Application of the Travel Cost Method to Estimate the Economic Value of Brasília National Park

Abstract

Ecological parks in Brazil are facing financial difficulties due to a disputed public budget for their administration. In this context, the environmental valuation of Brasília National Park is important for the development of financing instruments. The aim of this study is to estimate the economic value of the recreational use of Brasília National Park and to determine the price–demand elasticity among visitors residing in the Federal District. This involves estimating travel costs through regression analysis using cross-sectional data collected via questionnaires administered to park visitors. The results reveal a significant impact of travel cost on park demand, in which a 1% increase in travel costs reduces the park’s visitation rate by 4.1%. The economic value of Brasília National Park was estimated at approximately USD 25 million per year, equivalent to around BRL 140 million annually, based on an exchange rate of USD 1.00 = BRL 5.50 as of April 2020.

1. Introduction

Brazil is the country that has the greatest biodiversity of fauna and flora on the planet. There are more than 100 thousand animal species and almost 50 thousand plant species known to science [1]. This wealth, which is difficult to measure and is of little known value, is a cause for global concern and interest in view of its ecological, genetic, social, economic, scientific, educational, cultural, recreational, and esthetic value. As in other countries, the main means used by Brazil to protect natural resources is in situ preservation through the creation of conservation units [2].

According to [3], the first conservation unit in Brazil appeared in 1937 with the creation of Itatiaia National Park in Rio de Janeiro, and since then, conservation units have spread throughout Brazil. In the case of Brasília, the initial milestone occurred with the creation of Brasília National Park (PNB) on 29 November 1961, about a year after the inauguration of the city. PNB arose from the need to protect the water bodies of the city’s water supply system and keep the vegetation in its natural state as this is an urban park that experiences expressive visitation throughout the year. The additional reasons that led public authorities to establish the park at that time were its contribution to the balance of climatic conditions and to prevent soil erosion [4].

Within environmental management, the economic valuation of the environment emerges as a tool of great importance as it estimates the values of environmental goods and services, offering quantitative and tangible parameters for decision making. These parameters contribute to the elaboration of environmental policies and make environmental management more objective and pragmatic.

Objectively, the economic valuation of the environment is developed through two strands: declared preference methods and revealed methods. In the first strand, individuals provide information through direct questions about their willingness to pay for a resource, using methodologies such as choice modeling or contingent evaluation [5]. Revealed preference methods are based on observed behaviors and indirectly obtained data, such as the travel cost method (TC).

The advantage of using the TC method lies in its ability to estimate the price–demand elasticity for visits to the natural asset. This is an important estimate for administrators to be able to estimate the impacts of travel cost on the number of visits and the total revenue of a protected area.

Price elasticity of demand measures the degree of variation in the quantity demanded of a good in response to changes in its price. In general terms, when the price increases, demand tends to decrease; when the price decreases, demand tends to increase. In the context of visits to natural areas, several studies have found that this demand is inelastic—that is, it is not very sensitive to price changes [6,7,8,9,10,11]. On the other hand, some authors have identified elastic demand, which is more sensitive to cost variations [12,13], while others report inconclusive results [14]. An inelastic price elasticity of demand for visits indicates that an increase in price may lead to higher revenue as the number of visitors does not significantly decrease. Conversely, elastic demand suggests that visitors are more sensitive to changes in travel costs, meaning that an increase in cost results in a proportionally greater reduction in visitation rates to the environmental asset.

Although Brasília has about 99 green areas that include conservation units and urban parks, no studies were identified that used the TC method to measure values of direct use and elasticity of recreational areas in natural environments in the city. PNB is an ideal area for the application of TC method as it receives visits from national and foreign tourists. PNB has perfect places for swimming, walking, cycling, running, picnic, and meditation, as well as areas for observing the fauna and flora of the Cerrado biome. The attractions of PNB and the profile of its visitors impact the number of visits.

The TC method and the contingent valuation method (CV) have been widely used in environmental valuation studies to estimate the use value of recreational sites such as national parks. Examples of such studies include [4,8,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30].

The objectives of this study are to estimate the economic value of recreational use of PNB, to verify the applicability of the administrative divisions of the Federal District (DF) using the zonal approach of the travel cost method, and to analyze the sensitivity of park visitors to the variation in travel cost. This is because, according to [31], valuing recreation would justify charging any fees to enjoy the space, which is precious information for managers to verify the impact of travel cost on the number of visits. In addition, research on price–demand elasticity for visits to natural areas is incipient in the Brazilian capital.

This study employs a quantitative, non-experimental research design grounded in environmental economics, specifically using the travel cost method to estimate the recreational use value of Brasília National Park (PNB). The approach includes a structured survey to collect primary data from park visitors and an econometric analysis to estimate consumer surplus and travel demand elasticity. The TC method is an appropriate tool for valuing the direct-use benefits provided by natural resources as it captures visitors’ revealed preferences and allows for the estimation of a monetary value based on their willingness to pay for access to the environmental goods and services offered by Brasília National Park. Therefore, the application of the TC method to Brasília National Park will enable an estimation of the recreational demand function and the annual economic value associated with its use, providing empirical evidence to support public policies for urban conservation management.

Thus, the research questions are

I.  

What is the direct use value of Brasília National Park for its visitors?

II. 

How does travel cost influence the frequency of visits to the park?

III.

Does the current entrance fee reflect the recreational value perceived by visitors?

IV.

Is the price elasticity of demand for visits to Brasília National Park elastic or inelastic?

So, the hypotheses to be tested are as follows:

I.  

The coefficient for travel cost is negative and statistically significant, reflecting its inverse relationship with visitation rates, meaning the frequency of visits to PNB decreases as the travel cost increases.

II. 

The estimated consumer surplus per visit exceeds the current entrance fee, indicating underpricing.

III.

The price elasticity of demand for visits to Brasília National Park is inelastic, reflecting the unique importance of the park to its visitors and the lack of close substitutes. As a result, changes in travel cost will lead to relatively smaller changes in the quantity of visits demanded.

Data was collected through face-to-face surveys conducted with a sample of 300 visitors at the entrance of PNB. The questionnaire included sections on demographic characteristics, the number of visits, and travel expenses. The TC method was applied using a Log–Log regression model, with visitation rate as the dependent variable and travel cost, income, and age as independent variables. Diagnostic tests (e.g., Shapiro–Wilk, Breusch–Pagan, and Durbin–Watson) were used to validate the model’s assumptions, ensuring the robustness and reliability of the results.

