Finding a Best Conservation Park Entry Fee for Kruger National Park

Finding a Best Conservation Park Entry Fee for Kruger National Park Gardner Brown 1 and Johane Dikgang 2 Abstract Whereas most park valuation studies simply value a park our goal is to maximize net revenue. Kruger National Park is regarded as a firm "exporting" products to foreign clientele. In trade theory a firm gets to charge different prices in different countries. Here we have to have one price for all foreigners. The travel cost of an individual serves as an indirect determinant of price. We are estimating the price to charge for the site. We trick this out with travel costs for a TRIP not the SITE. We use a Poisson and Negative Binomial models count data specification of the recreational demand function, as the number of visitation trips taken is a non-negative integer. Our results indicate that the revenue maximizing daily entry fee to charge international visitors who can afford to visit is US$266, and US$106 (2014 prices) based on the whole population zone. Nonetheless, both estimates indicate that there is room to substantially raise Kruger entry fees. In reality, the park agency is unable to charge the revenue maximizing price due in particular to competition from other parks, both locally and regionally. Nonetheless, the fact that we found that the fees could be increased significantly over and above the current fees to maximize the revenue collection is important. Keywords: Kruger, international, price, revenue, travel cost. 1 Department of Economics, University of Washington. Seattle, Washington, United States of America. Emails: gbrown@u.washington.edu. 2 Department of Economics and Econometrics, University of Johannesburg, Johannesburg, South Africa. Emails: jdikgang@uj.ac.za. Funding from ERSA (Economic Research Southern Africa), and Sida (Swedish International Development Cooperation Agency) is gratefully acknowledged. 1

1. Introduction Big game parks in Africa levy entry fees on visitors entering the park. The entry fee or the fee for conservation is so low that the park authorities do not cover the costs of managing the park (see - Laarman and Gragersen, 1996; Schultz et al., 1998; Scarpa et al., 2000; Naidoo and Adamowicz, 2005). This implies that most park fees are underpriced. This creates what many would regard as a perverse phenomena: some of the world s poorest countries such as Botswana, Kenya, Namibia, Tanzania and South Africa are subsidizing the very predominantly rich visitors from the world s wealthiest countries. The median annual income in our survey of visitors is over US$75,000. It is a pricing policy that few would enthusiastically defend publically. Our intent is to estimate a more defensibly appropriate pricing policy for game parks illustrated by an analysis of foreign tourists visiting Kruger National Park in South Africa. The research has three focal points. First, whereas most park valuation studies simply value a park our goal is to maximize net revenue and we defend that objective. We are aware of the criticism that is usually leveled against studies seeking to maximize park revenue. The critics point out that such a study ought to focus on maximizing consumer surplus. We had that question happen in another context, that firms maximize revenues, so that solves that problem. Thus, Kruger National Park is regarded as a firm "exporting" products to foreign clientele. To the best of our knowledge, there are few papers that have been published that maximize revenues for the park, thus our study is important. What would have been really terrific was if we had the demand curve for South Africans tourists. Then we could have "derived" and estimated two price policies for Kruger. The two-price policy would have made this study even more unique. Nonetheless, we borrow the shape from a study by Dikgang and Muchapondwa (2013), and scale it to Kruger for illustrative purposes. We expect the slope on price to be significantly negative. We expect it to show that entry price should be dramatically larger. 2

