Group Title: general methodology for analyzing demand for outdoor recreation with an application to camping in Florida state parks
Title: A general methodology for analyzing demand for outdoor recreation with an application to camping in Florida state parks
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Title: A general methodology for analyzing demand for outdoor recreation with an application to camping in Florida state parks
Physical Description: xi, 179 leaves : ill. ; 28 cm.
Language: English
Creator: Jennings, Thomas A., 1939-
Copyright Date: 1975
Subject: Camps -- Florida   ( lcsh )
Parks -- Florida   ( lcsh )
Outdoor recreation -- Florida   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Thomas A. Jennings.
Bibliography: Bibliography: leaves 175-178.
General Note: Typescript.
General Note: Thesis (Ph. D.)--University of Florida, 1975.
General Note: Vita.
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Bibliographic ID: UF00098673
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000329088
oclc - 02976018
notis - ABV8650

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The author's gratitude is owed to many persons whose

assistance and encouragement were indispensable to the com-

pletion of this work. Special thanks go to Dr. Kenneth C.

Gibbs for his counsel and guidance throughout the Ph.D. pro-

gram. Gratitude is also expressed to the other members of

the author's committee, Dr. W. W. McPherson, Dr. John E. Rey-

nolds, and Dr. J. P. Heaney, for their invaluable suggestions

and patient editing of the earlier manuscripts.

Appreciation must likewise be extended to Mr. Ney

Landrum, Mr. Jim Pearce, and countless other personnel of

the Florida Department of Natural Resources throughout the

State for their unhesitating willingness to lend expert ad-

vice and provide access to the State Park files.

To Miss Carolyn Crook and Mrs. Pam Bunde, who did

most of the telephone interviewing, the author owes a debt

of gratitude for service beyond the call of normal secretar-

ial duties.

Appreciation is also extended to the Department of

Food and Resource Economics and the Agricultural Experiment

Station for the financial and other assistance without

which none of these words would be written.

Finally, very special thanks to the author's wife,

Diane, for her help, support, and patient endurance of the

long periods of separation and a life style less than befit-

ting a lady of her quality.


ACKNOWLE; Fr E' T ; .............. ....................... ii

LIST OF TABLES.................................... vi

LIST OF FIGURES............................ ........ viii

ABSTRACT ..................................... ... ix


I. INTRODUCTION ......................... ....... 1
The Problem .............................. 1
Objectives............................... 3
Importance and Innovations............... 4
Area of Study............................. 5
Preview of Subsequent Chapters ........... 6

RESEARCH .................................. 9
Direct Versus Indirect Methods ........... 10
The Hotelling-Clawson Approach ............ 11
The Pearse Approach....................... 14
The Gibbs-Edwards Approach................ 15
Some Final Observations................... 18

Basic Definitions......................... 20
Quantity Concepts.................... 20
Facility Price and Ancillary Costs... 22
Toward a More General Theory ............. 23
Conventional Precedents.............. 23
The Basic Implicit Model ............. 24
Relationships Between Facility
Price and Ancillary Costs ................ 25
Ideal Price Proxies .................. 25
Travel Costs Reconsidered............. 27
On-Site Costs Reconsidered........... 31
Ancillary on-site costs
assumed a price.................. 31
Sources of variation in
on-site costs..................... 34


Critical Costs and Prices......... 38
Leisure-Time Constraints.............. 41
Variation in Utility Functions........ 42
Other Related Prices .................. 44
Summary and Implications.............. 44

IV. SELECTION OF THE SAMPLE................... 47
Criteria for Selection of Sample Parks.... 47
Determination of Sample Size.............. 51
Stratifying the Sample.................... 55
Geographical Stratification........... 55
Seasonal Stratification............... 56
Drawing the Sample........................ 58
Concluding Observations.................... 64

Length of Stay per Visit (Dy) ............. 66
Frequency of Visits (V)................... 66
Daily On-Site Costs (Es) .................. 66
Use Fee (U)............ .............. 66
Daily Ancillary On-Site Costs (As).... 67
Adjusted Travel Costs (rEt)............... 69
Visitor Income (I) ........................ 71
Prices of Alternatives to Recreation
at Given Facilities (Px).................. 72
Utility Variables (T)..................... 73
Seasonal Dummy (S) .................... 73
Proximity-to-Sea Dummy (L)............ 74
Group Size (N)........................ 74
Leisure-Time Availability (C)......... 76
Value and/or Type of Fixed
Recreation Equipment (X).............. 77
Visitor Dummy (D)..................... 77
Time-of-Week Dummy (W) ..... ... 77
Critical On-Site Cost (Es or (Es/N)*) .... 78
The General Statistical Model ............. 78
Review of Testable Hypotheses......... 80
Algebraic Equation Forms .............. 82
Conclusion: The Explicit
Statistical Model..................... 85

RECREATION DEMAND MODEL................... 87
The Dv Relationship............... ........ 88
Critical On-Site Cost..................... 102

The V Relationship........................ 104
The Complete Estimated Models ............ 111
A Final Observation on Travel Cost....... 118

DEMAND MODEL................ ............ 120
Using the Model for Prediction............ 120
Variation in On-Site Cost ............ 121
Variation in Use Fee.................. 130
Seasonal Variation in Demand.......... 132
Estimation of Recreation Values .......... 138
Value Received from Northern Parks... 141
Value Received from Southern Parks... 146
Illustrative Example of a Value-Based
Fee Policy................................ 149

VIII. SUMMARY AND CONCLUSIONS................... 154
Summary .................................. 154
Conclusions .............................. 156
Limitations and Suggestions for
Future Research............ .... ......... 160

APPENDICES................... ................... 165

CITED REFERENCES.................................. 176

ADDITIONAL REFERENCES............................. 178

BIOGRAPHICAL SKETCH ............................... 180


Table Page

1 Sample of Representative Parks from
Florida's State Park System, 1973 ......... 49

2 Method of Allocating Recreationist
Interviews among Sample Parks and Seasons. 57

3 Breakdown of Seasons.................. 59

4 First Coefficient Estimates of the
Length-of-Stay (Dv) Relationship:
Florida State Parks, 1973 ................ 89

5 Second Coefficient Estimates of the
Length-of-Stay (Dy) Relationship:
Florida State Parks, 1973 ................. 97

6 Comparison of Dv Relationship Estimated
with and without the Travel-Cost
Adjuster, r............................... 100

7 Coefficient Estimates of the Frequency-
of-Visits (V) Relationship with Adjusted
Travel Cost: Florida State Parks, 1973... 105

8 Coefficient Estimates of the Frequency-
of-Visits (V) Relationship with
Unadjusted Travel Cost: Florida
State Parks, 1973 ......................... 108

9 Mean Values and Standard Deviations
of the Variables for the Samples of
Florida State Park Campers, 1973.......... 114

10 Prediction of the Change in Usage per
Visitor Group Due to a 50-Cent Increase
in Group Daily On-Site Cost............... 125

11 Prediction of Aggregate Change in
Recreationist-Days per Year Due to
a 50-Cent Increase in the Visitor-
Group's Daily On-Site Cost................ 127

12 Prediction of the Change in Fee Revenues
Due to a 50-Cent Increase in the Camp-
site Fee per 12-Hour Period............... 129

Table Page

13 Estimated Value of Camping to the
Recreationist-Group: Northern Parks....... 145

14 Estimated Value of Camping to the
Recreationist-Group: Southern Parks....... 148


Figure Page

1 Location of Sample Parks.................. 50

2 Illustration of Consumer Surplus.......... 140

v i i i

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



Thomas A. Jennings

March, 1975

Chairman: Dr. Kenneth C. Gibbs
Major Department: Food and Resource Economics

Theoretical and empirical models of recreation

demand are developed and the latter estimated for camping

in Florida State Parks. Each model consists of two struc-

tural equations--one explaining length of stay per visit,

the other frequency of visits per month--and an identity

which combines the two structural equations into a rela-

tionship explaining the individual recreationist's total

usage per time period.

Development of the theoretical model leads to

criteria favoring the recreationist's variable daily on-

site cost as the proxy price for recreational facility use.

Applicability of the models to analyzing demand of the

multiple-destination recreationist is achieved by intro-

duction of an adjustment factor applied to travel cost.

Data for estimating the statistical models were

obtained from a survey of past campers to Florida's State

Park System.

Separate estimates are made of the demand for use

of State Park campgrounds north and south of Orlando,

Florida. In addition two versions of the basic model are

estimated for each group of sites; one specifying travel

and on-site cost per recreationist group and the other

specifying those costs on a per-person basis. Estimates

of the structural equations are obtained by multiple linear


The empirical results of specifying costs on a per-

person basis are very nearly the same as those of specify-

ing them on a per-group basis. In general both versions

of the empirical model conform to expectations based on

theory and previous empirical research. While length of

stay is inversely related to both on-site cost (the price

proxy) and travel cost, both frequency of visits and usage

per time period are directly related to travel cost. Some

new empirical evidence of the role of leisure-time con-

straints is presented which suggests that they are of minor

consequence to the recreationist's demand for particular


Seasonal variation in demand and derived value

(consumer surplus) estimates is markedly more pronounced

for the visitor to State Parks north of Orlando. Implica-

tions of this and other characteristics of the empirical

models are examined from the standpoint of their applicabil-

ity to fee-setting policy.



The Problem

Natural resources available for outdoor recreation

comprise a part of society's material wealth. The abun-

dance of such resources in Florida has made recreation a

mainstay of the State's economy [12, p. 5]. It is a sig-

nificant source of export earnings, as it is the primary

attraction to the more than 21 million out-of-state tour-

ists annually, a number three times greater than Florida's

resident population [12, p. 5]. Such considerations arouse

interest in more precise quantitative measures of the econ-

omic value of outdoor recreation.

The economic value of a good exists when buyers

are willing to pay non-zero supply prices to sellers of

the good. The buyer's willingness to pay is summarized

in the demand relationship, which explains quantities pur-

chased for final consumption as a function of the good's

own price and other relevant variables. The demand rela-

tionship also has many additional uses as a predictor of

consumer behavior. The public sector has a need for esti-

mates of the demand relationship for formulating current

operational policies and for planning future facilities.

It has long been politically accepted that the public sec-

tor's responsibilities require substantial participation

in the outdoor recreation industry, including direct own-

ership and operation of common-property recreational lands.

Demand estimates are essential tools for governmental

planning and policy making aimed at securing the "maximum

benefits" (however defined) from lands already in public

use and from the dwindling endowment of lands convertible

to public use.

This study originated from a felt need for improved

estimating procedures in general and for improved estimates

of the demand for camping and associated recreation at

Florida State Parks in particular. Planners in the Divi-

sion of Recreation and Parks of the Florida Department of

Natural Resources indicated a need for the following infor-


1. Estimates of economic value for a given type

of facility to its patrons.

2. Economic criteria for setting campground fees

based on demand and/or value received by


3. Economic criteria for a more rational distri-

bution of fee-revenue quotas among the various

parks and seasons.

Such needs call for reliable estimates of the demand for

recreation at the facilities of interest.

While existing methodologies include some recent

advances which seemed applicable to needs of the Florida

planners, the adaptability of those techniques to that

type of study area remained largely unexplored. Perusal

of the literature reveals, moreover, a scarcity of standard-

ized procedures for specifying a recreation demand model and

interpreting (for purposes of practical application) the

estimates of such a model. Differences of opinion exist

over such basic issues as how to define a recreation quan-

tityunit, how to measure the price of a recreation quantity

unit, and how to handle the leisure-time constraints. In

consequence, the development of a methodology was as much a

purpose of this study as the application to the Florida

State Parks.


