Cold Water

Fishing,

Region

7 a

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45

50

60

70a

74

Number of

Trips

28,417

20,322

16,184

13,640

12,250

11,390

10,755

10,369

10,063

9,829

9,312

9,074

8,045

0

Total

Revenue

($)

0

101,613

161,848

204,608

245,000

284,757

322,667

362,926

402,536

442,341

465,635

544,471

563,167b

0

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist activity in the region. value for the

Added

Cost

Per Trip

($)

40a

45

50

60

70

80

90

100

110

120

130

0

5

10

15

20

25

30

35

140

150

160

Number of

Trips

601,710

515,834

453,276

405,293

369,539

339,183

312,360

295,743

280,639

237,222

219,676

191,311

153,821

126,271

120,786

115,051

110,156

106,005

91,662

41,850

25,249

0

Total

Revenue

($)

Regions

Included at the Given

Added Cost

.

0

2,579,181

4,532,786

1,2,3,5,6,7

1,2,3,5,6,7

1,2,3,5,6,7

6,079,434 1,2,3,5,6,7

1,2,3,5,6,7

7,390,841

8,479,655

9,370,893

10,351,099

1,2,3,5,6,7

1,2,3,5,6,7

1,2,3,5,6,7

11,225,685b

1,2,3,5,6,7

10,675,097 1,2,3,5,7

10,983,939 1,2,3,5,7

11,478,784c

1,2,3,5,7

10,767,509

1, 3,

7

10,101,703

1

10,870,793

11,505,195

12,117,228

12,720,613d

11,916,175

5,859,054

1

1

1

1

1

1

3,787,361

0

1 none a

Nondiscriminating monopolist price for the state. b

Nondiscriminating monopolist value for the state. c

Although this value is the largest total revenue and thus technically the nondiscriminating monopolist value, it has been rejected as unreasonable.

One of the alternate high points at the added cost of $40 is used. See discussion in the text. d

This value is the second highest total revenue but has been rejected as the most reasonable nondis- criminating monopolist value since it is not signi- ficantly different from the value at an added cost of $40, and Region

6 is not included.

24

TABLE

17.

ESTIMATES OF RESOURCE VALUES FOR

USE IN

WARM WATER FISHING AT

ALTERNATIVE ADDED

COSTS, BY

GAME AND FISH REGIONS, 1970.

Activity and

Region

Warm Water

Fishing,

Region

1

Warm Water

Fishing,

Region

2

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45

50

60

70

80

90

100

110a

120

130

140

141

0

5

10

15

20

25

30

35

40

45a

50

52

Number of

Trips

20,503

18,335

16,674

15,163

14,056

13,060

12,248

11,602

11,161

9,880

9,548

8,392

8,023

7,495

7,081

6,941

6,832

6,113

3,595

542

0

32,959

19,725

15,228

12,800

11,691

10,986

10,548

9,890

9,712

9,153

4,836

0

Total

Revenue

($)

0

98,625

152,287

192,011

233,826

274,658

316,468

346,155

388,486

411,927b

241,849

0

0

91,678

166,745

227,456

281,132

326,502

367,453

406,094

446,449

444,634

477,447

503,533

561,663

599,607

637,314

694,198

751,539b

733,646

467,436

75,990

0

TABLE

17.

(CONT'D)

Activity and

Region

Warm Water

Fishing,

3

Added Cost

Per Trip

($)

0

5

10

15

20

25

30

35

40

45

50

60

70

80

90

100

110

120

130

140

150

160

170

180 a activity b

200

216

Number of

Trips

0

252,741

477,351

681,482

869,890

1,043,285

1,205,799

1,357,994

1,499,162

1,631,085

1,759,391

2,015,657

2,261,046

2,490,856

2,705,480

2,910,529

3,107,250

3,296,723

3,487,114

3,682,057

3,881,291

4,082,630

4,288,063

4,499,578 b

4,719,628

4,378,779

0

35,187

33,594

32,300

31,135

30,060

29,105

28,247

27,472

26,823

26,300

25,875

25,516

25,223

24,997

24,840

21,893

0

55,347

50,548

47,735

45,432

43,494

41,731

40,193

38,799

37,479

36,246

Total

Revenue

($)

Nondiscriminating monopolist price for the in the region.

Nondiscriminating monopolist value for the activity in the region.

25

TABLE

17.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

TABLE

17.

(CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Activity and

Region

Warm Water

Fishing,

Region

4

Added Cost

Per Trip

($)

0

5

10

15

20

25a

30

35

Warm Water

Fishing,

Region

5

30

35

40

45

50

60

70a

80

90

0

5

10

15

20

25

94

Warm Water

Fishing,

Region

6 0

5

10

15

20a

25

30

31

Number of

Trips

83,284

67,294

57,751

51,682

47,703

42,616

30,031

0

405,535

365,156

331,907

304,732

287,735

267,175

255,561

240,799

231,112

223,028

216,458

205,217

192,853

165,072

25,505

0

20,503

14,497

10,047

8,221

6,369

3,806

273

0

0

1,825,781

3,319,073

4,570,981

5,680,116

6,679,381

7,411,293

8,427,983

9,244,510

10,036,272

10,822,946

12,313,047

13,499,751b

13,205,778

2,295,481

0

Total

Revenue

($)

0

336,470

577,516

775,237

954,078

1,065,400b

900,955

0

Activity and

Region

Warm Water

Fishing,

Region

7

Added Cost

Per Trip

($)

0

5

10

15

20

25a

30

35

40

44 a

Number of

Trips

125,138

93,217

71,969

62,208

53,290

42,673

19,713

11,418

5,701

0

Total

Revenue

($)

0

466,086

719,690

933,121

1,065,800

1,066,849b

591,400

399,652

228,070

0

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

0

72,487

100,479

123,321

127,397b

95,152

8,218

0

26

Number of

Trips

743,269

628,772

551,311

500,238

464,338

422,047

368,567

312,508

295,165

278,307

266,029

247,203

233,176

203,702

62,646

36,046

35,079

33,585

30,418

26,842

25,875

25,516

25,223

24,997

24,840

21,893

0

TABLE

18.

THE VALUE OF WARM WATER FISHING

IN

ARIZONA

AT

ALTERNATIVE ADDED

COSTS,

1970.

TABLE

19.

ESTIMATES OF RESOURCE

VALUES FOR USE

IN

GENERAL RURAL

OUTDOOR RECREATION

AT

ALTERNATIVE ADDED

COSTS, BY GAME AND FISH

REGIONS, 1970.

Added

Cos t

Per Trip

(s)

0

140

150

160

170

180

190

200

216

45

50

60a

70

80

90

100

110

120

130

25

30

35

40

5

10

15

20 a b

Total

Revenue

(s)

0

3,143,868

5,513,136

7,503,609

9,212,239

10,551,227

10,801,586

10,949,296

11,806,677

12,523,918

13,361,633

18,832,237b

16,322,460

16,296,241

5,638,275

3,604,727

3,858,789

4,030,369

3,954,550

3,758,047

3,881,291

4,082,630

4,288,063

4,499,578

4,719,628

4,378,779

0

Regions

Included at the

Given

Added Cost

1, 3

1, 3

1, 3

1, 3

1, 3

3

3

3

3

All

All

All

All

All

All

All

1, 2, 3, 5, 7

1, 2, 3, 5, 7

1, 2,

3, 5

1,

2,

3, 5

1,

3, 5

1, 3, 5

1, 3, 5

1, 3

3

3 none

Nondiscriminating monopolist price for the state.

Nondiscriminating monopolist value for the state.

Activity and

Region

General

Rural

Outdoor

Recreation

Region

1

Added Cost

Per Trip

(s)

224,943

197,247

192,161

187,194

182,347

177,620

172,795

168,294

163,287

159,035

154,902

146,694

139,255

132,348

127,424

123,426

120,202

116,950

111,751

109,531

106,836

104,888

103,254

101,937

98,766

96,844

37,539

0

60

70

80

90

100

110

120

30

35

40

45

50

130

140

150

160

170

180

190

200a

250

264

0

5

10

15

20

25

Number of

Trips

Total

Revenue

(s)

0

986,236

1,921,613

2,807,922

3,646,956

4,440,504

5,183,852

5,890,303

6,531,490

7,156,608

7,745,134

8,801,679

9,747,915

10,587,847

11,468,199

12,342,621

13,222,290

14,034,098

14,527,711

15,334,458

16,025,456

16,782,142

17,553,253

18,348,769

18,765,615

19,368,992b

9,384,969

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the activity in the region.

27

Activity and

Region

General Rural

Outdoor

Recreation,

Region

2

Added Cost

Per Trip

($)

40

45

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200a

250

262

0

5

10

15

20

25

30

35

TABLE 19. (CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

TABLE 19.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED COSTS.