Second, we set forth our version of the travel cost method used to determine the optimal price and explain how our method and the empirical setting of the analysis ameliorate some of the criticisms of the travel cost method. Third, we show the exceptional discrepancy between the actual conservation entry charge per day and the optimal price that should be charged. Over a wide range, demand for park entry is inelastic. Consider that airfare is $1302 or more for virtually all international visitors, the tour package that includes visits to the game park is $3761 or more and the scale of the entry fee for Kruger is $25 per day where they typically stay for a couple of days, an amount lower by more than an order of magnitude. Our idea is that SANParks should maximize revenue, so should set the price for international tourists where the elasticity of demand is equal to 1, and for the residents maximize consumer surplus (i.e. set price equal to marginal costs MC). The obvious is that the price depends on the weights of visitation at the different zones. In trade theory a firm gets to charge different prices in different countries. Here we have to have one price for all foreigners. We are not aware of any literature where countries are constrained to charge one price in two or more different markets, where elasticities differ. We would ideally like to know what the average cost per visitor is at Kruger, where the cost refers to running the park and not the rondevals (i.e. accommodation), restaurants and all other services. 2. The Travel Cost Method The classical stated virtue of the travel cost method (TC) compared to rivals such as contingent valuation (CV) or stated preference (SP) is that TC is lodged in the indirect revealed preference of consumer actual behavior. Hotelling s (1947) profound insight developing the travel cost method was that observed behavioral differences in consumers travel cost behavior give rise to observed different rates of actual participation in a recreation site while CV or SP studies rely on hypothetical nonmarket behavior. 3

Chase et al. (1998) have argued that methods such as contingent valuation and stated preference are more flexible than the travel cost method because the former can capture non-use values. True enough if we were interested in determining a total value of a site. However, our intent is a marginal objective - to determine an optimal price to charge for entry into Kruger Park. Obtaining estimates of existence value is not appropriate for solving this problem. Moreover, as long as something like an individual s existence value is not a function of use value, then we are not guilty of omission, not considering a social externality of increasing price that could result in the marginal loss of existence value. One of the criticisms of the travel cost model is the difficulty encountered when the site to be valued is part of a trip with more than one destination. How does one estimate the travel cost for one of the joint products? That is not our problem, given our objective. Most other TC studies seek a total value of a particular site for typically a non-market use like a park versus the total value of an alternative allocation of the land for timber cutting. Our objective is different. We are interested in the optimal price to charge for entrance into Kruger. Our survey asks respondents about travel costs of the whole tour package in order to enjoy Kruger if they are taking a tour as most are. If visitors are not part of a tour package, or if the utility of Kruger is separable from the utility of the other components of the tour then the multiple destination element is not a problem. A few words about the goal of setting a conservation fee or entry price that maximizes revenue are in order. Why not maximize consumers surplus, as most studies do? A few exceptions include Dikgang and Muchapondwa (2013) and Chase et al. (1998) who find that one park should increase its price to increase revenue, another should decrease the fee and a third park was pricing approximately correctly. A study by Alpizar (2006) used historical data to compute the optimal common entrance fees for national parks in Costa Rica. Alpizar (2006) found that price discrimination between residents and nonresidents could successfully maximize social welfare and even meet a set revenue target. A study by Naidoo and Adamowicz (2005) simulated fee increases and estimated entrance fees that maximized tourism revenue to Mabira Foresty Reserve in Uganda. 4

It is important to emphasize that the Kruger Park product is being sold to foreigners. It therefore is appropriate to treat Kruger as any other South African revenue-maximizing firm exporting a product to another country. The fact that Kruger is the property of the South African government, we judge, has no bearing on the appropriate objective function. 3. Approach The travel cost of an individual serves as an indirect determinant of price. Most importantly, the relevant population for any country should not include people who cannot afford to visit Kruger. We know the income of people who do come. For an accurate measure of population, we included the population in each country where income is US$75 000,00 (i.e. median income) or more. By measuring how visitation varies with price, TC, one can estimate a demand function for a destination. Visitation rates, V, from different origins are regressed on travel costs, TC, and socioeconomic shift variables, X: V = f (TC, X) (1) We run a model where TC is added to Time Costs to create a single variable, namely Full Total Costs and one where we only run TC. If the parameters associated with TC are the same as those associated with Time Costs, then equation 1 is deemed valid. The distribution of the visitation trip (i.e. dependent variable) for international visitors is typical of count data. We use a Poisson and Negative Binomial models count data specification of the recreational demand function, as the number of visitation trips taken is a non-negative integer. We start our analysis with the Poisson model, but are aware of the over dispersion issues. According to Winkelmann and Zimmermann (1998) the Poisson model is criticized for implicitly assuming that the variance of the dependent variable is equal to its mean (i.e. no over dispersion). This assumption rarely holds due to 5