This paper is organized as follows: the next section describes the study area and outlines the methodological procedures adopted for applying the travel cost method to Brasília National Park. The following section presents the statistical results, including the estimated demand function, the calculation of consumer surplus (CS), and the price elasticity of demand for park visits. The subsequent discussion interprets the main findings and compares them with similar studies conducted in Brazil and abroad. Finally, the paper concludes with reflections on the park’s potential as an economic asset and the implications for public policy aimed at achieving the sustainable management of urban conservation units.

2. Materials and Methods

2.1. Study Area

PNB is located in the northwestern portion of the Federal District, the capital of Brazil, approximately 10 km from the center, and it has an area of 42,389.01 hectares, comprising about a third of the capital’s territory. The park faces another protected area, the Cafuringa Environmental Protection Area, and borders the state of Goiás. The park is accessed via the Estrada Parque Indústria e Abastecimento—EPIA, geographically located between the parallels 15°35′ and 15°45′ south latitude and between the meridians 47°55′ and 48°55′ west longitude (Figure 1).

2.2. Calculation and Sampling Method

The sample size was calculated using the method presented in [32], which considers a confidence level of 95% and a standard sampling error of the formula of 5% according to Equation (1):

$$\mathrm{n}={\displaystyle \frac{\mathrm{N}}{1+\mathrm{N}{(\epsilon )}^2}}$$

(1)

where n = sample size; N = population size; ε = sampling error.

The study considered the size of PNB’s population and its carrying capacity based on the availability of the two pools. When one swimming pool was available, the allowed amount of visitors was 2000; if both were available, the limit increased to 3000. Thus, N was considered a population equal to 2000 visitors as one of the pools was always unavailable during the application of the questionnaires. A sampling error of 5% (which is the standard of the formula) was used; therefore, 334 questionnaires were applied on the spot without replacement.

The questionnaires were administered in February and March 2020, shortly before the first lockdown measures were implemented in the Federal District due to the COVID-19 pandemic. For comparison, the straight-line distance between the entrance of Brasília National Park (PNB) and the entrance of Chapada dos Veadeiros National Park (PNCV) is approximately 174 km, as measured using Google Earth Pro (version 7.3.6.9796).

According to historical visitation data for PNCV provided by Chico Mendes Institute for Biodiversity Conservation (ICMBio), tourism activity was completely halted between April and July 2020. With the gradual reopening of public spaces, August 2020 marked the return of visitors to the park; however, recovery was limited. The number of visitors that month (2952) was approximately 51% lower than the average for non-pandemic years (6017 visitors), highlighting the significant decline in visitation during the initial phase of reopening.

Tourism began to recover in 2021, when the number of visitors nearly doubled from 37,992 (in 2020) to 75,349—reaching approximately 95% of the pre-pandemic level observed in 2019. Visitation stabilized in 2022, with figures nearly identical to the previous year, and in 2023, the park surpassed its 2019 visitation levels, indicating full recovery and consolidation of tourism activity.

Before data collection, a license was requested from ICMBio to analyze the work and authorize research to be carried out within the park. With the application approved (license No. 73959-1), the interviews took place near the reception, which is close to the entrance/exit of the pools. All visitors who passed through the reception were approached with a brief explanation of the work. The main questions that constituted the questionnaire were gender, age group, situation in the labor market, higher level of education, monthly income by minimum wage range, location of residence, amount spent on commuting in BRL, number of visits made, and group size.

2.3. Travel Cost Method

This method estimates a demand function for the number of visits based on travel cost, as shown in Equation (2), to calculate consumer surplus, a measure of public welfare [17]. This demand function relates the number of travels taken (r) to the travel costs (${tc}_r$), substitute site costs (${tc}_s)$, income (y), and the vector of demographic variables (z).

$$r=f ({tc}_r{,tc}_s,y,z)$$

(2)

A regression model is used to explain how the independent variables $({tc}_r,{tc}_s,y,z)$ influence the number of trips taken (r). Therefore, the independent variables tested in the model were based on Equation (2):

$$r={\beta }_{{tc}_r}\times {tc}_r+{\beta }_{{tc}_s}\times {tc}_s+{\beta }_y\times y+{\beta }_z\times z$$

(3)

where ${\beta }_{{tc}_r},{\beta }_{{tc}_s},{\beta }_y,{\beta }_z$ = coefficients to be estimated.

Moreover, it is expected that the coefficient of travel costs will be negative (${-\beta }_{{tc}_r}$), indicating an inverse relation between travel costs (${tc}_r)$ and the number of trips taken (r). This supports the premise of the TC method, which states that an increase in travel costs leads to a decrease in recreational demand.

Based on Equation (2), it is possible to estimate the impact of increasing travel costs on the visitation rate to the environmental asset under evaluation. The TC method relies on the premise that the number of visits decreases as the cost of traveling to the site increases [33]. Thus, an inverse relationship is established between the number of visits (r) and the travel cost (${tc}_r$), which serves as a proxy for price, as illustrated in Equation (4). This relationship allows for the inference of the population’s willingness to pay for site access based on visitation rates, through the integration of the recreational demand function. The result of this integration is the consumer surplus, which represents the economic value attributed to the use of the site.

$${tc}_r=f\left(r\right)$$

(4)

The consumer surplus, or access value (applicable to any functional form), is defined as the area under the demand curve between an individual’s actual travel cost and the choke price, that is, the price level at which the number of trips drops to zero, as illustrated in Figure 2. Area A represents the individual’s total consumer surplus for trips to the site, which is the difference between their total willingness to pay (A + B) and the actual cost of the trips (B). This surplus reflects the individual’s access value to the site. Simply put, it represents the additional amount each visitor would be willing to pay beyond what they actually spend to visit the site [8].

Understanding consumer surplus allows for an assessment of the costs and benefits under different market conditions and the formulation of public policies aimed at influencing consumer behavior [34].