Number of

Trips

464,093

403,285

387,574

372,211

357,116

342,452

328,135

314,168

300,682

290,310

281,451

265,388

250,603

236,593

223,921

214,708

206,684

199,445

193,226

187,658

182,267

177,855

173,718

169,987

167,325

164,734

74,669

0

Total

Revenue

($)

0

2,016,429

3,875,741

5,583,170

7,142,339

8,561,300

9,844,076

10,995,898

12,027,315

13,063,964

14,072,551

15,923,317

17,542,221

18,927,470

20,152,922

21,470,871

22,735,319

23,933,430

25,119,509

26,272,257

27,340,053

28,456,934

29,532,135

30,597,673

31,791,788

32,946,847b

18,667,340

0

Activity and

Region

General Rural

Outdoor

Recreation,

Region

3

Added Cost

Per Trip

($)

0

25

30

35

40

45

5

10

15

20

50

60

70

80

90

100a

110

120

128

Number of

Trips

95,174

71,706

62,736

56,343

51,415

47,897

45,396

43,190

41,235

39,544

38,106

35,718

33,696

32,057

30,830

29,286

26,042

17,299

0

Total

Revenue

($)

0

358,532

627,360

845,147

1,028,318

1,197,449

1,361,890

1,511,660

1,649,400

1,779,508

1,905,335

2,143,090

2,358,759

2,564,603

2,774,771

2,928,689b

2,864,678

2,075,967

0 a

Nondiscriminating monopolist price for the activity in the region. b

Nondiscriminating monopolist value for the actitivy in the region.

28

Activity and

Region

General Rural

Outdoor

Recreation,

Region

4

Added Cost

Per Trip

($)

0

25

30

35

40

45

50

60

70

5

10

15

20

80

90a

100

106

General Rural

Outdoor

Recreation,

Region

5

35

40

45

50

60a

70

73

0

5

10

15

20

25

30

TABLE 19. (CONT'D)

RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

TABLE

19.

(CONT'D) RESOURCE VALUES AT ALTERNATIVE

ADDED

COSTS.

103,890

72,517

62,302

54,773

49,135

41,884

38,853

36,414

34,310

32,536

30,961

28,520

26,154

24,919

23,763

18,795

0

Number of

Trips

737,094

599,680

552,333

507,260

477,566

450,609

429,032

412,181

394,333

362,043

328,754

275,240

16,168

0

Total

Revenue

($)

0

362,586

623,022

821,605

982,711

1,047,115

1,165,596

1,274,511

1,372,419

1,464,139

1,548,058

1,711,238

1,830,804

1,993,529

2,138,720b

1,879,535

0

0

2,998,400

5,523,338

7,608,912

9,551,338

11,265,230

12,870,968

14,426,354

15,773,354

16,291,945

16,437,702

16,514,449b

1,131,822 o

Activity and

Region

General

Rural

Outdoor

Recreation,

Region

6

Added Cost

Per Trip

($)

0

5

10

15

20

25

30a

35

39

General Rural

Outdoor

Recreation,

Region

7

35

40

45

50

60

70

80a

90

98

0

5

10

15

20

25

30 a activity b activity in in the region. the region.

Number of

Trips

599,533

499,198

463,962

438,217

411,607

380,481

349,139

122,804

O

160,106

123,616

104,362

91,080

80,323

71,825

65,238

59,547

54,912

51,326

47,980

42,424

38,868

34,390

24,022

0

Total

Revenue

($)

0

2,495,993

4,639,628

6,573,256

8,232,145

9,512,035

10,474,190b

4,298,157

Nondiscriminating monopolist price for the

Nondiscriminating monopolist value for the

0

0

618,082

1,043,623

1,366,205

1,606,479

1,795,647

1,957,146

2,084,168

2,196,519

2,309,703

2,399,034

2,545,464

2,720,767

2,751,233b

2,162,030

0

29

TABLE 20.

THE VALUE OF GENERAL RURAL OUTDOOR

RECREATION

IN

ARIZONA AT ALTERNATIVE

ADDED

COSTS, 1970.

Added

Cost

Per Trip

($)

30

35

40

45

50

60a

70

80

90

100

110

120

130

140

150

160

170

180

190

200

250

264

0

5

10

15

20

25

Number of

Trips

2,384,833

1,967,249

1,825,430

1,707,078

1,609,509

1,512,768

1,428,588

1,156,598

988,759

934,794

882,154

793,984

504,744

460,310

429,960

386,215

352,928

333,694

304,977

297,189

289,103

282,743

276,972

271,924

266,091

261,578

112,208

0

Total

Revenue

($)

Regions

Included at the Given

Added Cost

0

9,836,258

18,254,325

25,606,217

32,190,286

All

All

All

All

All

37,819,280

39,647,220

41,606,715

43,365,509

45,239,076

47,085,388

48,946,442

All

42,857,718

All

40,481,051

39,550,497

42,065,867

44,107,814

All

1,2,3,4,5,7

1,2,3,4,5,7

1,2,3,4,5,7

47,639,237b 1,2,3,4,5,7

35,332,288 1,2,3,4,5,7

1,2,3,4,7

36,824,682

38,696,642 1,2,3,4,7

38,621,716

38,822,287

40,043,495

1,2,3,4

1,2,3

1,2,3

1,2

1,2

1,2

1,2

1,2

1,2

50,557,403 1,2

52,315,839e

1,2

28,052,309

1,2

0 none a

Nondiscriminating monopolist price for the state. b

Nondiscriminating monopolist value for the state. c

Although this value is the largest total revenue and thus technically the nondiscriminating monopolist value, it has been rejected as unreasonable.

The,al- ternative high point at an added cost of $60 is used.

See discussion in the text.

30

RESOURCE VALUES

IN

ALTERNATIVE

USES

The analysis revealed that in Arizona 4,905,384 household for purposes of rural outdoor recreation generating

$243,236,558 of consumer surplus value in 1970.

This value represents the total net benefits of the state's natural resources in use for outdoor recre- ation by

Arizona residents

(Table

3). optimum combination of products will change if the relative prices of any two products change.

The general theoretical economic model is quite clear. The problems are in

(1) empirically estima- ting the transformation functions between producing timber, grazing, recreation and water for a given watershed and

(2) estimating product demand functions.

The nondiscriminating monopolist method provides the maximum total revenue that could be extracted at a single price as set by an agency such as the

Arizona

Game and Fish Department. The monopolist price for 1970 was found to vary from about

$5 per household for general hunting to about

$60 per and general rural can play in warm water fishing, outdoor recreation activities when a price was selected for the state as a whole

(Table

4).

The total nondiscriminating monopolist value of the state's natural resources in use for outdoor recreation by Arizona residents was $91,582,973.

It is not suggested that the administrative agencies should raise fees to the point where reve- nue is maximized. There are serious equity consider- ations that should be made before any increases in fees could be justified. However, the nondiscrimi- nating monopolist value gives a resource value that may be compared to values of alternative products of the land resource if decisions relative to com- peting uses must be made. ing, represent only three of the possible uses of the forest, range land, and water resources in Arizona.

Other alternatives include such uses as timber pro- duction, water production, and cattle grazing on the forest lands, water production and grazing on the desert ranges, and agricultural, municipal and industrial uses of the water. or

The significance of this study is the role it developing public land policies. Hunt- fishing and general rural outdoor recreation

Often these uses of the resource are to a given cost, i.e., unrelated complementary to each other.

In these cases the values of two uses on the same set of resources would be additive no problem of decision making about resource use arises.

However, sometimes the various uses are competitive, and more of the pro- duct of one use can be achieved only at the sacri- fice of some of the product of another use.

Where such a multiple exists on a given resource base, the economic comes one of problem be- maximizing the value of output relative relative to the given resource base. In economic terminology, the product relationship must be solved.

The solution to this problem involves specifying the substitution rela- tionships between products, at all levels of output of each, specifying the relevant demand function for each product, and then solving for the optimum com- bination of products to produce.

Obviously, the

Research in estimating product transformation functions for Arizona watersheds is proceding by personnel of the Rocky Mountain Forest and Range

Experiment Station and the

University of

Arizona

[for example, see O'Connell and Brown, 1972]. Eco- nomic values and /or demand functions for grazing and water are available from past work by Martin and

Jefferies

[1966] and Kelso, Martin and

Mack

[1973], respectively. Valuation of timber, forage and water on National Forest Lands are summarized by O'Connell

[1972]. This current study contributes demand func- tions and value estimates for many types of rural outdoor recreation.

IN

THE VALUE OF SURFACE AREA

ALTERNATIVE RECREATION

USES

It is not appropriate to attempt a detailed analysis of the general trade problem herein.

Rather, the discussion is limited to converting the value estimates presented in the previous section into values per square mile of land (for hunting), values per surface acre of water

(for fishing), and values for total surface area for general rural out- door recreation, in order to better set the value estimates in context with other uses of the land and water resources.

