• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Demand for outdoor recreation
 Visits relationship
 Estimates of value to visiting...
 Summary and conclusions
 References
 Back Cover














Title: economics of water-oriented outdoor recreation in the Kissimmee River Basin
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Title: economics of water-oriented outdoor recreation in the Kissimmee River Basin
Physical Description: Book
Creator: Gibbs, Kenneth C.
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Publication Date: 1975
Copyright Date: 1975
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Volume ID: VID00001
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Table of Contents
    Front Cover
        Page i
    Title Page
        Page ii
    Table of Contents
        Page iii
    List of Tables
        Page iv
    List of Figures
        Page v
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Demand for outdoor recreation
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    Visits relationship
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
    Estimates of value to visiting recreationists
        Page 47
    Summary and conclusions
        Page 48
        Page 49
    References
        Page 50
        Page 51
    Back Cover
        Page 52
Full Text
Bulletin 769 (technical) May 195

.A: Io

A 'f






















"he Economics of Water-Oriented
outdoor Recreation in
'he Kissimmee River Basin



[enneth C. Gibbs

Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J. W. Sites, Dean for Research
-~- -





- -
















J. W. Sites, Dean for Research

















THE ECONOMICS OF WATER ORIENTED
OUTDOOR RECREATION IN THE
KISSIMMEE RIVER BASIN


Kenneth C. Gibbs
Associate Professor
Food and Resource Economics
Institute of Food and Agricultural Sciences
University of Florida





This report is a part of the study "An Optimum Water
Allocation Model Based on an Analysis for the Kissimmee River
Basin," Florida Water Resources Center Project Nos. B-005-
FLA and B-007-FLA. The project is funded by the Office of
Water Resources Research, U. S. Department of Interior, the
Central and Southern Florida Flood Control District and the
Florida Agricultural Experiment Stations. The project is con-
cerned with the allocation of water over space and time and
among several different uses within the Kissimmee River Basin.



This public document was promulgated at an annual cost of
$1,695.81, or a cost of 840 per copy to present procedures
and results of estimating value of outdoor recreation and its
relationship to water level for management policies.









TABLE OF CONTENTS

Page
LIST OF TABLES .. ........ ..... iii

LIST OF FIGURES iv

INTRODUCTION 1
Objectives ... .... 3
Demand Analysis .. 3

DEMAND FOR OUTDOOR RECREATION 11
Theoretical Model 12
On-site Costs 13
Travel Costs ..... 14
Selection of the Sample ...15
Sample Size 16
Allocation of the Sample 16
Explanation of the Variables 20
Number of Recreation Days (Y) .21
Travel Costs (T) ...... .. .. .22
On-site Costs (C) .22
Income (m) .......... .... ........ .. .. 23
Size of the Recreation Group (n) 23
Application of the Model.... ..... .... 24

VISITS RELATIONSHIP ...28
Definition of Variables ..... .......... ... .. ........ 30
Number of Visits (V) ..30
Water Level (WL) . .... ....... 36
Temperature (T) .. .. ... ... . 39
Rainfall (Ra). .. .... .... 39
Wind Velocity (Wv) 40
Empirical Results .. .. .. ... ... 40
Estimating Total Recreational Use of the River Basin 42

ESTIMATES OF VALUE TO VISITING RECREATIONISTS 47

SUMMARY AND CONCLUSIONS 48

REFERENCES -.................. .............. 50

iii









LIST OF TABLES

Table Page

1 Estimated percent of use by time period, Kissimmee River Basin 17

2 Estimates of intensity of use for lake groupings as a percent
of total use, Kissimmee River Basin, 1970 .. 18

3 Number of interviews for each lake grouping by time periods
for each access point, Kissimmee River Basin 19

4 Average values of variables estimated for outdoor
recreationists in the Kissimmee River Basin, 1970 26

5 Lakes and respective access points used in the sample study,
the Kissimmee River Basin, 1970.. 29

6 Estimated number of visits at each sampled access point,
by time period, from February 1, 1970, through June 19, 1971,
in the Kissimmee River Basin ... ............. .. 33

7 Total number of vehicles observed, total number of counts,
and total number of people recorded at counters located at
boat ramps (Group I) and fish camps (Group II)
in the sampled area, during the period of January 31, 1970,
to January 31, 1971, in the Kissimmee River Basin 36

8 Determining the correction factors; number of cars
per number of counts and average number of people per car,
during the period of January 31, 1970, to January 31, 1971,
in the Kissimmee River Basin 37

9 Derived estimate of the number of visitors at each sampled
access point, in the Kissimmee River Basin, during
the period of March 1, 1970, through March 14, 1971 38

10 Summary of all weighted average daily overflight counts,
by time period, for the sampled area in the Kissimmee
River Basin between January 31, 1970 and January 31, 1971 43

11 Overflight observations, on Lakes Gentry, Tohopekaliga,
and Marian, in the Kissimmee River Basin for the time period
November 14, 1970, through December 12, 1970 ....44

12 Weighted average overflight counts for the time period
November 14, 1970, through December 12, 1970 of the
three sampled lakes in the Kissimmee River Basin ..... 44

13 Seasonal estimates of total number of visitors to the
Kissimmee River Basin, in 1970 based on the estimated
percentage value derived by the use of overflight counts ... 45

14 Estimating the percent of recreationists utilizing the
three lakes by the use of overflight counts (season III),
in the Kissimmee River Basin, 1970 --.--.-..-...-.. -... -- ...-.... ..-- 46

iv








LIST OF FIGURES

Figure Page

1 The Kissimmee River Basin, Florida ....... .................... ... 2

2 An Indifference Curve for Commodities Qi and Q .................. 4

3 The Consumer's Budget Constraint .....................-............... 6

4 Maximization of Consumer's Utility .... 8

5 Quantities of Qi Purchased at Various Prices ...... .. ........ 9

6 The Consumer's Demand Curve for Commodity Q1 ...... .. 10

7 An Illustration of Consumer's Surplus .--...... -.......... ............ 10

8 Optimal Combinations of Recreation and nonrecreation
commodities for a consumer faced with variable on-site costs ...... 13

9 Estimated demand function and consumer surplus for an
average individual recreationist, Kissimmee River Basin, 1970 ..... 28

10 Hypothesized relationship of water level to recreation-visits,
Kissimmee River Basin -.. .---.---...--- ---. .-----..--. .---------.. --. 37






























V












THE ECONOMICS OF WATER ORIENTED OUTDOOR
RECREATION IN THE KISSIMMEE RIVER BASIN

INTRODUCTION
In the past recreation was taken for granted and was in-
cidental to much water resource planning. Many recreational
developments came about more through accident than design:
recreational use was not considered a major factor. Today,
government water projects attract many million recreational
visitor-days of use a year. They are bordered with camps, parks,
swimming areas, marinas, docks, launching ramps, and many
other public facilities. The agencies involved in water resources
planning have come to accept recreational use as a major factor
to be considered in water resource development projects, but
the process of determining the economic value of such use has
been the subject of much controversy. The evaluation of benefits
from recreation has recently been given attention by economic
researchers. One of the primary purposes of this study was to
estimate recreational values of water in the Kissimmee River
Basin.
The Kissimmee River Basin (see Figure 1) is located in the
central portion of Florida. The basin is bordered roughly with-
in the boundaries of Orlando on the north, Lake Okeechobee
on the south, the Sunshine State Parkway on the east, and
U. S. Highway 27 on the west. The geography of the area is
such that rainfall within the area drains primarily into the
Kissimmee River, its small tributaries, and associated lakes.
These lakes, as well as the Kissimmee River itself, furnish water
for municipalities, agricultural uses, industrial processes, and,
of course, recreational activities. The upper Kissimmee River
Basin is located in proximity to a large metropolitan area as
well as one of the nation's major amusement attractions. The
central portion of the basin contains some smaller cities and
towns, while the lower end of the basin is somewhat remote from
population areas.
Water in the Kissimmee River Basin can be controlled by
the Central and Southern Florida Flood Control District. Vari-
ations in water level have an influence on all uses of the water.
Water oriented outdoor recreation is one of the primary uses
of this basin.
Two types of recreationists utilize the Kissimmee River
Basin Waters. There are recreationists actually living (either
permanently or during vacation and holidays) on lakefront

1









W ^ORLANDO TITUSVILLE



DISNEYWORLD COCOA ATLANTIC
N\ OCEAN
KISSIMMEE E.LAKE
\ % TOHOPEKALIGA \
LAKE{ \ EAU GALLIE
TOHOPEKALIGA
HAINE\S MELBOURNE
CITY
LAKE CYPRESS
LAKE
HATCHINEHA
LAKE
WALES LAKE
ROSALIE LAKE .LAKE, VERO BEACH
SKISSIMMEEI JACKSON
TIGER L..%\ L.MARIAN .





CALE. \ LA O OBEE EE
L.WEOHYAKAPKA

AVON PARK J n

SEBRING
LAKE
ISTOKPOGA *OKEECHOBEE





SCALE
6 o LAKE OKEECHOBEE
S0510i 20
Figure 1.-Kissimmee River Basin, Florida.
2








property, and those traveling to the area primarily to partake
in recreational activities from publicly accessible facilities. For
both types of recreationists the primary water-based activities
include fishing, waterskiing, boating, and swimming. Visiting
recreationists also enjoy camping. This bulletin focuses on visit-
ing recreationists.1

Objectives
In order to efficiently allocate the water in a river basin,
knowledge of benefits to alternative uses of various management
schemes is necessary.
It was the purpose of this bulletin to present procedures
for estimating the economic value of outdoor recreation and
apply these to the Kissimmee River basin. In addition, the
impact of variations in water level on recreational values was
derived.
The demand for outdoor recreation in the Kissimmee River
Basin was determined by estimating the average demand func-
tion for a visit to the basin and then expanded to include all
visits during 1970. In addition, the aggregate demand was
functionally related to water level. In this way, estimated dollar
impacts to recreationists can be postulated by utilizing tenta-
tive water levels of a particular allocation scheme. Procedures
used in this endeavor include interviews with recreationists in
order to obtain estimates of the annual value of recreation. To
maintain as much homogeneity as possible, recreationists were
analyzed separately for each of four time periods: (1) February
through May, (2) June through September, (3) October through
November, and (4) December through January. A summary of
the fundamentals of demand analysis will precede the presen-
tation of the demand for visiting recreationists.

Demand Analysis
Assume that there is one consumer and two commodities,
Q, and Q,. It is also assumed that the consumer prefers to have
as much of each commodity as possible. The objective of the
consumer is to maximize his satisfaction, subject to a con-
straint the amount of money he has available to purchase
the two commodities in a given time period.
All of the information concerning the consumer's satisfac-
tion is contained in his utility function. A utility function ex-
1Details on waterfront residents can be found in References, subsequent
numbers in brackets refer also to References. [2].