The consumer surplus can be calculated using Equation (5):

$$CS ={\int }_{{tc}_r}^{{tc}_r^{*}}f({tc}_r,{tc}_s,y,z)\partial {tc}_r$$

(5)

where ${tc}_r$ = current travel cost; ${tc}_r^{*}$ = choke price; and $f({tc}_r,{tc}_s,y,z)$ = demand function.

Thus, the recreational use value of Brasília National Park will be calculated by multiplying the estimated consumer surplus by the total number of visits to the park in 2019.

2.4. Research Design

After collecting data from visitors, the study proceeded with the construction of the demand function for recreation using the zonal travel cost method in order to estimate the economic value of PNB. The dependent variable of the zonal model was the number of visits to PNB. However, the dependent variable was converted into visitation rates by zones of origin—in this case, the zones were the administrative regions of the Federal District, detailed below. Visitation rates by zones were calculated by the ratio between the number of visits belonging to each zone and its number of inhabitants; then, it was multiplied by a thousand. The number of inhabitants of the zones was extracted from the PDAD provided by the Planning Company of the Federal District (2018) [35].

Unlike other Brazilian states, the federal capital does not have municipalities, and to facilitate the administration of its territory, the DF is divided into 33 administrative regions. The administrative regions of the Federal District were grouped, using the QGIS 3.28.11 software, into six zones of origin, with distance intervals defined by concentric circles based on the boundaries of the Federal District and PNB (Figure 3). Since distance was measured in a straight line by the location points of each administrative region, these points were provided by the State Secretariat for Urban Development and Housing of the Federal District. Thus, the application of the administrative regions in the travel cost method was verified.

Because the nearest administrative region is within a radius of approximately 5 km from the entrance of PNB, this value was used as a distance interval from the zones of origin. Only zone VI had a 10 km gap, as areas with an administrative region were avoided. As PNB is inserted in the administrative region of the Plano Piloto that could affect the visitation rate, it was divided into the following neighborhoods: Northwest, North Wing, and South Wing. Visitors from other states had their questionnaires evaluated regarding their permanence at work. However, the questionnaires of visitors from the state of Goiás, which has surrounding cities, were eliminated, as they did not belong to any zone, as well as the questionnaires with unanswered questions. Therefore, this study focuses only on the questionnaires of residents of the Federal District. The administrative regions and neighborhoods belonging to each zone of origin and their respective distance ranges are presented in

Table 1. Zone of origin of each administrative region of the Federal District and their distance intervals.

Source Zones	Distance	Administrative Regions and Neighborhoods of the Plano Piloto
I	0–5 km	Northwest (neighborhood); SIA.
II	5–10 km	Asa Norte (neighborhood); Asa Sul (neighborhood); Varjão; North Lake; Cruise; Southwest/Octagonal; SCIA/Structural.
III	10–15 km	Guará I and II; Park Way; Vicente Pires; Candangolândia; Sout Lake.
IV	15–20 km	Bandeirante Nucleus; Riacho Fundo; Águas Claras; Taguatinga; Botanical garden; Itapoã; Paranoá; Sobradinho I, Sobradinho II, Fercal.
V	20–25 km	Riacho Fundo II; Ceilândia; Fern.
SAW	25–35 km	Recanto das Emas; Range; Brazlândia; São Sebastião; Planaltina; Santa Maria.

.

As the visitation rate by zones was established as a response variable, the independent variables tested in the model were the average travel cost of each zone and the socioeconomic variables (monthly income and mean age by zones). The midpoints of monthly income and the age of the zones were used for the prediction. Thus, the models tested were based on Equation (6).

$$Nv=f(CVm, R, I)$$

(6)

where Nv = visitation rate per zone; CVm = average travel cost per zone; R = yield per zone; and I = mean age per zone.

The average travel costs per zone (CVm) were represented by the sum of the explicit expenses resulting from visitation to the park. These explicit expenses corresponded to the entrance fee, fuel and food added to the cost of individual travel, and the value of time only for those who declared themselves to be active in the labor market. The calculations of the individual travel cost and the value of each visitor’s time are explained below. The individual travel cost, adapted from [16], considered as a calculation of the distance to and from the visitor’s place of origin to the park, was obtained by the straight line from the location points of the administrative regions to the entrance. This amount was multiplied by the cost per kilometers driven (USD 0.23/km) that the Uber app company charged in the DF to standardize vehicle expenses; thus, we avoided extending the interview with the visitor. The result was divided by the size of the group and the time, in minutes, that the visitor took to reach the entrance of the park, considering its midpoint. The size of the group included the respondent and their companions. The calculation of the individual travel cost is illustrated in Equation (7).

$$CV={\displaystyle \frac{Div\times Crod}{T\times Tg}}$$

(7)

where CV = cost of an individual trip; Div = the round-trip distance; Crod = cost per kilometers driven; T = group size; and Tg = time spent.

In the calculation of the opportunity cost in time, also adapted from [16], one third of the salary was considered as an amount intended to be recreated [33,36]. Monthly income was divided by the working time of 220 h per month worked—based on 8 h of work per day from Monday to Saturday, according to Decree-Law No. 5452 of 1 May 1943, considering that all visitors active in the labor market had this normal working duration. This value was multiplied by the time in minutes it took the visitor to get to the entrance of the park. The time value formula is illustrated in Equation (8).

$$VT={\displaystyle \frac{T}{60}}\times 2\left[{\displaystyle \frac{1}{3}}.{\displaystyle \frac{W}{220}}\right]$$

(8)

where VT = time value; Tg = time spent; and W = monthly income.

With the variables defined, four functional forms were tested based on Equation (6). The model that presented the best fit was used based on the criteria for choosing the Shapiro–Wilk normality test, Breusch–Pagan homoscedasticity, and Durbin–Watson residual autocorrelation. The significance of the coefficients determined by the t-test; the suitability of the model determined by the F-test; the highest coefficient of determination, R²; the Akaike information criterion (AIC); and the Bayesian criterion (BIC) were also considered as the criteria of choice.

After choosing the model, the consumer surplus was estimated, representing the area under the demand curve for recreation. In this case, the consumer surplus was obtained by the defined integral of the chosen model, illustrated in Equation (9).

$$\underset{CVma}{\overset{CVmb}{\int }}f\left(CVm, R, I\right)dCVm$$

(9)

where CVm = average travel cost per zone; CVma,b = average travel cost per minimum and maximum zone; R = yield per zone; and I = mean age per zone.