Table

21 presents estimates of the land and water areas available for hunting and fishing in

Arizona, classified by Region. Except for the total area of a Region, all figures are "ballpark esti- mates", but they are the best available. If the value estimates for whole

Regions, presented in the previous section, are divided by these estimates of surface area, the data of Table

22 are generated.

The estimates of Table

22 show the average value of a unit of surface area in a particular Region in use for a particular activity in 1970, when valued by the nondiscriminating monopolist procedure. For example, one square mile

(one section) of huntable deer range in Region

1 had an average value of $95 in use for hunting deer.

At the same time, huntable range for other big game in Region

1, some of which overlaps and some of which is separate from the deer range, was worth $94 per square mile. The weighted average value of all huntable area in

Region

1 for all types of hunting was

$159 per square mile. The weighted average value for a square mile of all area

31

TABLE

21.

SURFACE AREA OF ARIZONA AVAILABLE FOR RURAL

ACTIVITY,

1970.

OUTDOOR RECREATION ACTIVITIES,

BY REGION

AND

Region

1

2

3

4

5

6

7

Total Areas

18,526

26,182

11,678

16,251

11,091

13,513

16,543

Huntable Areaa

Deer

Other Big Gamed

3,635 square miles

5,100

14,710

5,270

6,400

11,000

2,500

1,800

9,000

5,550

8,850

7,565

7,500

8,850

All

Gamec

5,900

16,900

8,600

9,600

9,000

8,400

13,000

Surface Acresb of

Cold Waters Warm Waterc

- - - surface acres

- - - -

5,250 2,470

8,100

10,000

6,100

14,650

4,650

2,000

250

770 e

350

38,375e

State 113,784 53,415 44,315 71,400

26,370 66,545 a

Square miles of available hunting area include those areas generally open to the public at all times.

There are instances when an area of considerable size may be open for a short duration for a specific hunt, but is normally closed.

For instance, the

Fort Apache Indian Reservation

(2601 sq. mi.) in Region

1 is open for the elk hunt, but closed at other times.

Again, in Region

4, the Air Force Bombing Range

(2500 sq. mi.) is open for five or so sheep hunters, but is closed the rest of the year. b

Surface acreage of water in

Arizona includes only that which is inside the Arizona border. The

Colorado River Lake area includes only that which is in

Arizona.

If the total surface acres of Lake

Powell, Lake Mead and others were included, the total would be over 300,000 surface acres.

Those lakes which are both cold water lakes and warm water lakes have been divided on a percentage.

If, for example, a

1,000 acre lake is equally important for both classifications, 500 acres are assigned to the warm water category and 500 acres are assigned to the cold water category. Surface acres of all streams and rivers, including all of the area of the Colorado River adjacent to

Arizona, are included in the estimates. c

Source: Carr (1973).

All estimates are ballpark estimates, but are the best available. d

Estimates of huntable range are extremely rough except in the area of the Salt comprising parts of Regions

1, 2, 5 and

7.

Estimates for the Salt

(1973).

Watershed were made by Hammond e

Regions

5 and

7, both abounding Roosevelt Lake, are valued as a single region. is less than the sum of the values of deer and other big game, since the total huntable area in

Region

1 is larger than the deer and other big game hunting areas, and the value of small game, waterfowl and general hunting in Region

1 is relatively small.

Regions

5 and

6 have very large values per square mile for all hunting because of the very high demand for small game hunting in the two Regions, relative to the total huntable range.

The weighted average value for the total area of huntable range in the state was $194 per square mile.

Fishing values are computed on the basis of total surface acres of water. By far the highest

32 value per surface acre are the cold waters of Region

1, including the White Mountain streams and small lakes. Values in Regions

2 and

3 are much smaller per surface acre, where total cold water is more plentiful relative to economic demand.

No value is shown for Region

4, not because cold water would not have a value in

Region

4, but because there is no cold water in southwest Arizona, including the

Yuma and Gila Bend areas. Region

5 has some cold water, but Region

1 is adjacent and generally a more pre- ferable cold water fishing area; thus the low value per surface acre. Regions

6 and

7, in southern Ari- zona have little cold water but are near the popu- lation center of Tucson which generates fishing de- mand. Thus Regions

6 and

7 have high values per surface acre for cold water fishing.

TABLE

22.

VALUES OF SURFACE AREA AVAILABLE FOR RURAL OUTDOOR RECREATION

IN

ARIZONA, BY REGION AND

ACTIVITY, 1970.

Average Nondiscriminating Monopolist Value of

Region

1

2

3

4

5

6

7

Deer

Hunting

Other Big

Game Hunting dollars per square mile

95

97

30

27

17

183

91

94

42

159

49

12

All

Huntingb

159

127

30

103

594

479

159

Cold Water

Fishing

-dollars per surface acre-

2,423

334

102

184

1,621

731

Warm Water

Fishing

304

68

322

229 c

364

380c

General

Rural

Outdoor d

Recreation

-dollars per

1,045

1,258

250

132

775

1,489

166

State

70 46

194 426

283 417 a

Sections of huntable range are composed of different mixes of big game animals as follows:

Region

1

--

Mostly elk, antelope and turkey.

Lion and bear occupy considerable area. Smaller areas of javelina.

Region

2 --

Mostly elk, antelope and turkey.

Lion and bear occupy considerable area. Smaller areas of javelina and bighorn sheep.

Region

3

--

Mostly antelope and bighorn sheep.

Lion occupy a considerable area. Smaller areas of bear, turkey and elk.

Region

4 --

Mostly javelina and bighorn sheep.

Lion are restricted to smaller areas.

Region

5 --

Mostly javelina.

Lion occupy a considerable area.

Smaller areas of elk, turkey, bear, antelope and bighorn sheep.

Region

6

--

Mostly javelina. Smaller areas of lion, bear, turkey, antelope and bighorn sheep.

Region

7

--

Mostly javelina. Lion occupy a large area.

Smaller areas of elk, antelope, bear and turkey. on b

Include small game, waterfowl and general hunting, as well as deer and other big game. Values depend mix of hunting values compared to total hunting area. c

Regions

5 and

7, both abounding Roosevelt

Lake, are valued as a single region. d

Computed on the basis of all surface area, not just rural area; therefore, values are underestimated.

The major underestimation would be in

Regions

5 and 6, which contain Phoenix and Tucson, respectively.

The values for warm water fishing are much more stable across the state. Region

2 includes the

Colorado River and thus a relatively large area, but much of this area is inaccessible to fishermen

(e.g., that area within the Grand Canyon), and so the aver- age surface acre has relatively little value.

Re- gions

3 and

4 also include the Colorado River, but here the River is quite accessible.

Competition for warm water fishing is high and so is the surface acre value. Regions

5 and

7 both surround and abound the major warm water lakes in Arizona, Roose- velt, San Carlos, Canyon, Saguaro and Apache, and are treated as one region. These Lakes are near the major population centers of the state,

Phoenix and

Tucson, and have the highest value per surface acre even though they also have the greatest number of acres available.

Estimates for the average value of a square mile of area for general rural outdoor recreation

(ex- cluding the value for hunting and fishing) must be considered underestimates, especially in Regions

5 and

6.

These values were computed as the total value for the Region, divided by the total area of the

33

Region including urban area.

Except in

Regions

5 and

6 which include the metropolitan areas of Phoenix and Tucson, respectively, urban area is an extremely small percent of the total. However, none of the estimates consider that much rural land is inacces- sible to recreators also. The value of general rural outdoor recreation is a weighted value for both land and water based activities and is computed on the basis of the total of the land and water surface area.

The weighted average value per square mile for the state was $417 in

1970.

The authors hasten to reemphasize that all values presented in Table

22 are rough estimates and many conceptual problems could arise in comparing these values to values of the same land and water poses. Still, it is argued that the esitmates give a reasonable idea of approximate money values. As discussed at the beginning of this report, the value of outdoor recreation is not "priceless

", but is reflected in the prices that people are willing to pay for the experience.

The estimates of Table

22 give reasonable estimates of these magnitudes. using indices from USDA [1971, 1972]). Prices of public lands, classified by public agencies

(i.e.,

State lands, Forest Service land and Bureau of Land

Management lands) were obtained from Martin and

Jefferies

[1966].

Prices were weighted by the per- centages of each type of land in the area [Dickerman and Martin,

1967].

The average value of all lands for ranching is the annual equivalent

(at

6 percent interest) of the average sale price of all ranches, including deeded land as well as the rights to public land permits, also as developed by Martin and Jefferies

[1966] and reported in Dickerman and Martin

[1967]. Whole ranches were selling for the average price per sec- tion

(640 acres), while the marginal price represents the value of an additional section of public lands when added to a typical ranch in the area.

The values for hunting are the total nondiscri- minating monopolist values for the Game Regions di- vided by the estimated number of sections of huntable range as defined in Table

21.

A FEW ROUGH

COMPARISONS

The analysis is limited to a brief and rather rough comparison of land resource values when used in cattle ranching and hunting and the value of water resources in fishing versus in irrigated ag- riculture. These comparisons are for illustrative purposes only.