3






presses the relationship between satisfaction, or utility (U), and
the quantity of commodities Q1 and Q2 consumed:
U = U(q, q) (1)

where q, and q2 refer to the amounts of Q1 and Q2 consumed.
Indifference curves are a helpful analytical device. They are ob-
tained by holding the level of utility constant, and observing the
various combinations of the commodities that are consistent
with the fixed level of utility.
Uo = U(q,, q2)
(2)
where Uo refers to a constant level of utility. The indifference
curve depicted by Equation (2) is shown in Figure 2.
Q2





5-- D



4-
I
I




I I
2--- -- C


1 I I
I I i U0
I IUo

1 2 3 4 5 1
Figure 2.-An indifference curve for commodities Q, and Q2.
4







Indifference curves show the different combinations of Q1
and Q. that yield equal satisfaction to the consumer. He is in-
different, or has no perference, between the combinations of
Q1 and Q2 that lie on the indifference curve.
It should also be noted that all combinations of Q, and Q2
which lie above and to the right of Uo are preferred to those
combinations along Uo, since the consumer enjoys more of at
least one of the commodities. For example, Points B and C in
Figure 2 yield a higher level of satisfaction than Point A, since
the consumer has more of one commodity and the same amount
of the other. Therefore, Points B and C must lie on higher in-
difference curves. Likewise, all points below and to the left of
Uo are less preferred combinations of Q1 and Q, than those lo-
cated on Uo.
The indifference curve Uo in Figure 2 represents only one
of an infinite number of indifference curves for the consumer.
All of the indifference curves are referred to as an indifference
map. Again, the curves above and to the right of another in-
difference curve represent higher levels of utility or satisfaction
to the consumer.
Some of the more important properties of indifference
curves should be noted. The shape of the indifference curve can
be shown to be downward sloping and convex to the origin.
Another point worth noting is that indifference curves
cannot intersect. Since the curves reflect different levels of
satisfaction, two curves passing through the same point indi-
cate that one combination yields two different levels of satis-
faction to the consumer.
The concept of indifference curves contains all possible
combinations of commodities Q1 and Q2 that the consumer could
conceivably consume. However, it may not be possible for the
consumer to choose all combinations since he is constrained by
the amount of money he has available to purchase the two com-
modities.
To determine the consumer's attainable set, assume that
he has M1 dollars to spend on commodities Q, and Q,. If the
consumer chooses to purchase commodity Q1 only, he can obtain
M,/p, units, where pi represents the unit price of commodity
Q,. Similarly, if he chooses to purchase Q, only, he can obtain
M,/p2 units. The budget constraint faced by the consumer is:

M, = q1p, + q2p2
(3)

5








Q2





P2





M1 = q1 P + q2 2







Q1
M1/P

Figure 3.-The consumer's budget constraint.

Equation (3) is illustrated in Figure 3. The consumer is able to
purchase any combination of the two commodities in the set
bounded by the horizontal and vertical axes and by the line
representing Equation (3). This portion of the commodity space
represents the consumer's attainable set. The slope of the budget
constraint can be determined from Equation (3) :
dq2 p1
dq, p2 (4)

From Equation (4) and Figure 3, it can be seen that a
change in the price of either commodity will change the slope
of the budget constraint line. However, a change in the con-
sumer's money income will cause a parallel shift of the budget
constraint.

6








We are now ready to determine the "most preferred" com-
bination of commodities Q, and Q2. The consumer will choose
the combination of commodities to maximize his utility, given
his income constraint. This is equivalent to maximizing the fol-
lowing function:
V = U(q,, q2) + A(M1 q1p, q2P2) (5)

where x is the Lagrangean Multiplier. The conditions for maxi-
mizing constrained utility are fulfilled when the partial deriva-
tives of Equation (5), with respect to qi, q2, and x are set equal
to zero:
aV aU
-- p = 0 (6)
aq, aq1

aV U
= X = 0 (7)
aq2 aq2

S= M, -qlp, q2P2 = 0 (8)
ax
The consumer maximizes his constrained utility by consum-
ing those quantities of Q, and Q. that satisfy Equation (8) and
the following first-order condition:
au aU pi
S- (9)
dqi dq2 P2

That is, Q, and Q2 will be consumed until the ratio of their
marginal utilities equals the ratio of their respective prices,
and all income is spent.
The maximization of constrained utility is illustrated graph-
ically in Figure 4. The consumer's budget constraint is super-
imposed on his indifference map. Money income is M1, and the
price of commodities Q1 and Q, are pi and p2, respectively. In-
difference curve U, represents the highest level of utility that is
attainable with the given budget constraint. Therefore, the con-
sumer will maximize his utility by consuming q, units of Q1,
and qO units of Q,.
The consumer's demand curve for a commodity may be
derived from his indifference map. A demand curve is a sched-
ule that shows the various quantities that the consumer will
purchase at various prices.

7








Q





P2




Iq U4
U3

U2
I UI



P1
Figure 4.-Maximization of consumer's utility.
Assume the price of commodity Q2 and money income are
fixed at p, and M,, respectively, while the price of commodity
Q1 is varied. As shown in Figure 5, the quantity of Q1 purchased
will vary as its price varies. When the price of Q1 is pl the
consumer will purchase q? units of the commodity. When the
price of Q1 increases to p; and p" the individual will purchase
only q' and qt units, respectively. Thus, as the price of Q1 in-
creases, the consumer purchases less of the commodity. The
individual's demand curve is derived by plotting the various
prices and the respective equilibrium quantities purchased, as
shown in Figure 6.
It should be noted that the derivation of the demand curve
is contingent upon the continued optimizing behavior of the
consumer. This is illustrated by the tangencies at Points A, B,
and C in Figure 5. Any changes in the consumer's utility func-
tion, income, or the price of commodity Q, will shift the indi-

8







vidual's demand curve for Q1. A market demand curve for a
commodity is obtained by horizontally adding the demand curves
of all individuals in the market.
One other concept needs to be discussed before introducing
the demand model for recreation. It is "consumer surplus."
Begin with the notion that a consumer pays a price for a com-
modity. This can be illustrated by an individual's demand curve
DD, as shown in Figure 7. Assume that the market price for the
commodity is two dollars. At that price, the consumer demands
five units of the commodity. He pays two dollars for each of the
five units of the commodity. However, the consumer's demand
curve shows that he would be willing to pay more than two
dollars for the first unit of the commodity. In fact, the consumer
would be willing to pay six dollars. However, since the first



Q2




Mi





-3-3





U3
U2
I\ U,
MI M, M| Q
q, q q !, 4 Q! -
PI Pt P
Figure 5.-Quantities of Q, purchased at various prices.
9









price
.t D
I


P2---





P?---------;----r---\


I I
D

S____Quantity of
q, q, qO Q1 purchased

Figfure 6.-The consumer's demand curve for commodity Q,.


price ($)





7 D


6 --
I
I I
4 ---+----

3 --4----I-----

PM= 2 ---- ---- -

I I I


I 2 3 4 5 6 Quantity
Figure 7.-An illustration of consumer surplus.

10








unit, like all other units, is sold at the market price of two
dollars, the consumer receives six dollars worth of satisfaction
for only two dollars. Thus, he enjoys a "surplus" by receiving
excess benefits from the first unit. The same situation exists for
the second, third, and fourth units. The difference between the
price the consumer is willing to pay for the units of the com-
modity and the price he actually has to pay for them is called
"consumer surplus." Consumer surplus is used later in this study
to estimate some of the values associated with the demand for
outdoor recreation.

Demand For Outdoor Recreation

Demand for recreation, in the absence of an efficient mar-
ket, has been estimated in two ways: the direct and indirect
methods. In the direct method, the recreationist is asked how
much he would be willing to pay for a specified amount of recre-
ation. The indirect method (utilized in this study) involves
estimates of willingness to pay for recreation by observing the
amount a recreationist actually spends in order to participate
in a recreational experience.
Total recreational usage of an area can be defined as the
product of the number of days a recreationist uses a recreational
site per visit and the number of visits to a recreational site:2

days visit total visitor days total
x = recreational
visit time period time period usage

The number of days per visit can be considered the quantity
variable in a demand relationship and the daily on-site costs a
price variable. Based on the demand relation for an average
visit, the aggregate demand for recreation can be derived by
expanding according to the number of visits.3 For purposes of
this study, it was assumed that the impact of water level on
2Recreation "visitors-days" and recreation "visits" are defined by the
U.S. Forest Service as follows (1) "A recreation visitor-day consists of
12 visitor-hours, which may be aggregated continuously, intermittently, or
simultaneously by one or more persons. The visitor-hours contained therein
must be spent by persons in any activities, except those which are a part
of, or incidental to, the pursuit of a gainful occupation;" (2) "A recreation
visit is the entry of any person upon a site, or area of land or water, gen-
erally recognized as an element in the recreation population. Visits must be
made in order to engage in any activities, except those which are a part of,
or incidental to, the pursuit of a gainful occupation" [1].
SAn alternative method of deriving aggregate demand would be to
relate the number of visits to price and other relevant variables, and then
solve simultaneously with the days per visit relation. This was not done
due to voids in data.

11








recreational values is realized on the number of visits rather
than the length of stay per visit. Thus, a value per visit was
estimated and then the relationship between water level and
visits was utilized to relate water level to recreational value.

Theoretical Model

The theoretical model for the length of visit relationship
is based on traditional concepts of consumer behavior theory.
In order to participate in an outdoor recreational experience,
the recreationist' incurs two types of costs. It is assumed that
it is necessary to pay a certain charge, T, before consumption
of recreation, Y, is possible. The charge, T, is not dependent on
the quantity of Y purchased. It can be considered a payment
for the privilege of purchasing Y. That is, a recreationist will
pay a certain cost per day, C, while consuming recreation (on-
site costs) and he will incur travel costs, (fixed cost), T, in
order to get to the recreation site.
Travel cost includes transportation costs, cost of food and
lodging and other costs enroute to the recreation site. The cost
of travel to the recreation site, T, competes with the cost of
other commodities consumed. Thus, the budget constraint faced
by the recreationist is:

m = CY + T +Pq m,C,q > 0 Y,T > 0 (10)
Where m is income of the recreationist, C is daily on-site costs,
Y is number of days per visit at the site, T is travel cost, q is all
other goods consumed and P is price of all other goods.
The maximization of a recreationist's constrained utility
is determined by the same technique employed in traditional
consumer behavior theory except that travel cost enters into
the equation. The budget constraint:

m T = CY + Pq (11)

shows how the'travel cost, T, affects the available income. By
consuming Y, the recreationist will have less income available
than if he only consumed q. The travel cost, T, can only be zero
if no recreation is consumed since any amount of recreation
will generate some travel cost.5
4The "recreationist" can be defined as a recreation group or an
individual. For purposes of this bulletin, the recreation group is considered
the decision making unit. In a subsequent section the individual recrea-
tionist is referred to in order to isolate the influence of group size.
sThis is true even if an individual walks to a recreation site. His
travel cost, in this case, is very small but is still positive.

12








On-site Costs
A change in the on-site recreation costs, C, and the cost of
other nonrecreational commodities, P, will have an effect on the
quantity of recreation days per visit. A change in C or P will
result in a change in the slope of the budget constraint line.
In Figure 8, travel costs are fixed at T = To and the level of
income, m, and the price of other commodities, P, are held con-
stant at m and P", respectively. Only C is variable so that the
effect of C on the quantity of recreation days per visit demanded
can be seen.
On budget line, BC", the recreationist would prefer not to
consume any recreation since he could achieve a higher level of






0







2 m-T \
c5 p \


z
L)I







d d .