Then, the result was multiplied by the number of visits made to PNB in 2019 to obtain the recreational use value of the park by the zonal method. According to the park’s administration, the number of visits made in 2019 was 251,521. The study conducted in [15] served as a reference for the estimate of consumer surplus. The price–demand elasticity for visits was obtained based on the calculation of elasticities suggested in [13] for the models presented in

Table 2. Price–demand elasticities per visit for the zonal models tested.

Models	Price–Demand Elasticity
Linear: $\mathrm{N}\mathrm{v}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{C}\mathrm{V}\mathrm{m}+{\mathrm{B}}_2\mathrm{R}+{\mathrm{B}}_3\mathrm{I}+\mathsf{\epsilon }$	${\beta }_1\left({\displaystyle \frac{CVm}{NVm}}\right)$
Lin-Log: $\mathrm{N}\mathrm{v}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{L}\mathrm{n}\mathrm{C}\mathrm{V}\mathrm{m}+{\mathrm{B}}_2\mathrm{L}\mathrm{n}\mathrm{R}+{\mathrm{B}}_3\mathrm{L}\mathrm{n}\mathrm{I}+\mathsf{\epsilon }$	${\beta }_1\left({\displaystyle \frac{1}{NVm}}\right)$
Log-Lin: $\mathrm{L}\mathrm{n}\mathrm{N}\mathrm{v}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{C}\mathrm{V}\mathrm{m}+{\mathrm{B}}_2\mathrm{R}+{\mathrm{B}}_3\mathrm{I}+\mathsf{\epsilon }$	${\beta }_1\left({CV}_m\right)$
Log-Log: $\mathrm{L}\mathrm{n}\mathrm{N}\mathrm{v}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{L}\mathrm{n}\mathrm{C}\mathrm{V}\mathrm{m}+{\mathrm{B}}_2\mathrm{L}\mathrm{n}\mathrm{R}+{\mathrm{B}}_3\mathrm{L}\mathrm{n}\mathrm{I}+\mathsf{\epsilon }$	${\beta }_1$

Where Nv = visitation fee; CVm = average travel cost per zone; R = average yield; I = mean age per zone; and β = the beta coefficient associated with the variable.

.

Given the lack of theoretical consensus on the most appropriate functional form [24], model selection should primarily be guided by the best econometric fit. To ensure the validity of the results, it is essential to verify key regression assumptions—such as homoscedasticity, absence of autocorrelation and multicollinearity, and normality of residuals—by applying robustness tests to the estimated models.

Studies applying the zonal travel cost method typically rely on Ordinary Least Squares (OLS), using diagnostic tests to identify the functional specification that best explains the variation in the dependent variable [18,37,38,39,40]. According to [41], OLS models must meet several assumptions: errors must be random with zero mean, exhibit homoscedasticity, show no autocorrelation, follow a normal distribution, have more observations than parameters, include variability in the independent variables, and present no multicollinearity.

Accordingly, robustness tests were applied to the estimated models to verify the fundamental assumptions of regression analysis based on the following criteria: normality of residuals (Shapiro–Wilk test), homoscedasticity (Breusch–Pagan test), and residual autocorrelation (Durbin–Watson test). In addition, model selection considered the significance of the coefficients (t-test), overall model fit (F-test), the highest coefficient of determination (R²), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC).

The Shapiro–Wilk test assesses whether the residuals of a regression model follow a normal distribution, which is an important assumption for valid statistical inference. A p-value greater than 0.05 indicates that the residuals are likely normally distributed, which is desirable; a value below 0.05 suggests a deviation from normality. The Breusch–Pagan test evaluates homoscedasticity, which indicates whether the variance of the residuals remains constant across observations. A p-value below 0.05 indicates heteroscedasticity, implying that the residual variance is not constant and may affect the reliability of the estimates. A p-value above 0.05 suggests that the residuals have constant variance, which is ideal for model robustness.

Autocorrelation occurs when the residuals of a regression model are not independent from one another, which can compromise the efficiency of coefficient estimates and invalidate statistical tests such as the t and F-tests, making inferences less reliable. The Durbin–Watson test is the primary method for detecting autocorrelation, with ideal values being close to 2; significantly lower values indicate positive autocorrelation, while higher values suggest negative autocorrelation.

The t-test assesses the individual significance of the coefficients of the explanatory variables, while the F-test evaluates whether the set of independent variables significantly contributes to explaining the dependent variable. The coefficient of determination (R²) indicates the proportion of variance in the dependent variable explained by the model, serving as a measure of model fit. Finally, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are used to compare different models, penalizing those that are overly complex—lower AIC and BIC values indicate better balance between model fit and parsimony.

The confidence intervals of the consumer surplus at 95% were estimated using the method proposed in [42] through Equations (10)–(12):

$$\mathrm{v}\mathrm{a}\mathrm{r}(\mathrm{E}\mathrm{C})=({{\displaystyle \frac{\partial \left(\mathrm{E}\mathrm{C}\right)}{\partial {\mathsf{\beta }}_0}})}^2\mathrm{v}\mathrm{a}\mathrm{r}\left({\mathsf{\beta }}_0\right)+({{\displaystyle \frac{\partial \left(\mathrm{E}\mathrm{C}\right)}{\partial {\mathsf{\beta }}_1}})}^2\mathrm{v}\mathrm{a}\mathrm{r}\left({\mathsf{\beta }}_1\right)+\left({\displaystyle \frac{\partial \left(\mathrm{E}\mathrm{C}\right)}{\partial {\mathsf{\beta }}_0}}\right)\left({\displaystyle \frac{\partial \left(\mathrm{E}\mathrm{C}\right)}{\partial {\mathsf{\beta }}_1}}\right)\mathrm{c}\mathrm{o}\mathrm{v}({\mathsf{\beta }}_0{\mathsf{\beta }}_1)$$

(10)

$$ECi=EC-1.96\times var\left(EC\right)$$

(11)

$$ECs=EC+1.96\times var\left(EC\right)$$

(12)

where ECi and ECs = the lower and upper limits of the consumer surplus, respectively; EC = an average estimate of the consumer surplus; var = variance; cov = covariance; β₀ = the intercept of the function; and β₁ = the coefficient of the variable of cost of travel.