They do not imply that the activities are substitutes or that use for one activity or the other would be an optimum solution, rather they sim- ply show that the value of the resources when used for recreation, a nonpriced product, compares favor- ably with the use of the resources in traditional market priced activities.

The hunting values do not reflect the value of the land in terms of the capacity of the land to pro- duce game.

Rather, the values reflect the magnitude of the demand determinants which in turn affects the degree of hunting participation.

It is the distri- bution of hunters and total participation on the given land resource that ultimately affects the value of the resource. For this reason, the Southern desert near Tucson has the highest value for deer hunting and the

Arizona strip in the northwest cor- ner of the state has a lower value. But, the Arizona strip is widely considered superior deer hunting ter- ritory.

Table

23 shows estimated values per square mile

(one square mile equals one section) of land used in cattle ranching, deer hunting, hunting of other big game, and all hunting for six ranching areas in

Arizona that are roughly congruent with the

Arizona

Game and Fish

Management Regions.

Figure

8 shows a map of the state defining the six ranching areas. The areas were selected on the basis of similar land characteristics for grazing.

The differences in values between areas given for grazing in Table 23 reflect the value of the land resource in cattle production; in the areas where grazing conditions are poorer, returns are lower than in areas which have prime grazing conditions.

In a similar fashion, the high values per sec- tion for grazing do not really reflect the produc- tivity of the areas for producing cattle, but rather more closely reflect the demand for cattle ranches by individual investors; that is, the demand for participation in ranching activity. (Differences in values between areas partially reflect productivity.)

As discussed by Martin and Jefferies [1966], land values created by the demand for ranches by the pub- lic far exceeds that value that would reflect the productivity of the land in producing beef for mar- kets. For example,

O'Connell

[1972] argues that the resource value for producing beef in the Central

Mountain Area

(Region

5) lies between

$63 per section and a high limit of $357 per section.

In this same area, Table 23 shows values of $15 per section for deer hunting, $159 per section for hunting other big game, and an average of $594 per section for all hunting activities.

The cattle ranching values within a single area were computed in two ways, thus giving a range in value.

The marginal value of public lands represents the annual weighted average price of public land grazing permits at the margin as seen by the indivi- dual cattle ranch investor, and as revealed by a sur- vey of ranch sales by Martin and Jefferies

[1966].

(Reported values were inflated to 1970 conditions

Comparison of the value of activities is even a water in alternative more complicated problem. For example, estimates of the value of water for use in irrigated agriculture as made by Kelso,

Martin and

Mack

[1974] are in terms of an acre

(a volume) of consumptive at the margin of use in agricul- ture.

The fishing values of Table

23 are in terms of dollars per average surface acre. Still some rough

34

TABLE

23.

COMPARISON OF CATTLE RANCHING, DEER HUNTING AND OTHER BIG GAME

HUNTING

VALUES FOR A SECTION

OF LAND

IN

SIX DIFFERENT CATTLE

PRODUCING AREAS

IN

ARIZONA, 1970.

Ranching Areaa

Western Desert

(Region

4)

Arizona Strip

(Region

2)

Southern Desert

(Region

6)

Central

Mountain

(Region

5)

Annual Value ofb

Cattle

Ranching

Marginal Value

Public Lands

Average Value of

All Lands

55

140

Average Nondiscriminating Monopolist Value of

Deer Hunting

Other Big Game

Huntingc

All

Hunting dollars per section

27 d

103

119

173

153

290

352

355

97

183

15

42

49

159

127

479

594

Central Plateau

(Region

1)

(Region

2)

Southeastern

Desert

(Region

7)

236

210

425

558

95

97

91

94

42

12

159

127

159 a

See Figure

8.

These ranching areas roughly compare to

Arizona Game and Fish

Management

Regions as listed below.

Arizona Strip is the upper part of Region

2.

Central Plateau is the lower part of Region

2 and the most huntable portion of Region

1.

Central

Mountain is mostly

Region

5.

Western Desert is in

Region

4.

Southern Desert is in

Region

6.

Southeastern

Desert is in

Region

7.

Ranch budgets are not available for the area equivalent to Region

3. b

Total sale prices annualized at

6 percent interest. c

See footnote a,

Table 22 for types of big game involved. d

No estimate.

35

®

Ranching Areas

FIGURE 8.

RANCHING AREAS

IN ARIZONA

Source:

Dickerman and Martin (1967) comparison may be possible.

If evaporation from the warm water lakes is about 6 acre -feet per year per surface acre, the average consumptive value of a surface acre of water used only for warm water fish- ing would be about $300 divided by 6 or

$50 per acre foot of consumptive use.

The marginal value of the acre foot of water would be lower than the average value. Still, it is clear that the marginal value in fishing must compare favorably with the marginal value in irrigated agriculture.

Solution to these problems of comparing re- source values in alternative used must await much further study. It is evident, however, that the demand for hunting, fishing and other rural outdoor recreation activities in

Arizona is creating a monetary value which recource use administrators must consider carefully in their plans for the future.

36

APPENDIX

A

DETAILS

OF THE ESTIMATION PROCESS

The .general method of this research was an adaptation of the

Clawson

[1959]

-

Hotelling

[1949] approach to estimating the demand for and value of outdoor recreation as described in a general con- ceptual manner in the text. This appendix focuses on details of the specific estimation process.

RESEARCH DESIGN

Given the decision to estimate the demand for all types of rural outdoor recreation in all areas of Arizona, the relevant population to sample for basic data became the total population of the state.

Brown and Nawas

[1972, 1973] have discussed im- proved estimates of outdoor recreation demand func- tions made possible by using observations on indi- vidual recreators rather than the traditional ap- proach of averaging individual observations within distance zones as with the original Clawson approach. They showed that with the more efficient use of individual observations, distance traveled

(a surrogate variable for travel time) could be in- cluded in the statistical demand equation without introducing problems of multicolinearity with vari- able trip costs.

The result of doing so was an improvement in the specification of the demand model, consequently reducing the specification bias of the estimated coefficients for the important variable

- cost variable, and resulting in a larger estimate of value for the value estimate was computed (nondiscriminating monopolist value or consumer surplus value).

For purposes of this study, the household, as a composite of its elements, was determined to be the rural outdoor recreation consuming unit.

The deci- sion to use this definition was based upon the as- sumption that the household is the decision unit.

Even though a member of a household can par- ticipate in a recreational activity on his own accord, the person still functions within the gen- eral decision of the household.

The household is the basic unit "that finances recre- ation out of a common household budget, and the decision to participate is presumed to have house- hold sanction"

[USDI, 1962].

In order to have adequate observations for each statistical demand equation, relatively large num- bers of responses from each area of trip origin in the state were desired.

Population in

Arizona is concentrated in two of the 14 counties. Thus, a random sample of households was selected within each of the

14 counties, the sampling rate per county adjusted to produce approximately 15,000 addresses to which to mail the

14

In the same paper they commented that while they had reduced the strong negative bias resulting from the, complicating factor of travel time and heterogeneity of participants among the various dis- tance zones, there remained the factor of substitute attractions. While the existence of substitute goods would shift a demand curve to the left, an increase in the price of substitute goods will shift the curve to the right. Thus, because the prices of substitute attractions were neglected, a negative bias remained in their estimates, conceptually the best made up until that time, 1972.

This current study of rural outdoor recreation throughout Arizona gave the opportunity to use a large number of individual observations including the mileage variable, as did Brown and Nawas.

In addition, by focusing on all types of rural outdoor recreation activities in all regions of the state, rather than simply on a single activity or a single recreation site as many previous studies have done, it was possible to include the prices of substitute attractions in the regression equations. To the authors' knowledge, this is the first time that sub- stitute attractions have been made an integral part of the evaluation process.

THE QUESTIONNAIRE

The recreation researcher has two alternatives available for accumulating primary data, direct interviews or mailed questionnaires.

The average cost of a direct interview necessary to obtain the information required for the overall study, including the gross expenditure information and socioeconomic data reported in

Gum et al. [1973], was estimated at

$30 to $40 compared to approximately

$0.30 for a mailed questionnaire.

The large number of responses required for this study and the imposed budget limi- tations necessitated the use of mailed questionnaires.

While decreased accuracy of responses was expected from mailed questionnaires, the total number of res- pondents that could be reached due to lower average costs was deemed significant.

The questionnaire was divided into three major areas:

(a) costs of socioeconomic characteristics,

(b) atti- tudinal characteristics toward hunting and fishing, and

(c) three sections relating to participation and participation in hunting, fishing and gener- al rural outdoor recreation activities. Socioeco- nomic characteristics included information concerning age, sex, marital status, education, income, occu- pation, length of vacation, number of children, and

37

number of days off during a normal work week. Ex- planations as to why a household did not hunt or fish more frequently composed the section on atti- tudinal characteristics.

Nonsportsmen tended to underrespond, the weighted average response bias factor over all

14 counties was 1.273.

