How Does Congestion Affect the Evaluation of Recreational Gate Fees? An Application to Gulf Coast Beaches

2. Conceptual Framework

We use a simple demand model to investigate how accounting for congestion affects the revenue raised and deadweight loss generated from gate fees. The model adopts a representative consumer approach and therefore does not permit us to consider distributional effect, although we investigate these concerns in our Gulf Coast application. Moreover, our model considers only the gross costs of gate fees and not the direct benefits to recreators from lower congestion levels at visited sites. These gains are proportional to the number of recreational trips ultimately taken and may be substantial in practice. Nevertheless, our model suggests that ignoring congestion feedback effects as in Ji et al. (2022) and Lupi, von Haefen, and Cheng (2022) will lead to overestimating the fee-induced demand response if people are willing to pay to avoid congestion. By implication, this implies that the revenue raised will be underestimated, and the deadweight loss will be overestimated if congestion effects are ignored. We also consider leakage of beachgoers to other recreation sites that are not subject to gate fees. In our view, this is an important effect to consider because, in practice, no fee will have complete geographic (or temporal) coverage. From a benefit-cost perspective, all benefits and costs from gate fees should be accounted for, so understanding how fees in one region might affect use, congestion, and welfare in others is important to quantify (Cesario 1980).

To begin, consider a representative consumer’s demand for a single site, x = g(p,c), where x is the number of trips, p is the travel cost, and c is congestion at the site, which, consistent with our Gulf Coast application, is operationally defined as trips per mile of coastline over a given time period (i.e., c = x/L, where L is miles of coastline). Recognizing that a gate fee or tax, F, influences aggregate congestion at the site by raising costs to all visitors, we can write demand as a function of entrance fees as follows: [1] Now consider a marginal change in F and its effect on demand. By totally differentiating equation [1] and rearranging, we see that [2] where captures the “partial equilibrium” demand response associated with the price change, and captures the demand response from congestion. Assuming the law of demand holds and that congestion is a bad, the denominator in equation [2] is greater than 1, and the full demand response to an increase in entrance fees, , is muted relative to the partial equilibrium demand response. As we show in Figure 1, this has important implications for the revenue raised and deadweight loss from gate fees.

For simplicity, Figure 1 approximates demand with linear functions. At a travel cost of p, demand is initially x_base. With the introduction of the gate fee or tax, the partial equilibrium demand response (ignoring congestion feedbacks) reduces demand to x_partial. Because all visitors are subject to the fee and reduce their demands accordingly, congestion levels at the site fall, and some of the pure price effect of the gate fee is mitigated, resulting in a net response of x_full. This implies that accounting for congestion feedback effects raises the estimated government revenue by F × (x_full − x_partial) and decreases the deadweight loss by approximately 0.5 × F × (x_full − x_partial) compared with measures using the partial equilibrium demand response that ignores congestion feedbacks.

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Figure 1

Demand Response to Gate Fee

If we extend the current analysis to a multisite framework, a related issue arises when the entrance fee or tax applies to only a subset of sites. This case is likely relevant when sites span multiple jurisdictions (e.g., across neighboring states or federal vs. statemanaged sites) and different jurisdictions adopt different policies. A particular concern is leakage, whereby the jurisdiction not adopting the tax experiences a net increase in demand for its sites, an often unwelcome spillover effect that exacerbates congestion concerns. To shed some light on this, consider the demand for two sites where only the first site is subject to an entrance fee (i.e., F₁). In this case, the overall demand effect of an increase in F₁ on the demand for trips to the second site is (see the Appendix for a formal derivation): [3] In general, not much can be said about the sign of and leakage, although intuition might suggest that the direct effect of the gate fee on demand for the untaxed site will likely dominate any indirect congestion effects, implying that leakage will remain a policy concern.

The discussion suggests that the effects of gate fees on recreational demand are threefold: (1) a pure price effect, whereby the fee reduces demand for the taxed good and (assuming the sites are substitutes) increases demand for the untaxed good (ceteris paribus); (2) a taxed site congestion effect, which increases demand at the taxed sites and decreases demand at the untaxed sites; and (3) a nontaxed site congestion effect, which likely reduces demand at the sites not subject to the tax and increases demand at the taxed sites. We can separately identify the welfare implications of these three effects by decomposing the compensating variation (CV) for a change from to [4] where E( ) is the expenditure function evaluated at different price and congestion levels. In particular, CV can be rewritten as [5] where the first line monetizes the welfare implications of the pure price effect, the second line monetizes the taxed site congestion effect, and the last line monetizes the nontaxed site congestion effect. Equation [5] will be helpful when interpreting the implications of accounting for congestion in our application, which we describe below.