event occurrence dependence or due to unobserved heterogeneity. Over dispersion may results in failures of standard goodness-of-fit tests 3. It is argued that before accepting the Poisson results, a test for the presence of overdispersion must be undertaken. The Negative Binomial models are often applied whenever over-dispersion is detected (Greene, 2002). The latter model has an additional alpha, which is used to test over-dispersion presence, so that when alpha=0, the model collapses to a Poisson model. As a result, this paper presents both models and prefers the Poisson model in the case where over-dispersion is not present. For each zone, typically an OECD country suppose, V! /N! = g TC! + P (2) where P is the optimal revenue maximizing price to charge and N! is the zone s population/1 x 10! because the visitation rate is measured in terms of visits per 1x10!. Please note that N! consists of two sub-groups, namely, the proportion of the population that can afford to visit, and the whole zone population. Total revenue is: π =! P g N! (3) which is maximized by setting the derivative of (3) with respect to P to find the optimal price, P*. Not surprising revenue is maximized for P where the elasticity of demand = 1. It is instructive to note that the demand for Kruger is constructed by obtaining the area above the travel cost from each origin or zone to use Hotelling s term for each chosen region. So the demand function we are working with is net of costs of access to the park. Relatively early on, researchers including Cesario and Knetsch (1970) and McConnell (1975) set forth the argument that the full price of recreation included the monetized 3 A significant (p<0.05) test statistic from the goodness-of-fit indicates that the Poisson model is not suitable. 6

time cost of the trip along with the out of pocket travel cost. Reasoning from his study, McConnell argues that to estimate the value of time carefully, researchers ought to inquire about a respondent s time constraint if any and about alternative uses of one s time. We omitted such questions because the questions for the direction of our study involving the importance of substitutes (not discussed herein) exhausted the respondent s patience and concentration. Among the greater uncertain parameters of the travel cost model method is the opportunity cost of time. It is natural to assume it is the wage rate, particularly if the analysis involves a business trip (Cesario et al., 1970). It may be natural but is empirically wrong. Generally, the opportunity cost of time has been found to be less than the wage rate, perhaps because people enjoy the scenery if travelling to a recreation site, which creates a trip with multiple characteristics. Or perhaps it is because a commuter in a modal choice commuter study enjoys time away from ones family 4. And then there is the problem of retired people, of which there are very many in our sample of people on safari whose income budget constraint does not include hours worked. Our impression is that researchers in the past have assumed that the value of time was a fraction that varied between 20 to 45 percent of a calculated wage rate. An early study of modal choice by McFadden (1974) estimated that the opportunity cost of time was 32 percent of the wage rate. Larsen and Shaikh (2004) designed a quite interesting study in which the opportunity cost of time was not fixed and they estimated an elasticity of time with respect to the wage rate. Their time value was 32 40 percent for wage rates between $30 - $100 per hour. Our median calculated wage rate ranges from $45 - $84 per hour. Getting the opportunity cost of time right probably is less onerous in this research project because it is relatively less important compared to other travel cost studies in general and recreation park studies in general. This is because most of the foreign visitors to Kruger 4 McFadden provided this example during a University of Washington seminar shortly after the publication the New Science of Pleasure: Consumer Behavior and the Measurement of Well-Being (2013). 7