The range was 1.141 to

1.892.

The sections on hunting and fishing participa- tion inquired about species, game units hunted or fished, total number of trips and total number of days for each species. A page was included for cost information concerning lodging, food, transportation costs, and other variable expenses for the average trip for each species in each unit.

A map showing hunting units was provided by the Arizona

Game and

Fish

Department to assist respondents in recalling areas visited. The general rural outdoor recreation section also inquired about the type of activity, place, total number of days, total number of trips, total number of people and lodging, food, transpor- tation costs and other variable expenses.

The difficulties encountered when one goes to a large mail sample, stratified by counties, are obvi- ously formidable and invite response bias.

The authors were sorely tempted to concentrate on a completely random sample of a defined popula- tion such as hunting and fishing license holders as, for example, did the earlier Davis studies

[1962,

1967].

However, if a regression equation for each of eight activities in each of seven regions was to be estimated, if alternative activities were to be included in the regression models, and if the par- ticipation, expenditures and socioeconomic character- istics of nonhunters and nonfishermen were to be characterized, the large sample of the total popu- lation, stratified by location, was necessary.

RESPONSE AND RESPONSE

BIAS

Total usable responses to the 14,713 mailed questionnaires were 2,926 or 19.9 percent of the mailing. Usable response was about 0.6 percent of the total state population of households, ranging from a response of 3.79 percent in a large, sparsely populated county to

0.18 percent in the most metro- politan county. Since response to the mailing was not 100 percent, there was the possibility of response bias.

Other types of bias due to nonresponse are possible. For example, response rates may have varied with income, education, age, etc. Except for sampling nonrespondents there is no way to adjust for these latter sources of possible bias.

However, since among respondents these socioeconomic variables were not highly significant in explaining partici- pation rates, one could conclude that nonresponse associations with these variables would not greatly affect the estimates.

RESULTS OF THE STATISTICAL ANALYSIS

ies.

Respondents were classified into five categor-

The categories were those households who pur- chased one or more hunting license only, those who purchased one or more fishing license only, those who purchased both hunting and fishing licenses but did not have a combination license, and those who did not purchase any licenses at all. By comparing response data with actual licenses sold, it was found that households owning a combination license, the avid sportsmen, responded at a rate of slightly over twice their proportion in the population. Thus, it was assumed that within each county, combination license- a random fashion, but at a statewide rate of slightly over two times their actual frequency in the population.

Their responses were adjusted downward by a factor of 0.4596.

Households who were only fishermen also over- responded slightly. Their bias factor was 0.8547.

Households which only hunted underresponded and were thus assigned a bias factor of 1.1920.

A weighted average bias factor of 1.0010 was computed for the households which had both hunting and fishing licen- ses but did not own a combination license. derived out of a possible

56

(7 regions times

8 activities).

Skips occurred where there were less than

25 observations. The number of observations per equation ranged, for hunting, from

25 to 268; for fishing, from 53 to 615; for general rural out- door recreation, from 210 to 644. As

Brown and

Nawas [1972] noted, R2 values were not high. The ranges and means for the equations selected as the

"best" for each region and activity

(14 alternative formulations were tried for each demand equation) are as follows: hunting,

29 equations with R2's of

.09 to .82, mean

= .33; fishing,

13 equations with

R2's of

.07 to .59, mean

= .32; general rural out- door recreation,

7 equations with R2's of

.21 to .40, mean

= .32.

However, interest was not specifically in obtaining high R2 values but rather in the re- liability of the estimated structural parameters, especially those of the cost variable from which the value of the resource itself is derived under the

Clawson

[1959, 1949] approach.

Given the response rate for each of the 14 counties and the six statewide bias factors for license holders, it was possible to estimate the number of nonlicense- in each county and thus, to compute a response bias factor for nonsportsmen in each of the 14 counties.

In searching for stable, significant, cost coefficients, each demand relationship was estimated with

14 alternative selections of variables as de- scribed in Table

24.

The dependent variable was always household and the cost variable (vari- ables

1 and

2) was the average cost of the trip to that region for that activity, so that, under the second stage of the analysis, added costs could

38

TABLE

24.

VARIABLES INCLUDED

IN

EACH OF

14

EQUATIONS

FIT TO THE DATA ON EACH ACTIVITY

IN

EACH REGION.

Variablesa

Dependent Variable

Number of trips for activity i to on j i n

1970

1

2

3

4

5

6

Selection

7

8

9

10

11

X X X X X

X

X

X X

Independent Variables

1

.

Average variable cost of trips ij

2

.

(Variable #1)2

X X X X X X X X

X

X X X X X X X X

X

3.

Average round trip mileage ij

4.

(Variable #3)2

5.

Total days of outdoor recreation taken in 1970

X X X X X X X X X

X

X X

X X

X X X X

X X

X

X X

X X

X X

6.

Total dollars of outdoor recreation variable expense i n

1970

9.

Total recreation variable expense as a proportion of income

10.

Average variable cost of all other hunting trips

X

X X X X X X

7.

Average variable cost of all other recreation trips taken, excluding trips ij

X

8.

Total recreation days as a proportion of vacation days

X X

X

X

X

X

X

X X

X X

X

X

11.

Average variable cost of all other fishing trips

X

X

X

X

12. Average variable cost of all other general rural outdoor recreation trips

13. Age

14.

(Age)2

X X

X

X

15. Vacation

16.

(Vacation)2

X

X

17. Education

18.

(Education)2

19. Income

20.

(Income)2

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

12

13 14

X

X

X

X

X

X

X

X

X

X

X

X

X

X a

Data relate either to total household (e.g. cost data) or to head of household

(e.g. age).

39

have the practical interpretation of an entry fee per auto into the resource region for the purpose of a particular activity.

When mileage

(tre time) is excluded from the equation, the cost coefficients are usually larger than when mileage is included as a variable. Under either case, the cost coefficients may be highly significant.

Thus, estimates of recreational values per trip derived from grouped data, as they usually have been derived in the past, will usually under- estimate the value of the resource since mileage (a surrogate for travel time) cannot be included in the equation without problems of multicolinearity.

There will be exceptions, however, depending on the type of activity and the distances involved. For example, small game is usually hunted relatively close to home.

For small game hunting in most Ari- zona regions the coefficient on mileage was not sig- nificant and the introduction of this variable into the equation led to higher estimates for the coef- ficients on cost and thus, to lower estimates of value.

Variable

5, total days of rural outdoor recre- ation taken in the year, proved quite important in stabilizing the cost coefficients.

The coefficient on total days was consistently positive and highly significant, especially for the activities of fish- ing and general rural outdoor recreation where "t" values were as high as 12.

This variable may be viewed as a surrogate for positive "tastes and pre- ferences" for rural outdoor recreation. Inclusion of this variable tends to lower the size of the cost coefficients, though by not nearly as much as the inclusion of mileage, and to raise the estimated value of the resource. including Variable

7 was chosen as the equation with the least specification bias if Variables

1 and

2 were statistically significant.

If the cost vari- ables of that equation were not significant, selec- tion 13 was the second choice. If the cost vari- ables in the first two selections were not signifi- cant, selection

14 was used. In a few cases, se- lections without statistically significant coef- ficients were used in order to obtain a value for the region and activity, if the coefficients were of the right sign and the demand equations developed looked reasonable when compared with equations for other regions for the same activity.

EVALUATING

THE

RESOURCE

In the approach to recreation demand, the statistical de- mand curve (which describes the demand for the total recreation experience) is used to estimate a second demand curve which describes demand for the specific resource or activity itself.

For example, the statistical demand curve for the total experience of hunting deer in

Region

7, is used to develop a demand curve that describes the alternative quan- tities of deer hunting trips that would be made to

Region

7 at alternative additional costs- -for ex- ample, at alternative entry fee charges.

Of course, access to the region for the activity is now free, and probably always will be, but one wished to know how much households would pay and participate if a were charged.

Mechanically, each regional activity was evaluated as follows:

Inclusion of the other variables listed in

Table

24 did not have consistent results. One vari- able might be highly significant for a particular activity in a particular region and not significant elsewhere. Inclusion or exclusion did not materially change the size of the estimated cost coefficients.

However, in many cases, Variable

7, the

"average variable cost of all other rural outdoor recreation trips taken," was positive and significant.

In

Table

25 are listed the regression coef- ficients for costs and the prices of alternative activities, along with their corresponding "t "2 values, number of observations involved, and R values for each of three selections for each acti- vity and region where estimation of a statistical demand equation was at all successful. In each case the coefficients are shown for selection 14 where the only independent variables were costs and costs squared. Each case also shows the coefficients of selection 13 where mileage was also included as in- dependent variables. The other selection shown is the "best" equation that includes

Variable

7, the cost of alternative outdoor recreation trips.

The selection actually used in the evaluation process described below is footnoted. The best equation

1..