3. Empirical Application

Our empirical application uses data collected by researchers associated with the natural resource damage assessment for the 2010 Deepwater Horizon oil spill (English et al. 2018). As part of that assessment, two general population phone surveys were used to collect recreation data for roughly 2,000 miles of coastline stretching from Texas to Georgia in 2012-2013 (Figure 2). Over 41,000 adults (≥ 18 years) residing throughout the contiguous (lower 48) United Sates provided information on over 27,500 primary-purpose recreational trips that serve as the foundation of our analysis. Table 1 provides summary statistics for the trips. Importantly, about 17% of trips were for more than one day, and a nontrivial number of trips involved one-way driving distances of over 1,000 miles. These two factors led to the construction of travel costs in a novel way that reflects the reality that individuals may choose to drive or fly to their preferred recreational destination. As described in English et al. (2018), separate estimates of flying and driving from each resident’s home to every coastal destination from Texas to Georgia were constructed. It was assumed that everyone within a one-way driving distance of 500 miles of their destination drives, but beyond 500 miles, individuals may choose to fly or drive. Using the reported frequency of flying to recreation sites in the data, an expected travel cost was constructed for every origin-destination pair, where weights proportional to the frequency of flying from alternative distance bands and varying by household income and size were used to construct a weighted average of flying and driving travel costs.

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Figure 2

Sampling Region for Recreational Trips

Note: Survey respondents reported recreational trips to highlighted shoreline areas (i.e., Texas to Georgia).

The current analysis modifies the recreation data used by English et al. (2018) in two key ways. First, while the researchers aggregated the 2,000 miles of coastline from Texas to Georgia into 83 sites, we use a more disaggregated site definition of 167 sites. Second, we disaggregate the data temporally and estimate separate models by three-month quarters. This disaggregation adds to the richness of our data and allows us to consider the behavioral and welfare implications of alternative gate fees at finer spatial and temporal scales.

A second key difference between English et al. (2018) and our analysis is that, given our focus on gate fees, we must construct a measure of congestion for every site by quarter. Our approach recognizes that site congestion is more a function of user days than trips, a distinction that is especially salient when a nontrivial fraction of trips are multiday, as is the case with our data.² This raises two key issues: (1) for many trips in our data set, we do not observe trip duration (i.e., the number of recreation days); and (2) the length of a trip is endogenously chosen by recreators (McConnell 1992). To avoid these difficulties, we make the simplifying assumption that trip duration is a function of one-way driving distance. To be more precise, we group trips for which we observe the count of recreation days into one of six cells based on one-way driving distance (< 50 miles, 50–100 miles, 100–250 miles, 250–500 miles, 500–1,000 miles, and > 1,000 miles). For each cell, we estimate the mean number of recreation days and use these means to construct the total number of user days from the trip data for each site in a quarter. We note that these trip durations are monotonically increasing with distance and range from 1.02 days for trips < 50 miles and 4.84 days for trips ≥ 1,000 miles, which is consistent with the observation of McConnell (1975). When forecasting how congestion changes with gate fees, we assume these one-way driving distance/recreation user day relationships are deterministic, which obviates the endogeneity issue that we alluded to previously.

Another advantage of using a more disaggregated model is that it allows us to specify congestion in a more refined way. In particular, congestion clearly has spatial and temporal dimensions that we should account for. As Bujosa et al. (2015) point out, a 10-square-mile site with 1,000 visitors is far less congested than a 1-square-mile site with 1,000 visitors. To translate this estimate of the aggregate number of user days by site and quarter into a daily per mile of coastline congestion measure, we divide it by 90 days and the site’s estimated coastline length, L.³ Our data suggest that there are about 1,245 daily visitors per coastline mile for the average site in our application, although some sites in some quarters have well over 20,000 daily visitors per mile of coastline.