have out of pocket per person reported travel costs exceeding $1300 and non-travel costs of the trip exceeding $2000. Like most other researchers, our trail to delineating the opportunity cost of time begins with observing some measure of annual income and follows through to an estimate of the value of an hour. Such a transformation requires knowing weeks worked per year, days worked per week and hours worked per day. Since the vacation length of Europeans is a month or more while the American vacation centers closer to two weeks, individuals across travel zones can exhibit substantial variation. Recall that the observation for our travel cost study is the aggregation of sampled individuals in this zone. Fortunately, there is an OECD database that provides estimates of hours worked per year for each country and this allows us to estimate a wage rate for each country. As for the transformation of these estimated wage rates into a time value, we allow the estimation procedure to resolve this uncertainty. Specifically, our estimate of total travel cost TC! is a linear combination of time cost and reported travel cost for each zone. In fact we use the median reported travel cost for each zone. Some people in a given zone report high travel cost because they have flown business or first class. This introduces an additional product, quality of air service. We avoid a model with multiple characteristics by using the median travel cost observation for each zone because naturally it gives lower weight to the upper values. TC! = 0.3 time costs + reported TC (4) For each Zone! ; time cost (i.e. 0.3 of the wage rate) = the product of hour time cost and the length of the flight from Zone! to Johannesburg the time to Kruger from Johannesburg is the same for all so need not count - well some could drive but expect that s a distinct minority. Hour time cost! = γ Annual Income! (5) 8

γ = γ/(!"#!"#.!"#$.!""#$!""#!" ) (6) where Annual Income! is the subjective value of time. Now that represents the usual assumptions about the opportunity cost of time equal to a range of 20% - 45% of the wage rate. Whereas others have to make assumptions about the three unknowns in the denominator, we remain agnostic. That is, we will estimate the standard travel cost regression in equation 5 allowing γ in the time cost portion of the dependent variable to vary from 0.00015 to 0.00032 based on our subjective guess of the likely possible range of the denominator s values. We then choose the equation with the γ providing the best statistical fit. The range of values above are built on using McFadden s time cost of 30-45 percent of the wage rate (McFadden, 1995); vacation length between 2-4 weeks and a rough range for the U.S. and Europe respectively, of 7-8 hours per day in recognition of some variation across countries. Average income and median travel cost for each zone are substituted for missing values in the estimation procedures. The hours worked per year per zone are shown in table 1 below: Table 1: Average annual hours worked per worker in each zone Zone Hours Worked 2013 $ Value of an Hour EU 1549 48 UK 1669 45 U.S. East 1788 84 U.S. Mid- West 1788 84 U.S. West 1788 63 4. Kruger National Park Kruger is home to the big five, has the biggest accommodation facilities, tarred roads and an international airport. It is the flagship of SANParks managed parks and by far the largest park in South Africa. The park has a wide variety of attractions comparable only with the best in Africa. Although the park is in Mpumalanga province, it is relatively close to Johannesburg/Pretoria both in the Gauteng Province, only 440km away. 9

Kruger has the second highest number of park visitors after Table Mountain national park, accounting for 29.7% percent of total visits. However, given that Table Mountain main attraction is the mountain itself, and that it does not boast of abundance of wildlife, its visitation demand is not of interest in our study. 5. The Survey A face-to-face survey was undertaken in July 2014 in the broader Kruger area. We used electronic questionnaires instead of paper-based questionnaires. To be more specific, we used tablets during the fieldwork. A survey was conducted with randomly picked park visitors (only park goers, and those who already paid to get to the park) at the Kruger National Park. Due to the vast size of the park, the surveys were mainly carried out at the gates, accommodation facilities and designated resting sites inside the park. We also conducted surveys in lodges within close proximity to the park. A total of 322 international visitors were surveyed. Our sample composition is in line with the visitor profile at the park. Thus, the top 5 countries are the Netherlands, United Kingdom, Germany, France and the United States of America. In addition to data from the travel cost, the survey collected data on visitor demographics. The questionnaire was designed such that it would provide the necessary information for calculating travel costs and visits per million. The respondents were asked what their approximate round-trip travel cost they paid to get to South Africa from where their trip originally started. Thus, they were asked to reveal their travel cost per person in their currency. Visits per million and median travel costs are shown in table 2 below. 10