Finally, the recreational use value of Brasília National Park (PNB) was estimated by multiplying the aggregate consumer surplus by the number of visits to the park in 2019, a total of 251,521 visits, according to the park administration.

$${TEV}_{PNB}={EC}_{total}\times P$$

(13)

where ${TEV}_{PNB}$ = the economic value of PNB; ${EC}_{total}$ = the aggregate consumer surplus; and $P$ = 251,521 visits.

3. Results and Discussion

3.1. Sample Description

The sample considered respondents from the Federal District and was characterized by socioeconomic variables: gender, age group, situation in the labor market, level of education, and income. From this characterization, it was possible to identify the profile of the interviewees, contributing to the understanding of the economic value attributed to PNB by the travel cost method.

A total of 34 questionnaires were discarded because the respondents were not residents of the Federal District and/or the questionnaires were incomplete. Therefore, this study had a sample of 300 questionnaires in which a sampling error of 5.3% prevailed. The non-resident visitors to the DF came from the states of São Paulo, Goiás, Rio de Janeiro, Bahia, Acre, Espírito Santo, Minas Gerais, Ceará, Tocantins, Amazonas, Piauí, and Alagoas, in addition to other countries, such as Mexico, England, and Germany. The socioeconomic information of the PNB interviewees is detailed in

Table 3. Socioeconomic information of the PNB interviewees.

Socioeconomic Data		Number of Visitors	Percentage (%)
Sex
Male		175	58.3
Female		125	41.7
Age group
Under 19 years old		10	3.3
19–29 years old		67	22.3
30–39 years old		78	26.0
40–49 years old		54	18.0
50–60 years old		52	17.3
Over 60 years old		39	13.0
Labor market situation
Retired		40	13.3
Unemployed		22	7.3
Student		30	10.0
Working		197	65.7
Education level
No education		1	0.3
Incomplete elementary school		3	1.0
Complete elementary school		8	2.7
Incomplete high school		10	3.3
Complete high school		47	15.7
Incomplete higher education		34	11.3
Complete higher education		197	65.7
Monthly income
Up to 1 minimum wage—minimum wage in 2020: BRL 1045.00 (USD 190.00)		35	11.7
Between 1 and 2 minimum wages		45	15.0
Between 2 and 5 minimum wages		70	23.3
Between 5 and 10 minimum wages		82	27.3
Between 10 and 20 minimum wages		49	16.3
More than 20 minimum wages		19	6.3
	R2	PBIAS	CE
AWY efficiency	0.64	−11.11	−0.14

.

According to Table 3, the sample had a higher proportion of male respondents (58%). This group made more than seven thousand visits to the PNB in the last 12 months and, consequently, had an expenditure of USD 1163.87 incurred during visitation. In another study, in Parque Olhos D’Água, in the Federal District, the authors [4] also observed a predominance of males in their sample, corresponding to 54% of the interviewees. Still, according to Table 3, 52% reported being 39 years of age or younger, with the predominant age group being between 19 and 39 years, corroborating the study carried out in [15] with the contingent valuation method to obtain the willingness to pay of visitors to PNB. Also, in their study, the authors of ref. [31] found that the Masouleh Forest Park in Iran had the highest visits in this age group. However, there was a low demand for visits from people under the age of 19 and over 60 years old.

Another important highlight was the number of active visitors in the labor market, which represented 66% of the total sample. Retirees, on the other hand, with more free time available compared to others, represented 13% of the sample. Only 2% declared that they work and study, and 1% reported being retired and working. Ref. [43] also reported a high frequency of active visitors in the labor market and a low incidence of students and retirees in the Serra do Mar State Park. Therefore, it is more likely that people active in the labor market have dedicated part of their time to recreation in the park.

Regarding the level of education of the interviewees, 93% of the respondents declared that they had completed high school, and 66% stated that they had completed higher education. According to the Planning Company of the Federal District (2018) [35], most inhabitants of the Federal District have completed high school and higher education, with a predominance of people with the highest levels of education. This result was also similar to that in [15]. Therefore, due to the high academic level of the inhabitants of the Federal District, its residents were more interested in visiting the park, corroborating the results of [31,44].

Regarding monthly income, the majority of respondents (73%) reported having an income above two minimum wages, but half had an income below and above five minimum wages, and the predominant monthly income was between five and ten minimum wages. Considering its average points, the household income for PNB visitors was USD 1304.67. Including the size of the group, the average income per visitor was around USD 489.25, which is in line with the Planning Company of the Federal District (2018) [35], as the household income for the population of the DF is around USD 1129.01, and the average value per person is USD 451.16, considering a salary of USD 173.45. There was a low demand for visits by people with an income of more than 20 minimum wages, followed by visitors with an income of up to 1 wage. A determinant that contributes to the low attendance of people with lower purchasing power in parks is the price of admission [15]. Therefore, increasing the price of admission reduces the frequency of visits by people with lower incomes.

In summary, the average visitor to Brasília National Park (PNB) is male, approximately 30 years old, possessing a high level of education and a family income of around five minimum wages. These findings are consistent with previous studies on ecotourism and urban park visitation.

3.2. The Economic Value of Recreational Use of the National Park of Brasília

Analyzing Figure 4, the sample revealed that about 32% of the interviewees came from the Plano Piloto, a region that covers the Asa Norte, Asa Sul, and Northwest neighborhoods. The fact that these neighborhoods are close to PNB and house visitors with the highest levels of education and income contributed to this frequency of visits. According to the Planning Company of the Federal District (2018) [35], the Plano Piloto was the third region of the DF with per capita income, in addition to being one of the regions with the highest levels of education. Among the neighborhoods of the Plano Piloto, Asa Norte presented more than half of the responses, with 63%. Overall, Asa Norte accounted for 20.33% of the sample, in agreement with the results of [15]. On the other hand, Noroeste and SIA had the highest rates of visitors per inhabitant, followed by Asa Norte and Lago Norte. Thus, there was more possibility for visitors from these places to go to the PNB than visitors from other regions of the Federal District. Visitors from the regions farthest from the PNB, such as Brazlândia, Planaltina, Gama, and Santa Maria, regions with a gross labor income of between one and two minimum wages and complete high school education, represented 4%, and the other regions showed somewhat similar qualities.