2U r \U2

BCC BC
b c -\ d \

___ ___ i T0
b -''- T c T d m - T
y C Y C' Y C"
RECREATION
Figure 8.-Optimal combinations of recreation and nonrecreation commodities
for a consumer faced with variable on-site costs.

13








utility by foregoing recreation and consuming mO/po units of
nonrecreation. The recreationist could achieve this higher level
rather than the point (M-T) -.-p since any recreation involves
a cost To that must be incurred before recreational activities can
occur. If no recreation is consumed, then the potential recrea-
tionist has To more dollars of income to spend on nonrecreation
units. This is a discontinuity in the budget constraint. A decrease
in C from CO to C' is represented by the iso-income line BC'.
After the price decrease, the utility level of U, is reached and
can be obtained in two ways. First, the recreationist can con-
sume no recreation and be at the point mo--p or he can consume
Y = ye, q = qc. The recreationist would be indifferent between
these two choices since he would remain on the same utility
level regardless of his decision.
Decreasing on-site costs further gives the iso-income line
BC". This will change the optimal budget to Y = yd, q = qd.
Thus, as the price of recreation decreases, the quantity of recre-
ation demanded increases. At any value of C where C < C', the
recreationist will prefer to consume a combination of recreation
and nonrecreation commodities rather than solely nonrecreation
commodities. For any value of C where C > C', the consumption
of recreation would be excluded from the budget, i.e., any iso-
income line to the left of BC'. The price of a recreation unit at
the point where a recreationist is indifferent between recreation
and nonrecreation, C' in this case, is defined as the "critical"
on-site cost (C*). The effect of a change in C on the amount
of recreation will depend on the magnitude of the critical price.
For a given utility function, the critical value of on-site recrea-
tion cost depends on the level of income, the price of other
commodities, and the cost of travel.

Travel Costs

A change in the cost of travel will be viewed in a different
manner than a change in on-site recreation costs due to the fact
that a travel cost must be incurred before any recreation is
consumed. By varying the travel cost, T, a different budget con-
straint is imposed for each value of T. Referring to Equation
(11), it can be ascertained that high levels of T will leave less
income to be spent on recreation, Y, and all other commodities,
q, whereas lower levels of T will make more income available.
It can be hypothesized that as travel costs decrease the
amount of recreation (and nonrecreation goods) will increase
within a certain range due to the effect of more income being

14








available for the consumption of Y and q. This is because a de-
crease in travel cost can be looked upon as an increase in income.
One hypothesis that will be tested is that a recreationist
will spend fewer days at the recreation site per visit as his costs
of travel increase. Since the number of visits a recreationist
makes is not explicitly accounted for by the measure of recrea-
tional use (days at site per visit), the reverse hypothesis may
have some validity. That is, as the travel cost increases the
recreationist may spend more days at the site per visit and make
fewer visits. He may substitute days at the site for trips to the
site and thus cause the reverse hypothesis to hold.
At a certain level of T, the potential recreationist is in-
different between consuming recreation and not consuming recre-
ation. This level of travel cost has been labeled the critical travel
cost, T*. It is so designated since at a level of travel cost below
T*, the recreationist will consume some level of recreation in
order to maximize his utility while at a level above this cost, he
will not consume any recreation.
The theoretical model can now be summarized. The quantity
of recreation demanded per visit is related to travel cost, T, on-
site cost, C, the cost of a unit of other commodities, P, and in-
come, m.

Y=Y (T, C, P, m) for: C < C* (12)
T
The theoretical concepts will be applied to data collected
from recreationists using the Kissimmee River Basin in 1970.
A discussion of the sampling procedure used to secure a repre-
sentative sample of recreationists and activities is presented in
the following section.

Selection Of The Sample

Certain socioeconomic data were needed from recreationists
using the Kissimme River Basin to derive the variable used in
the theoretical model. This section presents the proportional
sampling technique that was devised to select certain sites and to
randomly select recreationists to obtain the needed information.
This technique was developed since it would have been physically
impossible to interview all the recreationists even on selected
lakes. The selection of the sample with respect to size and alloca-
tion was based on the entire year, even though four time periods
were examined independently.

15







For sampling purposes, the Kissimmee River Basin was
divided into three sub-basins: the upper, central, and lower sub-
basins corresponding to their geographic location from north to
south. The division into sub-basins, in effect, stratified the
sample area. Within these three strata, various lakes were chosen
in order to collect data on the water-oriented outdoor recreation
activities. The lakes to be included in the sample were chosen to
represent a cross section of all outdoor recreation activity that
takes place within the Basin.
In the upper sub-basin, Lakes Mary Jane and Hart were
chosen as the sampled lakes. In the central sub-basin, Lakes
Tohopekaliga, Hatchineha, Tiger, and Kissimmee were chosen.
The lower sub-basin included the Kissimmee River. (By inter-
viewing on a river rather than a lake the diversity of the sample
was increased in that it provided a sample of bank fishermen,
which are prevalent in this particular area.) In choosing the
sampled areas, an effort was made to include some relatively
inaccessible sites as well as those that border urban areas. The
objective of the study was to measure the recreational value of
the total basin so that by choosing some remote areas, which are
part of the total basin, a better picture of the type and amount
of outdoor recreation that takes place within the Basin will be
obtained.
After the lakes were selected, each access point to these
lakes was considered as a site where interviews of outdoor recre-
ationists could be taken. These access points were sites where
public access was available. They included fish camps, boat
ramps, and campgrounds that had or furnished access to the
selected lakes.

Sample Size
In order to determine the sample size that will give statis-
tically reliable estimates of the variables to be estimated, the
amount of error that could be tolerated in the sample estimates
was ascertained. Since more than one variable was to be esti-
mated, one variable had to be chosen in order to determine the
size of the sample to be taken. For our purposes, the average
length of stay per person was used. It is believed that this was
the most important variable and that by satisfying the size
requirement for this variable, the required precision for the
study would be obtained. A sample size of approximately 1000
was deemed adequate to estimate the demand for each time
period. This sample size applies to the entire year and needs to
be proportioned according to time periods and sites.

16








Allocation of the Sample
The year was divided into four time periods to better re-
flect the various activities in the basin. Data from two agencies
were used to determine the percentage of yearly use that occurred
during each time period. The Central and Southern Florida Flood
Control District (FCD) maintain boat locks on the Kissimmee
River. Boats must pass through locks in order to pass from the
lower to the upper river, or vice-versa. Yearly data of all boats
that pass through the locks were used to construct Table 1.
Independent estimates by the Florida Game and Fresh Water
Fish Commission wildlife officers corroborated the data obtained
from the FCD.

Table 1.-Estimated percent of use by time period, Kissimmee River Basin.

Time period Percent of yearly use

February May 35
June September 25
October November 26
December January 14
Total 100


From Table 1 it can be seen that 35 percent of the recrea-
tional use of the area occurred during February through May,
25 percent during June through September and so on. The num-
ber of interviews was apportioned according to the percent of
total use that occurs during each time period. For example, time
period one has 35 percent of the total use, so 35 percent of the
total interviews, or 350, were taken during this particular time
period.
Discussions with officials of the Game and Fresh Water
Fish Commission and with long time residents of the area in-
dicated that the various lakes included in the survey had different
amounts of use. This would be reasonable to expect due to the
remoteness or accessibility of particular lakes and particular
recreational activities. The intensity of use for the lakes, which
are grouped according to similar characteristics, is presented in
Table 2.
The number of interviews conducted at each lake grouping
during each of the four time periods were determined by using
the percentage of use that occurs during each time period as
well as the percentage of use at each lake grouping.

17








Table 2.-Estimates of intensity of use for lake groupings as a percent of
total use, Kissimmee River Basin, 1970.

Lake Percent of Use

Kissimmee
Hatchineha 57
Tiger

Tohopekaliga 20

Mary Jane
Hart 7

Kissimmee River 16
Total 100


Every public access point to the chosen lakes was considered
a site where samples were to be taken. These sites ranged from
only one access point on Lake Mary Jane to eleven on the Lake
Kissimee group. In order to allocate properly the samples among
the various sampling sites, some measure of the intensity of use
for each site was needed. Again, using estimates provided by
officers of the Game and Fresh Water Fish Commission, Table
3 was constructed.
The number of interviews to be conducted at each site is
given in Table 3. As an example, during the first time period, 200
interviews from the Lake Kissimmee Group were needed. Within
this grouping, there are eleven public access sites where samples
were taken. Since 24 percent of the total use at the Lake Kissim-
mee Group for time period one was from Camp Mack, 24 percent
of the 200 interviews, or 48, were taken there. The remaining
time periods and site allocations can be similarly ascertained.
One further step was needed in the sampling procedure.
Usage of these various sites is likely to be different on weekdays
than on weekend days and holidays. The number of interviews
for a particular site were allocated according to weekend day
or weekday usage in order not to give equal weighting to all of
the days of the week. Data from Moss Park were used to divide
the number of interviews equitably according to weekend day
or weekday usage.6 These data indicated that approximately three
times as many people use the park on a given weekend day than
6Moss Park, a county park located at Lakes Hart and Mary Jane, has
kept yearly records of visits. From these records, the number of weekday
and weekend visitors was obtained. This was the only source of data
available.