A new demand curve for each individual household was estimated, using the house- hold's observed number of trips as maximum trips at zero cost. The household's de- crease in trips was estimated as costs in- creased, until the household's trips became zero or started increasing.

(The estimate would begin increasing in certain cases where the statistical demand curve reached a minimum before touching the cost axis.

Since an increase in activity in response to increased cost is not logical, estimated activity was set at zero if the minimum point was reached before estimated activity reached zero.) This procedure utilized the actual number of trips taken by a household and its actual costs per trip to define the household's individual demand curve. Only the two regression coefficients on cost are eliminating specification bias in developing the sta- tistical demand equation.

All independent variables other than the cost variables are ignored since the effects of these shifter variables are included by computing individual demand functions starting with actual trips at zero added cost. That is, each individual household in the sample,

40

Actual trips

-

changein

trips

= estimated new trips

Change in trips

=

-b1(added cost) -2b2(original cost x added cost)

-b2(added cost)2 where

Derivation of the computational equation is as follows:

Let T1 = estimated trips at actual cost

T2

= estimated trips at added cost

Therefore, Change in trips = T1

-

T2

T1 - T2 = a

+ b1(OC)

+ b2(OC)2 b

1 is the coefficient of variable

1

(Table

1) b2 is the coefficient of variable

2

(Table

1) added cost

=

1, 2, 3,

.

.

. ,

1,000 original cost is the observed value of variable

1 for the individual household

-[a + b1(OC

+

AC)

+ b2(0C +

AC)2] where OC is original cost

AC is added cost a is the regression constant bl,b2 are defined as shown above

2.

Estimates for each individual household were expanded by the relevant response rate and adjusted by the relevant bias factor.

Thus,

T1

- T2 = a-a

+ bl

(OC) - bl(OC)

- bl(AC)

3.

Expanded and adjusted individual demand curves were aggregated.

4.

The aggregate number of trips and the associated total revenue were printed out at each level of added cost.

5.

The nondiscriminating monopolist value

(maximum total revenue) and associated added cost were selected by inspection.

+ b2(OC)2 -b2[(0C)2-2(0C)(AC)-(AC)2]

=

-b1(AC)

-

2b2(0C)(AC)

- b2(AC)2

6.

The consumer surplus value was the cumu- lative sum of estimated trips since trips were estimated for each additional dollar of added cost until total estimated trips became zero.

41

TABLE

25.

REGRESSION COEFFICIENTS,

"t" VALUES,

NUMBER OF OBSERVATIONS AND R2'S FOR THE STATISTICAL

DEMAND EQUATIONS.

Demand Equations

1

Independent Variable

2

7

Number of

Observations

R2

Deer Hunting, Region

1

Selection

5a .021827

(1.27)

152 .43

Selection

13

Selection

14

-.029720

(3.71)

-.104140

(3.79)

-.132790

(5.64)

.000665

(3.20)

.000669

(2.97)

.000809

(3.81)

152

152

.25

.23

Deer Hunting, Region

2

Selection 6a .011431

(0.70)

268

.24

Selection 13

Selection

14

-.029841

(3.42)

-.022110

(2.75)

-.038508

(6.31)

.000034

(2.97)

.000027

(2.33)

.000048

(5.08)

268

268

.19

.14

Deer Hunting, Region

3

Selection

6

.011971

(0.62)

112 .33

Selection

Selection

13

14a

-.032488

(0.98)

-.035066

(1.02)

-.091092

(2.96)

-.000134

(0.36)

.000101

(0.26)

.000641

(1.77)

112

112

.22

.14

Deer Hunting, Region

4

Selection 6a .001468

(0.21)

61

.13

Selection

Selection

13

14

-.015683

(0.61)

-

.006989

(0.28)

-.006650

(0.28)

-.000041

(0.19)

-.000054

(0.25)

-.000051

(0.24)

61

61

.05

.03

Deer Hunting, Region

5

Selection

6

-.035651

(1.60)

88

.19

Selection

13

Selection

14a

-

.077799

(1.27)

-.091347

(1.49)

-.156070

(3.19)

.000125

(0.14)

.000273

(0.31)

.001130

(2.51)

88

88

.17

.13 a

This selection was used in computing the values for the regional activity.

42

TABLE 25.

(CONTINUED) STATISTICAL DEMAND EQUATIONS.

Demand Equations

1

Independent Variable

2

Deer Hunting, Region

6

Selection

9a

Selection

13

Selection

14

-

.045295

(2.17)

-.041460

(1.97)

-.046001

(2.43)

Deer Hunting, Region

7

Selection

Selection

10a

13

Selection

14

-.032970

(3.53)

-.030462

(3.22)

-.027966

(3.43)

Other Big Game Hunting, Region

1

Selection

5

-.005526

(0.54)

Selection

Selection

13

14a

-.007835

(0.78)

-.025424

(2.91)

Other Big Game Hunting, Region

2

Selection 5a

-.060328

(1.70)

Selection

13

-.056087

(1.64)

Selection 14a

Other Big Game Hunting, Region

5

Selection

5

-.024663

(1.20)

Selection

13

-.065591

(2.60)

Selection

14a

-.014014

(0.82)

-.021262

(1.27)

.000190

(1.40)

.000187

(1.35)

.000212

(1.65)

.000102

(2.28)

.000097

(2.13)

.000087

(2.10)

.000002

(0.20)

.000005

(0.68)

.000019

(2.63)

.000269

(1.37)

.000233

(1.16)

.000279

(1.64)

.000040

(0.36)

-.000004

(0.41)

.000070

(0.82)

7

.005756

(0.40)

.016505

(2.54)

.020574

(1.17)

.041230

(1.39)

-.034713

(1.11)

Number of

Observations

120

120

120

165

165

165

128

128

128

117

117

117

67

67

67

R2

.15

.07

.07

.13

.10

.09

.23

.10

.09

.19

.15

.07

.25

.09

.04

43

TABLE 25.

(CONTINUED) STATISTICAL DEMAND EQUATIONS.

Demand Equations

1

Independent Variable

2

Other Big Game Hunting, Region

6

Selection

5

-.027138

(1.01)

Selection

13

-.028262

(1.14)

-.051700 Selection

14a

Other Big Game Hunting, Region

7

Selection

6a

-.092214

(1.27)

Selection

14

-.054583

(1.11)

Small Game Hunting, Region

1

Selection 5a

Selection

Selection

13

14

-1.350200

(2.90)

-.649130

(1.18)

-.733510

(1.78)

Small Game Hunting, Region

2

Selection

5a

Selection

Selection

13

14

-.346760

(3.14)

-.360150

(3.26)

-.305530

(3.00)

Small

Game Hunting, Region

3

Selection 13a

Selection

14

Small Game Hunting, Region

4

Selection

6

-1.303100

(1.68)

-.906630

(1.41)

Selection

Selection

13a

14

-.493270

(1.42)

-.857040

(2.01)

-.888070

(2.68)

.000249

(1.01)

.000255

(1.06)

.000423

.000537

(0.70)

.000382

(0.60)

.022460

(1.01)

.012876

(0.69)

.003793

(0.99)

.007200

(1.52)

.007536

(1.83)

.029603

(2.34)

.011498

(0.73)

.012013

(1.01)

.003208

(2.92)

.003388

(2.78)

.002393

(2.11)

7

.004758

(0.35)

-.013278

(2.01)

.249030

(2.03)

.005907

(0.10)

.271390

(3.72)

Number of

Observations

90

90

90

64

64

70

70

70

118

118

118

81

81

104

104

104 a

This selection was used in computing the values for the regional activity.

R2

.14

.13

.09

.12

.12

.12

.09

.08

.43

.09

.09

.15

.14

.09

.23

.05

44

TABLE 25.

(CONTINUED) STATISTICAL DEMAND

EQUATIONS.

Demand Equations

1

Independent Variable

2

Small Game Hunting, Region

5

Selection 9a

Selection

13

Selection

14

-.326510

(2.88)

-.303790

(2.45)

-.221460

(2.36)

.002674

(1.85)

.002543

(1.59)

.001741

(1.24)

Small Game Hunting, Region

6

Selection lla

7

.037761

(1.71)

Selection

Selection

13

14

-.362480

(1.96)

-.525920

(2.73)

-.525530

(3.41)

.003771

(1.17)

.006116

(1.82)

.005901

(2.27)

Small Game Hunting, Region

7

Selection 9a .074278

(0.76)

Selection 13

Selection

14

-.606780

(2.08)

-.360510

(1.19)

-.531080

(2.86)

.004997

(1.75)

.002695

(0.87)

.004068

(1.70)

General Hunting,

Region

1

Selection 9a .146040

(1.11)

Selection

13

Selection

14

-.803450

(1.32)

-.656940

(0.99)

-.382840

(0.76)

.011851

(1.02)

.008320

(0.66)

.003559

(0.34)

General

Hunting, Region

2

Selection

5

.090947

(0.45)

Selection

Selection

13a

14

-.847640

(1.19)

-1.039800

(1.70)

-.451530

(0.99)

.023066

(1.01)

.037362

(2.02)

.015618

(1.11)

Number of

Observations

192

192

192

169

169

169

129

129

129

35

35

35

39

39

39

R2

.28

.08

.05

.23

.06

.05

.20

.09

.09

.24

.14

.04

.32

.09

.08

45

TABLE 25. (CONTINUED)

STATISTICAL DEMAND EQUATIONS.

