Sustainable tourism development: A dynamic model incorporating resident spillovers

Abstract

The ongoing debate on over-tourism shows that developing more sustainable forms of tourism is not only relevant for environmental reasons but it would also create important spillovers benefitting residents within the economic and social domain of sustainability. Based on this broad idea, we develop a theoretical model of sustainable tourism considering the well-being of locals incorporating external effects and trade-offs with less sustainable forms of tourism. We employ a dynamic model of resident well-being, where utility is derived from consumption, tourism quality (e.g. better restaurants, hiking trails), and the number of tourists visiting. A benevolent regional government maximizes the representative resident’s well-being by choosing the rate of consumption, the number of tourists visiting (e.g. number of beds), and the rate of investment in tourism quality. Our results depend crucially on the initial number of tourists and state of tourism quality. Suppose the initial state of tourism quality is below its long-run optimum. If initial visitor numbers are small so that increasing them raises residents’ well-being directly through consumption (i.e. more tourism supply and cultural exchange raises resident’s marginal utility of consumption), the optimal strategy is to invest in tourism quality and to increase the number of tourists over time, as quality changes. If initial visitor numbers are large, increasing them further reduces the resident’s marginal utility from consumption (e.g. booked-out restaurants, crowed hiking trails, etc.) and the optimal strategy is to increase tourism quality over time but to reduce the quantity of visitors. Our general finding is that quantity and quality may move in tandem or in opposite direction, depending on current state and residents’ preferences. If over-tourism means that residents’ well-being is negatively affected by an increasing number of visitors, the model suggests that ongoing investment in tourism quality while reducing numbers will maximize residents’ well-being. We show that the first-best optimum, achieved in a centrally planned economy, can be replicated in a decentralized economy by using time-varying tax rates. This ensures that (i) the steady state of the first-best optimum is reached and that (ii) the speed of convergence to steady state is socially optimal.

Keywords

dynamic optimal taxation over-tourism spillovers sustainable tourism

Introduction

Over-tourism has become an intensely debated issue. It describes destinations experiencing too many tourists such that the environment, residents, and even the visitors will suffer. Dubrovnik and Venice are often cited as destinations experiencing extremely high visitor numbers and thus over-tourism (e.g. Panayiotopoulos and Pisano, 2019; Seraphin et al., 2018). In this context, calls for a more responsible and sustainable tourism development are made, which also benefit the local environment and its residents within the economic and social domain of sustainable development. Based on this general idea, we develop a theoretical model of sustainable tourism development explicitly considering the well-being of locals by including external effects and trade-offs with less sustainable forms of tourism based on high tourist numbers. In this context, over-tourism phenomena serve as an example of an unsustainable state of tourism development and are a sufficient but not a necessary condition for the conclusions derived from the theoretical model. The problem we address is how to pave the way toward a more sustainable tourism development identifying appropriate tourism policy incentives which will address tourism flows.

Growth in tourism associated with an increasing number of tourists contributes to the local economy’s income. In turn, the accommodation needs of an increasing number of guests and an appropriate infrastructure is met by building new hotels, roads, shopping areas, and so on. As visitor numbers grow, facilities such as restaurants, bars, specialty stores are built pleasing tourists and residents alike. Thus, via investments, the quality of existing tourism services improves, creating a new supply. Increasing capacities of tourism facilities and growing visitor numbers have various effects, both economic and noneconomic, on the host country or region. Thus, an improved infrastructure, more, better and diversified leisure facilities, restaurants, and the exposure to different cultures of foreign visitors can generate positive spillover effects toward locals. However, massive streams of tourists can turn local residents’ life into a nightmare (Chao et al., 2005), despite an improved infrastructure and better service quality. Moreover, tourism can lead to a degradation of nature, which in turn lowers quality of life (QOL) both for residents and tourists. Thus, tourism and nature (the environment) can be in conflict, in coexistence or in symbiosis, as Budowski (1976) categorizes in his classic article.