18









Table 3.-Number of interviews for each lake grouping by time periods for
each access point, Kissimmee River Basin. a


Number of interviews
Time periodearly
Yearly
Lake Group Access point 1 2 3 4 total

Kissimmee, Mack 48 34 36 19 137
Hatchineha, Lester 40 28 30 16 114
and Tiger Oasis 20 14 15 8 57
Port Hatchineha 34 24 25 14 97
Marie 20 14 15 8 57
S-65 20 14 15 8 57
Tiger Fish Camp 6 4 5 2 17
Pennington 4 3 3 1 11
Grape Hammock 2 1 1 1 5
Kissimmee Park 4 3 3 1 11
Shady Oak 2 2 2 1 7

Sub-total 200 141 150 79 570

Lake Scotties 21 15 16 8 60
Tohopekaliga County Ramp 14 10 10 6 40
Red's 9 6 7 4 26
Jannis 10 8 8 4 30
Bank Fishing 1 1 1 1 4
2-lane Ramp 4 2 3 1 10
3-lane Ramp 7 5 5 3 20
Yacht Club 4 2 3 1 10

Sub-total 70 49 53 28 200

Mary Jane
and Hart Moss Park 24 18 18 10 70

Kissimmee Joe and Wanda's 22 16 17 9 64
River O'Kissimmee 17 12 13 6 48
FCD Camp (North) 11 8 9 4 32
FCD Boat Ramp 6 4 4 2 16

Sub-total 56 40 43 21 160

Total 350 248 264 138 1000


a Derived from estimates of use by Game and Fresh Water Fish
Commission Wildlife officers.


on a weekday. Included in the classification of weekend days was
the total number of holidays that occur during the year. Dividing
the year into weekdays and weekend days plus holidays yielded
110 weekend days and holidays and 255 weekdays. To obtain
the percentage of people who use the area on weekend days plus
holidays and weekdays, add 330 (110 x 3) to 255 and divide

19








by the total.7 This results in an estimate that 56 percent of the
use of the area occurs during weekends and holidays and 44 per-
cent during weekdays.
From data in Table 3, the number of interviews to be con-
ducted at a particular site during the weekends and holidays
and the number to be conducted during the weekdays was cal-
culated. This was done by multiplying the previously calculated
number of interviews for each site by the percentage for the
type of day desired. Using the prior example of 48 interviews
to be conducted at Camp Mack for time period one, the number
of interviews for weekend days and holidays can be calculated
by multiplying by 56 percent (i.e., 27). The number of weekday
interviews can be similarly found by multiplying by 44 percent.
In order to determine when the interviews should be con-
ducted, weeks were randomly selected from each month for each
time period. For example, 21 weekday interviews [(.44) (48)]
were needed for Camp Mack for the first time period. Since there
are four months in this time period, dividing four into the 21
weekday interviews gives approximately 5 weekday interviews
needed per month.
This sampling procedure was used to measure accurately
the outdoor recreational activities on a proportional basis. In
summary, the proportional sampling procedure was designed by
determining the percentage of total use by time periods, lake
groupings, interview sites, and finally by weekend days and
holidays or weekdays. By determining the proportion of use for
these various areas, it was hoped that a better cross section of all
activities that occur, along with the intensities of the activities,
will be accurately reflected by,the sample.8
The data from the questionnaire were used to determine
certain economic and sociological parameters that are necessary
to estimate economic value. The next section describes these
parameters and how they are derived.

Explanation Of The Variables
The following variables were calculated using data obtained
through the use of a questionnaire. The questionnaire (see Ap-
7Since there are 3 times as many people who use the park on any given
weekend day or holiday than on weekdays, this gives a weight of 3 to be
applied to the weekend days.
8Interviews were conducted by a private company, The Management
Team, using questionnaires developed for this particular study. The inter-
viewers were instructed to observe the activities at each site where they
conducted interviews and to interview those people engaged in each activity.
This gave a good cross section of the activities.

20








pendix) was administered to recreationists engaged in outdoor
recreation using the sampling procedures established in the
previous section. A close examination of the questionnaire indi-
cates that a large number of variables were measured. The price
of other goods variable, P, discussed above was not included in
the measurement since in a given year this is constant. The esti-
mated model will not reflect this variable. Only the following
variables were utilized in this study:

Y = number of recreation days per group
T = travel costs per group
C = on-site costs per group
m = income
n = size of recreation group

Number of Recreation Days (Y)
The number of recreation days per visit was measured by
determining when the recreation group arrived and when they
planned to leave. The time of arrival and departure was used to
determine the total number of days and hours the recreational
group planned to stay at the site. To avoid a problem in termi-
nology a day was defined as a 12-hour period. Using a 12-hour
period, divided into tenths of a day, provides a more accurate
reflection of the actual time spent. For example, if a group of
five recreationists visited a site from 6:00 a.m. until 6:00 p.m.
on the same day, this would constitute five recreation days.
Recreationists were also asked the minimum amount of time they
would spend at the site, considering the cost, distance and time
involved in traveling to the recreation site.9
In preliminary results obtained using the questionnaire data
to derive the variables, there appeared to be two separate sample
groups. These two groups are composed of those recreationists
that spent more than 90 days at the recreation site and those
that spent less than 90 days.
The group that: spent over 90 days was removed from the
analysis since it was believed that they did not fit the definition
of a recreationist for purposes of this study. This group con-
tained observations which were characterized by low incomes

"gIn a very few instances due to unforeseen circumstances some recrea-
tionists actually spent less time at the recreation site than they stated as a
minimum. Where this occurred the questionnaire was not used or the mini-
mum of days was set equal to the actual days spent at the site. Some of
the circumstances which created these few situations were severe weather
conditions, accidents, and other unforeseen events.

21








and retirement ages, and thus fit more closely the definition of
a resident than a recreationist. With these observations removed,
the total usable observations from the sample was 950.

Travel Costs (T)

The cost of travel to get to and from the recreation site in-
cluded food and lodging enroute and the cost of operation of
vehicles that transported the recreation group to the site. In
determining the cost of food and lodging enroute, questions were
asked concerning the amount of food brought from their home
for consumption enroute, food purchased while enroute, the
length of trip in days or hours, and the cost of lodging enroute,
whether in the form of camping fees or motel fees. With regard
to the operation of a vehicle, the origin of the trip was asked so
that a distance from the point of origin to the recreation site
could be ascertained. This distance in miles was multiplied by
$.07.10 Intrinsic in all of the costs is the number of people in the
recreation group. Total transportation costs plus the total
costs of the group for lodging, meals, and other miscellaneous
items in traveling to and from the site were added to calculate
travel costs for the group, T. In order to be more accurate in
determining the cost of food enroute, the cost of food that would
have been consumed at home was subtracted." In some cases
the cost of food eaten at home exceeded the cost of food enroute.
This, of course, would give a negative travel cost if it were the
only component. On perhaps a dozen interviews where vehicle
costs were nonexistent and food costs at home exceeded food
consumed enroute, a negative travel cost ensued. Negative travel
costs were not used in the study. In no case did the costs amount
to less than minus $.07 per person. For purposes of computation
negative costs were set equal to $.01. Results were not altered
by this decision.

On-site Costs (C)

On-site costs included the cost of food consumed at the site
for all members of the group minus the estimated cost of food
consumed at home. Camping fees, cabin rentals, and motel costs
10The seven cents per mile includes the cost of gas and oil for the
trip plus minor maintenance. It does not include depreciation, taxes, or
insurance which would be incurred regardless of the decision to participate
in a recreational experience or not [3].
"Cost of meals eaten at home was based on USDA estimates for
various income levels [4, 6].

22








were also included in on-site costs. In addition, any cost directly
attributable to participation in the recreation experience was
considered an on-site cost. This includes, but is not limited to:
launching fees for boats, rental of boat slips or dockage, rental
of such items as skis, cushions, motors, boats, and other articles.
Also included in on-site costs was the cost of operating a boat.
This was determined by asking the recreation group how many
outboard motors they had and how many gallons of gas would
be used per day. Multiplying the number of gallons of gas by
$.42 yields the cost per day of operating the boat.12 All of these
costs were added and where applicable divided by the number
of days at the site to give C, the on-site cost per day per group.

Income (m)
The recreationist's income was estimated by determining
an income category that most closely corresponds to the family
income of the respondent. This includes all working members
of the family. It was believed that the total income of the recrea-
tionist's family would be a more important factor in recreation
decisions than the income of the primary wage earner alone.
The income ranges listed are before tax incomes. No attempt
was made to allow for income taxes since there could be a great
divergence depending on exemptions and deductions. Obtaining
the required information on these items would be extremely
difficult considering the reluctance shown by some people in list-
ing a simple income range.
The actual income used in the analysis was the midpoint
of the income range. As an example, $9,500 was used as the in-
come for the $9,000-$9,900 range. The incomes given by the
respondents were used in determining the cost of food consumed
at home since USDA estimates of the cost of food per day is
based on the income of the consumer.

Size of Recreation Group (n)
The determination of the number of people in the group
was by direct question. In most cases the recreation group was a
family consisting of a father, mother, and one or more children.
In other cases the group consisted of scouts, and similar groups.
No distinction was made as to the composition of the group,
however.
12The average price of a gallon of gas plus the required oil for mixing
outboard fuel amounted to 42 cents per gallon. This estimate was obtained
from a range of costs given by marina operators and boat owners.

23








Application Of The Model
The dependent variable (Y) is defined as the number of
visitor days a recreational group spends at the recreation site
per trip. Thus, Y = ny, where y is the number of days per per-
son per visit and n is the size of the recreation group. Since Y
is determined by two separate variables, a per capital equation
to utilize a single dependent variable is needed:

y = y(t, c, m, n, D,, D,, D,) (13)
Where,
t = travel costs per person
c = daily on-site costs per person
m = income of the recreationist
n = number of persons in the recreation group
f1 for each observation in season II
S 0 for all other seasons
01 for each observation in season III
D. 0 for all other seasons
[1 for each observation in season IV
D 0 for all other seasons
Due to prior evidence that the demand function may not be
linear, a semi-logarithmic regression equation was estimated
where the dependent variable, y, was in natural log form and the
independent variables were non-logarithmic. The estimated de-
mand relationship is given as: 13
In y = 2.183 + .0260 t** .051 c** + .00001 m*
(.0014) (.010) (.000005)
1**
-1.399 -- .229 D,* .258 D2* .368 D3** (14)
(.172) (.114) (.120) (.129)

R2 = .351 F = 72.7 Degrees of freedom = 942
The D,, D2, and D3 variables represent zero-one variables
to account for the differences among time periods. For example,
DI explains how the demand relationship would be different
between time periods one and two. This indicates that one could
expect recreationists to spend an additional 1.3 days (derived
by taking the antilog of .229) per visit in time period two over
time period one. Similarly, the length of stay would decrease in
both periods three and four compared to one.
r1Standard deviations are presented in parentheses under the coeffi-
cients. Significance of the coefficents are indicated by ** (1 percent level )
and (5 percent level).

24








Equation (14) contains on-site cost, travel cost, income,
number of recreationists in the group, plus time period variables.
In this equation the sign of the coefficient of travel cost, t, is
positive and significant at the 1 percent level. This indicates that
as travel costs increase $10.00 the recreationist will increase his
stay at the site by 1.2 days." Since the number of visits is not
explicitly accounted for, recreationists will likely substitute more
days at a site per visit for additional trips as travel costs in-
crease, as previously stated.
The sign of the coefficient of on-site costs, c, is negative
and significant at the 1 percent level. As the price of a day of
recreation increases it is estimated that the number of days spent
at the recreation site will decrease. From Equation (14) an in-
crease of $1.00 will result in a decrease in the number of days
spent at the site of 1.1 days.
The sign of the coefficient of m, the recreationist's income,
is positive. This indicates that as incomes go up, the number of
days a recreationist will spend at the site increases. As in the
two examples previously given, a $1,000.00 increase in income
results in a 1 day increase in the time spent at the recreation
site per visit. This indicates that even though income is signifi-
cant in determining length of stay, the number of days at the
site is not very responsive to small changes in income.
The coefficient of the variable 1/n is negative, indicating
that as the group size increases the number of days spent at the
recreation site per visit increases. This can perhaps be explained
by the hypothesis that larger groups usually indicate families
taking vacation time while individual recreationists usually
spend less time.
Equation (14) was used to determine a demand function
for outdoor recreation. The demand function for outdoor recre-
ation is a relationship between the quantity of recreation con-
sumed (days at a site per person per visit, y) and various prices
of recreation (on-site costs per person per day, c) taking into
account all other variables. The demand curve for an average
individual was determined by holding all independent variables
in Equation (14), except c, at their means. The means of the
dependent and independent variables are summarized in Table 4.
The value of c* is needed to determine consumer surplus
from the demand function for outdoor recreation. To compute
this, recreationists could be asked to estimate the maximum on-
site costs they would be willing to pay before they would choose

14Derived by taking the antilog of the product of (10) (.026).