The respondents made more than 11 thousand visits to PNB between 2019 and March 2020, totaling a travel cost of more than BRL 12 thousand. The resident respondents of the Plano Piloto made more than four thousand visits in this period. The fact that the Plano Piloto is close to the park contributed to this number of visits, in addition to being the region that obtained the highest cost in visitation, about USD 568.93. Next come the administrative regions of Ceilândia, Águas Claras, Sobradinho I, Taguatinga, and Lago Norte, which had costs of USD 199.74, USD 175.85, USD 136.2, USD 97.78, and USD 94.02, respectively.

Table 4. The visitation rates and average travel costs of the zones adjacent to PNB.

Zones	Distance (km)	Population	Visits in %	Visitation Rate (Visitors Per Thousand Inhabitants)	Average Travel Cost (USD/Zone)	Average Yield (USD/Zone)	Mean Age
I	0–5	12.420	7.2	67.1	3.43	1763.7	46.3
II	5–10	356.617	58.1	18.9	5.81	1638.9	43.7
III	10–15	267.247	16.3	7.1	5.99	1270.3	40.2
IV	15–20	740.307	14.2	2.2	9.44	1053.1	37.2
V	20–25	751.478	2.9	0.5	12.77	592.6	32.4
SAW	25–35	737.673	1.3	0.2	13.15	745.4	32.5

shows that the visitation rate per zone decreased the greater the distance to PNB. This trend was also observed in the average cost of travel in each zone. It was noted that, as the intervals from the visitor’s zone of origin to the park increased, the average travel cost increased, which can be explained by the income levels, as they decreased with the distance to the PNB. It was also observed that there is an inverse relationship between the visitation rate per zone and the cost of travel per zone, something expected for these two variables. According to Table 3, visitors from administrative regions belonging to zones I and II were more likely to attend the PNB more. The values in the table below were used in the prediction of the zonal model.

Regarding the proposed zonal model, the variables of average income and average age by zone were not significant, neither together nor separately; thus, both socioeconomic variables were removed from the predictive analysis, in agreement with other studies [33,45,46]. Perhaps the heterogeneity of income and age among the administrative regions interfered with this result. The authors of [47] warned that the variation between the zones is not homogeneous. Thus, the dependent variable visitation rate was predicted only with the average cost of travel per zone. The summary of the regression analysis is presented in

Table 5. Results of the regression analysis and statistical tests for all estimated models.

	Linear	Lin-Log	Log-Lin	Log-Log
Intercept	57.82 *	175.52 **	5.86 ***	16.68 ***
CVm	−0.90 **	−42.87 **	−0.10 ***	−4.14 ***
R2	58.34%	74.71%	97.18%	95.65%
BIC	55.15	52.15	9.49	12.08
AIC	55.77	52.78	10.11	12.70

(***) Significance < 0.001. (**) Significance < 0.05. (*) Significance < 0.1 according to the t-test.

, in which it is observed that, in all models, the regression coefficient of CVm was significant and presented a negative sign. In other words, this means that an increase in the average cost of travel per zone would result in a drop in demand for recreation. The results of the model tests are presented in

Table 6. Results of the statistical tests applied to the estimated models.

Tests	Linear	Lin–Log	Log–Lin	Log–Log
Shapiro–Wilk	0.96 (0.81)	0.97 (0.91)	0.85 (0.16)	0.93 (0.60)
Durbin–Watson	1.29 (0.03) *	1.30 (0.03) *	2.47 (0.53)	2.50 (0.55)
Breusch–Pagan	3.80 (0.05)	3.09 (0.08)	0.26 (0.61)	0.07 (0.79)
F-Test (p-value)	5.60 (0.08)	11.82 (0.03)	137.6 (0.00)	87.98 (0.00)

(*) Non-significant test for its p-value.

.

The linear model was not the most suitable for this study. Although it explained the data well and had the assumptions of normality and homoscedasticity of the waste met, it violated the independence of the waste. The Lin–Log model obtained a significant CVm coefficient and a high R² value, and the residuals were homoscedasticity and normally distributed. However, the Durbin–Watson test for this model identified the presence of autocorrelation in the residuals while violating the hypothesis of the classical linear regression model, which states that the residuals are not independent, and the presence of autocorrelation made it seem like the coefficients were significant. The results of the two models corroborate the work of the authors of [8], who also found insignificance in the same models but with a constant variance problem; on the other hand, both regression models were significant according to the F-test.

On the other hand, the two models with log in the dependent variable obtained excellent fits, with significant coefficients and a high R² value. In addition, they showed normality of the residuals by the Shapiro–Wilk test (p-value > 0.05), as well as the absence of constant variances and independence of the residuals. The F-test, for both models, confirmed the quality of the adjustments given the significant p-value. Thus, both models were quite similar; therefore, we decided to use the Log–Log model in this study, even with the AIC and BIC adjustment values being slightly higher than in the Log–Lin model, which was similar to the decision of the authors of [8]. Similarly, the authors of [46,47,48] also opted for the Log–Log model.

The advantage of using the Log–Log adjustment is its ability to allow a direct combination with the price–demand elasticity per visit [8]. Logarithm models are quite popular in econometrics [41]. Thus, according to the regression coefficient of the chosen model, visitors to PNB living in the Federal District had a demand for visits or elastic recreation. This means that visitors to the Federal District were sensitive to variations in the cost of travel, that is, an increase of 1% in the cost of travel resulted in a reduction of 4.1% in the rate of visits to PNB. Therefore, PNB experienced a reduction in demand per visit due to the increase in the price of the determinants of travel cost, encompassing food, ticket price, fuel, and travel time.

The study presented in [12] carried out in the Lake Nakuru National Park in Kenya also considered the demand for visits to be elastic. The authors obtained price–demand elasticities for visits that were inelastic for foreigners and elastic for residents of the country. Due to the proximity of the park to the administrative regions and the vast amount of green area that the DF has, it is notable that resident visitors would be more sensitive to the cost of travel due to the Brazilian capital offering alternatives for recreation, in addition to the existence of many residences with swimming pools, especially in the administrative regions of Lago Norte and Sul.