It is difficult to assess the external effects associated with tourism, since no markets for them exist. Often, they are clear externalities, implying benefits or costs that tourists or firms confer on others without paying or receiving any compensations. Because these side effects are not accounted for in the market, externalities can lead to individual decisions that are not optimal for a society as a whole. To improve the welfare of residents, it is therefore important to implement appropriate policies to deal with externalities such as nature degradation or crowded infrastructures, directly affecting the welfare of local residents. This article addresses the issue of optimal policy options in a regional economy to cope with externalities caused by tourism. In the formal model we develop, over-tourism may serve as an example of a situation in which residents’ well-being is negatively affected by high visitor numbers.

The list of externalities associated with tourism is long. Externalities which negatively affect residents’ welfare are, for example, crowding and congestion of roads, public transportation and cities, noise, litter and pollution, property destruction, pollution, increased water consumption, changes in community appearance, landscape changes, nature degradation, for example, caused by overbuilding, wildlife depletion, damage to cultural resources, land loss, increased urbanization, and increased crime rate. On the other hand, tourism can have beneficial impacts, enhancing residents’ living. Examples for such positive externalities are infrastructure development including more or better leisure facilities, designated parks, a greater recognition of the importance of saving historical buildings, pollution control, more and/or cleaner beaches, cultural exchange, better public health systems, or simply higher living standards in the host economy. It is thus evident that tourism generally disrupts social, cultural, and environmental systems, and that noneconomic impacts of tourism often tend to be negative as a whole, whereas economic side effects are normally perceived as positive (see Figini et al., 2007).

As the many examples reveal, tourism simultaneously creates both positive and negative externalities. Candela et al. (2008) define them as “multiple externalities” or “intersecting externalities” in the sense that any net external effect inherent with tourism can be positive or negative depending on the level of tourism (e.g. if the costs of congestion and degradation of nature are smaller or larger than the economic and social benefits of tourism). By their very nature, externalities are not properly accounted for when tourism firms decide on tourism development in terms of the quantity of tourism services produced for tourists.

Hence, the tourism service market, on which prices equilibrate supply and demand, typically will not operate optimally from a social point of view. The same is true with respect to tourism firms’ investments into quality improvements as a form of tourism development. When deciding on how much to invest, each firm considers only its own benefits from an increase in quality and rationally does not consider any additional benefits or costs such quality improvements may create for other tourism firms and for local residents. To correct the market failures that these “multiple externalities” produce, some form of market intervention is necessary. Policy can use its instruments to improve the overall performance of the economic system in the direction of what is socially optimal.

For our theoretical model to follow, tourism quality and improvements in tourism quality are important concepts. Via investments, the quantity and quality of existing tourism services are raised and facilitate a growing number of visitors with economic and noneconomic effects on the host region. In this context, tourism quality will incorporate positive and negative external effects of tourism development. In practice, any indicator to measure tourism quality will be complex, difficult to identify and it depends crucially on the regional context (e.g. in terms of economic diversity, environmental sensitivity, and social cohesion). Uysal and Sirgy (2019) argue that QOL indicators can be seen as performance indicators to pave the way toward sustainable resource use and development in tourism. In the context of their paper, we argue that an index of QOL indicators related to tourists, residents, employees in tourism, and hospitality may also serve as a measure for tourism quality. This index of QOL indicators includes multiple externality aspects as outlined above and thus can operationalize our concept of tourism quality. While we recognize the importance of tourism quality to develop our model, it would be beyond the scope of the current article to specify a detailed indicator measuring tourism quality.

In economics, it is well-known that externalities can be internalized by using taxes or subsidies. Thus, to correct a negative externality associated with tourism services, a tourism tax could be imposed. Palmer and Riera (2003) as well as Aguiló et al. (2005) report that an “ecotax” (tourism tax) of about one Euro per day and head was introduced to address the negative effects of mass tourism on the Balearic Islands. Gooroochurn and Sinclair (2005) provide a comprehensive typology of tourism taxes (e.g. entry/exit tax, bed night tax, occupancy tax, accommodation tax, service tax, ecotourism tax). To internalize a positive spillover from a firm’s quality investments to other firms and residents, quality could be subsidized.