25








Table 4.-Average values of variables estimated for outdoor recreationists
in the Kissimmee River Basin, 1970.

Days per Daily Minimum
Time visit Travel on-site Income Group days per
period (y) a cost (t) cost (c) (m) size (n) visit a

Feb.-May 7.95 20.16 3.25 11,782 3.07 4.01
June-Sept. 5.16 7.80 2.41 10,079 3.27 2.08
Oct.-Nov. 3.75 7.16 3.38 10,048 2.77 1.98
Dec.-Jan. 4.38 17.31 3.66 11,997 3.06 2.58
All periods 5.64 13.38 3.23 10,964 3.06 2.78

a Measured in terms of 12-hour periods.
not to recreate, given everything else constant, but it is believed
that they would not answer this question without undue biases.
On the other hand, recreationists had a good idea of the minimum
length of time they would be willing to stay at the site. Thus,
critical on-site cost was estimated by obtaining the minimum
number of days recreationists were willing to recreate, all other
things fixed. This corresponds to the maximum price they would
be willing to pay on a demand curve. The minimum number of
days, y*, was substituted into the demand function to solve
for c. The minimum number of days, y*, was calculated to be
2.78 days for all periods. The critical on-site cost, c*, was cal-
culated to be $17.77. This is the maximum amount of on-site
costs a recreationist would pay to engage in outdoor recreation
given his travel costs and all other things equal.
The average demand function for recreation using the mean
values for variables, can be written as:

y = e1.929 .051c for c < $17.77 (15)

Equation (15) is derived with all independent variables
held at their mean (except on-site cost). This includes D1, D,,
and D3. Thus, this relation is based on the average recreationist
over all time periods. If, however, the demand relation for a
particular time period were desired, a zero or one should be
substituted for the Di variable. For example, for time period
one all D variables equal zero. The demand relation for time
period one holding all other variables at means appropriate to
time period one, is:

y = e2.198 .051C (16)

For period two, D, is set equal to one and D2 and D, are zero.
Similarly, for periods three and four, D. is one and D3 is one,

26








respectively. If an analysis of recreational values called for a
particular time period, then it is preferable to use values of
variables associated with that period.
Figure 9 illustrates the consumer surplus derived using the
average demand function for an individual recreationist, on a
per visit basis, in the Kissimmee River Basin during 1970. The
value per visit is based on the theory of consumer surplus and
is the shaded portion of Figure 9. Consumer surplus is based
on the concept that the price a rational person pays for some-
thing can never exceed the price he would be willing to pay
rather than do without it. The annual value per visit can be
calculated as:

Average 17.77
Value = (e1.929 .051 ) dc (17)
per visit J 3.23
$59.91

The economic value of recreation for an average individual
in the Kissimmee River Basin, computed from Equation (17),
is $59.91. This value relates to that amount of worth accruing
to recreationists visiting the Kissimmee River Basin in 1970
over and above the required on-site expenses. Travel cost, income,
and group size have influence on this value in that they jointly
determine the position of the demand function. If average in-
comes were to increase, for example, then the average demand
curve would shift upward thus increasing the value estimates.
[The exact impact of increasing incomes can be predicted by
utilizing the coefficient on the income variable in Equation
(14).] Similar effects can be seen for the other independent
variables.
As previously discussed, the main interest in this study is
the aggregate demand for the total number of visitor-days per
year. The preceding model is appropriate for explaining the
average number of visitor-days per visit. That is, it pertains to
an individual, not to the population of users. The aggregate de-
mand, or total number of visitor-days as a function of on-site
costs can be obtained by multiplying Equation (13) by the annual
estimated number of visits (VT ) to the Basin during the
year (or by each time period). The aggregate demand model can
then be specified as:

VT y = f(t, c, m, s, n, D,, D2, D3) For c < c* (18)
Total economic value may then be calculated by multiplying the

27









C+= 17.77











y e1,.929-.051 c
y= e
0



I-
c,
z-
o C 3.23












0 y =2.78

DAYS PER VISIT
Figure 9.-Estimated demand function and consumer surplus for an average
individual recreationist, Kissimmee River Basin, 1970.

average consumer surplus by VT The focus of the next section
is the estimation of VT .

VISITS RELATIONSHIP
A procedure was developed to carry out the estimation of
the average number of visits per year. In addition, the relation-

28








ship between the number of visits and other factors, primarily
water level, was estimated.
A multiple linear regression model was used to explain the
relationship between the number of recreational visits to the
Kissimmee River Basin and selected physical variables. The
model was formulated as follows:

V =V ( WL WV Ra, T, D D2 ) (19)
Where:
V = number of visitors during a set time period
WL = water level
WV = wind velocity
Ra = rainfall
T = temperature
DI = 1 for each observation in season II"
0 for all other seasons
D. = 1 for each observation in season III
0 for all other seasons
The observations for each variable in the models were accumu-
lated into two week intervals.
It was necessary to limit the collection of data pertaining
to both the dependent variable V and the independent variables
(WL, T, W Ra ) to an appropriate representative seg-
ment (sampled area) of the Kissimmee River Basin. It was
decided that an adequate representative sector of the river basin

Table 5.-Lakes and respective access points used in the sample study, the
Kissimmee River Basin, 1970.

Lake Access points

Gentry 1. County boat ramp
Tohopekaliga 2. Two lane boat ramp
3. Three lane boat ramp
4. Fish camp I
5. Fish camp II
6. County boat ramp
Marian 7. Fish camp III
8. Fish camp IV

15Only three time periods were recognized in estimating the visits
relationship due to the nature of the data. Time periods 3 and 4 were
combined. Thus, time period 3 now refers to October- January.

29








consisted of three distinct lakes (see Table 5). The degree of
usage and size of the lake were the criteria for distinguishing
the sampled lakes. Lake Gentry is representative of small lakes,
Lake Marian medium sized lakes, and Lake Tohopekaliga large
lakes.

Definition Of Variables

The following sections will briefly discuss each variable
used in the analysis. The empirical results will be presented fol-
lowing the discussion of the variables.

Number of Visits (V)

The dependent variable (V) is the estimated number of
people using the lake facilities for recreational purposes. The
use of a lake facility includes such activities as launching a boat
from a ramp, water skiing, swimming, hiking, fishing, or just
"passing the time of day" along the shoreline. Therefore, the
variable V is an estimate of the total number of visitors (or
visits) that attend the lake or its immediate surroundings to
participate in a type of recreational activity during a set time
period. ( VT is the estimated annual visitations.)
It should be noted that a visit to the river basin was defined
as any entry of a person upon a recreational site in order to
participate in any activity other than those associated with the
pursuit of a gainful occupation. If, for example, a group of three
recreationists arrived at a site, in one car, this would be recorded
as three visits regardless of how many days they stayed at the
site. Thus, a particular visitor can be counted one or more times
during the year depending on how often he visits the river basin
throughout the year.
The method chosen to estimate the number of people utiliz-
ing the facilities of a sampled lake (V) was to conduct a traffic
count survey. The survey consisted of data gathered by eight
mechanical traffic counters at selected locations. A traffic
counter was placed at all public access points on each of the three
lakes. The access points were located at organized fish camps,
county boat ramps with parking facilities, and at two and three
lane boat ramps with no parking facilities. The analytical pro-
cedure for estimating the number of people using a lake will now
be described.
The data obtained directly from the traffic counters had
to be adjusted in order to obtain an estimate of the number of
people using the area rather than just the number of axles that

30








tripped the meter. The analysis of adjusting the traffic count
data was carried out in three basic steps. First, a correction
factor was determined to account for the fact that car-s are
counted at least twice once while launching boats and once
removing boats. In the cases of the two and three lane boat
ramps, the cars were counted four times. This is due to the fact
that these ramps do not provide parking facilities within the
metered area. Thus, after the recreationist launches his boat, he
must cross the meter another time in order to park his car.
When returning to load his boat, he will again contribute two
more crossings. In the other six locations, parking is available
within the metered area. Therefore, the counts recorded at the
two and three lane boat ramps with no parking facilities were
divided by four; and the counts at the remaining six locations
by two.
The second step was to calculate a correction factor to
account for trailers which contribute extra counts on the traffic
meter. If this were not adjusted, the estimate would be biased
upward. This correction can be performed by determining the
following ratio:
number of cars
Correction factor =number of ars
number of counts

Since the number of counts, number of cars, and number of
trailers were estimated from the sample study, the correction
factor was computed with existing data.
The third step was to determine the average number of
people per car. This factor was established from a sample of cars
chosen and the number of people per car counted.
It should be noted in one location (Fish Camp I), a portion
of the people were permanent residents or lived in rental units
for a considerable length of time. Inclusion of these people in the
estimated counts would bias the estimate upward due to their
frequent trips out of the metered area. Thus, the estimate for
this traffic counter was reduced by observing the percentage of
people crossing the meter that actually utilized the recreational
facilities. This was calculated by recording the number of people
entering the area for recreational purposes versus the total
number of people visiting this location. It was estimated that
only 42.5 percent of the counts recorded on the meter were ap-
plicable to outdoor recreationists at this area. Thus, the counts
were multiplied by .425.
Once all correction factors were determined, the readings
on the traffic meter were multiplied by each factor. This opera-

31








tion provides an estimate of the number of people using a specific
access point during a given time period.
In equation form, the analysis can best be described as
follows. The equation for the two and three lane boat ramps is:
number of
estimated counts number average
number registered of cars number
of people = by meter per of people
per by meter
time period per number per car
time period of counts

The equation for Fish Camp I is:
number of
estimated counts number average
number registered of cars number .4
of people by meter per of people [.4251
time period per number per car
time period of counts

The equation for all other entrances is:
number of number
estimated counts of cars average
counts of cars number
number registered 1/2 per of people
of people by meter number per car
per
time period per of counts
time period

Finally, to estimate the total number of people using an
entire lake for a particular time period, the adjusted counts for
each meter at that lake were summed.
The adjusted values of visitation at each access point, for
all time periods, are shown in Table 6. The derivation of the
values in Table 6 can be exemplified by applying the above
equations to the traffic survey data taken only during the period
of March 1, 1970, to March 14, 1970. This is done merely to
illustrate the procedure. First, as shown in Table 7, the total
number of vehicles observed, total number of counts contributed
by the vehicles and the total number of people are recorded. It is
necessary to calculate these values since they are utilized to de-
rive the desired correction factors. It should be noted that due
to the lack of data, it was assumed that the locations could be
combined into two groups. The two lane, three lane, and county
boat ramps comprise group I, and the other four entrances con-
stitute group II. In Table 8, the number of cars per number of
counts and the average number of people per car, for each access
point, are shown. Table 9 derives a numerical estimate of the
number of visits at each sampled access point during the desired
time period. The total number of people visiting Lake Gentry

32







Table 6.-Estimated number of visits at each sampled access point, by time period, from February 1, 1970, through June 19, 1971,
in the Kissimmee River Basin.