This dissertation has three specific objectives:

(1) to develop a general model of outdoor recreation demand

for particular facilities; (2) to empirically estimate par-

ameters of the model with data pertaining to actual campers

at selected Florida State Parks; and (3) to illustrate the

applicability of the empirical model to some typical needs

of recreation facility planning and management--specifically,

the needs for facility value estimates and for criteria

to guide pricing policies.

Importance and Innovations

The main thrust of this study was toward the de-

velopment of a methodology of general applicability to

many types of recreation facilities, including but not

limited to Florida State Park campgrounds. At the same

time, the Florida State Parks represent a more common or

duplicatable type of recreation facility than those to

which previous methodologies have been applied. The pur-

pose of greater generality is well served by the chosen

study area. It illustrates problems that cannot be ignored,

as may have been justifiable for the more nearly unique and

unduplicatable types of facilities analyzed in previous


The model that emerges from consideration of those

problems necessarily incorporates some novel features.

One feature is the use of two equations to explain the

separable components of recreation quantity (visits and

days per visit in this study) and the use of a theoretic-

ally chosen algebraic form which permits the derivation

of a facility demand equation from estimates of its sep-

arable components. Careful analysis is also made of the

theoretical relationships between the price of a facility


and the associated recreation costs commonly used as

surrogates for hypothesized changes in a facility's own

price. Out of this approach comes the introduction of

a travel-cost adjuster, a feature which enables applica-

tion of the model to facilities used largely by non-single-

destination recreationists. More specific theoretical sug-

gestions for the use of proxy prices in prediction and

value estimation are offered. The role of leisure-time

constraints is also explored and some new empirical evi-

dence of their importance presented.

Area of Study

The general study area consists of the 36 Florida

State Parks (including two State Forest Areas) with camp-

grounds. This area covers a large geographical domain--

virtually the entire State of Florida. The recreational

opportunities offered by those parks are as diverse as

the State itself, which possesses not only the longest

coastline of the 48 contiguous States, but a multiplicity

of inland lakes and streams and a terrain that includes

hilly pine forests, swamps, hammocks, lush prairies and

subtropical islands. Climate ranges from the temperature

north where the seasons are well demarcated by temperature

to the subtropical south where seasonal change is measured

more by the ebb and flow of out-of-state tourists. The

tourist seasons are virtually reversed between northern

and southern Florida with summer as the high-demand season

in the north, and winter as the high-demand season in the


Apart from such variation in resource base, all

State Park campgrounds possess certain characteristics

in common. They all provide opportunities for being out

of doors overnight, for socializing and making new ac-

quaintances, for communing with nature, and so forth. All

sites offer some water-based recreation or are near enough

to such facilities for commuting. Such common attributes

suggest the reasonableness of conceptualizing demand models

for groups of campgrounds or for the "average" campground

of a particular group. Such is the nature of demand ana-

lyzed in this study, which presents two separate demand

models; one for northern parks and one for southern parks.

The dividing line between northern and southern parks dis-

tinguishes between the two major climatological zones of

Florida (temperate and subtropical) and falls approximately

on the latitude of Orlando, Florida. Thus northern parks

include all parks north of Orlando and southern parks all

those south of Orlando.

Preview of Subsequent Chapters

The analysis presented in the following chapters
proceeds in three stages: theory, measurement, and

application. Chapter II is a review of major past studies.

It is both a search for theoretical precedents and a sum-

mary of needed theoretical refinements. In Chapter III,

building upon the discussion of Chapter II, is presented

the development of a general theoretical model to serve

as a basis for analysis of the recreationist's demand for

recreation at a given type of facility.

Measurement is the topic of Chapters IV and V. In

Chapter IV the selection of the sample is described, includ-

ing the procedures used in selecting the set of representa-

tive parks, determining sample size, and drawing the sample.

The discussion of Chapter V draws upon the theoret-

ical model to develop a statistical model of recreation

demand. The variables to be measured are described along

with problems of measurement and explicit specification of

the model.

Application involves estimating the parameters of

the statistical model on the basis of a sample and inferring

knowledge from the estimates. The estimating procedure,

basic empirical results, and statistical problems encount-

ered are presented and discussed in Chapter VI. The dis-

cussion of application is extended in Chapter VII to some

illustrative examples of the model's relevance to recrea-

tion facility planning and management.

Major conclusions and results from all previous

chapters are summarized in Chapter VIII. In this chapter


the limitations of the study are also discussed and some

suggested topics for future research in the area of out-

door recreation demand analysis are listed



Public outdoor recreation is not marketed in the

sense of ordinary goods. Many public recreation facili-

ties are free to the individual patron, others charge

only nominal facility use fees. Even those which, like

the Florida State Parks, charge fairly substantial camp-

site fees seldom change them. In order to estimate the

value of a facility's use a demand model must be able to

relate quantity demanded to the entire range of prices

that could be collected from the recreationist without

driving him away from the facility altogether. Actual

variation in facility use fees comes nowhere near to

spanning that range, or any range sufficient to estimate

the price slope of the facility's demand function. This

condition poses one of two major problems that have had

to be surmounted. The other major problem is the need to

quantify recreation, an intangible substance in many if

not most aspects. This chapter reviews past approaches

to these and other problems.

Direct Versus Indirect Methods

Perhaps the most obvious approach to determining

the price slope and range of a demand function would be

to ask recreationists by means of personal interview how

much they would be willing to pay for their use of a

facility rather than do without it. This is the so-called

"direct method". The problem with this approach is in its

application. Hypothetical questions tend to elicit hypo-

thetical answers based on the respondent's own assumptions.

The respondent may overstate his willingness to pay if,

for example, he thinks he might thereby help promote im-

provement or duplication of favored facilities. On the

other hand he might understate his willingness to pay if,

for example, he feared his answer might be used to justify

a hike in facility use fees. The inability to quantify

such biases casts doubts on the accuracy of estimates

based on a direct approach, even though the aim of the

approach is theoretically sound.

Indirect methods involve the use of some surrogate,

or proxy for facility price. More precisely, the recrea-

tionist's willingness to pay is based on observation of

costs he actually incurs in recreating at a facility. Such

a method is employed by the present study and by most previ-

ous studies. For this reason a more detailed review of past

indirect approaches is in order.

The Hotelling-Clawson Approach

For purposes of this study the "Hotelling-Claw-

son" approach refers to all methods that include the

costs of traveling to a facility from various distance

zones as all or part of the facility price proxy. While

Hotelling [18] is credited with the original idea (as ex-

pressed in a letter of 1949 to the U.S. National Park

Service), Clawson's [6] study became the most widely noted

example of its early application. The first step in the

basic procedure is to define concentric zones around the

facility such that the cost of traveling to the site is

approximately the same for all residents of a given zone.

Then a relationship is established between the costs of

traveling from the various zones and the proportion of

people within each zone who visited the site over a given

time period. From this relationship a demand curve is

derived in effect by assuming that a use fee equal to the

travel cost differential between two zones would reduce

the participation rate from the nearer zone to the rate

actually observed from the farther zone. In this way the

number of visits from each zone is estimated as a function

of such hypothetical fee changes and the aggregate facility

demand curve is obtained by horizontal summation of the re-

sulting schedules for all zones.

The basic approach just outlined is essentially

empirical, as pointed out by Edwards et al. [8]. It re-

lies heavily upon the tendency of large aggregates to

exhibit more uniform behavior with respect to a given

influence, namely travel costs, than may smaller sub-

sets of those aggregates. By dealing with such large

populations of people as exist within a given zone, the

influence of other important variables of demand may be

largely averaged out of the picture.

Understandably, refinements of the Hotelling-

Clawson model have included examples of adding additional

explanatory variables, for example family income [3] and

other socio-economic variables, to account for such things

as the quality of the recreational experience [26]. Brown

et al. [3] also enlarged the definition of travel costs

to include not only transportation costs but all en route

costs between a site and the visitor's point of origin.

These so-called "transfer costs" include such things as

food and lodging en route and constitute in general what

is meant by travel costs used in more recent studies of

the Hotelling-Clawson procedure. A noteworthy example is

Clawson and Knetsch [7].

Burt and Brewer [5] have examined the Hotelling-

Clawson approach from the vantage points of rigorous neo-

classical demand theory and value concepts and expanded

it by developing a system of demand equations for alterna-

tive sites in a given geographical region. Their appli-

cation to water-based recreation in Missouri also pro-

vides a useful illustration of econometric principles

involved in estimating such equations.

None of those refinements, however, have chal-

lenged two of the most disturbingly restrictive assump-

tions, namely, (1) that the recreationist's response to

a use fee would be exactly the same as to an equal change

in transfer costs, and (2) that the transfer costs are

incurred solely for the purpose of recreating at given

facilities. Clawson pointed out that total trip costs

represent the price of a "total recreation experience"

[7, p. 33] which includes not only recreation at a given

facility but such additional enjoyments as may accrue

from travel and reflection on the sojourn before and

after its undertaking. Burt and Brewer [5] pay heed to

this latter problem by defining recreation quantity as

total visitor-days including travel time, but this makes

it ultimately more difficult to conceptualize the value

of a facility per se.

The problems with the Hotelling-Clawson approach

have stimulated searches for alternative indirect methods.

Two of these, the Pearse approach and the Gibbs-Edwards

approach, will now be described.

The Pearse Approach

Pearse [23] has proposed a method for estimating

consumer surplus without a demand curve. A demand curve

could, however, be derived from his consumer-surplus

estimates. The method involves dividing the sample of

recreationists into several income groups and estimating

consumer surplus for each income group as the average

difference between the "fixed cost" (which includes travel

cost) of each group member and the highest fixed cost which

is paid by the assumed marginal participant of the income

group. Multiplying this average consumer surplus by the

number of participants in the given income category and

following the same procedure for all income groups gives

the Pearse measure of consumer surplus earned from recre-

ation in the study area. A literary interchange between

Pearse [24] and Brown and Nawas [4] makes clear that

Pearse is still estimating the value of the Clawsonian

type of total recreation experinece rather than the value

of a facility per se. More disturbing is the dependency

of Pearse's consumer-surplus measure on the width of his

income groupings. In general, the narrower the range of

incomes defined for each group, the smaller the estimated

consumer surplus, which would disappear altogether were

every income in the sample defined as a category. In view

of this latter point alone, the Pearse approach seems con-
signable to the realm of historical curiosities.

The Gibbs-Edwards Approach

Another group of writers, exemplified by Gibbs

[15] and Edwards et al. [8], divide total variable trip

costs into travel costs, i.e., all costs incurred while

en route to and from the facility, and daily on-site

costs, i.e., the costs per day incurred while actually

recreating at the facility. These two components are

then expressed as separate explanatory variables, with

on-site costs the choice of facility price proxy. This

approach represents a theoretical improvement in light

of the fact that the typical facility use fee is itself

a daily on-site cost, whereas travel costs are off-site

costs. Empirical results of these and other studies

confirm, moreover, significantly different types of recre-

ational response to those two types of costs.

Unlike a facility use fee, however, a recreation-

ist's other daily on-site costs are to a considerable ex-

tent subject to his own discretion. Thus the question

arises whether daily on-site costs are more like a price

than like, say, a utility variable. While the empirical

results have generally confirmed expected characteristics

of a price, the theoretical basis for expecting such char-

acteristics needs clarification.

1See also, for example, Gibbs and Conner [16] and McGuire [21].