Before moving on to a discussion of our modeling framework, it is worth briefly discussing the structure of the gate fees that we consider in our policy simulations. Consistent with our specification of congestion, we assume gate fees are charges on a per user day basis, meaning a person on a long weekend trip who visits the beach on three consecutive days pays triple the amount a person on a single-day trip pays. We assume the charge applies to visitors of any coastal area in Mississippi, Alabama, and the Gulf Coast side of Florida (Perdido Key to Key West), excluding the coastline from Apalachicola to just north of Tampa, where sandy beaches are largely absent. Recognizing that many user fees provide discounts for locals, we assume residents of these three states pay a $5 daily fee for access, whereas those coming from other states pay a $10 daily user fee. Because our data only include trips for adults aged 18 and older, we assume that children do not have to pay the fee.

4. Modeling Framework

Our recreational model builds on the revealed preference approach introduced by Timmins and Murdock (2007). In a site selection model, they model how congestion arises from a Nash bargaining framework in which individuals make choices given expectations about the decisions of others. In equilibrium, expectations of congestion match realized congestion for every individual and site, and assuming congestion is a bad, a Nash equilibrium exists. We extend the Timmins and Murdock model by allowing the total trips to all sites (i.e., participation) to be endogenous. We do so within the repeated discrete choice framework (Morey, Rowe, and Watson 1993), whereby the time horizon of choice (e.g., three-month quarter) consists of a series of choice occasions. On each choice occasion, an individual makes a discrete choice of whether to take a recreation trip, and if so, a conditional choice of which site to visit. Because these decisions are made across multiple choice occasions and aggregate demand is the sum of these separate choices, the total quantity of trips and their distribution across multiple sites is endogenous. We assume that conditional on taking a trip, preferences can be represented by the following indirect utility function: [6] where tc_ij is individual i’s travel cost to site j, c_jq is the total count of user days per mile of beach at site j in quarter q, δ_jq is a fixed effect for site j and quarter q that nonparametrically controls for unobserved and observed site characteristics in that quarter, and ε_ijqt captures idiosyncratic factors specific to the individual, site, quarter, and choice occasion t. Note that congestion and unobserved site characteristics in a quarter are perfectly correlated and thus cannot be separately identified without additional structure. Following convention in the recreation literature, the utility associated with not taking a trip is specified as a linear function of demographic variables (z_i) specific to individual i and an idiosyncratic error: [7] Assuming the idiosyncratic errors are random draws from the GEV variant of the type I extreme value distribution, the probability taking a trip to site j on choice occasion t in quarter q is [8] The probability of not taking a trip is [9] Estimation of model parameters proceeds by maximum likelihood and incorporates the population weights for each person in the sample.

With these parameters in hand, we could, in principle, follow Timmins and Murdock (2007) and recover the marginal (dis)utility of congestion through a second-stage regression that decomposes the alternative specific constants into part worths associated congestion and other observed site characteristics. Because unobserved site characteristics are likely correlated with these observable characteristics, the regression suffers from a classic endogeneity problem. To address this, Timmins and Murdock (2007) adopt an instrumental variables approach that uses nonlinear functions of the observed characteristics of neighboring sites as instruments, as do Phaneuf, Carbone, and Herriges (2009) and Melstrom and Welniak (2020), whereas Bujosa et al. (2015) use a control function approach. We do not estimate the congestion parameter through either approach but evaluate the sensitivity of gate fees to alternative calibrated parameter values that are consistent with different assumptions about what people would pay to avoid additional congestion on a beach trip. Given the relatively small number of recreation studies using credible econometric methods and data to estimate the marginal value of congestion, our approach allows us to speak to the issue of how much demand, welfare, and revenue change across a range of plausible parameter values.

Our calibration of the congestion parameter works as follows: On a trip, the willingness to pay (WTP) to avoid a change in current congestion levels is [10] If we have an econometric estimate of β_tc and assume a change in congestion ∆c, we can back out the congestion coefficient, β_c, for alternative WTP values. We assume ∆c corresponds to a doubling of congestion levels at the average site in our data set and consider alternative WTP values for avoiding this change that range from $0 to $25 in $5 increments. We evaluate gate fees for each of the implied values for β_c.⁴ It is important to note that the linearity of equation [10] in ∆c rules out the possibility of convex congestion costs (i.e., a doubling of congestion at a congested site has a larger effect on demand and welfare than a doubling of congestion at an uncongested site). In this way, it is likely that the implied demand and welfare effects of congestion reported in the next section may be conservative relative to a richer model that allows for such nonlinearities.