Demand Equations

1

Independent Variable

2

General Hunting, Region

3

Selection 6a

Selection

Selection

13

14

-4.312600

(2.12)

-2.490400

(1.37)

-1.433000

(1.51)

.155230

(1.99)

.070285

(1.02)

.033165

(0.93)

7

-.498290

(1.29)

General

Hunting, Region

5

Selection

6

1.101900

(2.05)

Selection

Selection

13a

14

-.873450

(0.87)

-3.155100

(2.17)

-3.021700

(2.45)

.011485

(0.51)

.057678

(1.85)

.056941

(1.91)

General

Hunting, Region

6

Selection 5a .098011

(0.87)

Selection

13

Selection

14

-1.158300

(2.97)

-

.972310

(2.62)

-.839700

(2.57)

.041093

(2.88)

.033801

(2.60)

.028247

(2.41)

General Hunting, Region

7

Selection 5a .372070

(1.06)

Selection

13

Selection

14

-1.143400

(2.83)

-.900640

(2.03)

-.612810

(1.63)

.017562

(2.40)

.012363

(1.67)

.008253

(1.23)

Waterfowl Hunting, Region

1

Selection 5a

-

.062078

(0.59)

Selection

13

Selection

14

-.528890

(2.23)

-.626300

(1.49)

-.509250

(1.62)

.007677

(1.19)

.010950

(0.85)

.007049

(0.94)

Number of

Observations

29

29

29

25

25

25

43

43

43

33

33

33

31

31

31 a

This selection was used in computing the values for the regional activity.

R2

.43

.17

.15

.26

.18

.14

.82

.18

.17

.80

.33

.25

.49

.16

.11

46

TABLE 25.

(CONTINUED)

STATISTICAL DEMAND EQUATIONS.

Demand Equations

1

Independent Variable

2

Waterfowl Hunting, Region 2

Selection

10a

Selection

Selection

13

14

-1.307300

(3.07)

-1.235100

(2.92)

-1.001800

(2.46)

.032468

(2.60)

.026859

(2.33)

.019799

(1.75)

7

-.144790

(1.16)

Waterfowl Hunting, Region 4

Selection

6

.378100

(1.28)

Selection

Selection

13a

14

-.641530

(0.83)

-2.023300

(2.07)

-2.221100

(2.92)

.003052

(0.17)

.032650

(1.38)

.036635

(2.27)

Waterfowl Hunting, Region

7

Selection

7a

Selection

13

Selection

14

-.514030

(2.11)

-.323230

(1.18)

-.194020

(1.10)

.005999

(1.61)

.003114

(0.75)

.001904

(0.54)

Cold Water Fishing, Region

1

Selection la .091348

(2.45)

Selection

13

Selection

14

-.084474

(2.88)

-.101260

(3.38)

-.184030

(8.20)

.000264

(2.17)

.000324

(2.54)

.000633

(5.82)

Cold Water Fishing, Region

2

Selection 6a

.051678

(1.49)

Selection

13

Selection

14

-.259000

(2.07)

-.214260

(1.72)

-.407750

(4.65)

.002024

(1.75)

.001462

(1.22)

.002944

(2.92)

Number of

Observations

32

32

32

35

35

35

34

34

34

615

615

615

273

273

273

R2

.41

.38

.24

.32

.16

.12

.25

.11

.09

.65

.27

.26

.39

.11

.09

47

TABLE

25.

(CONTINUED) STATISTICAL DEMAND EQUATIONS.

1

Independent Variable

2

Demand Equations

Cold Water Fishing, Region

3

Selection

9a

Selection

Selection

13

14

-.446700

(2.16)

-.676200

(3.05)

-.849570

(4.93)

.002811

(2.03)

.003692

(2.40)

.004768

(3.62)

7

-.359930

(1.95)

Cold Water Fishing, Region

5

Selection

13

Selection 14a

-

.024399

(0.20)

-.200170

(2.19)

-.000485

(0.29)

.001633

(1.56)

Cold

Water Fishing, Region

6

Selection

4a

Selection

13

Selection 14

-.272580

(1.02)

-.244290

(0.83)

-.206340

(0.79)

.002890

(0.48)

.003556

(0.53)

.002999

(0.49)

Cold Water Fishing, Region

7

Selection 4

Selection

Selection

13a

14

-.147030

(1.15)

-.328560

(1.98)

-.436890

(3.24)

.000988

(1.05)

.002176

(1.75)

.002890

(2.65)

Warm Water Fishing, Region

1

Selection

9

Selection

14a

-.011660

(0.25)

-.083853

(2.19)

-.000047

(0.22)

.000297

(1.49)

.017823

(2.98)

Warm Water Fishing, Region

2

Selection 13

Selection

14a

-.134460

(0.22)

-

.685470

(1.94)

.000082

(0.10)

.006443

(1.18)

Number of

Observations

116

116

116

58

58

64

64

64

91

91

91

115

115

75

75 a

This selection was used in computing the values for the regional activity.

R2

.17

.10

.26

.06

.08

.07

.41

.24

.21

.31

.04

.02

.54

.14

.12

48

TABLE 25. (CONTINUED) STATISTICAL DEMAND

EQUATIONS.

1

Independent Variable

2

Demand Equations

Warm

Water Fishing, Region

3

Selection

10a

Selection

Selection

13

14

-.227410

(1.87)

-.212540

(1.77)

-.371300

(3.88)

.000529

(1.67)

.000488

(1.56)

.000826

(2.98)

7

.100770

(0.88)

Warm Water Fishing, Region

4

Selection

5a

Selection

Selection

13

14

-.686270

(2.09)

-1.098600

(2.57)

-1.303800

(3.61)

.010298

(1.81)

.014640

(1.94)

.017717

(2.60)

.050253

(0.97)

Warm Water Fishing,

Region

5

Selection

9a

.047864

(1.82)

Selection

Selection

13

14

-.152440

(2.92)

-.140900

(2.60)

-.191420

(4.53)

.000801

(2.30)

.000733

(1.98)

.000998

(3.07)

Warm Water Fishing, Region

6

Selection

6

Selection

Selection

13

14a

-.271580

(1.52)

-.228640

(1.32)

-.355060

(2.45)

.004328

(1.20)

.003635

(1.02)

.005405

(1.74)

.078143

(1.70)

Warm Water Fishing, Region

7

Selection 6a

Selection

Selection

13

14

-.431280

(3.71)

-.204210

(1.20)

-.334080

(2.66)

.004853

(2.62)

.002509

(0.91)

.003944

(1.74)

-.158850

(4.08)

Number of

Observations

137

137

137

133

133

133

310

310

310

53

53

53

224

224

224

R2

.24

.08

.08

.59

.06

.05

.29

.21

.16

.17

.17

.11

.55

.14

.13

49

TABLE

25.

(CONTINUED) STATISTICAL DEMAND EQUATIONS.

1

Independent Variable

2

Demand Equations

General Rural Outdoor

Recreation, Region i

Selection

9a

Selection

Selection

13

14

-

.016351

(1.71)

-.014215

(1.46)

-

.067280

(8.75)

.000031

(1.31)

.000025

(1.04)

.000132

(5.78)

7

.013951

(1.59)

General

Rural

Outdoor

Recreation, Region

2

Selection

1

.038740

(2.23)

Selection

13a

Selection

14

-.012980

(0.86)

-.028694

(1.98)

-.107390

(9.32)

-.000012

(0.34)

.000055

(1.54)

.000219

(6.77)

General Rural

Outdoor

Recreation, Region

3

Selection la .063990

(1.49)

Selection

13

Selection 14

-.203320

(2.66)

-.134970

(1.68)

-.323680

(5.25)

.000799

(2.14)

.000528

(1.29)

.001253

(3.39)

General Rural Outdoor

Recreation, Region

4

Selection

1

.088883

(2.19)

Selection

13

Selection

14a

-

.046533

(0.38)

-.091952

(0.81)

-.303000

(3.71)

.000145

(0.21)

.000256

(0.39)

.001424

(2.64)

General Rural Outdoor

Recreation, Region

5

Selection

6

Selection 14a

-.027490

(0.54)

-.100480

(2.38)

-.000201

(0.38)

.000689

(1.36)

-.028899

(1.57)

Number of

Observations

644

644

644

767

767

767

277

277

277

210

210

210

472

472 a

This selection was used in computing the values for the regional activity.