Also in contrast to the Clawsonian type of model,

the focus of these studies has been on visitor-days actu-

ally spent at the site (per visit or per time period) as

the recreation quantity variable. This vistor-day repre-

sents a more homogeneous recreation quantity unit than

either the Clawsonian visit (which does not take into

account differences among visitors' lengths of stay) or

visitor-days including travel time (which ignores obvious

differences in the quality of time spent traveling and

time spent at a facility). Visitor-days per time period

on site of a facility constitute a more accurate measure

of facility use intensity, the type of measure of greatest

relevance to recreation planning and management. This

visitor-day is also the conventional product unit on which

facility use fees are levied.

In general, the total usage equation has been ar-

rived at by specifying a single equation explaining vis-

itor-days per time period, for example, as by Edwards et al.

[8]. Theoretically it should be possible to derive a total

facility demand equation from separate equations explaining

visits and days per visit, which could provide additional

useful information about facility demand characteristics.

Gibbs [15] did provide estimates of both the visits and

days-per-visit equations, but did not attempt to derive

from them, or separately estimate, a relationship explain-

ing total visitor-days per time period.

The visitor-day measures time spent recreating,

which can mean time spent in a variety of pursuits depend-

ing upon the proclivities and skills of the recreationist.

Thus in general it is necessary to have some reasonably

homogeneous set of activities in mind when conceptualiz-

ing a recreation demand model using time spent as the

quantity measure. Alternative measures of recreation

quantity appear to suffer at least equally from the defect

of product heterogeneity. For example, Brown and Hammack

[2] have analyzed the demand for bagged waterfowl. It is

highly doubtful whether commodities such as ducks measure

the amount of recreation received by hunters as well as

the time spent hunting ducks.

Gibbs' model contains a novel procedure for empir-

ically delimiting the feasible range of his equation ex-

plaining days per visit as a function of travel and on-site

costs. The essential idea is that there exists some upper

limits to, or "critical" values of, those costs above which

the demand curve ceases to exist, and that the limits would

be reached at some finite quantity demanded. Specifically,

Gibbs hypothesized that (1) the critical on-site cost is,

ceteris paribus, directly related to the recreationist's

actual travel cost and (2) the critical travel cost is

directly related to actual on-site costs. For the single-

destination recreationist, with which previous studies have

been mainly concerned, such hypotheses seem plausible and

are supported by the empirical results. For multiple-

destination recreationists the critical costs may be

more strongly related to actual costs of visiting other

facilities on their itineraries. An easier way to ob-

tain the critical costs, and one that does not depend

upon such hypotheses, is to find out the minimum amount

the recreationist would be willing to recreate at the

facility and then to read from the demand estimate the

value of the price proxy that corresponds to that minimum

amount of recreation. Examples of this approach include

Gibbs and Conner [16] and McGuire [21].

Some Final Observations

Whatever their differences, a major common feature

of all the indirect methods discussed is the assumption

that the price of using a recreational facility can be

reasonably well reoresented by the costs of certain goods

and services which are purchased in conjunction with fa-

cility use. An implied corollary is that recreationists

would react to a change in a facility use fee in the same

way as they would react to an equal change in those ancil-

lary costs. This assumption is potentially subject to

both theoretical and empirical debate, which is singularly

scarce in previous literature.

Another similarity between previous studies is

the absence of suggestions on how to deal with the mul-

tiple-destination recreationist, that is, the recreation-

ist who visits other sites in addition to the given

facility on a single trip. Travel costs, which explain

so much of the individual recreationist's demand for a

single-destination facility, cannot be relied upon to

explain the demand for a facility visited on an itinerary

that includes other facilities. Since the aggregate de-

mand for many common types of facilities is substantially

composed of multiple-destination visitors, there is clearly

a need for including them in a general methodology.

The role of leisure-time constraints on recre-

ation demand is a topic that has drawn considerable expres-

sions of concern, but little in the way of practical sug-

gestions of what to do about them. Some theorizing has

been done, for example, by Wilson [27], who conceptualizes

outdoor recreation as a consumer-produced good and draws

the interesting, if implausible, conclusion that the search

for a facility price proxy is irrelevant. Whether leisure-

time constraints are at all important is debatable, since

no quantitative estimate of their importance to a recre-

ationist's demand for use of a given facility can be found

in previous literature.

This completes the summary of the historical con-

text from which the present study emerges. The next topic

is the development of a more general theoretical analysis.



The objectives of this chapter are to set forth

a general theoretical framework for analyzing recreational

demand and to establish guidelines for the use of travel

and/or on-site costs in estimating a market-equivalent

facility price.

It is necessary to begin with working definitions

of recreation quantity and price concepts. Following this,

basic questions are raised concerning how demand for recre-

ation can be modeled on the framework of conventional de-

mand theory. Then a general model is developed which

explores the theoretical relationships between the neg-

ligibly variable facility price and the related consumer

costs--namely, travel and on-site costs commonly used as

proxies for facility price. This model suggests answers

to the questions posed concerning the applicability of

conventional methodologies.

Basic Definitions

Quantity Concepts

Recreation is an intrinsically intangible essence,
the quantifiability of which is on par with that of love,

hate, and tolerance. However, the use of many types of

recreational facilities can be conceived as tangible,

measurable, and even marketable. It is the marketability

aspect of facility use, primarily, that commands the at-

tention of economists and defines the appropriate limits

of economic analysis. Most so-called "recreation-demand"

studies are, in fact, facility-use-demand studies.

"Use" can also imply many things, some tangible

and some not. For present purposes a unit of use will be

defined as a day spent patronizing a facility by a typical

visitor.2 This visitor-day is both an easily measurable

quantum and the one most commonly found to be the standard

pricing unit; examples being a daily entry fee or daily

campsite fees charged overnight visitors.

A theory of demand for use of a facility must

therefore explain variation in the number of visitor-days

taken per time period by patrons of a given facility.

From the individual visitor's standpoint there are actu-

ally two decisions to be made: One of how many visits to

make to the facility (how frequently to visit) and the

other of how long to stay on a particular visit. Let V

equal number of visits per time period and D equal days

per visit. Then total aunatity of recreation (usage)

demanded per time period is Ds, given by:

2The "visitor" in this quantum may refer to a single person, a
family group, or any other convenient decision-making unit of humanity.

(1) D = V D D

A complete theory of recreation demand should explain

variation in both V and D

Facility Price and Ancillary Costs

In practice the day-use, campsite, and other use

fees actually collected, or potentially collectible, from

patrons of public outdoor recreational facilities are pre-

cisely the type of charges that would be used to calculate

facility price schedules of privately owned and income-

oriented facilities. Such use fees are therefore defined

for present purposes as composing the facility price of a

visitor-day at any facility, even largely free public fa-

cilities. The facility price will hereinafter be desig-

nated "U", for "facility use fee".

In addition to facility use fees, the recreation-

ist incurs other associated, or ancillary, costs of re-

creating at a givenfacility. These ancillary costs are

for present purposes sorted into two categories; (1) on-

site costs and (2) travel costs. Ancillary on-site costs,

A comprise all tangible expenses of goods and services

consumed while actually recreating at the facility net of

the facility use fee U which, to repeat, has been desig-

nated the actual facility price. Travel costs measure

all costs incurred while traveling to and from the facility,

including expenditures for lodging, meals, and all other

purchases associated with traveling as well as transpor-

tation costs.

Toward a More General Theory

Conventional Precedents

In conventional demand theory the consumer chooses

a particular bundle of goods according to his preferences

as constrained by his money income and relative prices

of all goods that tempt him. Conventional theory of de-

mand for a particular good must therefore explain the

quantity demanded, say Ds, of the good as a function of

its own price U, consumer income I, the set of prices for

all other likely-to-be-purchased goods Pr, and individual

preferences, or tastes, T. In implicit equation form

this can be expressed as:

(2) Ds = Ds(U,I,Pr,T)

The task of adapting this model to the analysis

of outdoor recreation demand is the subject at hand.

There are six topics of concern: First is the already

mentioned decomposability of Ds into V and D Second

is the search for proxy prices to represent changes in

the negligibly variable facility price U. The logical

place to look for such proxies is in the set Pr of

related prices. Upon establishing some criteria of

appropriate proxies, travel and on-site costs are ex-

amined to see how well they may meet those criteria.

Third is the concept of critical costs, which determine

the relevant ranges of the demand model. Fourth is the

question of how to allow for the possible effectiveness

of leisure-time constraints in recreation demand models.

Fifth on the agenda are taste shifters, or ways to ana-

lyze changes in the recreationist's utility function.

Sixth, prices of substitutes and complements of a given

facility are considered. Because the roles played by

available choices of price proxies (on-site and travel

costs) have some bearing on all these issues, it is con-

venient to begin with a somewhat expanded model.

The Basic Implicit Model

A suggested demand model that incorporates all

the quantity and price proxies discussed thus far, as

well as the basic recreation demand relations investi-

gated by previous scholars, is presented in general as:

(3) V = V(U,As,Et,I,Px,T)

(4) Dv = D (U,As,EtI,PxT)

Ds = V Dv
s v

The variable As is the recreationist's daily ancillary on-

site cost, Et his total cost of traveling to and from the

site, I his annual income, P is the set of prices of all

relevant substitutes and complements for the facility,

and T is the set of taste variables, i.e., utility-func-

tion shifters. All other variables are as previously


In the past a major motive for including As, Et'

or both, among the independent variables was for their

assumed role as proxies for facility price U. The need

for a surrogate, or proxy, to represent the facility

price of site use arises from the practical problem of

inadequate variability of U to estimate its influence by

existing methods. Proposed solutions to the problem have

all relied on some assumption that the effects of changes

U on site use could be inferred from the effects of changes

in either ancillary on-site costs or travel costs or their

sum. The purpose of the following section is to review

those assumptions and to state conditions for their valid-


Relationships Between Facility
Price and Ancillary Costs

Ideal Price Proxies

In the context of conventional theory, As and Et

would be regarded as prices of related goods, that is, as

members of the set Pr in Equation (2). It is helpful to

begin with a clear understanding of the characteristics

required of these so-called prices for their use as facil-

ity price proxies.

If one price is an ideal surrogate, i.e., a per-

fect substitute for another, then in technical terms the

true coefficients of the facility price and proxy price

must be equal. Let travel cost be divided by recreation-

ist-days per visit for a moment so as to make their units

consistent with those of U and A Then if travel costs

per day on site, Et, and daily ancillary on-site costs,

As, are ideal proxies for U, it follows that:

Condition (1) DD Ds Ds
sEt aAs sU
IEj IA; = 3

Condition (2) aV aV aV
aE' A U
Ej @As D U

Condition (3) aD aD aD
v v v
E _As U

It would indeed then be possible to predict that the effect

of a hypothesized change in facility price would be identi-

cal to the effect of an equal observed change in either

of the proxy prices, Ef and As. The buyer would be behaving

as if he actually did conceptualize the price of a day's

recreation at a given site as equal to the sum, Et + As

+ U, or, as Clawson [7] later assumed, that the total

price of a visit to the site is viewed as (E' + As + U)

Dv'. In fact such behavior is both intuitively and theo-

retically unrealistic especially where comparison of

travel costs and use fees are concerned.

Travel Costs Reconsidered

Clawson recognized that the visit is also a proxy

for a "total recreational experience" which includes not

only recreation at a given site, but additional enjoyments

that accrue from travel itself. It also includes recre-

ation from other destinations for multiple-destination

patrons. Thus total travel costs of the recreationist

may overstate what he would be willing to pay for travel

solely to a given facility.