With the estimation or calibration of our model parameters complete, we turn our attention to identifying the congestion levels after a fee is introduced. There are two related questions here: Is there a unique Nash equilibrium with the fee? If so, how does one solve for it? As discussed in Bayer and Timmins (2005), the assumption that congestion is a bad guarantees that a unique Nash equilibrium exists.⁵ Solving for the new equilibrium with the gate fee can be achieved through a contraction mapping where the congestion estimates at each site are updated iteratively until they have converged to their true values, c^*. The algorithm we use works as follows: We initially assume congestion levels are fixed at their pretax level, c⁰, and then solve for the implied congestion levels with the gate fee, . We repeat this step by solving for and update our congestion estimate in the following way: [11] where d is a dampening parameter, 0<d<1. We repeat this step until abs|c^j − c^j-1| ≤ k, where k is a small positive value, which implies the contraction mapping has converged to c^*.

Once we have solved for the new equilibrium level of congestion, we can monetize the full change in economic value induced by the gate fee using the well-known “log-sum” formula as presented in English et al. (2018).

5. Results

Table 2 reports first-stage parameter estimates for the travel cost (β_tc)and dissimilarity (λ)coefficients across alternative models, with the other parameters not reported for brevity. In the first column, all participation and site choice data are pooled across the four quarters, whereas the remaining four columns report separate models by quarter. Focusing first on the travel cost coefficient, we find that it is consistently negative and significant. The dissimilarity coefficients, which by theory must fall between 0 and 1, are centered around 0.2 and highly significant. The ratio of the dissimilarity coefficient to the travel cost parameter, which is approximately the per trip value for a small site (Haab and McConnell 2002), is lowest in summer.

Table 3 reports key findings from our simulations. These results are aggregated across the four quarters and represent annual predictions for calendar year 2012. We focus first on column (1), where we assume the per trip WTP to avoid a doubling of congestion is 0, which is the implicit assumption in Ji et al. (2022), Lupi, von Haefen, and Cheng (2022), and the vast majority of published recreation studies investigating access fees. Our model predicts that the gate fee will raise $424 million in revenue from 44 million trips, which corresponds to an average gate fee of roughly $9.65 per trip. Relative to the pretax baseline, the fee generates a 22.4% reduction in trips at Gulf Coast sandy beaches in Mississippi, Alabama, and Florida subject to the fee and a 6.9% increase in trips to other coastal areas in the six-state region. The behavioral response in terms of user days is larger—a 33.6% reduction in user days at taxed Gulf Coast beaches and a 10.8% increase at other coastal sites—suggesting that multiday trips, which are subject to higher average fees, are more affected by the gate fee than are single-day trips.

Table 3, column (1), also reports the CV associated with the gate fee, which equals $556 million. The decomposition of CV shows that this loss is entirely due to the increase in the price of recreation trips induced by the fee because, by assumption, congestion does not affect the marginal value of a trip. Finally, we report two measures of the efficiency costs of the gate fee. The first is net surplus, or the sum of revenue raised and CV, which equals −$132 million, or roughly 31% of the total revenue raised. The second measure is the traditional Harberger triangle measure of deadweight loss, ½ΔTrips_G × AvgFee, where ΔTrips_G equals the change in trips to Gulf Coast sandy beaches. This commonly used approximation of deadweight loss equals −$61 million, as reported in column (1). Given that recreators are assumed to not value changes in congestion in this case, there is no welfare gain from declines in congestions, and thus the two measures are comparable in theory. In practice, however, they diverge by a factor of 2. Our sense is that this difference is driven by the Harberger triangle’s reliance on average price and average change in trips, which masks the substantial heterogeneity that arises in our data and is accounted for in the CV calculations.⁶ Although quantitively different, both measures suggest that there is substantial excess burden generated by the gate fee.