Table 2: Sample visits, visits per million and median travel costs from each zone Zone Sample Visits Population Affordability 5 Populations (Millions) Visits/ Million Travel Cost EU 639 0.38 115.688417 6 1302 UK 103 0.46 29.798800 4 1512 U.S. East 171 0.22 25.780680 4 1800 U.S. Mid- 153 27.188850 2000 West 0.22 3 U.S. West 61 0.22 16.260750 4 2000 The estimated number of visitors against median travel cost is shown in figure 1 below: Median Travel Costs 1200 1400 1600 1800 2000 USA Mid-West USA West USA East UK 3 4 5 6 visitsmillionafford EUROPE Figure 1: Kruger visitation against median travel cost The importance of the figure is to show the strong bunching of observations for Europe, the UK and the USA so that we don t have very good variation and that s why there are few observations. 5 The median household income for our sample is $75 000. Thus, we define those who can afford as people with a household income of $75 000 or more. The percentages shown in the column is the proportion of the people in each zone that meet these criteria. 11

6. Results I think the following is right and it is interesting. We are estimating the price to charge for the site. We trick this out with travel costs for a TRIP not the SITE. But then we basically subtract the costs to get the willingness to pay (WTP) for the site. The TC Model uses annual visits per million as the dependent variable, and uses median travel costs and some demographic information as explanatory variables. The basic model would be to regress travel costs alone to estimate the visitation to the Kruger. The other factors that are likely to explain visitation rates include time costs, flight time, gender, education level, household income and number of members on the trip. The moment the appropriate explanatory variables have been identified, the regression equation yields the demand function for annual trips for the average visitor to the Kruger, and the area below this demand curve provides an estimate of the average consumer surplus. The average consumer surplus is multiplied by the total zone population to generate an estimate of total consumer surplus for the Kruger park. Most importantly, none of the demographic variables were significant with the exception of time costs. Thus, we ran a simple possible model, regressing visits on travel costs and time costs. A specific equation describing annual trips to Kruger is as follows: Visits /N! = β! + β! (TC! ) + β! (X! ) (7) where visits is the visitation per million and β! is the median travel cost and β! is time costs. We construct the aggregate demand function by summing up the consumer surplus of all the zones. The estimated demand function is reported in Table 3. As expected, the coefficient for median travel cost is negative and significant. The slope coefficient is the ratio of the proportionate change in annual visits per million to the real change in the explanatory variable. 12

Table 3: Regression estimates of the visits on travel costs to Kruger National Park on use Poisson - Negative Negative Negative Poisson Negative Poisson Full Afford Binomial - Binomial Binomial Whole Binomial Cost Afford Incorrect Full Total Sample Whole Whole Measure of Cost - Sample Sampl Time - Afford Afford Dependent Variable: Visitation/Million Travel Cost -0.001* -0.001* -0.001-0.001-0.0017** -0.0017** -0.0017** (0.0006) (0.0006) (0.0006) (0.0006) (0.0008) (0.0008) (0.0008) Time Cost (0.3) / 0.0001 0.0001 0.0001 0.0001 0.0003 0.0003 0.0003 Full Cost (0.0002) (0.0002) (0.0002) (0.0002) (0.0003) (0.0003) (0.0003) Cons 2.79*** 2.79*** 2.77*** 2.79*** 2.46*** 2.46*** 2.51*** (0.50) (0.50) (0.52) (0.52) (0.6465) (0.6465) (0.6401) Alfa 6 7.67e-22 7.67e-22 7.67e-22 5.26e-14 Pvalue 0.00 0.00 0.00 0.00 Log-likelihood -8.37-8.37-8.37-8.37-6.04-6.0-6.04 Pseudo R2-0.0452 0.0452 0.0449 0.0452 0.0442 0.0442 0.0448 Observation 5 5 5 5 5 5 5 Note: robust standard errors in parentheses; legend: * p<0.10; ** p<0.05; *** p<0.01 The table above presents six model specifications. Column 1 and 2 show Poisson and Negative Binomial models for the proportion of the population that can afford to visit the park. In column 3, we include the full time cost (i.e. incorrect measure of time) as an explanatory variable. Colum 4 shows results where we include the Full Total Costs (TC + Time Costs) as an explanatory variable for those who can afford. Column 5 and 6 on the other hand shows the Poisson and Negative Binomial models for the whole population zone. 6 Alpha is a measure of the dispersion parameter. This dispersion parameter can be obtained by exponentiating /lnalpha. In a case where the dispersion parameter is equal to zero, then the model reduces to the simpler poisson model. In a case where it, is significantly greater than zero then the data are over dispersed and are better estimated using a negative binomial model than a poisson model 13