Time period 1970
1-31 2-07 2-14 3-01 3-14 3-27 4-11 4-25 5-19 5-31 6-14 6-29
Access point to to to to to to to to to to to to
2-07 2-14 3-01 3-14 3-27 4-11 4-25 5-19 5-31 6-14 6-29 7-13

1. Lake Gentry 336 898 2272 1293 696 1212 1816 1916 1050 2118a 1324 1402
(county boat ramp)
a a
2. Lake Tohopekaliga 86 310 836 358 976 566a 636 701 289 408 183 112
(two lane boat ramp)
3. Lake Tohopekaliga 526 663 1292 947 1002 934a 982 945a 550 773 777 724
co (three lane boat ramp)
M a a
4. Lake Tohopekaliga 107 231 537 332 83 290 419 294 142 103 292 184
(Fish Camp I)
5. Lake Tohopekaliga 371 447 1433 1008 1246 1252 1182 1345 829 1087 830 912
(Fish Camp II)
a
6. Lake Tohopekaliga 340 680 2216 1620 1132 892 798 552 368 676 94 453
(county boat ramp)
7. Lake Marian 271 452 1697 3046 1229 815 744 823 381 826a 212 639
(Fish Camp III)
8. Lake Marian 186 222 473 591 720 702 206 81 64 444a 339a 278
(Fish Camp IV)

a It was necessary to estimate the number of visits by the use of a seasonal weighted average due to lack of data during that
time period.
b No data were collected from Lake Gentry and Marian during the time periods of 1-31 to 6-19 for 1971. Continued









Table 6.-Estimated number of visits at each sampled access point, by time period, from February 1, 1970, through June 19, 1971,
in the Kissimmee River Basin-Continued.

Time period 1970
7-13 7-27 8-11 8-24 9-06 9-19 9-30 10-14 10-31 11-14 12-03 12-12
Access point to to to to to to to to to to to to
7-27 8-11 8-24 9-06 9-19 9-30 10-14 10-31 11-14 12-03 12-12 12-26
a a a
1. Lake Gentry 1560a 1176 1530 760 1824 1012 1686 1042 224 400 320 404
(county boat ramp)
2. Lake Tohopekaliga 117 93 284a 162 273a 266a 338a 1052 184 402 76 222
(two lane boat ramp)
3. Lake Tohopekaliga 662 635a 602 559 537 449 632 916 754 1193 524 828
M (three lane boat ramp)
4. Lake Tohopekaliga 261 205 202 262 293a 295a 246 290 195 262 114 146
(Fish Camp I)
a a
5. Lake Tohopekaliga 1141 452 1369 834 1366 1302 1022 1286 1328 1754 609 1032
(Fish Camp II)
6. Lake Tohopekaliga 328 312 342 304 254 396 504 590 478 928 440 534
(county boat ramp)
7. Lake Marian 609a 460a 780 448 534 452 701 590 638 887 398 441
(Fish Camp III)
8. Lake Marian 220 246a 181 234 1320 339 398 529 572 874 351 600
(Fish Camp IV)







Table 6.-Estimated number of visits at each sampled access point, by time period, from February 1, 1970, through June 19,
1971, in the Kissimmee River Basin-Continued.

Time period 1970 (one week), 1971
12-26 1-08 1-23 1-31 2-14 2-27 3-13 3-31 4-19 4-30 5-22 5-29
Access point to to to to to to to to to to to to
1-08 1-23 1-31 2-14 2-27 3-13 3-31 4-19 4-30 5-22 5-29 6-19
1. Lake Gentryb 356 424 234
(county boat ramp)
a
2. Lake Tohopekaliga 251 111 81 168 100 81 2 9 12 12 13 23
(two lane boat ramp)
3. Lake Tohopekaliga 845 897 589 281 83 82 87 55 50 53 25 47
(three lane boat ramp)
4. Lake Tohopekaliga 141 183 101 1123 1381 2177 203 330 135 10 81 102
(Fish Camp I)
5. Lake Tohopekaliga 805 731 743 1020 1273 1273 2168 1374 1061 434 250 807
(Fish Camp II)
6. Lake Tohopekaliga 656 840 748 188 1000 52 45 28 17 304 64 209
(county boat ramp)
7. Lake Marianb 617 507 797
(Fish Camp III)
8. Lake Marianb 565 516 370 .. .. .
(Fish Camp IV)
9. Lake Tohopekaliga .... 199 314 322 102 157 104 87 42 85
(South Lake Tohopekaliga)
a It was necessary to estimate the number of visits by the use of a seasonal weighted average due to lack of data during that
time period.
b No data were collected from Lake Gentry and Marian during the time periods of 1-31 to 6-19 for 1971.








Table 7.-Total number of vehicles observed, total number of counts, and
total number of people recorded at counters located at boat ramps
(Group I) and fish camps (Group II) in the sampled area, during
the period of January 31, 1970, to January 31, 1971, in the Kissim-
mee River Basin.

Total number Total number Total number
Group of vehicles of counts of people

I 47 109.5 88
II 53 81.5 102



during the period March 1, 1970, to March 14, 1970, was 1293.0;
Lake Tohopekaliga attracted 4562.0 (this value is the sum of
counters 2 through 6); and Lake Marian had 3638.0 visitors.
The values for the remaining time periods listed in Table 6 can
be derived similarly.


Water Level (WL)
The main physical variable of interest is W L, the water
level of a particular lake. It is assumed that recreationists react
to variations in the water level. This is important due to the fact
that if the water level of a lake were too low or too high, the
recreationist may be unable to launch a boat from a ramp, for
example. The Flood Control District is interested in how recrea-
tion activity varies with the level of the water. If these levels
are determined, the FCD can allocate water among alternative
users to optimize the benefits from the use of water in the Kis-
simmee River Basin.
The hypothesized nature of the relationship between recrea-
tional visits and water level is presented in Figure 10. It was
hypothesized that the number of visits would increase as water
level increased from low water levels up to W L 1 ; from W L 1
to W L 2 the number of visits would not fluctuate with water
level; and above W L 2, maximum free storage level, the num-
ber of visits would decrease as the water level increases. It was
only possible to test the first part of the hypothesis due to the
lack of data during flood conditions. It was possible to obtain
from the Central and Southern Florida Flood Control District
daily measurements in feet above sea level of the water at the
nearest lock of each of the three sampled lakes. Specifically, for
Lake Gentry, the nearest water level data collecting center was

36








Table 8.-Determining the correction factors; number of cars per number of
counts and average number of people per car, during the period
of January 31, 1970, to January 31, 1971, in the Kissimmee River
Basin.


Number of cars Average number
Access point per number of people
of counts per car


1. Lake Gentry 47 .429 88 1.87
(county boat ramp) 109.5 47
2. Lake Tohopekaliga 47 88 1.
(two lane boat ramp) 109.5 -429 47 1
3. Lake Tohopekaliga 47 429 88 1.87
(three lane boat ramp) 109.5 47
4. Lake Tohopekaliga 53 102 1
(Fish Camp 1) 81.5 650 53 1
5. Lake Tohopekaliga 53 102
(Fish Camp II) 81.5 .650 53 1.92
6. Lake Tohopekaliga 47 88 8
(county boat ramp) 109.5 .9 47
7. Lake Marian 53 102
(Fish Camp 111) 81.5 .650 53 1.92
8. Lake Marian 53 102
(Fish Camp IV) 81.5 .650 1.92










to the




Low High
4- water water -
leel level
WL Water level WL2


Figure 10.-Hypothesized relationship of water level to recreation-visits,
Kissimmee River Basin.


at gate S-63. In the case of Lake Tohopekaliga, it was gate S-61,
and gate S-65 was the closest to Lake Marian (refer to Figure
1) [5].

37









Table 9.-Derived estimate of the number of visitors at each sampled access point, in the Kissimmee River Basin, during the period
of March 1, 1970, through March 14, 1970.
Total Correction Correction factor: Correction Estimated
traffic factor: to to account for factor: to number
counts account for trailers determine of
Access point recorded duplicate contributing number of people
for counts due to extra counts people per car for
time no parking (number of cars) (number of people) time
period facilities (number of counts) (number of cars) period
1. Lake Gentry 3224 .50 .429 1.87 1293.0
(county boat ramp)
2. Lake Tohopekaliga 1790 .25 .429 1.87 358.3
(two lane boat ramp)
3. Lake Tohopekaliga 4723 .25 .429 1.87 947.2
S(three lane boat ramp)
4. Lake Tohopekaliga 1523 .50 .650 (1.92) x (.425)a 332.2
(Fish Camp 1)
5. Lake Tohopekaliga 1616 .50 .650 1.92 1008.3
(Fish Camp II)
6. Lake Tohopekaliga 4039 .50 .429 1.87 1620.0
(county boat ramp)
7. Lake Marian 4882 .50 .650 1.92 3046.5
(Fish Camp III)
8. Lake Marian 948 .50 .650 1.92 591.5
(Fish Camp IV)


a Additional correction factor accounts for permanent and rental residents contributing extra counts (at Fish Camp I) to the
traffic survey.








Temperature (T)
Most people become disinterested in outdoor recreation
when the temperature is uncomfortably hot. Therefore, it is
hypothesized that as the maximum daily temperature increases,
the number of visits to the river basin will decrease.
It was impossible to attain an accurate reading at each lake.
The intention was to derive an average of the highest daily
temperature at each lake by considering the highest daily tem-
perature at each access point of the lake. The only data available
concerning daily temperature was obtained from the U.S. Depart-
ment of Commerce National Oceanic and Atmospheric Ad-
ministration. The nearest location for gathering the highest daily
temperature readings for Lake Gentry and Lake Tohopekaliga
was at the Kissimmee Climatological Station; while for Lake
Marian, the nearest was the Indian Lake Estates Climatological
Station [5]. It was assumed that maximum daily temperature
readings were the only readings that would influence recrea-
tional usage of the river basin. The other extreme point, the
lowest daily temperature, was not considered relevant due to the
general climate in this part of Florida and the type of recrea-
tional activities predominating in the area.

Rainfall (Ra)

In most cases, rainfall has an influence on outdoor recrea-
tional activities. As rainfall increases, outdoor activities along
the shoreline and on the lake are dampened, with only a few
"enthusiastic" recreationists engaging in activities. Such rec-
reational activities as picnicking and sports are usually disrupted
by thunderstorms. Thus, it was hypothesized that as the amount
of rainfall increases, the number of visits to the Kissimmee
River Basin will decrease.
Initially, a measurement'of rainfall at each individual sam-
pled lake was desired. Instead, a daily rainfall count at the near-
est lock, for each sampled lake, was the measurement obtainable.
For Lake Gentry, it was lock S-63; Lake Tohopekaliga, lock
S-61; and Lake Marian, lock S-65 [5]. The procedure to account
for rainfall entailed measuring rainfall in inches per day during
each time period, at each of the three locks. Note that in the
Kissimmee River Basin, rainfall occurs most frequently during
seasons I and II but not for long durations. The water level data
and all rainfall data were collected at the same locations.