In terms of elasticities, if E' is an ideal proxy for U, then
as (Et + U)
(EI + U) Ds must be uniquely valued for a given (E' + U)

regardless of the relative magnitudes of Et and U. If As is an ideal
aDs (As + U)
proxy, then (A + U) D is uniquely valued for given (As + U).
s s D
If both EC and As are ideal proxies for U, then a(E' + A + U)
t s
(E + As + U)
--0-.D s is uniquely valued for given (Ej + A + U). Similar

statements must also apply to the components of Ds, i.e., to V and D .

In theory it is the marginal travel cost of

visiting that facility to which the recreationist should

be sensitive. The marginal travel cost of a given facil-

ity may however range from total travel costs for the

single-destination visitor to near zero for the visitor

who views the given facility as merely a convenient place

for a necessary stop-over en route to major destinations

down the road. Deciding what portions of his total travel

costs are marginal costs of recreating at a given site is

similar to the problem of determining what portion of a

department store's overhead costs is a marginal cost of

merchandising a single item. The problem is that over-

head costs are fixed costs and marginal fixed cost is by

definition zero. Likewise the cost of traveling a par-

ticular itinerary represents a kind of fixed investment

in the access to recreational facilities along the way.

Having made the decision to travel a certain itinerary in-

cluding more than one recreational destination, the mar-

ginal travel cost of recreating at a given facility is in

a similar sense, approximately zero. In an intuitive sense,

however, to assume that no portion of his travel costs ex-

plain the average multiple-destination recreationist's

decision to recreate at a single facility seems as arbi-

trary as assuming that all of his travel costs are relevant

in explaining that decision.

An assumption deemed more plausible is that the

typical multiple-destination recreationist views the travel

cost of recreation at a given facility as less than his

total travel costs but greater than zero. He may, in fact,

arrive at this view while planning his itinerary, much as a

housewife plans her trip for a spool of thread to coincide

with a trip for more major shopping that takes her within

the vicinity of a notions shop. By making the investment

in the trip for major shopping, she reduces the marginal

cost of going for the spool of thread to a possibly non-zero,

but decision-feasible level.

The housewife's decision-feasible marginal travel

cost of obtaining a spool of thread is clearly related to

her evaluation of the thread's importance to her. Indeed,

the ratio of that marginal cost to the total travel cost of

her shopping trip provides a measure of sorts of the rela-

tive importance of the thread among her total purchases.

Conversely, given knowledge of her total travel costs and

a measure of the importance of thread relative to the im-

portance of all purchases made on the shopping trip, an

estimate of her decision-feasible marginal travel costs of

obtaining the thread could be derived. By the same line

of reasoning it may be possible to obtain an estimate of

that fraction of the recreationist's total travel cost

which is relevant to explaining his decision to recreate

at a given facility. Let r be the travel-cost adjuster,

Ms the importance of recreation at the given facility, and

Mo the importance of other recreation received from the trip.

Then r is in theory given by a function such as:

(6) r = ( +s
S o0

On the basis of the above argument it is hypothesized that

the variable r Et is in general superior to either Et

or zero as a measure of the recreationist's relevant travel

costs in his decision to recreate at the given facility.

This is one of the major hypotheses to be tested in this

study. The function, Equation (6), should be specified so

as to give r = 1 when Mo = 0, since when Mo = 0 the recre-

ationist is a single-destination visitor whose entire trip's

travel cost is allocable to his decision to recreate at the

given facility. Also, ideally r should be near zero for

all recreationists who consider the facility as purely a

place on the way to elsewhere.

The plausibility of near zero marginal travel costs

for certain nondestination recreationists presents one pro-

blem with conceptualizing travel costs as a facility price

proxy, even if the perfect travel-cost adjuster r could be

found. Also, the notion of travel costs as overhead still

lingers and raises doubts about their appropriateness as a

surrogate for facility price to even the single-destination

recreationist, particularly if facility price is conceptu-

alized on a daily-use basis. Unlike the typical facility

use fee, travel costs per day on site are obviously vari-

able with respect to length of stay. Such considerations

make travel costs especially difficult to cast in the role

of an approximate, much less ideal, facility price proxy.

On-Site Costs Reconsidered

The simple fact that a facility use fee is itself

an on-site cost directs attention to ancillary on-site

costs as a more logical candidate for the facility price

proxy. To employ them in this role requires some assump-

tions, however, which need to be made explicit in order to

give an idea of how nearly they may approach an ideal price

proxy. Obviously it has to be assumed that ancillary on-

site costs represent a price of something and are identifi-

able as some member of the set Pr of related prices speci-

fied in Equation (2). This assumption is examined later.

For the moment it is accepted in order to examine another

type of problem with the use of the price of one commodity

as a surrogate for the price of another.

Ancillary on-site costs assumed a price. With

reference to Conditions (1), (2), and (3), it helps to re-

flect on the nature of pairs of goods whose prices are

thus related. One possibility is that the goods be perfect

complements; in other words, that the daily recreation

received from expenditures for site-use privileges (i.e.,

the user fees defined as facility price) are perfect

complements to the ancillary inputs purchased with ancil-

lary on-site expenditures. A less stringent condition is

that the privilege of site use and ancillary on-site con-

sumables are either sold or bought as a package, though not

necessarily in rigidly fixed proportions. The cost of the

angler's daily bait and tackle consumption could, for ex-

ample, be an ideal proxy for the facility price of a given

site, but only if there were no alternative place at which

to fish. On this assumption a dollar-per-day change in the

cost of bait and tackle would change the rational consumer's

quantity of site usage by the same amount as would a dollar-

per-day change in the daily site-use fee, or facility price,


The assumption that the ancillary inputs bought

with on-site costs are specific to a given site is gener-

ally untenable. It takes only one other alternative site

at which to fish to make the daily bait and tackle costs

less than an ideal proxy for facility price. In many cases

a change in ancillary on-site costs better reflects a change

in the costs of recreation in general than of recreation at

4See footnote 3.
See footnote 3.

the given site.5 A general rise in ancillary on-site

recreation costs would therefore probably have less im-

pact on the quantity demanded of recreation at a given

site than would an equivalent rise in the facility price

of recreating at that specific site. Thus to the extent

that ancillary on-site costs include non-site-specific

costs it is hypothesized that the facility price coeffi-

cient of demand exceeds the on-site coefficient of demand;

i.e., that:

Condition (4) DV _V

Condition (5) Dv D v

Condition (6) Ds s
3U DAs

The hypotheses expressed by Conditions (4), (5),

and (6) are of extreme importance to the interpretation

of empirical estimates, including those presented in this

5Other on-site costs, for example food, may better reflect the
cost of subsistence rather than recreation per se. While netting out
subsistence costs is a serious practical problem, it need not be a
theoretical one. Thus for purposes of this discussion As is assumed
to contain no subsistence costs.

dissertation. They also rest on the assumption that As

deserves membership in the set Pr of Equation (2), in

other words, that As is predominately a related price

and not predominately a taste shifter. This arguable

assumption is the next topic of concern.

Sources of variation in on-site costs. It has

been hypothesized on theoretical grounds that the influence

of on-site costs on quantity demanded of recreation at a

given site is less than the influence of site use fees.

This is based on the assumption that on-site costs repre-

sent some price, that is, a member of the set Pr of Equa-

tion (2).

On-site costs are in fact an aggregate concept

defined as follows:

(7) As = PiX

where Pi is the unit price of the ith ancillary good con-

sumed on site, X. the daily quantity consumed of the ith

good on site, and n the total number of goods consumed on

site. In essence, then As is an index of related prices

which are weighted by the Xi for purposes of aggregation.

Unlike more familiar price indices, the price weights X.

are variable and possibly a greater source of variation

in As than are the prices.

The P. can be reasonably assumed given to the

individual recreationist, which is to say that he has no

monopsony power over their formation. The Xi, however,

are functions of the P., consumer income, and the para-

meters of consumer preferences, or utility function.

The correlation between consumer income and on-site

costs seems negligible in light of previous estimates (com-

mon sense suggests a weakly positive correlation). This

leaves the possibility that variation in the X. may be due

primarily to differences in preferences. In other words,

it is possible that differences between on-site costs of

recreationists are primarily a function of consumer pref-

erences instead of the unit prices of real ancillary inputs.

It follows that the observed relationship between

on-site costs and quantity demanded of recreation may be

less a facsimile of a price-quantity relationship than of

a taste-quantity relationship. The author deems this un-

likely although it is to be hoped that some future studies

will seek empirical answers to the question. For present

purposes an answer is suggested by reflection on the myriad

of possible relationships between consumer preferences, con-

sumption of ancillary inputs, and use of a given site. If

all patrons confronted identical P. it would follow that

differences between daily on-site costs of individuals are

due to differences in preference functions. In this hypo-

thetical case the range of plausible relationships between

on-site cost and site usage is enormous. At two extremes,

for example, would be (1) the recreationist who spends

more for ancillary inputs in an attempt to compensate for

the lack of enjoyments offered by facilities perceived as

of inferior quality and (2) the recreationist who spends

less for ancillary inputs at facilities perceived as in-

ferior in an attempt to conserve his resources for greener

pastures down the road.

If all recreationists were of the first type, the

observed correlation between on-site cost and site use

and its components would be negative on the presumption

that the more spent per day, the less desirable the site,

hence the less frequent the visits and/or the shorter the

stay per visit. If all recreationists were of the second

type, the observed correlation between on-site costs and

site use would be positive since, presumably, the more

spent per day, the more desirable the site, hence the

more frequent the visits and/or longer the stay per visit.

Lacking empirical evidence to the contrary, both

types intuitively are equally plausible, which suggests

that the influence (on site use) of tastes reflected in

the on-site costs is perhaps random. This must serve for

present purposes as a working assumption.6

It follows from this working assumption that, if all patrons of
a site were confronted by identical Pi, their behavior with respect to
on-site costs could be predicted equally well by substituting a set of
random numbers for the on-site costs.

Previous studies (e.g., [8], [15], [16], [21])

confirm an inverse relationship between on-site costs and

the components, V and D of facility patronage. Given

the working assumption that tastes reflected in on-site

costs exert a random influence on quantity demanded, this

systematic relationship resembles a price-quantity demand

curve. From the decision to live with that assumption

there follows a commitment to the premise that individual

recreationists indeed confront significantly different P..

In other words, one is led to conclude that ancillary on-

site costs do compose a price index, albeit an index that

contains a random component attributable to the variabil-

ity of consumer tastes for real ancillary goods.

Such are the assumptions behind the choice of an-

cillary on-site costs as the facility price proxy. This

choice is tantamount to respecification of the general

model (page 19) as follows:

(8) Dv = Dv(E ,Et,I,PxT)

(9) V = V(E ,Et,I,Px,T)

(10) Ds = V Dv

The variable, Es, equals U + As. Hence Es becomes the vari-

able facility price proxy on the working assumption that U

and As are additive in the sense of ideal price proxies.

It should be kept in mind that this last working assump-

tion is in violation of the hypothesis stated previously

that quantity demanded of recreation is probably less

elastic with respect to ancillary on-site costs than

with respect to facility use fees.

Critical Costs and Prices

Previous discussions of critical costs have dealt

with the range of the demand model with respect to on-site

and travel costs. The critical values of those costs, as

indicated in Chapter II, are upper limits above which the

recreationist would shun the facility altogether. An

equally pertinent issue is the relationship between the

critical facility price and critical values of facility

price proxies.

An answer is suggested by the hypothesis that use

and its components are probably more elastic with respect

to U than with respect to As because As likely represents

a less site-specific type of cost than U. If A were

totally non-site-specific, exceeding its critical value

would keep the recreationist away from all facilities.

Exceeding the critical site-specific use fee would merely

drive facility to another.