However, in other studies, it was observed that demand was inelastic. Using the individual approach of the cost of travel method, ref. [11] found a price–demand elasticity of −0.329 for the beach of Kenting National Park, Taiwan. Ref. [10] also found an inelastic demand (−0.1210; −0.2362) for Dachigam National Park in India, just as [49] obtained an inelastic demand for two national parks in Australia. Therefore, the concept of elasticity for recreation is quite different from other commodities, and estimates vary between places [50].

The estimate of the economic value of recreational use of PNB and the benefit to its visitors were calculated using the previous Log–Log demand function. It is reiterated that the consumer surplus was the area under the demand curve calculated by the defined integral of the function, and the average minimum and maximum travel costs by zones consisted of their lower and upper limits. Thus, PNB allowed for an estimated consumer surplus of USD 99.52, with a 95% confidence interval between USD 40.31 and USD 158.71. This amount was characterized as a desire for each visitor to effectively pay to travel to the park, as was the desire of visitors to the Água Mineral Park, Brusque, SC, who were willing to pay USD 95.16 (USD 1.00 = BRL 2.52 in 2002) [51]. This study was conducted in a Brazilian park distinct from PNB. Each park has its own peculiarity, and the surplus of consumers for these areas is different as the profiles of visitors change. This comparison not only demonstrated any discrepancy in the results but also demonstrated the existence of studies in Brazil with the same intent as this research.

In another study conducted in recreational areas in other countries ref. [33], it was estimated that visitors to the Sierra de Aracena and Picos de Aroche Natural Park in Spain were willing to pay USD 89.74 (USD 1.00 = EUR 0.81 in 2018)—the authors even used the zonal method. Likewise, visitors to Lake McKenzie were willing to pay USD 195.82 (USD 1.00 = AUD 1.24 in 2007) [46]. As there is no reference value for the PNB consumer surplus, this result was considered acceptable as the conservation unit is located in an urban environment with easy access, causing the cost of travel per zone to decrease.

Dividing the consumer surplus by the average number of visits (38.59), a consumer surplus of USD 2.58 per visit was obtained, with a 95% confidence interval between USD 1.04 and USD 4.11. The result was higher than the value found by the authors of [15] of USD 1.69, who used the CV method. However, the value would be within the confidence interval and validated the use of administrative regions as zones of the travel cost method. It is common for TC method estimates to generate values greater than the CV method; however, values, in some cases, will be within the confidence interval [52]. The authors of [53] detailed the main reasons why TC method estimates are higher than those of the CV method. One of them is the methodological variety of both methods. Another example is the study presented in [54], which showed that the travel cost method tends to produce higher estimates of recreational value compared to the contingent valuation method, reflecting differences in the perceived cost of the visit. The consumer surplus per visit was estimated at USD 3.11 using TC, resulting in an annual recreational benefit of approximately USD 94,229. In contrast, the average willingness to pay under the CV method was USD 1.73 per visit, totaling around USD 52,423 annually. Furthermore, the study presented in [12] also showed that the TC estimates of annual recreational value were higher than the CV estimates; they were USD 13.7–15.1 million compared to USD 7.5 million, respectively, for Lake Nakuru National Park.

The values of consumer surplus for visits are good suggestions for charging admission to the park, but it is worth remembering that the demand for PNB was determined to be elastic by the zonal method. PNB adopts some means to generate revenue, such as charging tuition, which is important for its operation.

The economic value of recreational use of PNB was USD 25 million/year (about BRL 137,667,504.14/year), with a 95% confidence interval between USD 10,138,582.85 and USD 39,918,669.25/year. This value confirmed, in fact, how valuable the unit was for the residents of the DF who traveled to the park for recreation, and these values attested to 2019 visitors’ willingness to pay for PNB.

In summary, the econometric model employed was a Log–Log regression, which demonstrated a strong statistical fit (R² = 95.65%). The Log–Log model demonstrated the best statistical and econometric performance among the models evaluated, being robust and suitable for analyzing the demand for visits to PNB. Diagnostic tests confirmed the model’s adequacy: the residuals were normally distributed (Shapiro–Wilk = 0.93; p = 0.60) and homoscedastic (Breusch–Pagan = 0.07; p = 0.79) and showed no autocorrelation (Durbin–Watson = 2.50; p = 0.55). Furthermore, the model was statistically significant overall, as indicated by the F-test (F = 87.98; p < 0.01). The independent variable tested in the model, the average travel costs per zone (CVm), was statistically significant and had a negative expected sign, confirming the hypothesis that this variable is statistically significant and that the frequency of visits to PNB decreases as the travel cost increases.

The Log–Log model allows the coefficients to be interpreted directly as elasticities. The price elasticity of demand was estimated at −4.1, suggesting a highly elastic demand: a 1% increase in travel cost leads to a 4.1% decrease in visitation frequency. This finding contradicts the assumption that PNB has few substitutes and reinforces the idea that visitors respond sensitively to cost changes, so the hypothesis that demand is inelastic is not supported.

Using the TC method, the estimated average consumer surplus per visit was USD 2.58, which is slightly above the current entrance fee of USD 2.54. This supports the hypothesis that visitors derive more value from the park experience than they pay for, indicating potential for revenue optimization without harming visitation levels.

Finally, the total recreational use value of the park was estimated at USD 25 million per year based on the aggregate consumer surplus multiplied by the number of visits to Brasília National Park in 2019 (251,521 visits). This substantial value highlights the importance of the park not only as an environmental asset but also as a significant contributor to social welfare and urban quality of life.

According to the study presented in [12], using the travel cost method, the average recreational value per visit was estimated at USD 68–85 for domestic tourists and USD 114–120 for international tourists, indicating that non-residents assign higher recreational value to the park. Moreover, the price elasticity of demand was found to be elastic for domestic visitors and inelastic for international visitors, suggesting that there is potential to increase entrance fees for international tourists without significantly reducing the number of visits. These findings imply that focusing solely on residents of the Federal District may underestimate the park’s total recreational value as it overlooks the higher willingness to pay of non-local and international visitors.

Similarly, the annual recreational benefit of Bukit Timah was estimated at approximately USD 5.8 million, with a consumer surplus per visit of around USD 1.58. In contrast, Jurong Lake Gardens showed a significantly higher annual benefit of about USD 44 million, with a per-visit surplus estimated at USD 11.17 (USD 1.00 = SGD 1.38 in 2017) [55]. For comparison, ref. [56] estimated even greater recreational benefits—approximately USD 1 billion annually for East Coast Park and around USD 279.7 million for Pasir Ris Park (USD 1.00 = SGD 1.57 in 2006).