39







Wind Velocity (WV)

As Wv increases beyond a certain point, it imposes a re-
striction on the maneuverability of sail boats and fishing lines,
and generally makes recreation less desirable. Therefore, it was
hypothesized that as wind velocity increases, the number of
visits to the river basin will decrease.
Data for wind velocity were not available at each lake.
The desired value was an average of readings at several locations
at each lake, of the highest mile per hour reading recorded dur-
ing the day; but the only attainable data for the entire river
basin came from the Herndon Airport in Orlando, Florida [5].
Thus the same measurement was used for each of the three lakes.
Three distinct procedures were established to utilize the
wind velocity values. The first method consisted of determining
the number of days the wind velocity was higher than the highest
mile per hour average for the year, during a particular time
period. The second method entailed calculating the number of
days the wind velocity was higher than the highest mile per
hour average during the particular time period in question.
For example, if the highest m.p.h. average for a specific time
period was 18.0, and four days in that time period received a
reading greater than 18.0 m.p.h., then the number of days the
wind velocity was higher than the highest m.p.h. average was
four. Note that the basic difference between methods one and
two is that the first procedure refers to the highest mile per
hour average during the year while the second refers to the time
period. The third method was to compute the average highest
mile per hour wind velocity for each time period. Again, it was
presupposed that only extreme wind velocity readings would
affect recreational activity and therefore, would be pertinent to
this study.
Empirical Results
A recreational use equation was estimated for the three
sampled lakes. The selection of the final equation was based
upon the extent to which it was believed to describe observed
conditions and upon statistical indicators of significance. The
remaining portion of this section is devoted to a discussion of the
estimated visits equation.
A zero-one dummy variable, L i, was introduced as an in-
dependent variable in the general model to differentiate among
the different types of lakes. The variable Li possesses a value
of "one" whenever the data being examined were collected from
the lake in question and a zero at all other times. Note that Lake

40







Tohopekaliga has no dummy variable since its value of "one"
or "zero" is implied in the regression equation. When estimating
recreational usage of lakes, other than those sampled by the
traffic survey, such characteristics as size of lake, distance from
population centers, and depth of water should be considered in
determining the proper value for Li.
The estimated regression equation is:
V = 766.2 + 22.07 W L ** 85.98 Ra 1.80 T* 43.08 D2*
(3.737) (54.35) (0.865) (14.39)
82.80 L,** 314.28 L2** (20)
(14.37) (35.56)
R = .687 degrees of freedom = 77 F = 28.14
where the variables are as previously defined.
The strongest correlation among the independent variables
occurred between the variables L, (dummy variable for Lake
Gentry) and WL (water level). This interdependence can be
justified, since the water level did not vary a great deal within
the lakes, with the exception of Lake Tohopekaliga, but rather
varied between lakes. Wind velocity was not utilized due to its
statistical insignificance.
The calculated R2 was .687 and the calculated F-value was
28.14, which is significant at the one percent level. The statis-
tical results support the original hypothesis that recreational
use of the lake varies directly with the water level and inversely
with the physical variables temperature and rainfall. As water
level (W L ) increases by one foot, recreational use of the lake
is estimated to increase by 22.07 visitors per day. Between sea-
son II and season III recreational usage of the lake will decrease
by 43.08 visitors per day due to the seasonal trends. There was
no evidence of a seasonal trend during the months of February
through September; thus the variable D, was deleted from the
final equation. This conclusion differs from the original hypo-
thesis that the year be divided into three seasons rather than
two. Also, the variables L, and L, behaved as predicted. That is,
the total number of visitors recorded decreased from Lake
Tohopekaliga to Lake Marian and from Lake Marian to Lake
Gentry by 82.81 and 314.28 visitors per day, respectively.
If an estimate of recreational use was desired, and not its
relationship to other variables, then this regression equation is
not needed. Only the procedures to calculate V from the traffic
counts is necessary. This study was especially interested in the
relationship between water level and recreational use due to an
interest in allocation.

41








Estimating Total Recreational Usage Of The River Basin
The preceding model refers to the total number of people
using the sampled lakes. It is of importance to estimate the total
number of people using the entire river basin during a particu-
lar time period. The main problem encountered in establishing
this value was that the traffic meter data were applicable only
to three lakes, and could not be used directly to estimate the
number of recreationists for the entire river basin. The method
of overflight counts" was therefore chosen to provide sample
data on the relationship between the number of people using
the three lakes and the total number of people using the river
basin.
The percentage of people in the entire river basin that
utilize the three lakes was established by first determining the
number of people, as computed by the overflights, for the three
lakes, during each seasonal period. Next, it was necessary to
calculate the number of people for the entire river basin, as esti-
mated by the overflights, during each season. Finally, the pro-
portion of people in the entire river basin who used the three
lakes was computed as the ratio of the number of people using
the three lakes to the total usage.
Once the proportion (P) was determined, the total number
of people using the river basin daily for each time period could
be calculated by multiplying the total number of people using
the three lakes by the factor 1/P.
The data consisted of a count of the number of people sight-
ed on boats and shorelines of each lake in the basin. In order
to sum the individual overflights to obtain an estimate of the
use over a period of time, the data were adjusted. The adjust-
ment was necessary because there are more weekdays than week-
end days or holidays in a given time period. This adjustment
was not applied to the traffic count data, since it was collected
over several weeks rather than at one point in time.
The general procedure for adjusting the overflight data was
characterized as follows. The overflight data during a particular
time period were divided into weekday and weekend counts.
Then each set was summed and the daily average computed.
Finally, both sets of counts were added together to derive a
weighted average of the total visitors per day for that time
period. The counts were weighted depending on the number of

16An overflight consisted of using a small airplane to observe and
count the number of people recreating on each lake during an instant in
time. This information was collected for each lake in the river basin at
different times of the day on selected days over a period of a year.

42







Table 10.-Summary of all weighted average daily overflight counts, by time
period, for the sampled area in the Kissimmee River Basin between
January 31, 1970, and January 31, 1971.

Daily Overflight Counts
Time period Lake Lake Lake
Gentry Tohopekaliga Marian

1-31-70 to 3-01-70 3.90 150.90 52.00
3-01-70 to 3-27-70 1.65 101.70 33.90
3-27-70 to 4-25-70 1.29 96.60 18.80
4-25-70 to 5-31-70 0.92 105.20 15.07
5-31-70 to 6-29-70 2.10 171.70 6.82
6-29-70 to 7-27-70 0.00 139.80 17.56
7-27-70 to 8-24-70 0.00 83.90 10.85
8-24-70 to 9-30-70 1.90 65.50 18.06
9-30-70 to 10-14-70 1.57 65.00 6.71
10-14-70 to 11-14-70 12.05 120.90 6.31
11-14-70 to 12-12-70 11.20 98.30 11.28
12-12-70 to 1-31-71 3.41 84.70 33.40


weekdays or weekend days and holidays in that time period. This
analysis was carried out individually for each lake. Some of the
time periods used in calculating the daily average overflight
counts were different than the time periods used in the traffic
survey. This was due to the lack of sufficient overflight data
during the designated time periods in the traffic study. For a
complete listing concerning the adjusted overflight data for all
time periods, see Table 10.
The procedure used to establish the adjusted overflight data
can be illustrated by considering the time period November 14,
1970, to December 12, 1970, as an example. During that time
period, five overflight observations for each lake were made.
These are summarized in Table 11.
In order to utilize these data, an adjustment must be made
for the fact that of the five observations, two were on weekends
and three on weekdays. For example, Lake Marian's weekend
observations consisted of 28 counts, and the weekday total was
30. Since two weekend values were observed during that time
period, the average count for the weekend was 14 visitors per

43








Table 11.-Overflight observations, on Lakes Gentry, Tohopo;.aliga, and
Marian, in the Kissimmee River Basin for the time period Novem-
ber 14, 1970, through December 12, 1970.


No. of people No. of people No. of people
observed on observed on observed on
Lake Gentry Lake Tohopekaliga Lake Marian
Date of
observation Weekday Weekend Weekday Weekend Weekday Weekend

11-15-70 18 162 8
11-21-70 11 245 20
11-25-70 3 12 4
12-02-70 16 83 12
12-11-70 10 50 14



day. There were three observations taken during the weekdays
between November 14, 1970, and December 12, 1970; therefore,
the average overflight count for the weekdays was 10 visitors
per day. Next, both averages must be weighted to account for
the fact that there are more weekdays than weekends and holi-
days in the time period. Thus, since 19 out of the 28 days in
that time period were weekdays, the average weekday value
was multiplied by 19/28. The weighted average weekday value
was (19/28) X (10) or 6.78 visitors per day. The average week-
end value was mutiplied by 9/28 since there were nine week-
end days in the time period. Therefore, the weighted average
weekend value was (9/28) X (14) or 4.50 visitors per day. To


Table 12.-Weighted average overflight counts for the time period November
14, 1970, through December 12, 1970, of the three sampled lakes
in the Kissimmee River Basin.

Weighted average for: Total
weighted
Lake Weekend Weekday average of
overflight overflight overflight
counts counts counts

Gentry 9/28 ( 14.5) = 4.66 19/28 (9.66) = 6.55 11.20
Tohopekaliga 9/28 (203.5) = 65.40 19/28 (48.3) = 32.90 98.30
Marian 9/28 ( 14.0) = 4.50 19/28 (10.0) = 6.78 11.28


44








Table 13.-Seasonal estimates of total number of visitors to the Kissimmee
River Basin, in 1970 based on the estimated percentage value
derived by the use of overflight counts.