In other words, the less site-specific the cost,

the more its increase is reflected in the cost of recreating

at all sites; hence the less the incentive to abandon only

the given facility. Conversely, the more site-specific

the cost, the greater its increase provides incentive to

seek out less expensive alternatives. From this it fol-

lows that, other things equal, the critical value of an

on-site cost component would be inversely related to the

specificity of that cost component to the given facility.

Hence the critical ancillary cost, A*, would exceed the

critical use fee, U*. In a situation where all observed

variation in Es is due to variation in As, it is thus

reasonable to assume that E* exceeds U* by some amount.

One point, however, must be clear: site specific-

ity is an issue only in a relative sense. If As and U

were equally site-specific--which is the same thing as

equally non-site-specific--then there would be no problem

with the rational consumer, whose demand would be equally

elastic with respect to a given change in the use fee and

in ancillary cost, and whose critical use fee for given

ancillary cost would equal the critical on-site cost, E*
As previously mentioned, the more unique the

facility, the better as a proxy for U. For the poorer

the alternatives to the given facility, the more specific

to that facility are the ancillary costs of recreating


For non-unique facilities Es may still be a good

proxy for U if the market happens to be characterized by

a form of price competition designed to maintain the rela-

tive market shares of all competing enterprises. Pure

competition would give this result although time would

have to be allowed for expansion or contraction of industry

capacity before a predicted equilibrium would be established.

Perfect oligopolistic price leadership would be an equally

suitable and more quickly responsive type of market situa-

tion for assuming Es a good proxy for U, on condition of

course that the given facility is one capable of exercis-

ing the price leadership. In either type of market struc-

ture the key lies in maintaining (i.e., assuming a type of

interdependence between) relative prices of all substitut-

able facilities. The greater the extent to which every

one's use fees vary in tandem, the less specific is a

given facility's price to itself.

Some degree of uniqueness and/or local prominence

among competing facilities is not atypical of many public

outdoor recreation sites. In the cases offacilities such

as Federal and State Parks, their very existence generally

can be attributed to the public sector's unique ability to

conserve large portions of unusual natural environments

and maintain a monopoly over them. The public facilities

may also plausibly exercise a degree of probably uncon-

scious price leadership over such establishments as commer-

cial campgrounds, whose own existences may be due largely

to the public park. Thus the assumption of non-site-specific

use fees and/or site-specific ancillary costs may not be

inappropriate in the cases of such facilities.

Leisure-Time Constraints

In conventional demand theory the consumer's op-

timizing choice among alternative bundles of purchases is

determined by his tastes and constrained by his income,

the latter expressed as a monetary budget constraint at

given prices of available goods. It follows that conven-

tional predictions of consumer purchases rest on projec-

tions of tastes, income, and relative prices. It has been

suggested [7, 27] that leisure-time availability may con-

stitute a more binding constraint than income on the quantity

demanded of recreation.

Surely not everyone has all the time he would wish

for all the recreation he could afford to buy. The impli-

cations of this for analysis of recreation demand at a given

site certainly merit consideration.7

Two points seem worth raising. First, consumption

of virtually all goods takes time, thus recreation is not

Indeed some of the writing on this subject seems almost existen-
tially fatalistic. Wilson [27], for example, presents a way to view
the problem in terms of an extension of neoclassical demand theory in
which recreation is conceived as a consumer-produced activity and he
draws the interesting, if implausible, conclusion that the question of
proxy prices for a facility may be irrelevant.

8Commodities and services for which there may be option demand
constitute a seeming exception.

unique in this respect. Second, income and time constraints

are inextricably interrelated for most people. Nearly every-

one performs some kind of work that could be hired out in

exchange for more leisure time. People who do some of

their own home-maintenance work provide an example.

Thinking about modeling an individual's trade-off

between income and leisure brings to mind a host of vari-

ables including such things as the nature of one's employ-

ment (e.g., time-clock puncher versus self-employed versus

retired), attitudes toward work, leisure, and alternative

uses of leisure time, and other social, cultural, and psy-

chological factors, all of which suggest that an undertaking

of major proportions would be required to do an adequate job.

In view of this and in keeping within the scope of this

study, the author will consign all such variables to the

realm of "random influence." People's opinions may count

for something, however, and a variable is easily incorpor-

ated to distinguish those who feel more bound by time from

those who feel more bound by income.

Variation in Utility Functions

Utility variables are the parameters of the con-

sumer's utility function and thus determine the shape of

the indifference curves on his preference map. In applied

demand analysis it is rarely plausible to assume constancy

of those parameters over a given sample of observations,

and this is especially true where each sample observation

is of a single consumer. Recognizing that each consumer

is an individual--which in economic terms means that no

two individuals have identical preference maps--variation

in utility parameters can be expected to exert a signifi-

cant influence upon the quantity demanded of recreation

at a given site.

A listing of possible proxies for utility-function

parameters would include characteristics of the site along

with characteristics of the visitor. The visitor, having

been defined as any convenient decision-making unit,may,

for example, incorporate various numbers of people, thus

group size suggests itself as one possible utility vari-

able.10 Visitor characteristics also include such things

as amount of durable equipment brought to the site, number

of children in the group, and type of equipment brought

It has been assumed that on-site costs themselves are subject to
variation due to differences in utility function parameters, but that
most of that influence can be treated as a random nature. See footnote
8, however. In general, prior evidence suggests that there do exist
utility variables which, while explaining little of the variation in
on-site costs, may still explain a significant part of the variation in
quantity demanded of recreation at a particular site.

10Some writers, e.g. Gibbs [15] and Edwards et al. [8], have argued
that, due to the variability of group size, travel and daily on-site
costs should be expressed on a per-person basis instead of a per-group
basis. Arguments for and against this adjustment are examined in Chap-
ter IV.

(e.g., tents vs. recreational vehicles). Site character-

istics include such things as location (e.g., seaside or

inland, type of climate), season of year, and type of

recreational activities available.

Other Related Prices

The prices represented by ancillary travel and on-

site costs by no means exhaust the list of relevant prices

whose variation could exert significant effects upon the

usage of a recreation facility. The typical facility is

both in competition with and complemented by other recre-

ational facilities.

Thus prices of those other facilities are a poten-

tially significant source of variation in the demand for

use of the given facilities. Such prices, or proxies for

them, should be incorporated as additional explanatory

variables to the extent that it is feasible to do so and

that seems warranted by nature of the study area. Further

discussion and illustration of practical ways to recognize

the role of some related prices in an empirical analysis

is contained in Chapter IV.

Summary and Implications

The objectives of this chapter were primarily the-

oretical but with a practical goal in mind, namely the

estimation of demand for a public recreational resource

that is sold under far less than the ideal circumstances

assumed by any basic market model of the "textbook" type.

Toward that end a general theoretical model was developed

and represented:

(11) Dv = Dv(E ,rEtI,P ,T)

(12) V = V(Es,rEt,I,Px,T)

(13) Ds V Dv for E < E*
s v s- s

This model is specified subject to a restriction on one

of its variables, namely, E < E*. In Chapter V a sta-

tistical counterpart of this model will be developed by

specification of empirical versions of its variables and

explicit equations for its relationships. Meanwhile the

procedures used to obtain data for the statistical model

are described in Chapter IV.



For a statistical version of the general theoret-

ical model some data are required. The problem was to

obtain a representative sample of data from a large study

area at reasonable cost in time and money. It was discov-

ered that State Park registration files contain names and

addresses of past campers, which raised the possibility

of a telephone survey of those campers as a possibly

justifiable way to cover a statewide system of facilities.

Alternatives were considered and preliminary experiments

tried with a telephone questionnaire. In the end the tele-

phone survey was adjudged the most efficient way for pur-

poses of this study. The next step was to decide which

campers to select and how many of them to interview.

Criteria for Selection of Sample Parks

The only link to past patrons of the State Park

campgrounds was the camper registration card kept at the

parks. Thus even for a telephone survey it was necessary

to go to parks for names and addresses. Both budgetary

and time constraints precluded traveling to all 36 State

Parks, thus making it necessary to select the sample of

campers from a sample of parks. To achieve representa-

tiveness, this selection was made in consultation with

the most knowledgeable people in the Division of Recrea-

tion and Parks of the Florida Department of Natural Re-

sources (hereinafter referred to as DNR). The final

selection is listed in Table 1 and the geographical loca-

tion of the sample of parks is shown in Figure 1. These

parks were selected according to the following criteria:

(1) The number of parks should be large enough

to adequately represent the spectrum of

recreational opportunities afforded in the

two broadly defined regions, north and south

(of Orlando). Based on recommendations of

DNR, six parks were chosen to represent parks

north of Orlando and four to represent Florida

parks south of Orlando.

(2) The sample of parks should be distributed

throughout the state with certain obvious

locational and other geographical distinc-

tions between subregions recognized. Thus

in the north, the Panhandle (Area I) was

recognized as one distinctive subregion, and

the remainder of Florida north of Orlando

Table 1

Sample of Representative Parks from
Florida's State Park System, 1973

Northern Parks

Southern Parks

Area I

Area III

St. Andrews

Florida Caverns

Ochlockonee River

Area II


Highlands Hammock


Area IV

Long Key

Fort Clinch

Bahia Honda

Gold Head Branch

Source: Selected after consultation with knowledgeable
personnel of the Division of Recreation and Parks
of the Florida Department of Natural Resources.

. Clinch


Highlands Hamock

o o Long
oo* Key
Bahia Honda

Figure 1. Location of Sample Parks

(Area II), as another. In like fashion, the

south was divided into the Florida Keys (Area

IV) and the remainder of Florida south of

Orlando (Area III). In sum, the parks listed

under a given "Area" subheading are deemed

equal to the task of giving all parks in that

area their due share of representation in the


(3) The sample parks should include numbers of

seaside and inland parks in approximate pro-

portion to their relative importance in terms

of representativeness of facilities offered

and patronized. The chosen seaside parks are

St. Andrews, Anastasia, Fort Clinch, Long Key,

and Bahia Honda. The remainder of the parks

in Table 1 are inland parks.

Determination of Sample Size

Since the primary purpose is to explain and predict

total number of visitor days, the sample size was chosen

with a view toward satisfying a desired precision on the

random variable, Ds V Dv. An approximate error of 10

percent in the estimate of Ds was deemed small enough to

assure reasonable usefulness of the estimator. Such a

choice is necessarily arbitrary in some degree, as are

other necessary working assumptions that enable use of

data. Fortunately some usable data were available from

a DNR survey of five State Parks which gives a breakdown

of the number of registered campers by the number of days

for which they registered during the fiscal year, July

1969 through June 1970.11 Although many campers make

multiple registrations and thus stay longer per visit

than individual registrations indicate, those data are

assumed to give a reasonable estimate of the variability

of the length of stay, D .

There was no available estimate of the number of

visits per individual camper. Therefore the total number

of visitors, with multiple counting of repeat visitors,

was assumed approximately equal to the number of registra-

tions. Lacking an adequate basis on which to estimate the

mean and variance of V, it was assumed for purposes of

sample-size determination that V was known and constant.

In essence this means that the sample size was chosen to

satisfy a desired precision on D days per visit, rather

than D days per year.

Although the overall distribution of Ds is clearly

not normal, owing to the obvious distinctions that can be

made between overnight, weekend, and bi-weekly campers, it

1Florida Department of Natural Resources, Division of Recreation
and Parks, "Campsite Statistics Survey," 1972. (Mimeograph)

was assumed that a given number of standard deviations

from the mean value, Ds, would bracket approximately the

same proportion of total observations as for a normally

distributed variable. With this assumption and the as-

sumption that V is known, the formula for calculating

the desired confidence limits (L) around the estimated

population mean, VD can be written for a given sample

size, n, as;

(14) L = VI +
v -

where a is the population standard deviation of days per
visit.12 This states, under the given assumptions, that

approximately 90 percent of all randomly drawn samples

of size n will have means within that indicated range.