We make use of the nested test for over-dispersion within the Negative Binomial model output. As can be seen in the output above, the model provides us with an additional parameter alpha so that if we fail to reject the null hypothesis that alpha = zero, then the Poisson is appropriate for modeling our count data above. To test the null hypothesis of no over-dispersion against the alternative of over-dispersion, we used the p-value. The negative binomial output s estimated implicit variance value term of the multiplicative heterogeneity (constant alpha) is about 7.67e-22 with a p-value of 0.000. Thus, the null hypothesis that alpha=0 is rejected and conclude that the variance of the dependent variable is statistically significantly different from the mean; hence a Negative Binomial is preferred. In our case, alpha is significantly not different from zero, suggesting that the Poisson distribution is appropriate. The value of the log-likelihoods is -8.37 for both models, which suggest that the two models are similar in terms of goodness of fit. The travel cost coefficient is negatively signed and statistically significant for both Poisson and Negative Binomial models. The results obtained in column 1 and 3 suggest that inclusion of the incorrect measure of time leads to an insignificant travel cost parameter relative to running the correct measure of time (0.3 of wage rate). As can be seen from column 1 and 4, the parameters associated with TC are the same as those of Time Costs; thus, we conclude that equation 1 is valid. The output in table 3 gives us (V = 2.79 0.0001TC) as the trip demand function. The park demand function is made up of the demand functions for the five zones. We construct the aggregate park demand function by summing up the consumer surplus of all the zones. The average visitor is estimated to receive $1 119 in consumer surplus per trip (calculated by the inverse of the coefficient for median Travel Cost). A worthy goal for our research is to be able to estimate the revenue maximizing entry fee for recreational sites. By doing 14

so, it allows decision-makers to adopt policies that would enable recreational sites to generate sufficient revenues so they could sustain themselves. Our research provides this much needed estimates - see the table below. Table 4: Revenue Maximizing Entry Fees for Kruger Zone Revenue Maximum Population (Millions) Weight % Revenue 7 Maximum Revenue Maximum Fee $ Fee $ Fee $ (Sub-Sample) (Whole Sample) 8 EU 1 488 115.688417 34 506 26 UK 1 278 29.798800 10 128 29 U.S. East 990 25.780680 21 208 121 790 27.188850 22 174 171 U.S. Mid- West U.S. West 790 16.260750 13 103 101 Total 5 336 115.688417 100 1 119 448 The revenue-maximizing price facing this demand curve ranges from $790 to $1 488. As indicated earlier on in our introduction, the park agency is unable to charge different prices in different zones/countries. Thus, the average price to charge all international visitors depends on the weights of visitation at the different zones. In the interest of getting a more accurate measurement of the revenue-maximizing fee that are of relative importance to each other, we calculate the weighted average. The weighted revenuemaximum price ranges from $103 to $506. Thus, the total weighted revenue maximizing entry fee for Kruger is $1119 (2014 prices). 7 The revenue maximizing fees based on the proportion of the population that can afford to visit Kruger National Park. 8 Revenue maximizing fees baaed on the total zone population. 15