Number of Proportion Number of
Season Lake visitors (Vi) (P) calculated visitors
at sampled lakes for season in river basin
Feb.-May Gentry 11,488 .375 30,635
Tohopekaliga 34,526 .375 92,069
Marian 13,280 .375 35,413
Sub-total 59,294 158,117
Jun.-Sept. Gentry 11,896 .326 34,491
Tohopekaliga 23,592 .326 72,368
Marian 8,508 .326 26,098

Sub-total 43,996 134,957
Oct.-Jan. Gentry 5,090 .231 22,035
Tohopekaliga 27,568 .231 119,342
Marian 10,351 .231 44,809
Sub-total 43,009 186,186
TOTAL VISITS (V T) 479,260


derive the total weighted average daily count, the individual
weighted average counts per day were summed. The total weight-
ed average was 11.28 visitors per day. Therefore, during this
time period, an average of 11.28 visitors per day was estimated
by the overflights at Lake Marian. The total weighted average of
the overflight counts for Lake Gentry, Tohopekaliga, and Marian,
during November 14, 1970, through December 12, 1970, are pre-
sented in Table 12. Note that Lake Gentry average 11.20 visitors
per day and Lake Tohopekaliga 98.3 visitors per day.
The estimated number of visitors to the Kissimmee River
Basin is presented in Table 13. A numerical example of the
above analysis as related to the months of October through
January, 1970-71, is included in Table 14.
During the same months, the traffic survey counts were
distributed among the three lakes as follows:


Lake Gentry 5,090 visitors
Lake Tohopekaliga 27,568 visitors
Lake Marian 10,351 visitors

Total 43,009 visitors



45







Table 14.-Estimating the percent of recreationists utilizing the three lakes
by the use of overflight counts (season III), in the Kissimmee River
Basin, 1970

Lakes People Percent of recreationists
per day utilizing the three lakes

Lake Gentry 18.84
Lake Tohopekaliga 183.75
Lake Marian 34.12

Total of three lakes 236.71
Total for river basin 1026.65
236.71

1026.65 = .231


To estimate the total number of recreationists for the year,
the seasonal totals were combined (see Table 13). When em-
ploying the overflight method, it is assumed that the proportion
of the number of people actually participating in water oriented
recreation (as observed by the overflights) to the total number
of recreationists utilizing the lake facilities is constant among
the lakes. Thus, if the overflight counts actually represent 40
percent of all recreationists at Lake Marian, it should also rep-
resent 40 percent of all visitors at Lake Gentry, and so forth.17
The relationship between total recreational visits and water
level can be formulated. The total visits (VT) is expressed
as a function of daily visitation at each sampled lake (Vi),
proportion of visits on sampled lakes to entire basin (Pj), and
the number of days in each of the three time periods (d aj):

3 3
S3 daj
VT = 2 V(i) ( (21)
i =1 j=1

where i refers to the three sampled lakes and j refers to the
three time periods. Expanding over the time periods, the rela-
tionship becomes:

3 3 3
3da da da
VT = (V) + (V) i) 2 + (Vi) (22)
i=1 Pl i=l P2 i=1 P3
iTOther methods could be utilized to estimate the number of visits for
the entire river basin. For example, the proportion of access points on the
three sampled lakes to the basin could be used. This was applied in [1].

46








By substituting Equation (20) into Equation (22), allowing L1
and L, to be zero or one depending on which lake is being con-
sidered, and similarly for the time period dummy variables, Di,
and holding the rainfall and temperature variables at their
means, the formulation can be expressed as:

VT = [3(-925.93) + 3(22.07) WL 82.8 314.28] 120
.375
[3(-925.93) + 3(22.07) WL- 82.8 314.28] 122


"+ [3(-925.93) + 3(22.07) WL + 3(-43.08) 82.8 (23)

314.281 123


where the number of days in the three time periods were 120,
122, and 123, respectively, and P, = .375, P. = .326, P, = .231
as shown in Table 14.
Each segment of Equation (23) represents a time period.
To estimate the changes in number of visits due to a change in
water level in time period one, multiply 21,187.2 times the change
in the level of the water. That is, it is estimated that for every
foot in elevation increase in water level, 21,187.2 more visits
will occur during February May on the average in the entire
Kissimmee River Basin. The estimates for time periods two and
three can be interpreted accordingly. It is important to realize
that these estimates apply only to drought conditions and not
flooding, due to the data used.
Equation (23) can be simplified to express total visitations
on a yearly basis as a function of water level:
VT = 3,962,699.23 + 81,219.81 W L (24)
If for example the water were at a mean value (for the
time over which data were obtained in this study) of 54.06 feet,
one would expect a total of approximately 428,000 visits an-
nually. If the water level were at the maximum observed (61.57
feet), approximately one million visits could be expected.

ESTIMATES OF VALUE TO VISITING RECREATIONISTS
The aggregate value was obtained by combining the an-
alyses of days per visit and number of visits.
Total (Annual) Value Number
Economic Value = per X of
Visit Visits

47








where, in this study, only the number of visits was related to
water level. Combining equations (24) and (17) gives an esti-
mate of economic value relating to water level:
Annual
Economic = ($59.91) ( -3,962,699.23 + 81,219.81 W L )
Value
where $59.91 is the estimated average value per visit as obtained
in a previous section. Thus, annual economic value for a water
level of 54.06 feet is estimated at $25.6 million, while at 61.57
feet it is approximately $62.2 million. The estimated relation-
ship indicates that no economic value would be forthcoming, due
to zero visits, at a water level as low as 48.79 feet above sea
level.1"
To obtain estimates of value for each time period it is neces-
sary to utilize the demand curve for the time period, and that
portion of Equation (23) pertaining to the particular time
period. If no relationship to water is desired, then the above re-
lationship to water level can be ignored and data in Table 13 can
be applied directly to obtain total values from the demand rela-
tionship. The total annual value to visiting recreationists for
1970 was estimated as:
($59.91) (479,260) = $28.7 million

SUMMARY AND CONCLUSIONS
Many levels of government are involved in providing rec-
reational opportunities. These opportunities range from small
city parks to the extensive national forest system. The funding
of these recreation sites, provided from taxes or the sponsoring
governmental body, must compete with funds needed for many
other services. For this reason, a great deal of interest has been
placed in the measurement of economic values of outdoor
recreation.
It was the purpose of this bulletin to present procedures for
estimating the value of outdoor recreation and apply these to
the Kissimmee River Basin. In addition, the impact of variations
in water level on recreational values was derived.
Demand for recreation, in the absence of an efficient mar-
ket was estimated by observing the amounts recreationists spend
in order to participate in a recreational experience.

18The lowest water level observed on Lake Tohopekaliga during an
extreme drawdown was 47.72 feet, thus, the above estimates seem reason-
able, since recreational activity was at a minimum.

48








Total recreational usage of an area can be defined as the
product of the average number of days recreationists use a
recreational site per visit and the number of visits to a recre-
ational site.
The number of days per visit can be considered the quantity
variable in a demand relationship and the daily on-site costs a
price variable. Based on the demand relation for an average
visit, the aggregate demand for recreation can be derived by
expanding according to the number of visits. For purposes of
this study, it was assumed that the impact of water level on
recreational values is realized on the number of visits rather
than the length of stay per visit. A value per visit was estimated
and then the relationship between water level and visits was
utilized to relate water level to recreational value.
The average demand function for recreation per visit was
estimated. This relationship is based on 1970 and was estimated
such that the separate relationship for each of four time periods
throughout the year could be evaluated. Based on the concept
of consumer surplus, a value per visit was estimated to be $59.91.
The relationship between total recreational visits and water
level was also formulated. By combining days per visit with
visits, the aggregate value is obtained as a function of water
level:
Annual
Economic = ($59.91) (-3,962,699.23 + 81,219.81 WL )
Value
As water level increases so does economic value. For example,
at a level of 61.57 feet (the maximum observed during 1970)
the annual economic value is estimated at $62.2 million.
The average annual economic value to visiting recreationists
in 1970 was estimated at $28.7 million. This estimate is a meas-
ure of consumer surplus enjoyed by recreationists visiting the
area. This figure does not measure the gross expenditures or
income to the area. It is merely a measure of the "surplus
satisfaction" accruing to the recreationist using the site over
and above their actual expenditures.
Information of this nature is valuable for use by decision
makers in allocating water among alternative uses. Recreation
is one of the prominent uses of water in many areas, as it is in
the Kissimmee River Basin. By lowering the water level to
provide for say, flood control, potential benefits to recreationists
are foregone. For every foot the water level is lowered, recrea-
tionists lose an average annual benefit of $4.9 million ($59.91
X 81,219.81). This highly sensitive relationship is related to

49








the shallow nature of the lakes in the basin and based on the
lowering of one lake during 1970. A change of one foot in eleva-
tion of the lakes results in many yards difference in the water's
edge. Thus, boat docks and ramps may be completely out of the
water with small variations in water level.
Even though the estimates presented in this bulletin are
based on data from the Kissimmee River Basin, the procedures
can be used in any area. It is becoming increasingly more im-
portant to attempt to allocate resources efficiently. By account-
ing for benefits by each use of water a more efficient allocation
is possible.


REFERENCES

[1] Behar, Morris. "Recreational Usage in the Kissimmee River Basin,
Florida." Unpublished Master's Thesis, University of Florida,
December 1972.
[2] Conner, J. R., J. E. Reynolds, and K. C. Gibbs. Activities, Character-
istics, and Opinions of Lakefront Residents: The Kissimmee River
Basin, Florida. Florida Agricultural Experiment Station Bulletin
755, January 1973.

[3] "The High Cost of Driving and What to Do About It," Changing
Times, 24 (September 1970), p. 37.
[4] U. S. Agricultural Research Service. "Food Consumption of House-
holds in the U.S.," Household Food Consumption Survey, 1965-
1966, (Report No. 1). Washington, D.C.: 1965, p. 212.
[5] U.S. Department of Commerce. National Weather Service, Office for
State Climatology, Local Climatological Data: Years 1970-1971,
Washington, D.C., 1972.
[6] U.S. Bureau of Labor Statistics. Consumer Price Index for May 1970.
Washington, D.C.: June 1970.

Additional References

Gibbs, Kenneth C. A Measure of Outdoor Recreational Usage, Food
and Resource Economics Department, Econ. Rept. 52, University
of Florida, August 1973.
Gibbs, Kenneth C. "The Estimates of Recreational Benefits Resulting
from an Improvement of Water Quality in Upper Klamath Lake:
An Application of a Method for Evaluating the Demand for Out-
door Recreation," Unpublished Ph.D. Dissertation, Oregon State
University, 1969.
Gibbs, K. C., and J. R. Conner. "Components of Outdoor Recreational
Values: Kissimmee River Basin, Florida," Southern Journal of
Agricultural Economics, Vol. 5 Number 1, July 1973, p. 239-244.
Gibbs, Kenneth C., and John F. McGuire, III. Estimation of Outdoor
Recreational Values, Food and Resource Economics Department,
Econ. Rept. 53, University of Florida, July 1973.

50









Grubb, Herbert W. and James T. Goodwin. Economic Evlauation of
Water-Oriented Recreation in the Preliminary Texas Water Plan.
Texas Water Development Board Report 84. Austin, Texas: Sep-
tember 1968.
McGuire, John F. III. "An Application of Two Methods to Estimate
the Economic Value of Outdoor Recreation in Kissimmee River
Basin." Unpublished Master's thesis, University of Florida, De-
cember 1972.
Morgan, J. and P. King. "Effects of Reservoir Operating Policy on
Recreation Benefits," Water Resources Bulletin 7: 98-117, August
1971.
Participating in Outdoor Recreation: Factors Affecting Demand
Among American Adults, Study Report 20, Outdoor Recreation
Resource Review Commission, Washington, D.C.: 1962.

Reiling, S. D., K. C. Gibbs, and H. H. Stoevener. Economic Benefits
from an Improvement in Water Quality. U.S. Environmental Pro-
tection Agency Socioeconomic Environmental Studies Series EPA-
R5-73-008. Washington, D.C.: U.S. Government Printing Office,
January 1973.
Stevens, J. B. Measurement of Economic Values in Sport Fishing:
An Economist's View of Validity, Usefulness, and Propriety. Paper
presented to the annual meeting of the American Fisheries So-
ciety, September 1968.
Stoevener, H. H. and L. J. Guedry. "Sociological Characteristics of
the Demand for Outdoor Recreation." Paper for discussion by
Technical Committee WM-59, San Francisco, California, March
1968.
Trice, Andrew H., and Samuel E. Wood. "Measurement of Recreation
Benefits," Land Economics (34) 1958, pp. 196-207.


























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