For present purposes a sample size that gives a 90 percent

probability that the sample mean will differ from the pop-

ulation mean by no more than 10 percent is deemed reason-

able. That is, the sample size, n, should be chosen so


(15) ^2Vo
(15) 2 < 0.1Vfv

Three of the parks surveyed in the "Campsite Sta-

tistics Survey" are north of Orlando and two are south of

12For a detailed explanation see, for example, [14].

Orlando. Those north of Orlando are St. Andrews, Gold

Head Branch, and Lake Griffin State Parks. Those south

of Orlando are Myakka River and Bahia Honda State Parks.

St. Andrews and Bahia Honda are seaside parks and the

others are inland. St. Andrews and Bahia Honda are in

the sample of parks used in this study. Those five parks

together accounted for 22 percent of the total yearly

patronage of State Park campsites, and for 19 percent of

the total number of existing State Park campsites during

the fiscal year, July 1971 through June 1972.13

Embracing the working assumption that those five

parks comprise a representative sample of the State Parks

gives a basis for estimating the size of an adequate vis-

itor sample. The mean and standard deviation of D were

not known, but could be estimated from the known values

of those parameters for the five parks of the "Campsite

Statistic Survey". On that basis, Dv was approximately

2.0 and 5 approximately 2.0, which implies a needed sample

size of about 400. In other words, according to Equation

n > 2V 20
1 VDv

n > 400

1Fort Pickens State Park, which became Fort Pickens National
Monument in 1972, does not figure in the bases of these percentages.

According to this criterion variation in the con-

fidence limits is relatively insensitive to changes in

the number of sample observations. For example, increas-

ing the number of observations from 400 to 500 would re-

duce the estimated confidence interval from 10.0 to 9.0

percent, while reducing the number of observations to 300

would increase the estimated confidence interval from 10.0

to about 11.5 percent. The marginal benefits to confi-

dence of a larger sample size were deemed insufficient to

justify the costs of additional interviews. To aim for a

smaller sample seemed unwise, however, due to the number

of parks being surveyed and the fact that certain small

and greatly underutilized parks could thereby wind up with

only a negligible number of observations allocated to them.

All things considered, a sample in the neighborhood of 400

visitors seemed reasonably adequate to represent the spec-

trum of visitor characteristics for the cost involved.

Stratifying the Sample

Geographical Stratification

The general basis for allocating sample observa-

tions among the 10 "representative" parks was proportional-

ity to total usage measured as recreationist-months per

year. Before that, however, the targeted number of

observations were divided equally between north and

south; that is, the goal was 200 observations from the

sample parks north of Orlando and 200 from those south

of Orlando. A strictly proportional allocation accord-

ing to usage would have given slightly more observations

to the south, but this was believed to be offset by the

larger number of northern parks and the need to assure

an adequate sample from certain northern parks with a

small amount of use. The 200 observations within each

of the two regions were, however, allocated to the indi-

vidual sample parks strictly according to use of those

parks. Those allocations are shown in Table 2 under the

heading, "Number of interviews targeted." For example,

from Table 2, the average number of campsites in use was

146 at St. Andrews during the high demand season, which

is equivalent to 730 recreationist-months, or 730/1890 =

.26 of the total recreationist-months supplied by the six

northern parks in the sample. Thus approximately 26 per-

cent of the 200 observations, or 53 interviews, were al-

located to St. Andrews for the high demand season.

Seasonal Stratification

Seasons were defined for the two general areas

north and south of Orlando. The distinction between sea-

sons is based on the same capacity utilization data sup-

plied for the fiscal year 1972, by DNR. Low season includes

Table 2
Method of Allocating Recreationist Interviews Among Sample Parks

Total usage

Average number
of campsites
in use

ist months

High Low High Low
Season Season Season Season

Proportion of
yearly all-
park usage
High Low
Season Season

Number of
High Low
Season Season

and Seasons,Florida 1973

Number of
High Low
Season Season Total

North Seaside
St. Andrews 146 39 730 273 .26 .10 53 20 44 20 64
Ft. Clinch 61 19 305 133 .11 .05 22 10 22 25 47
Anastasia 109 45 545 315 .20 .11 39 73 31 0 31

North Inland
Florida Caverns
Ochlockonee R.
Gold Head Br.


South Seaside
Bahia Honda
Long Key

South Inland

378 125 1890 875 .68 .33 137 64 117 60 117

102 57 510 399 .23 .18 47 36 34 47 81
54 27 270 189 .12 .09 25 17 13 13 26

175 .15 .08 29
105 .10 .05 20

16 25 17
10 21 10

264 124 1320 868

.60 .40 121 79 93 87 180

Source: Data from DNR.


those months in which the rate of campground usage was

below average for the year, high season includes those

months during which the rate of capacity utilization was

above the yearly average. Some of the individual parks

within a given region exhibited slight differences in

seasonal variation, but the uniformity of seasonal pat-

terns of parks within a given region is as striking as

the contrast between seasonal patterns of the northern

and southern regions. The breakdown of seasons is shown

in Table 3.

The objective of temporal stratification is to

represent the seasons, as well as location, on basis of

usage. Thus as quotas were established for sample visi-

tors from parks, so were they established for sample

visitors by season. The overall summary of the target

sample's stratification by region, park, and season, is

presented in Table 2.

Drawing the Sample

The first step in drawing the sample was to obtain

names and addresses of potential interviewees from the

registration cards in the State Park files. In drawing the

cards both seasonal and subseasonal stratifications were

accomplished by a chronologically systematic selection.

Step one consisted in arranging the cards in approximately

Table 3

Breakdown of Seasons
Florida State Parks, 1973

Area High Season Low Season

North April August (5 mo.) September March (7 mo.)

South December April (5 mo.) May November (7 mo.)

Source: Data from DNR.

chronological order, step two in dividing the total number

of cards by the number of needed sample observations from

the given park. That quotient tells which of the chron-

ologically ranked observations to select. If, for example,

a sample of 50 observations were needed from a park with

10,000 registrations per year, then 10,000/50, or every

200th observation would be drawn from that park, in chron-

ological order.

To allow for people without phones, no-answers,

busy signals, unlisted numbers, and non-communicative

respondents, it was decided to double the number of ad-

dresses taken from each park visited. Thus, continuing

with the example given in the preceding paragraph, every

100th card would be drawn on the assumption that half or

less of the addresses gleaned from State Park files would

fail to provide completed interviews.

Although it was the stated policy of DNR to require

that registration cards remain in State Park Files for at

least one year, certain individual Park Rangers proved un-

aware of the requirement. Consequently it was impossible

to cover all months of both seasons for all parks. For

the worst example, Anastasia held cards only from June,

1973, onward thus permitting only an attempt to meet the

high-season quota for that park. Had Anastasia not fortu-

itously been the next-to-last park on the name-and-address-
collection schedule (it was visited in late July, 1973) it

would have been dropped from the sample. To make up for

this loss, more than the targeted quota of names and

addresses were drawn from Fort Clinch's low-season camp-

ers. Fort Clinch is fortunately similar to Anastasia in

respects deemed sufficient to warrant this measure. For

all other parks an adequate number of cards from some

months of both seasons were available.

The next step was to find telephone numbers to

go with the names and addresses obtained from the registra-

tion cards. To that end both telephone directories and

long-distance information service were used in approximately

equal measure.

The actual interviewing (apart from protesting of

the questionnaire) was conducted from mid-July, 1973, to

late October, 1973. The telephoning was scheduled so as

to contact first those registrants whose visits were

farthest back in the time in order to minimize the ef-

fects of memory loss due to time. Calls were placed on

weekdays between the hours of 6:00 P.M. and 9:00 P.M. in

the respondents' own time zones. Those hours were adjudged

the most likely time to find people at home and not asleep

and also the time least subject to the female-bias14 invar-

iably noted in connection with telephone surveys.

1This refers to the likelihood of finding more women than men at
home during normal working hours.

Table 2 shows the success rate of the survey by

comparison of the actual numbers of interviews completed

with the targeted quotas. The disparities are noteworthy

in terms of lessons contained for future surveys of this


To begin with, the total number of successful

interviews falls short of the overall target by about 10

percent. Of the 200 interviews each targeted for north

and south, 177 were obtained for the north and 180 for

the south, for a total of 357 of 400 for the two regions

combined. While the number of unanswered telephones re-

maining on the total list exceeded this discrepancy, the

proportion of no-answers had risen to a point where the

benefits of an additional interview were deemed less than

the marginal cost of obtaining it. Thus in effect the

cause of the discrepancy was exhaustion of the lists of

potential respondents. The lesson is that more than twice

the number of names and addresses--perhaps two and a half

to three times--per needed interview should have been col-

lected from the park files.

Differences between shortfalls for the individual

parks and seasons can only be explained as a matter of

chance. Overfulfillment of quotas resulted from the

chronological sampling procedure, which in some instances

discovered as unexpectedly large number of cards for a

given season. For example, in the case of Bahia Honda,

cards from the high season were counted first. This led

to the decision to draw every 100th card to meet the

high-season quota. Logically, drawing every 100th card

should also meet the low-season quota, but since the low-

season file was considerably larger than expected (in

relation to the size of the high-season file), the actual

number of cards drawn exceeded the target number.1 This

windfall was later applied to making up for the overall

discrepancy for the southern region.

There are three possible reasons for such dispari-

ties between the expected and actual ratio of high-to-low-

season registrations. The least likely reason is that the

DNR data on campground usage is erroneous. More likely is

that the ratio had changed since the past year or so cov-

ered by the DNR data. An even more likely reason is that

some of the cards were missing due to the haphazard card

filing systems encountered at certain parks. There were

two instances of cards definitely unlocatable to the sur-

prise of everyone concerned.

At any rate, the shortfall is deemed of no serious

consequence and small enough to ignore in view of the

necessarily rough approach used to calculate the target

15There were also instances of surprise in the other direction
requiring that a repeat drawing be made from the file for a given

sample and the sensitivity of confidence to its size.

Concluding Observations

Telephone surveys suffer two obvious defects; one

is the problem of making people willing to divulge per-

sonal details to anonymous strangers, the other of making

willing interviewees remember those details. In addition,

telephone interviews are heretofore untried in this type

of demand study. Experience with the questionnaire used

in this study (which is reproduced in Appendix A) seems

encouraging enough to dispel much of the understandable

timidity against the telephone. Most interviewees ap-

peared pleased with the chance to have their answers

counted and eager to exercise their memories to that end.

Hindsight, moreover, is not necessarily less lucid than

understanding of current events.16

The data actually collected are described in

greater detail in the following chapter, in which the

statistical counterpart of the general theoretical model

is described.

1For more on the advantages and disadvantages of telephone surveys,
see Field [9], who also noted that, "Unlike many telephone interviews,
questions about leisure and outdoor activities generate enthusiasm.
Respondent reservation and aloofness to the interview did not material-
ize as noted in the literature."



In addition to data and some theoretical guidelines,

an empirical analysis requires two things, namely: (1)

a specific model showing interrelationships between vari-

ables and (2) a statistical estimating procedure to test

the model on the basis of the available data. This chapter

deals with the first requirement, that is, the development

of a statistical model. Estimating procedure is the subject

of Chapter VI.

