DETERMINING THE ECONOMIC FEASIBILITY OF PUBLIC RECREATIONAL DEVELOPMENTS AT BEAVER LAKE, ARKANSAS* Robert N. Shulstad and Thomas G.

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1 SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS JULY, 1977 DETERMINING THE ECONOMIC FEASIBILITY OF PUBLIC RECREATIONAL DEVELOPMENTS AT BEAVER LAKE, ARKANSAS* Robert N. Shulstad and Thomas G. Sawyer Beaver Lake is nestled in the midst of the Ozark the gross expenditure method generates large num- Mountains in the northwest corner of Arkansas. The bers, it lacks theoretical support. Many resource picturesque lake is actually a multi-purpose reservoir economists have turned to the Clawson-Hotelling constructed and maintained by the U.S. Army Corps procedure and have introduced a number of innovaof Engineers. The 28,220 acre lake offers eleven tions. Brown, Singh and Castle [3] introduced improved public access areas for use by recreationists. income- and distance, Stevens [12] the quality of the Six additional recreational areas have been planned, experience, Guedry [8] site characteristics, Brown to be built as demand requires [16]. and Nawas [2] use of individual observations and Costs for development of the six additional parks Gum and Martin [10] influences of substitute recreawere estimated by the Corps of Engineers as of July tional activities and a shifter variable representing 1974, to be $6.87 million [16]. tastes and preferences. On initiation of this research, two methods for For this analysis, the Gibbs methodology [5, 6, financing future recreational developments on reser- 7] was selected. Unlike the Clawson approach, the voirs were available. The first method requires agree- Gibbs procedure distinguishes between effects of ment of a local sponsor such as a state, county or city travel costs and on-site costs on the quantity of to pay at least 50 percent of the proposed recrea- recreation days demanded. Travel costs influence tional development costs and assume all costs for choice of making a trip or not, and limit the amount operations, maintenance and replacement of the of funds available once the recreational site is facilities. The second method allowed 100 percent reached. However, the same travel cost will be federal financing for recreational developments if a incurred whether the recreationist chooses to remain system of user charges could be expected to recover one day or five days. As long as the effective budget all operation, maintenance and replacement costs constraint allows choice of length of stay, deciding [15]. the number of days per trip will be based on effective Research objectives were to determine: (1) total on-site costs per day. demand for and economic value of publically pro- The Gibbs methodology implies a critical price at vided recreational areas on Beaver Lake, (2) the which consumers would be indifferent between economic feasibility of adding to the present system recreating or not recreating at the site. If prices and (3) the financial feasibility of local sponsorship exceed this "critical" price, the consumer would not through using a fee system. recreate at all because he could gain more satisfaction The choice of an appropriate recreation demand through not incurring any travel expenses and using estimation technique was not an obvious one. Recrea- his total budget for other items. tional administrators have generally estimated the The'critical price' divides the spectrum of possible value of a recreational development through measure- recreation prices into two mutually exclusive groups: ment of the gross volume of business generated. While prices at which the consumer would not recreate at Robert N. Shulstad is Assistant Professor and Thomas Sawyer was Graduate Assistant, Department of Agricultural Economics and Rural Sociology, University of Arkansas. *Paper presented to the Annual Meeting of the Southern Agricultural Economics Association, Atlanta, Georgia, February 7-9, Published with the approval of Director of the Arkansas Agricultural Experiment Station. 101

2 the site, and prices at which the consumer would number of visits per year (X 7 ), the reciprocal of the travel to the site in order to consume some recrea- number of recreationists in the party (X 8 ), and the tion. Similarly, the number of recreation days asso- season of the year (D 1 ), spring; (D 2 ), fall; (D3), ciated with this critical price can be considered a winter. "critical" level of consumption of recreation, since it Recreation demand is hypothesized to be of a divides the spectrum of recreation consumption into curvilinear nature and therefore the log form of the two exclusive groups: (1) levels of consumption less dependent variable was used. The following demand than the critical quantity which the consumer, given model was obtained where Z is the natural log of days income and costs of transportation, would never per visit. volunteer to consume, and (2) levels of recreation which he would volunteer to consume. Z = X1 * X 2 * For a comparison of the Gibbs and the Clawson X 3 ** X 5 approaches see Edwards, Gibbs, Guedry and Stoevener, 1976 [5] X X 7 * X 8 ** D1* THE MODEL D 2 ** D 3 * Sample and questionnnaire data were collected F-Value * R.44 *.01 through personal interviews with 271 recreating **.05 parties, representing 871 recreationists from July.10 (1) 1974, through July The sample was stratified to reflect representative proportions of activity, All predictive variables are significant at the ten season, access area and weekday versus weekend- percent level or less and carry the hypothesized sign. holiday