The total annual recreational value of Awash National Park, Ethiopia, was estimated at ETB 26,553,229 (approximately USD 970,263), with an average consumer surplus per visitor of ETB 1220 (approximately USD 44.57) [57]. The recreational value of Lawachara National Park in Bangladesh was estimated at Taka 476.44 million per year using TC [58].

In addition to the Teide National Park in Spain, the estimated recreational use value ranged from USD 25.5 million to USD 71.8 million, while the average consumer surplus per visit varied between USD 11.47 and USD 30.90 based on a 2015 exchange rate of 1 USD = 0.89 EUR [5]. Therefore, according to the recreational values, the administrative regions of the Federal District would serve as a means of estimating the economic values of recreational places by the zoned approach of the travel cost method in the Brazilian capital.

One of the main limitations of the studies used for comparison is that the TC method captures only the recreational benefits experienced by visitors, that is, the direct use value [59]. In other words, this method does not account for the hedonic values associated with parks [60,61,62], nor does it include non-use values such as option, existence, and bequest values [63,64].

The economic value of environmental resources stems from all their attributes whether or not they are associated with actual use. The total economic value (TEV) of a resource comprises use values, composed of direct use value and indirect use value, and non-use values, composed of option value, bequest value, and existence value.

Regarding use values, direct use value (DUV) refers to the immediate, tangible benefits obtained from the resource through activities like extraction, visitation, or other forms of direct consumption or production. In contrast, indirect use value (IUV) arises from the ecosystem services the resource provides, such as the protection of soil through forest conservation.

Regarding non-use values, existence value (EV) reflects the satisfaction individuals derive from simply knowing that a natural resource or species exists regardless of any current or future use. This value is often rooted in cultural, ethical, moral, or altruistic beliefs regarding the importance of preserving nature. Option value (OV) represents the value placed on preserving the possibility of using the resource in the future, particularly in contexts where its availability may be uncertain or threatened. Finally, bequest value captures the satisfaction individuals feel from ensuring the conservation of environmental resources for the benefit of future generations.

PNB has great ecotourism and economic potential due to its location, in addition to having natural pools and samples of the flora and fauna of the Cerrado biome. Due to this, in the sample of resident visitors, numerous expenses above USD 18.18 were found, with a maximum of USD 29.09, and a travel cost of USD 31.63, which is surprising because PNB is located in an urban environment. However, these values are explained by the high purchasing power of visitors. PNB also received visitors from other states and countries, as shown in this work. This highlights the importance of PNB for the local economy, fitting into one of the categories of conservation units that received the most visits in Brazil. To date, it is the fourth most visited park in the country over the years, behind only Tijuca, Iguaçu, and Jericoacoara.

The recreational use economic value of PNB was close to other studies in parks that used the zoned approach. If a ticket price were charged for the number of visits made in 2019, based on the values of consumer surplus per visit mentioned above, the park would have an estimated gross revenue of USD 686,880.99 in the same year, with a 95% confidence interval between USD 292,678.98 and USD 1,081,540.3. The economic value of recreational use is reflected only in the economic value of direct use of the park for recreation, not having measured the value of non-use or the values of existence and option, which, together, would provide the total economic value of the environmental resource.

4. Conclusions

The average visitor to PNB is male, aged around 30 years, with a high level of education and with an average income of five minimum wages. The identified profile is the same as that which is observed in other ecological parks, reflecting a public concerned with physical and mental health, attracted by sports activities that are allied to ecological tourism.

Using the TC method, the estimated economic value of the park’s recreational use is approximately USD 25 million per year, with an average consumer surplus of USD 2.58 per visit. This figure aligns with the park’s current ticket price (USD 2.54), suggesting a pricing policy that is consistent with profit maximization without significantly reducing visitation. Furthermore, the hypothesis that the consumer surplus per visit exceeds the current entrance fee is supported.

The chosen econometric model (Log–Log) demonstrated strong statistical validity (R² = 95.65%), normal residual distribution, and the absence of autocorrelation and heteroscedasticity, confirming the robustness of the findings.

The estimated price elasticity of demand was −4.1, indicating elastic demand: a 1% increase in travel cost leads to a 4.1% decrease in visitation rates. Although the study claims that PNB has few competitors due to its privileged location, favorable climate, and an apparent lack of alternatives that combine tourism and sports activities, the results suggest otherwise. The demand for visits to PNB was found to be elastic, indicating that visitors are sensitive to changes in price. This type of demand typically implies the existence of nearby substitute goods, such as other parks, green areas, and recreational options within the Federal District. Therefore, even though the park may have unique attributes, the data show that increases in costs significantly reduce visitation frequency, challenging the notion that PNB faces limited competition.

This behavior highlights the importance of considering access costs in public policy planning. The analysis also revealed that visitation rates decrease as the distance from the origin increases, with visitors from the closest zones showing the highest visitation frequencies.

One of the main limitations of this study is inherent to the TC method itself, which allows for the estimation of the economic value of direct use only, without capturing non-use values (option value, bequest value, and existence value) or indirect use values, which are essential components of the total economic value (TEV) of an environmental resource. Additionally, the presented estimates do not account for the benefits generated by visitors who reside outside of the Federal District, which may have led to an underestimation of the consumer surplus. Another limitation lies in the difficulty of comparing the results with those of other studies due to the particularities of each recreational site, which differ in terms of visitor profiles, income levels, local currencies, education levels, and proximity to the recreational area. Nevertheless, the findings of this research were proven to be consistent with those of other referenced studies that also applied the TC method, reinforcing the reliability of the results.

Although this study focused solely on residents of the Federal District, the estimated values confirm the park’s importance as an urban ecological and recreational asset. Further studies are recommended, including visitors from other regions and incorporating meteorological variables (temperature, relative humidity, and precipitation) that influence visitation patterns and complementary methods, such as contingent valuation, to estimate non-use values and indirect use values, thus capturing the TEV of the conservation unit. More research would also allow for the comparability of results and the consolidation of the methodology.