The theoretical model presented and discussed in

Chapter III is as follows:

(16) Dv = D (E,, rEt, I, P T)

(17) V = V(ES, rEt, I, Px, T)

(18) Ds = V Dv for E < E*
s s- s

The variables will now be defined and discussed in terms

of the types of data available for estimating the model.

For this study most of the data on these variables were

obtained by the telephone questionnaire.

Length of Stay per Visit (0v)

In principle the length of stay per visit should

have been obtainable from the camper registration cards

kept by State-Park personnel. In practice, however, time-

in and time-out (especially the latter) were not always re-

corded and there was the additional problem with visitors

reregistering for extensions of stay, hence the problem of

locating all cards for a given visitor. Length of stay

was determined from the questionnaire within a half-day

(six-hour) interval.

Frequency of Visits (V)

Since the estimates in this study are of demand

for groups of State Parks, and seasons were recognized

for their probable influence over the type of visitor and

the frequency of visits, the questionnaire asked for the

number of recreation trips per season which involved camp-

ing at any State Park within the defined geographical

group. This was then converted to a visits-per-month

basis since the seasons are of unequal length.

Daily On-Site Costs (Es)

Use Fee (U)

The range of variation in the daily use fee paid

by Florida State Park campers in 1973 is so limited as to

make user fees inappropriate as a separate explanatory

variable. The basic campsite fee is $3.50 per day.

Those who use sites with an electrical outlet pay an addi-

tional fifty cents per day. One park (Highlands Hammock)

has a so-called "primitive" area that can be rented for

$1.50 per day, but this is the only Florida State Park

with such an option. While it happens to be included in

the sample of parks used in this study, the campers who
use the primitive area are negligible in number. In

view of this condition it was decided to incorporate user

fees and ancillary on-site costs into the single variable,

Es. This is based on the working assumption, which is

necessary to consider ancillary costs as a proxy for U,

that the consumer reacts the same to a given change in

total daily on-site costs whether the source is a change

in facility price or in prices of ancillary goods.

Daily Ancillary On-Site Costs (As)

Total ancillary on-site costs for the entire visit

were obtained with the questionnaire. These are the sum

of (1) the visitor's best estimate of his total expenditures

17"Primitive" is a misnomer for this particular site. It is
actually a partially cleared and largely bleak stretch of what ap-
pears once to have been a scrub-pine forest. Truly primitive areas
would probably command more patrons at higher prices.

for food, beverages, and other grocery items actually con-

sumed while camped on a site regardless of where those

items were purchased and (2) his best estimate of the

value of all other goods and services consumed on-site

regardless of where purchased. The respondent was reminded

of some typical things in the latter category in an effort

to aid his memory of these costs. Total ancillary costs

per visit were then divided by length of stay, Dv, to ar-

rive at As, the daily ancillary on-site costs.

No attempt was made to account for differences

between normal "at-home" costs of certain items, for ex-

ample food, and the on-site costs of equivalent items.

While it is probably true that the costs of meeting normal

subsistence standards are generally higher away from home,

it is less than obvious that campers apply the same sub-

sistence standards at home and away. Thus the usefulness

of excluding at-home subsistence costs from on-site costs

(as some studies have attempted, for example Gibbs [15])

is difficult to gauge. There arises again the question of

how expensive it would be to make such allowance in a rea-

sonably nonarbitrary manner. Rather than attempt spur-

iously precise adjustments to already approximate data,

no such transformation was attempted on the variable, As.

Adjusted Travel Costs (rEt

The recreationist's total travel costs, Et, include

all variable costs of the sojourn away from home net only

of his on-site costs, E Thus they include the visitor's

best estimates of (1) transportation costs of the total

time away from home not spent at a given site, (2) all

lodging costs incurred en route to and from the site, (3)

all food and grocery expenses of consumption en route,

and (4) all other costs of items consumed on the trip but

not at a given site.

For many patrons of Florida recreational facili-

ties a State Park is neither the sole nor the major desti-

nation. Total travel costs thus tend to explain consider-

ably more than a part of demand for the given facilities.

In view of this, only a fraction of total travel costs are

counted toward recreation at the site. That fraction, r,

is the ratio of the total necessary round-trip (directly

to the site and back home) travel time, T1, plus time at

the site, D to total time away from home, T2. In other

words, the travel-cost adjuster, r, is given by:

(19) r = (T1 + D )/T2

Thus time is used to measure the relative importance

specified in the theoretical travel-cost adjuster, Equation

(6), of Chapter III. This admittedly arbitrary adjustment

is deemed less arbitrary than using total unadjusted

travel costs in explaining demand for a site that serves

multiple-destination visitors.

Total actual time away from home (trip time) was

determined with the questionnaire. Total necessary round-

trip travel time was estimated on the basis of the Rand-

McNally [25] and American Automobile Association [1] Maps

and the Official Highway Map of the State of Florida [10].

The first two sources contain estimates of average driving

times between points in North America and the Southeastern

United States, respectively, and those estimates were used

wherever possible. For in-state and border-state visitors

it was frequently necessary to estimate some portions of

driving times on the bases of distance and the author's

own considerable travel experience in those areas.

The driving times charged in the map sources [1,

10, 25] are all between points no more than 12-hours dis-

tant and thus include no allowance for overnight stop-over

times of visitors from more than a feasible day's drive

away. Estimates of total necessary travel time for the

visitor considered as a hypothetical single-destination

visitor thus contain a downward bias which is directly

related to actual estimated driving time. No attempt was

made to correct for this bias in calculating the travel-

cost adjuster, since what may be considered a normal day's

driving time is so highly variable among individuals that

it is impossible to estimate, with any reasonable precision,

the number and length of overnight stop-overs which would

be taken by a given visitor on a sole-destination trip.

Visitor Income (I)

Visitor income used in this analysis is the personal

income (i.e., including income taxes) of the respondent's

own family. A better estimate of actual purchasing power

would have been disposable income (i.e., excluding income

taxes) but it was thought that a typical respondent would

be more aware of his family's before-tax income than of

how much income taxes they pay. In view of the complexities

of federal, state, and local income tax codes, no attempt

was made to derive disposable income from personal income.

A possibly more serious omission is the failure to

account for incomes earned by nonfamily members of the re-

spondent's visitor group. Of course, not all visitors in-

clude nonfamily income earners, but some do. It was, how-

ever, deemed imprudent and doubtfully productive to further

tax the respondent's patience and knowledge with questions

18In theory T1 should be equal to Td + T2, where Td is necessary
driving time and Ts is necessary stop-over time that would be expended
were the visitor a sole-destination visitor. In practice, since Ts
cannot be estimated, T1 = Td. On the average Td and Ts are directly
related; hence the downward bias in r as a function of necessary travel

of such a personal nature about nonfamily associates.

Prices of Alternatives to Recreation
at Given Facilities (P )

The ancillary goods associated with on-site and

adjusted travel costs are essentially complementary with

use of a given facility. Equally important are prices of

alternative commodities, i.e., those that compete with the

given site for the visitor's patronage. Especially of in-

terest to the Florida Parks system are the alternatives

afforded by other campgrounds, especially private ones, in

a competitive vicinity. In practice the opportunities af-

forded by those alternatives are so diverse as to make im-

practical the specification of a few exemplary user fees

to represent the prices of them all.

In the short run it is generally safe to assume

that most of the variation in user fees of private facili-

ties is seasonal. Private purveyors of recreational ser-

vices in Florida are amply sophisticated in the profitable

art of seasonal price variation, as perusal of any major

hotel chain's rate schedule confirms.19 In general the

year can be divided into two seasons: "high season" for

19See for example [19]. Since an already significant and grow-
ing number of private campgrounds are owned by large corporate enter-
prises, including many of the major national hotel chains, a trend
toward similarly complex rate schedules for private campgrounds seems

the period of high demand during which high private rates

are in effect, and "low season" for the period of low de-

mand and low private rates. Thus the qualitative variable

S, which is the seasonal shifter used in this analysis can

be reasonably assumed to explain some of the variation in

recreational usage due to seasonal variation in the prices

of alternative campgrounds.

Utility Variables (T)

The consumer's utility, or preference, function

can not be directly estimated, although changes in some

of its parameters can be represented by several variables

reflecting differences in site characteristics and visitor

characteristics. Both site and consumer characteristics

are related to seasonal change. Other site characteristics

are geographical. Other consumer characteristics include

number of people in the visitor group (group size), leisure-

time availability, value and/or type of fixed recreation

equipment owned, and time of the week during which the

visitor uses the facility (weekend versus other use).

Seasonal Dummy (S)

The seasonal shifter can also be viewed as a

utility variable since consumer tastes for recreation

change with the seasons (which of course provides the

privately exploited opportunities for seasonal price

variation). Of course S is a catch-all variable for all

seasonally induced reactions by both buyers and sellers

of recreation.

Proximity-to-Sea Dummy (L)

Among the most obvious qualitative differences be-

tween Florida State Parks are those between seaside and

inland parks. The qualitative variable, L, is incorporated

to help account for those differences.

Group Size (N)

The group, being by definition the irreducible

consumer decision unit, becomes the analogue to the con-

sumer of conventional demand theory. Carrying out the

analogy, the group-alias-visitor has a preference map de-

picting group tastes for all goods including recreation

at a given site. Among the quantifiable characteristics

of this visitor's preference function is group size. Thus

group size emerges as a taste shifter by definition of

the group as the consumer decision unit.20

It would seem to follow that the other variables--

including on-site and travel costs--should be expressed

on a per-group basis. Other writers (e.g., [8, 15]) have

20The concept of a group preference map finds precedent in the
community indifference curve of international trade theory.

opted for dividing those costs by group size and express

the group decisions as a function of costs per person.

The rationale for expressing costs on a per-person

basis is stated as a need to reduce the variation in those

costs that vary with group size [15, p. 35, 36]. This ad-

justment does reduce the variation in some cost data which

is due to group size. At the same time, some costs per

person are perhaps more variable with respect to group

size because of size economies. An example would be travel

costs, in which transportation expense is important. Trans-

portation cost per person declines as the number of persons

per vehicle increases short of the point at which an addi-

tional vehicle would be needed, and by far the great major-
ity of groups would travel in a single vehicle. Lodging

expense per person is also subject to economies of group

size. Typical hotel and motel rates incorporate additional-

person charges per room which are far less than the single-

person rate, hence per-person lodging expense declines un-

til group size reaches the point at which an additional

room would be taken. Campground fees are typically invar-

iant with respect to group size up to the maximum permitted

per site and very few groups attain that size. Size econ-

omies doubtless also influence such individual on-site

Of course this does not apply to common carriers such as buses
and airplanes, that collect fares on a per-person basis. All of the
recreationists interviewed for this study traveled by private land

costs as food expense (especially for campers, who typi-

cally do much of their own food preparation) and rental

and operation of durableequipment, for example power boats.

For groups that include nonfamily income earners,

family income understates group income. Since income has

an influence on the consumer's demand as a function of

costs, it may be that expressing costs on a per-person

basis is more justified because costs per person are more

indicative of family costs than are costs per group in

such cases [15]. Most camping groups, on the other hand,

probably do not include nonfamily income earners.

In the end, group costs are probably positively

correlated, while per-person costs are negatively corre-

lated, with group size. Lacking evidence that either cor-

relation is significantly stronger than the other, or

that either correlation is even significant, it seems

preferable to include both cost specifications in the


Leisure-Time Availability (C)

The qualitative variable, C, distinguishes be-

tween those recreationists who cited time and those who

cited income as the primary constraint on their recrea-

tion at such State Parks as the ones of interest.