participation based on 1973 visitation data Leisure time is omitted from the model due to its received from the Corps of Engineers [13, 14]. correlation with income and size of group.' A six page questionnaire was administered by The demand function for the average Beaver graduate students through interviews at the eleven Lake recreationist can be expressed in terms of price developed access areas. Questions concerned number (on-site costs) by holding all other variables at their and composition of each group, reason for visit, travel mean and solving equation (1) for days per visit. The costs and on-site costs broken down by category, average demand function is: income, length and number of visits per year and amount of leisure time available. A series of direct ) questions concerning expected use of new parks and Brown and Nawas [1] have shown that expanwillingness to pay for activities at new parks were also sion of the average individual demand curve will asked. underestimate the value of the recreational expe- Since records and dates were critical to the rience unless all individuals have exactly the same accuracy of data concerning investment expenditures, characteristics as measured by the other independent the investment portion of the questionnaire was variables. mailed to the participants after they returned home. To avoid this problem each individual's own Through use of a mail survey procedure developed by characteristics were used in equation (1) and a Christenson [3], a total response rate of 76 percent demand curve estimated for each recreating party in was obtained with a usable response rate of 58 the sample. percent. The consumer's critical price was calculated by Ordinary least squares regression was used to asking each repondent the minimum number of days he estimate the demand for recreation days per visit (Y) would spend at Beaver Lake per visit. By substituting as a function of travel costs per trip (Xi), on-site the individual's minimum days into his demand costs per day (X 2 ), income (X 3 ), leisure time (X 4 ), function, maximum on-site costs a party of recreationsite characteristics (X 5 ), investment cost (X 6 ), the ists is willing to pay per day can be determined. 2 1 While exclusion of the leisure time variable may result in specification bias within the model, its inclusion within the model definitely did result in multicollinearity problems. I have chosen to avoid the certainty of multicollinearity. Other researchers have hypothesized the importance of the leisure time variable. However, none have found it to be of great significance; thus, any specification bias would be minimal. 2 The following assumptions are implicit in the above argument: (1) the utility function of the consumer is such that recreation at the site can be expressed as one argument while all other goods and services, excluding transportation to the site, aggregated as Hicks-Allen "money" is the other argument, (2) the indifference curves appropriate to this utility function intersect the "money" axis but are asymptotic to the recreation axis or some line parallel to, but above, the recreation axis, and (3) the act of traveling to the site, in and of itself, is not a source of utility to the consumer [5, p. 7-8]. 102

3 The demand function for each party can then be parks to new parks would undoubtedly take place, integrated from actual on-site costs to critical price to but would represent a transfer of benefits within the determine the consumer surplus received by the park system rather than an increase in benefits. party. 3 The additional six parks are estimated to cost Following this procedure, individual consumer $6.87 million with annual operation, maintenance surplus estimates were summed and divided by the and replacement set at $43,455 per park. Assuming total sample to produce a mean individual consumer an eight percent discount rate and an expected life of surplus of $70.43 per party visit. Since the sample was 20 years, the marginal benefit-cost ratio for the six stratified by activity, season, park and weekday- additional parks is Additional parks would not weekend, the data received should be representative be economically feasible if they rely solely on of user population. increased visitation from present park users. Visitation data show 391,954 party visits to This marginal benefit-cost ratio is important to improved access areas on Beaver Lake during the overall decisions made by the Corps of Engineers Thus, net benefits of publicly provided outdoor regarding construction of the six proposed parks. It recreation at Beaver Lake are estimated to equal would be the appropriate decision mechanism, $27,605,320. This is the value of benefits received assuming the present parks are adequate to meet net of actual costs to the recreationist. normal increases in visitation (10.6 percent per year) which have been occurring and can be expected to continue. ECONOMIC FEASIBILITY ECONOMIC FEASIBILITY OF OF NEW NEW PARKS PARKS Present parks are beginning to reach capacity and Addition of new parks would be considered cannot be expected to accommodate normal growth, economically feasible if the value of discounted thus benefits from this normal growth allowed with benefits received is greater than discounted costs new parks must be considered in the benefit-cost incurred. analysis. Under conditions of limited capacity for Recreationists at the existing parks were shown a increasing visitation the addition of six new parks map designating proposed locations of six additional would have a benefit-cost ratio of 3.05 and