R2

.30

.29

.24

.40

.16

.12

.37

.13

.07

.34

.22

.11

.21

.02

50

TABLE 25. (CONTINUED)

STATISTICAL DEMAND EQUATIONS.

1

Independent Variable

2

Demand Equations

General Rural Outdoor

Recreation, Region

6

Selection

3a

Selection

Selection

13

14

-.127300

(1.74)

-.212040

(2.51)

-.263390

(4.18)

.001661

(1.74)

.001941

(1.68)

.001913

(2.30)

7

.028565

(2.27)

General

Rural Outdoor

Recreation, Region

7

Selection

3 .026531

(2.05)

Selection

Selection

13

14a

-.044647

(1.25)

-

.032982

(0.88)

-.112650

(4.30)

.000286

(1.06)

.000137

(0.51)

.000574

(2.51)

Number of

Observations

465

465

465

357

357

357

R2

.21

.10

.06

.39

.06

.05

51

APPENDIX

B

RELIABILITY

OF THE VALUE ESTIMATES

The estimates of value depend on the reliability of the two regression coefficients, b

(on variable cost) and b (on variable cost squared).

Table

25 reports the2regression coefficients used and their associated

"t" values.

In general, a "t" value of

2.0 or higher indicates that the regression coef- ficient is that is, it is un- likely to actually be equal to zero. Most coef- ficients used in computing values had "t" values of

2.0 or higher.

The standard error of each coef- ficient is not reported, but may be easily computed as standard error

(se)

- coefficient t value

Thus,

2 a

4b1 is the "expected value" for the nondiscri- minating monopolist value. For a coefficient one standard error higher than estimated

(b1

+ se), the

2 a value

-

4(b

1

+ se)

, a smaller estimate of value.

Likewise, for a coefficient one standard error lower than estimated

(b1 - se), the

2 value

=

4(b a- se)

'

2 a larger estimate of value.

The nondiscriminating monopolist value esti- mates are computed as the maximum possible size of added cost times visits as estimated from the ag- gregate demand curve, which in turn, was estimated as the sum of the individual demand curves. The range on the

"expected value" of the nondiscrimi- nating monopolist value estimate may be computed as follows:

The ratio of the larger value to the

(the value reported herein) is a2 a2

4(b1

+ se),//4b

1 bl b1

+

se expected value

The ratio of the smaller value to the expected value is

First, assume the simple case of a linear in- dividual demand curve

(the coefficient b1 is assumed negative and b is assumed equal to zero).

Visits are estimated ks

V= a-b1

C a2

4(bl - se) a

2 b1 bl b1 - se where

Therefore, if one assumes a plus or minus one stan- dard error variation in b1, 68 percent of the time

V = estimated visits a = actual visits at zero added cost

C = added cost b1 = the estimated regression coefficient

Thus, nondiscriminating monopolist value

(VAL) is computed as

VAL

=

2

VC

= aC - b1C the value derived will fall between b

1 b

1

+ se b

1 b1 - se and times the estimated value. Further, it can be shown that the difference between the lower pos- sible value and the estimated value will always be less than the difference between the higher possible value and the estimated value.

To find maximum VAL, set

8C - a

-2b1C

= 0

At maximum value

C= a

2b1

If the individual demand curves are linear, the relationships described above will also hold for the aggregate demand curve. Also, the same ratios will hold for the estimates of consumer surplus.

V= a

2 a

, a

Max VAL

=

2b1 2 a

2

4b1

In the more general case, where the individual demand curves are curvilinear, the range and distri- bution of the values computed from the aggregate demand curve can be established exactly only by nu- merical methods. The authors are making such esti- mates but to present them herein would make this report too voluminous.

However, bl is not estimated without error.

An intuitive argument about the range in esti- mated value in the general case leads to the judgment

52

that the relative range in values would be about the same as in the simple linear case.

First, the smallest value would be where the true values of the coefficients were larger than estimated for the linear term and smaller than estimated for the squared term. The largest value would be where the true value of the coefficients were smaller than estimated for the linear term and larger than esti- mated for the squared term. Thus, the variation on the linear terms is the same as in the simple case, and, since the optimum price is likely to be fairly low and associated with a relatively large number of visits, the nondiscriminating monopolist value is likely to occur on the more linear portion of the demand curve before the squared term takes much effect.

Therefore, a reasonable approximation of the possible range in value would be to simply ignore the squared term and estimate the range as in the simple case.

For example, for hunting deer in

Region

1, if one ignores the coefficient b2, an assumption of one standard error leads to a range in the esti- mate for the nondiscriminating monopolist value of from 0.788 to

1.369 times the value reported.

53

APPENDIX

C

VALUES COMPARED

TO

GROSS EXPENDITURES

As discussed in the Foreword, the gross expen- diture method of valuing recreational activity was rejected in this study as being conceptually in- correct.

These data are needed, however, as inputs into the statistical demand equations used and have been summarized for statistical purposes in

Research

Report

No.

270

[Gum, et al., 1973]. has

One reason that the gross expenditure method been popular, to quote from Clawson and Knetsch

[1966], is that "such estimates are likely to yield large figures, which give the impression of a large

-recreation business. Indeed, this is often one of their chief purposes."

Past studies of recreation demand, using the traditional with the data averaged within distance zones, have given nondiscriminating monopolist and even consumer surplus values that were smaller than the gross expenditure estimates.

Thus, at least in some quarters, the gross expendí- ture method remained popular in spite of its con- ceptual inadequacy. because of specification bias even though the gener- al method itself was conceptually correct.

In this in Table

26. study the newer individual observation approach was used and specification greatly im- proved. The results in terms of comparisons of value with the gross expenditure method are shown

Nondiscriminating monopolist values compare favorably with gross expenditure values for most activities. The monopolist values are larger in total, tend to be about as large or larger for the more important activities involving considerable travel and other expense, and are significantly smaller only for those minor activities of waterfowl and general hunting where travel and other expense is relatively minor. Consumer surplus values are very much larger than gross expenditures in total and for all activities except waterfowl and general hunting. For these two activities the values are of similar magnitudes.

However, Brown and Nawas

[1972,

1973] have shown, as discussed in Appendix

A, that previous studies using the traditional Clawson approach have significantly underestimated values

The comparability of the two sets of estimates are mere coincidence. One method of estimation has an acceptable conceptual base, the other does not.

However, the comparisons do show that as the newer methods are adopted, the recreation demand approach may compete successfully on the basis of public relations as well as on its conceptual base.

TABLE

26.

NONDISCRIMINATING MONOPOLIST

AND

CONSUMER SURPLUS

VALUES COMPARED TO ACTUAL VARIABLE

EXPENDITURES,

BY

ACTIVITY, ARIZONA, 1970a

Activity

All

Hunting

Deer

Other Big Game

Small Game

Waterfowl

General

All

Fishing

Cold Water

Warm Water

General Rural

Grand Total,

Outdoor Recreation

All

Activities

Variable

Expenditures

$14,404,064

4,512,211

2,650,100

5,355,458

620,608

1,265,687

$23,422,915

14,065,759

9,357,156

$36,966,767

$74,793,746

Nondiscriminating

Monopolist

Value

$13,885,814

3,717,064

2,034,966

7,752,495

127,412

253,877

$30,057,922

11,225,685

18,832,237

$47,639,237

$91,582,973 a

Expenditures and values are those of and for Arizona residents only. Expenditures and values of and for nonresidents are not included.

Consumer

Surplus Value

$34,480,415

11,246,250

6,100,267

15,651,167

580,882

901,749

$64,374,326

30,244,477

34,129,849

$144,381,917

$243,236,558

54

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W.

W., The

Economic

Value of Hunting and Fishing in Arizona in 1956,

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No.

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Arizona

Game and Fish Department, Phoenix,

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1958.

Boyet, Wayne

E. and George

S.

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E. M.

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Future, Inc., Reprint No. 10, February

1959.

Clawson,

Marion and Jack

L.

Knetsch, Economics of Outdoor Recreation,

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1966.

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Research, the

University of Arizona, Tucson,

1962.

Davis,

William

C.,

Values of Hunting and Fishing in Arizona in 1965, College of Business and Public

Administration, the

University of

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William

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C.

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1973.

Hotelling, Harold, "The Economics of Public Recreation,"

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Prewitt Report, Land and Recreation Planning

Division, National Park Service, Washington,

D.

C., 1949, mimeo.

Kelso,

Maurice

M.,

William

E.

Martin and Lawrence

E.

Mack, Water Supplies and Economic Growth in an

Arid

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University of Arizona Press, Tucson,

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E. and Gene

L.

Jefferies, "Relating Ranch Prices and Grazing Permit Values to

Ranch Pro- ductivity," Journal of Farm Economics, May

1966.

O'Connell, Paul

F.,

"Valuation of

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The Annals of

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1972.

O'Connell, Paul

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Harry

E.

Brown, "Use of

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E.

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Department of Agriculture, Farm Real Estate Market Developments, CD-77, July 1972.

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E.

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56

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