Value and/or Type of Fixed Recreation Equipment (X)

The value of the visitor's fixed recreation equip-

ment has been suggested as an independent variable with

influence similar to that of visitor income. It was

deemed impractical to attempt collection of such data with

a telephone questionnaire. The camper registration card

does not record whether the visitor camped in a tent or

a recreation vehicle. Assuming that in general the value

of tents and associated paraphernalia is less than the

value of recreational vehicles, and that tent campers may

have other characteristics distinguishing their utility

functions from those of recreation-vehicle campers, the

qualitative variable, X, was specified to represent such


Destination-versus-Non-Destination-Visitor Dummy (D)

The questionnaire also asked the respondent to

specify whether the given site was a major destination

or whether he was just passing through. The qualitative

variable, D, was specified to distinguish between major-

destination and non-major destination visitors.

Time-of-Week Dummy (W)

It is also hypothesized that weekend visitors to

the State Parks may possess preference functions different

from those of other visitors. Thus the qualitative variable,

W, distinguishes visitors who camped for two and a half

days (five twelve-hour periods) or less on the weekends

(Friday through Sunday) from all other visitors.

Critical On-Site Cost (E* or (E /N)*)

The critical on-site costs set upper limits to

the range of the component demand equations. Since it

is the maximum value of the facility proxy price that the

recreationist would be willing to pay, it follows that

the recreationist could not be induced to stay less time

per visit than the length of stay that is associated with

that critical cost. The minimum acceptable length of

stay, Dvm, was determined with the questionnaire. Since

the calculation of E or (E/N)* is a derivation from the

estimated model, further discussion is more appropriately

deferred to Chapter VI, which presents the empirical


The General Statistical Model

In terms of the variables just described, the

implicit statistical model becomes:

Model I

Ov = D (Es, rEt, 1, N, S, D, X, C, L, W)

V = V(Es, rEt, I, N, S, D, X, C, L, W)

Ds = V D for E < E*

Model II

Dv = Dv(Es/N, rEt/N, I, N, S, D, X, C, L, W)

V = V(Es/N, rEt,N, I, N, S, D, X, C, L, W)

Ds = V D

for Es/N < (Es/N)*

where the variables are defined as follows:

Dv = the recreationist's length of stay per visit
in 12-hour periods

V = the number of visits per month

Es = daily on-site costs of the recreation group

rEt = adjusted travel cost of the recreation group

Et = total travel cost and

r = the travel-cost adjuster which is the
ratio of Dy plus minimum round-trip travel
time to total time away from home

I = recreationist's family income







N = number of persons in the recreation group

S = a seasonal dummy

D = a major-destination-camper dummy

X = a tent-camper dummy

C = a time-constrained-camper dummy

L = a park-location dummy

W = a weekend-camper dummy

E* = the critical, or maximum, on-site cost the
recreationist would be willing to pay per group

(E /N)* = the critical on-site cost the recreationist
would be willing to pay per person.

Next follows a review of hypotheses about these models.

Review of Testable Hypotheses

Economic theory and existing empirical evidence

suggest that these models possess certain characteristics

that can be stated as testable hypotheses. Of special

interest are the hypotheses discussed in Chapter III con-

cerning the dependency of the quantity proxies on the

price proxies, namely, that when other things are equal:

(HI) Both number of visits, V, and days per visit,

Dv (and thus Ds) are inversely related to

on-site costs, Es.

(H2) Number of visits, V, and total usage, Ds,

are inversely related to adjusted travel

costs, rEt.

(H3) Days per visit, Dv, is directly related to

adjusted travel costs, rEt.

Hypotheses (H1) and (H2) need rest only on the assumptions

that recreation is a normal (i.e., not inferior) good and

that Es and rEt represent prices of goods that are essen-

tially complementary to the recreational services provided

by the given facilities. Hypothesis (H3) is based on the

concept of travel costs as a type of fixed investment in

on-site recreation. The greater the fixed investment per

visit, the greater the number of days per visit needed to

recover that investment.

Further reflection on the relationship between

travel costs and demand as a function of Es suggests the

possible applicability of Marshall's [22, p. 8] principle

of lower elasticity of items less important in the con-

sumer's budget, namely that:

(H4) The on-site cost elasticity of demand is

inversely related to adjusted travel costs

for all quantity proxies.

Proceeding down the list of independent variables,

it is hypothesized that:

(H5) All quantity proxies are directly related

to visitor income, I.

Hypothesis (H5) follows from the normal-good assumption.

Plausible hypotheses about some of the qualitative

variables are fairly obvious in view of their descriptions.

For example, when other things are equal all quantity

proxies are expected to be:

(H6) Positively related to the seasonal dummy,

S, where S = 1 for high season and S = 0

for low season.

(H7) Negatively related to type of fixed recrea-

tion equipment where X = 0 for recreation

vehicle and X = 1 for tent.

(H8) Positively related to the destination dummy,

D, where D = 1 for destination visitor and

D = 0 for non-destination visitor.

Algebraic Equation Forms

Past experience in the estimation of outdoor rec-

reation demand suggests that basic demand relationships

are curvilinear. The simplest types of curvilinear equa-

tions to estimate are logarithmic forms, and in fact log-

arithmic forms have performed well in previous studies.

A logarithmic equation form is especially well adapted to

the model used in this analysis for which the form chosen

must meet the following criteria: (1) It should be pos-

sible to derive an explanatory equation for Ds from the

equations explaining Dv and V. (2) The form chosen should

enable valid tests of all hypotheses. The simplest and

most economical (in terms'of the number of parameters to

estimate) form that meets both criteria results in a

slight modification of the constant-elasticity-of-demand

function. In general the constant-elasticity demand

equation is:

C(26) Y cX 1 c2 c n
(26) Y = X1 X2 ... X = c I X.
n oi=1 1

where Y is quantity demanded, c is a constant or shift

parameter, X. (i=l,...,n) is a price or other independent

variable, and c. (i=1,2,...,n) is the elasticity of demand

with respect to Xi. This function is, of course, linear

in logarithms.

To illustrate, Dv would be related to the three

independent variables, Es, rEt, and I, as follows:

(27) Dv = c Es (rEt) 2 3

The modification which makes the elasticity of E a func-

tion of Et consists in defining c1 = bI + d rEt so that:

b1 + d1 rEt c2 c3
(28) Dv = cE 1 (+ rEt ) 2 3

This is the simplest form of a regression equation which

permits testing of all hypotheses listed above, including

(H4). It is also linear in logarithms.

(29) In DV = In co + b In Es + d1 rEt In Es + c2 In (rEt) + C3 In I

The interaction term, d1 rEt In Es may create more prob-

lems with multicollinearity than it is intended to detect

between adjusted travel costs and the elasticities asso-

ciated with on-site costs. At this stage of the art of

recreation demand estimation however, such experimentation

does not seem amiss.

Given a visits relationship of the same algebraic

form, namely:

b2 + d2 rEt a2 a3
(30) V = a Es (rEt) 2

and the identity which gives D :

(31) Ds = V Dv

it is a simple matter to derive from Equations (29) and

(30) an equation explaining Ds as a function of the same

independent variables:

(bl + b2) + (dl + d2) rEt (c2 + a2) (3 + a3)
(32) Ds = d oaoEs (rEt)3

With this the groundwork is now complete for speci-
fication of the explicit statistical model.

Conclusion: The Explicit Statistical Model

In explicit logarithmic form, the statistical

to be estimated in two versions (one using group

and the other using individual costs) is as follows:

Model I

In Dv = In a10 + all In Es + al2rEt + a13 1n

(rEt) + a14 In I

(33) + a15 In (1/N) + b11 S + b12 D + bl3 X + bl4 C

+ b15 L + b16

In V = In a20 + a21 In Es + a22 rEt In Es + a23 In (rEt) + a24 in I

(34) + a25 In (1/N) + b21 S + b22 D + b23 X + b24 C

+ b25 L + b26 W

(35) lnD = In V + In Dv

In Dv = In a10 + all In

for E < E*
s- s

Model II

(Es/N) + al2(rEt/N) In (Es/N)

+ a13 In (rEt/N) + a14 nI + a15 In (1/N) + b11 S



+ b12 D + b13 X + b14 C + b15 L + b 16

In V = In a20 + a21 In (Es/N) + a22(rEt/N) In (Es/N)

+ a23 In (rEt/t) + a24 In I + a25 In (1/N)

+ b21 S + b22 D + b23 X + b24 C + b25 L + b26 W

(38) In D = In V + In Dv
s v

for Es/N < (E /N)*

The variables are as defined previously on pages 78 and

79. The actual estimation of this model is the topic of

Chapter VI.



The principal empirical results are estimates of

the structural equations explaining days (twelve-hour

periods) per visit, Dv, and visits per time period, V.

Separate estimates of the D and V relationships were

obtained for the two groups of parks north and south of

Orlando, thus providing an opportunity to compare the

model's performance for analyzing recreation demand in

two distinctly different regions. The structures of

these relationships were estimated by the method of ordi-

nary least squares. All variables employed in the equa-

tions were described in Chapter IV. Since there exists

a difference of opinion as to whether on-site and travel

costs should be expressed on a per-group or per-person

basis, estimates were obtained and compared for both


For each estimated equation the residuals were

examined for nonspherical disturbances. In general the

assumption of random errors seems tenable. There is some

evidence of heteroskedasticity in estimates of the visits

relationship, suggesting a geometrically positive correlation

between the error term and number of visits. There was

no attempt to correct for this since a vast majority of

observations fall in a small range of visits within which

homoskedasticity can be reasonably assumed. Thus the

problem was not deemed serious and t-values were assumed

to give acceptable indication of the statistical signifi-

cance of individual coefficient estimates.

No significant problems with multicollinearity

were encountered. Thus the decision whether to delete a

variable with a very low t-value had to rest on grounds

of (1) its theoretical importance in the equation, (2)

its significance in the equation for the other region,

and/or (3) its significance in an alternative specifica-

tion. Each estimate will now be presented and discussed,

The Dv Relationship

Estimates of the Dv relationships with all vari-

ables except time-constraint-versus-income-constraint

dummy, C, included are given in Table 4. Es is the daily

(per twelve hours) on-site costs of the group, rEt is ad-

justed travel costs, I is income, N is group size, S is

the seasonal dummy, D, the destination dummy, X, the tent-

versus-recreation-vehicle dummy, L is the seaside-versus-

inland dummy, and W the weekend-versus-other-camper dummy.

The standard errors of the coefficient estimates are given

Table 4
First Coefficient Estimates of the Length-of-Stay
(Dy) Relationship: Florida State Parks, 1973

In Es In (E /N) In (rEt) In (rEt/N) rEt In Es (rEt/N) In (Es/N)

Northern Parks

(39) (Group costs)

(40) (Per-person

-2.347 -.412***


Southern Parks

(41) (Group costs)

(42) (Per-person

.522 -.520***


Source: Sample data.


10 percent level.
5 percent level.
1 percent level.














Table 4 continued

of 2
Equation In I In (1/N) S D X L W Freedom F R

Northern Parks

(39) .188*** .163*** .183*** .748*** -.085 -.077 .102 166 39.765 .706***
(.069) (.078) (.072) (.074) (.075) (.084) (.084)

(40) .193*** .030 .185** .748*** -.086 -.076 .109 166 39.374 .703***
(.069) (.094) (.072) (.075) (.075) (.084) (.085)

Southern Parks

(41) -.104 -.082 -.081 599*** .213 -.117 -.060 169 26.228 .608***
(.067) (.096) (.088) (.092) (.085) (.091) (.144)

(42) -.105 -.309** -.080 .593*** -.128 -.128** -.108 169 25.356 .605***
(.067) (.120) (.088) (.093) (.086) (.093) (.144)

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