construcimproved access areas on Beaver Lake. They were tion would be economically feasible. then asked if they would use the new areas if they Economic feasibility does not assure financial were developed. If yes, would they spend more feasibility. While total benefits received by users may recreation days at Beaver if the new areas were exceed costs, only a discriminating monopolist would developed? If yes, how many more? Recreationists be able to secure revenues equal to total benefits. The who indicated they would use the new parks said Corps of Engineers or a local sponsor would be they would spend an average of 2.17 additional days expected to charge a uniform fee to all users. at Beaver. The average for the entire sample was.74 additional days per party per year. The value of net benefits received from these additional days can be IMPACT OF A FEE SYSTEM considered the marginal benefits which could be The impact of a fee system on number of days attributed to the additional parks. Average net demanded was determined for each party by subbenefits received per party per visit was estimated to stituting individual on-site costs plus change in costs equal $70.43 while the average visit was 3.65 days. into the demand function. If on-site costs per party Net benefits per day were estimated to equal $19.30 are increased by one dollar, days per visit will decline per party. by 0.04 days. This reflects the average of the There were 41,258 recreating parties at Beaver individual changes in demand. Similarly, increases of Lake in Based on.74 additional days per party, $5 and $10 per day will decrease length of the $589,247 in net benefits per year could be antici- average visit by 0.19 days and 0.36 days per visit, pated from the additional parks. This figure assumes respectively. no substitution occurs from present parks to new These decreases in number of days demanded parks and no increase in visitation other than the.74 with increases in on-site costs are as expected, not days per year per party. Substitution from present great. Once a recreationist has made the trip to the 3 The demand curve estimated using the Gibbs methodology may be referred to as a "more-or-less" demand curve, as it indicates the quantity of recreation consumed at various prices of recreation, given that the consumer chooses to recreate at all [5, p. 10]. On-site costs were adjusted for normal at home expenditures for food. 4 Six additional parks, while the palnned number, is not necessarily the optimal level of investment for the Corps to engage in, but given that this level of investment is being considered, the benefit-cost ratio should be greater than or equal to one for the investment to be made. 103

4 area for a weekend or vacation, an additional $5 or with the total revenue which could be generated per $10 per day will not send him home. However, party per year through use of the additional fee. knowledge of a fee system which adds to on-site costs In 1974, an estimated 1,431,653 camping days could be expected to influence the decision to make were spent at improved access areas on Beaver Lake. the visit. This impact is examined in the visits model. While a certain amount of on-site costs were incurred there were no use fees charged. If a use fee of $2.50 Visits per year X 1 * X 3 * per day per party had been imposed, it is estimated X X 5 that only 1,262,907 recreation days would have been demanded, generating revenues of $3,157, If X X* fees were increased to higher levels, days spent will D D 2 decrease, but total revenues will continue to increase D 3 * up to a user fee of $12 per day per party. Based on F- Value = 10.3' R 2 =.39 (4) the estimated demand functions, visitation would drop from its present 35 recreation days per party per year to 16.8 days per party per year. The maximum By holding all variables except on-site costs at total revenue which could be produced from a their means, the following equation for number of uniform fee at improved access areas is estimated to visits per year is generated: be $8,300,000. Visits per year X2 (5) In 1975, the Corps of Engineers imposed a fee of $2.50 for camping at improved access areas. The Under the present fee system, average number of demand model would have projected a decrease of 6 visits per year is By increasing on-site costs by percent in visitation, other things equal. Actual $1.00 per day, visits drop to Additional fees of visitation decreased by 8.6 percent. $2.50 and $5.00 per day would decrease the number of visits per year per party by.90 and 1.79, respectively. FINANCIAL FEASIBILITY FOR By examining effects of changes in on-site costs LOCAL SPONSOR on both visits and average days per visit, the overall Under present requirements, the Corps of Engiimpact on recreation days per year can be deter- neers will develop a new park if a local sponsor will mined. This joint effect is shown in Table 1 along provide fifty percent of the construction costs and TABLE 1. EFFECTS OF CHANGE ON-SITE COSTS ON AMOUNT OF RECREATION DEMANDED AND TOTAL REVENUE PER PARTY, BEAVER LAKE, 1974 a Change in Change in Recreation Days Total Revenue Added Length of Number of Demanded per per Fee/Day Visit Visits/Year Party/Yearb Party/Year $ 0.00/day.00 days.00 visits C NOTE: Mean recreation days demanded per year was 34.70, mean visits per year was , mean length of visits was days. Recreation days (column 4) is derived by multiplying the length of visit at the increased fee times the number of visits per year at the increased fee. For example: an added fee of $12 per day will decrease length of visit by 0.43 days and number of visits by 4.3 visits. These decreases make the length of visit days ( ) and the number of visits ( ). By multiplying these figures ( x ) the number of recreation days per party per year (16.77) is obtained. aassumes fees at similar sites on other lakes in the region would also be increasing to maintain a competitive price situation within the recreational industry. No allowance has been made for the impact of the decrease in number of visits on the length of the visit. As a result the actual impact of price changes on total recreation days demanded per year is over-estimated and the number of recreation days per party estimated in the table is biased downward. CFee that generates maximum revenue. 104