Our study differs from previous studies as it estimates the revenue entry fees using two distinct sample groups. The weighted maximizing fees for the whole sample population ranges from $26 to $171, with a total weighted maximizing entry fees of $448. 7. Conclusion The Kruger National Park is a world-renowned comparable with the best in Africa. This is one of a few studies to quantify the benefits and optimal price to enter the park. We develop a zonal cost approach. The park agency is unable to charge $1 119 as it only captures the aggregate park demand function. When we estimate a value using a park demand function, we have to divide by mean number of days, we are looking for say 4.2 days average stay in Kruger. Our results indicate that the daily revenue maximizing daily entry fee to charge international visitors is US$266, hence there is room to substantially raise Kruger entry fees. Inherently, the revenue maximizing fees based on the whole zone population is significantly less than our preferred sub-group (i.e. based only on those who can afford), at $106. Most TC studies estimates entry fees based on the whole population zone, hence the latter estimates are comparable with estimates from most TC studies. Nonetheless, the estimated entry fee of $106 based on the whole population zone echoes our earlier concluding remarks from our preferred sub-group estimates, that there is room to significantly increase the fees. In reality, the park agency is unable to charge the revenue maximizing price due in particular to competition from other parks, both locally and regionally. Nonetheless the fact that we found that the fees could be increased significantly over and above the current fee to maximize the revenue collection is important. This additional amount can be used to reduce the over realize of parks on public funding. In conclusion, this study implies that Kruger has an economic potential far greater than its realized economic earnings. This situation is not specific to Kruger but applies to other parks both in South Africa and in the region. 16

Of crucial importance in our future work is the issue of seasonality. The top five markets for South African parks are European, United Kingdom and the United States. However, the holiday season for these regions differ, thus future data collection should be carried out during the year to ensure a truly representative sample of international tourists. 17

References Alpizar, F. 2006. The pricing of protected areas in nature-based tourism: A local perspective. Ecological Economics 56, 294-307. Brown, G.M., and Mendelsohn, R. 1984. The Hedonic Travel Cost Method. Review of Economics and Statistics 66 (3): 427 33. Cesario, F.J. and Kenetsch, J.L. 1970. Time bias in recreation benefit estimates. Water Resource Research 6: 700 704. Cesario, F. J. 1976. Value of Time in Recreation Benefits Studies. Land Economics, 52, pp 291 297. Chase, C., D. R. Lee., W. D. Schulze., and D. J. Anderson. 1998. Ecotourism Demand and Differential Pricing of National Park Access in Costa Rica. Land Economics 74 (4), 466-482. Dikgang, J and Muchapondwa, E. 2013. Estimation of optimal conservation fees for international park visitors in the Kgalagadi Transfrontier Park, ERSA working paper 393. Greene, H. W. 2002) Econometric Analysis (5th ed.). Upper Saddle River, New Jersey: Prentice-Hall. Hotelling, H. 1947. The Economics of Public Recreation. The Prewitt Report, National Parks Service,Washington. Laarman, J. G. and Gragersen. H.M. 1996. Pricing Policy in Nature-Based Tourism. Tourism Management 17 (4), 247 254. L.Carr and Mendelson, R. 2003, Valuing Coral Reefs: A Travel Cost Analaysis of the Great Barrier Reef, Ambio, 32,5 353-357 Naidoo, R., and. Adamowicz. W.L. 2005. Economic benefits of biodiversity exceed costs of conservation at an African rainforest reserve. PNAS. 102, 16712 16716. Scarpa, R., Chilton, S.M., Hutchinson. W.G. and Buongiorno. J. 2000. Valuing the recreational benefits from the creation of nature reserves in Irish forests. Ecological Economics 33: 237 250. Schultz, S., Pinazzo, J., and Cifuentes. M. 1998. Opportunities and limitations of contingent valuation surveys to determine national park entrance fees: evidence from Costa Rica. Environment and Development Economics 3: 131 149. 18

Smith, V.K., Desvouges, W.H., and Fisher, A., 1986. A comparison of direct and indirect methods for estimating environmental benefits. American Journal of Agricultural Economics 68, 280. Winkelmann, R. and Zimmermann, K.F. 1998. Is Job Stability Declining in Germany? Evidence from Count Data Models. Journal of Applied Economics 30: 1413-1420. 19