We turn to the second column, where we assume the per trip WTP to avoid a doubling of congestion levels on a trip is $5. Comparing these results with those in the first column, we find several differences. First, the gate fee raises an additional $30 million (7.1%) in revenue under the assumption of a $5 WTP to avoid a doubling of congestion relative to a $0 WTP. This increase is driven more so by a smaller decline in trips to the taxed beaches (−18.4% vs. −22.4%) than a higher average fee per trip (which rises by only $0.17, or 1.8%). Second, leakage, or the increase in trips to nontaxed sites, is smaller in column (2) relative to column (1) (4.6% vs. 6.9%). Third, a similar pattern of behavioral differences arises if one focuses instead on user days instead of trips. Fourth, the welfare losses to consumers (i.e., CV) are greater by $10 million (or 1.7%) when recreators have a $5 WTP to avoid a doubling of congestion. The decomposition suggests that, while there are significant additional benefits ($99 million) from the reduction in congestion levels at the taxed sites, there are even more ($108 million) additional costs associated with the higher congestion levels at the untaxed sites. Finally, the efficiency measures suggest that the net benefits (revenue raised plus CV) of the gate fee are higher (or less negative) when congestion is a disamenity to recreators. The Harberger triangle measure of deadweight loss, which does not account for the welfare gains from reduced congestion, remains substantially below the sum of revenue raised and CV.

We consider the final four columns of Table 3, where WTP is gradually increased in $5 increments from $10 to $25 to avoid a doubling of congestion. Comparing these results with those reported in the first two columns reveals several interesting trends. First, revenue raised increases with WTP for avoided congestion, although at a declining rate. In particular, revenue raised increases by $16 million when moving from column (2) to (3) (WTP changing from $5 to $10) but only by $9 million when moving from column (5) to (6) (WTP changing from $20 to $25). This trend appears to be due more to the gradual increase in the predicted number of trips to taxed beaches (which increases from 46 to 50 million between columns [2] and [6]) than to the more modest increase in the average fee per trip (which increases from $9.83 to $10.07). Second, we also find that leakage to non-Gulf Coast beaches declines as the value for avoided congestion increases, and these patterns are similar if we focus on user days as our relevant metric.

Third, the welfare costs of the gate fee as measured by CV decline as recreators’ value for avoiding congestion increases. The decline seems to decelerate with higher values for avoided congestion. The decomposition results suggest that the welfare gains from less congestion at the taxed sites trend upward, while the welfare losses from more congestion at the nontaxed sites trend downward. However, the gains from the reduced congestion at taxed sites grow faster than the losses at taxed sites. The net result is that overall welfare losses to recreators decline to such a degree that, combined with the gradual increases in revenue raised, social welfare (Revenue Raised + CV) is positive when recreators value congestion reductions most highly: $8 million and $39 million in columns (5) and (6), respectively. This implies that when recreators value avoided congestion highly, gate fees can be potential Pareto improving, even when the revenues are only returned in a lump sum. Finally, it is worth pointing out that the value of the Harberger triangle approximation as a proxy for welfare change degrades with higher values for avoided congestion to the point that it can be misleading in sign and magnitude; again, see columns (5) and (6). This result is attributable to the increasing welfare gains to recreators from reduced congestion that the Harberger triangle approximation does not take into account.

Table 3 also shows results for implied price elasticities associated with the fee regime. Elasticities for the complex pattern of price changes are approximated by taking the percentage change in total Gulf Coast beach trips and dividing by the percentage change in average price. A similar calculation is performed for the total trips to all beaches (final row). With no congestion effects, as in column (1), the Gulf Coast beach trips are elastic, with an elasticity of about 1.8, which is similar to the elasticities reported in Lupi, von Haefen, and Cheng (2022). When looking at total trips, the results are inelastic because the change in total trips is lessened by the substitution from Gulf Coast to non–Gulf Coast beaches, where prices do not change. Because the simulations include increasing amounts of congestion effects, the Gulf Coast beach trips become less elastic, and at a WTP for avoiding a doubling of congestion of $25, as in column (6), Gulf Coast beach trips are inelastic due to the net effects of the price and congestion changes.

In terms of the distribution of benefits and costs, the underlying demand model reported in Table 2 controls for several observable demographic characteristics that influence trip taking, allowing us to examine the effects of the fee regime by race, geographic origin of trips, and income. These results are presented in Tables 4 and 5. Beginning with Table 4, nonwhites, who make up 25% of the sample, take only 17% of total trips with the gate fee but reduce their demand by relatively more compared with whites (17%–28% vs. 11%–21% depending on scenario considered). Nonwhites, however, bear a modestly smaller percentage of total welfare losses (CV) from the fee relative to their population share (21%–24%) and pay a lower percentage of gate fees (20%–21%). As a whole, these results do not suggest that gate fees are disproportionately born by minorities.