5 provide for operation, maintenance and replacement rate, the local sponsor revenue-cost ratio would equal once constructed. The question is whether adequate 1.45 to one. Substitution from existing parks to new revenue can be generated to cover these expenses. parks would increase this ratio. Total visitation to improved access areas at Thus, construction of two additional parks on Beaver has increased at an average rate of 10.6 Beaver Lake is found to be both economically percent from 1967 through However, present feasible for construction by the Corps of Engineers parks are beginning to reach capacity and cannot be and financially feasible for participation of a local expected to accommodate this normal growth in sponsor on the 50:50 plan, provided present parks are visitation. Based on the 10.6 percent normal growth near capacity. The revenue-cost ratio considering rate, 118,285 additional camping days could be both federal and local costs is.92 to one. Present expected at new parks during Based on the regulations do not require an examination of financial $2.50 per day per camping party fee now in effect, an feasibility at the national level, however. annual revenue flow of $295,713 would result. Two Recreation demand at Beaver Lake, Arkansas was new parks would be required to accommodate this estimated through use of the Gibbs methodology. growth, given present visitation at existing parks of Unlike the Clawson approach, it allows for the 101,445 camping days per year per park. differential impacts of travel costs and on-site costs on Average construction costs are estimated to equal the demand for recreation days per visit. The estimate $1,145,000, implying a cost to the local sponsor of of benefits received from recreation are of the same $572,500 per park plus $43,455 for operation, general magnitude as those developed through the gross maintenance and replacement costs per year. expenditure method or the Clawson approach as Assuming a 20-year life and an eight percent discount modified and used by Gum and Martin [9]. REFERENCES [1] Brown, William G. and Farid Nawas. "Impact of Aggregation on the Estimation of Outdoor Recreation Demand Functions," American Journal of Agricultural Economics, 55, , [2] Brown, William G., Farid H. Nawas and Joe B. Stevens. The Oregon Big Game Resource: An Economic Evaluation, Corvallis: Oregon State University, Special Report 379, [3] Brown, William G., Ajmer Singh and Emery N. Castle. An Economic Evaluation of the Oregon Salmon and Steelhead Sport Fishery, Corvallis: Oregon State University Press, [4] Christenson, James A. A Procedure for Conducting Mail Surveys with the General Public, Raleigh: North Carolina State University, [5] Edwards, J. A., K. C. Gibbs, L. J. Guedry and H. H. Stoevener. "The Demand for Non-Unique Outdoor Recreational Services: Methodological Issues," Technical Bulletin 133, Agricultural Experiment Station, Oregon State University, Corvallis, Oregon, May [6] Gibbs, Kenneth Charles. The Estimation of Recreational Benefits Resulting from an Improvement of Water Quality in Upper Klamath Lake: An Application of a Method for Evaluation the Demand for Outdoor Recreation, Ann Arbor: University Microfilms, Inc [7] Gibbs, Kenneth Charles and John F. McGuire, III. "Estimation of Outdoor Recreational Values," Gainesville: Food and Resource Economics Department, University of Florida, Economic Report 53, [8] Guedry, Leo Joseph, Jr. The Role of Selected Population and Site Characteristics in the Demand for Forest Recreation, Ann Arbor: University Microfilms, Inc., [9] Gum, Russell L. and William E. Martin. "Problems and Solutions in Estimating the Demand for and Value of Rural Outdoor Recreation," American Journal of Agricultural Economics, November [10] Martin, William E., Russell L. Gum and Arthur H. Smith. "The Demand for and Value of Hunting, Fishing and General Rural Outdoor Recreation in Arizona," Tuscon: Agricultural Experiment Station, Technical Bulletin 211, [11] Pindyck, Robert S. and Daniel L. Rubinfield. Econometric Models and Economic Forecasts, New York: McGraw-Hill, [12] Stevens, Joe Bruce. A Study of Conflict in Natural Resource Use: Evaluation of Recreational Benefits as Related to Changes in Water Quality, Ann Arbor: University Microfilms, Inc., [13] U.S. Army Corps of Engineers. Monthly Recreational Visitation Data, Project-Beaver Lake, Little Rock: Southwestern Division, Corps of Engineers,

6 [14] U.S. Army Corps of Engineers. Monthly Recreational Visitation Data, Project-Beaver Lake, Little Rock: Southwestern Division, Corps of Engineers, [15] U.S. Army Corps of Engineers. Draft-Operation and Maintenance Environmental Statement-Beaver Lake, Arkansas, Little Rock: Southwestern Division, Corps of Engineers, [16] U.S. Army Corps of Engineers. Updated Master Plan for Beaver Lake, July 1975, Little Rock: Southwestern Division, Corps of Engineers,