In addition, Table 4 breaks down the distributional effects of the proposed gate fee by locals (i.e., residents of Mississippi, Alabama, and Florida) and nonlocals. Locals account for 9% of the sample but take 88%–90% of total trips after the gate fee is implemented. Their reduction in trips is much lower relative to nonlocals, ranging from 3% to 14% compared with 48%–59% for nonlocals. Locals bear about half of the welfare losses from the fee and pay almost two-thirds of all gate fees. However, given that they take the vast majority of trips, it appears that the structure of the gate fee considered—which is proportional to user days and discriminates against non-locals—is effective at shifting the burden of the tax to nonlocals.

Finally in Table 5, we consider the distributional effects across income quintiles. In our empirical model, trip taking is positively influenced by income, with higher-income groups having the largest probability of visiting a beach.⁷ This implies that the poorest income quintile takes only 14% of total trips under the gate fee. However, the poorest quintile reduces their demand by the highest percentage (25%–37%) and bears a disproportionate amount of the total welfare losses. The second-lowest income quintile actually bears a higher percentage of total CV (27%) and total fees (27%), although they take a higher percentage of trips (24%). On the other hand, the highest income quintile takes 22%–23% of total trips but bears only 13%–14% of the welfare losses and 14%–15% of the fee payments. To gain further insight into the distributional effects of the gate fees by income, we aggregate the bottom two and top two quintiles. This reveals that the lowest 40% of incomes take a modestly lower percentage of total trips (38%), experience a steep decline in trips after the fee’s introduction (13%–24%), bear 51%–53% of the welfare losses, and pay 48%–49% of the total gate fees. This contrasts with the upper 40%, who take a slightly higher percentage of trips (41%–42%), experience a smaller decline in trips after the fee is implemented (5%–13%), and bear only 28%–30% of the CV losses and 30%–32% of the gate fees. Consistent with Ji et al. (2022) and Lupi, von Haefen, and Cheng (2022), these results suggest that gate fees are generally regressive, even when congestion feedback effects are taken into account.

6. Conclusion

This special issue of Land Economics is focused on the need for a significant and reliable revenue stream to fund maintenance and repair projects on public lands throughout the United States. Our article contributes to this theme by focusing on an appealing revenue-raising instrument—an access or gate fee— that not only generates funds for maintenance and repair but also mitigates the persistent problem of congestion. By introducing a gate fee, one can address both concerns simultaneously. Economists have long recognized this virtue, but our collective understanding of the behavioral, welfare, revenue-raising, and distributional implications of these taxes remains relatively primitive. We advance our understanding of gate fees by developing a simple conceptual framework that predicts the likely behavioral and welfare effects of these fees, building a detailed recreation demand model of participation and site choice for shoreline recreation from Texas to Georgia, then evaluating a gate fee for sandy beaches in Mississippi, Alabama, and Florida that is proportional to the number of user days. We identify three distinct behavioral channels that arise from a gate fee—a pure price effect, a taxed site congestion effect, and a nontaxed site congestion effect—that combine to determine the overall social costs of such a fee. In our empirical analysis, we find that substantial revenue can be raised with such a fee, and accounting for how a fee is likely to change congestion levels can reduce the social costs of the fee substantially. In fact, if people have a relatively large WTP to avoid congestion, these fees can be potentially Pareto improving. Moreover, our distributional analysis suggests that gate fees are generally regressive, do not disproportionally affect minorities, and benefit locals at the expense of visitors from further away.

There remains much to do to further economists’ understanding of gate fees, and we identify two areas that seem promising to us. First, our limited understanding of the marginal value of reducing congestion at beaches and other resources suggests the need for more research. This will require additional data collection efforts and clever identification strategies, and the work by Timmins and Murdock (2007) and Bujosa et al. (2015) certainly represents a good start. We also believe that stated preference approaches like Boxall, Englin, and Rollins (2003) can add significant insight, especially in terms of how the value of congestion varies across individuals, sites, and recreational activities. Second, our study investigates one possible gate fee but does not search across alternative gate fees to determine which fee structure is optimal from a net benefits perspective. Once one sets identifying an optimal gate fee as a target, several questions arise: (1) What are the potential gains of allowing the fee to vary across time and space? (2) Should gate fees vary by time of day and the level of aggregate use? (3) What are the social costs of exempting children or seniors from the fee? (4) Should locals be provided a discount relative to nonlocals? Economists have made some progress in answering these questions in the context of energy and water consumption demand, but the implications of alternative fee structures merit further study in the recreation context.