There is a large and growing literature analyzing QOL and well-being in tourism reviewed by Uysal et al. (2016). They note that there is still a research gap on how levels of tourism development affect the perceived impact of tourism and QOL for residents. While we do not intend to close this gap, we further underpin this research need with our model from a theoretical point of view emphasizing the external effects associated with tourism development. In our modeling approach, levels of tourism development relate to the quantity and quality of tourism services produced for tourists.

Uysal et al. (2012) relate the QOL effects on destination residents to the literature on tourist area life cycles inspired by Butler (1980) which proposes that tourist destinations follow a recognizable cycle of evolution from the initial stages through tourism development, consolidation, stagnation, and decline or rejuvenation. The policy implications following from our theoretical model can be seen as a way to mitigate tourism development in a more sustainable way leading to a consolidation of visitor numbers but avoiding decline.

The objective of tourism taxes is twofold: to generate revenue and, as already indicated, to correct market failures. While taxation of tourism can be an important source of government revenue, deserving an analysis on its own, we focus our attention on addressing externalities to achieve a sustainable tourism development and thus a more desirable social outcome. If such interventions in tourism markets are done properly, overall welfare in the host region and residents’ QOL may improve substantially.

Of course, the analysis of optimal tourism taxation is not new. In a static partial equilibrium framework, Pintassilgo and Silva (2007) and Candela et al. (2007) derive optimal tourism taxes. With multiple, intersecting externalities, the social optimum may be replicated using taxes or subsidies. However, a static, partial-equilibrium framework neglects any repercussion of tourism and of taxation across different economic entities and across time. Piga (2003) uses a dynamic partial equilibrium model to explicitly link tourism, its use of natural resources and policy intervention. He derives optimal taxation rules for different strategic settings. Cerina (2007) analyzes dynamic optimal taxation with respect to environmental sustainability, using a small open economy model without capital formation and foreign borrowing. Because of the specific functional forms assumed, the optimal tourism tax is time invariant. A dynamic model of a growing small open economy completely specialized in tourism production is developed by Gómez et al. (2008), focusing on tourism taxation as an instrument to internalize environmental impacts and to increase long-run welfare along a balanced growth path.

In contrast, our focus is on sustainable tourism development from a resident’s point of view, as tourism affects residents’ well-being in various ways. Of course, this is an inherently dynamic issue, as tourism streams and the quality of tourism service supplies may continuously change and evolve over time, determining tourism firms’ profits, influencing firm owners’ income, and affecting residents’ well-being.

To the best of our knowledge, papers on dynamic models of sustainable tourism are rare. Casagrandi and Rinaldi (2002) build a nonlinear mathematical model, describing the dynamics of tourists, the environment and tourism services, and how they influence sustainability, but their model is based on behavioral relationships and lacks microeconomic foundations. Johnston and Tyrrell (2005) construct an intertemporal optimization model along the lines of the dynamic renewable resource literature. They consider the relationship between environmental quality and the number of visitors and how these affect profits and utility and use a simple framework, where environmental quality is negatively affected by the number of visitors but may increase due to environmental renewal. Thus, environmental quality is controlled by using the number of visitors as a policy instrument. Johnston and Tyrrell (2005) show that the profit-maximizing “industry sustainable optimum” differs from the utility-maximizing “resident sustainable optimum.” In another paper, Tyrrell and Johnston (2008) extend their model by including resiliency in ecological–environmental quality, economic–fiscal quality, and social–cultural quality of tourism destinations. From a modeling point of view, both are dynamic partial equilibrium models. Their common thread is a focus on ecological and environmental rather than economic issues. Moreover, the question of how a socially optimal sustainable tourism development can be achieved by implementing proper policies is not addressed.

Our article provides an important contribution to the analysis of sustainable tourism development including residents’ well-being. It extends and enriches existing models in four dimensions. First, we consider ‘“intersecting externalities” in a dynamic general equilibrium framework, based on micro-foundations, taking account spillovers and trade-offs and how they change over time. As we will see, the optimal policy leading to the social (first-best) optimum are time-varying taxes or subsidies depending on the types and the signs of the spillovers and trade-offs. Second, we explicitly consider how quality of tourism services can be changed over time by incurring costly investments into quality. Third, in contrast to previous work, we explicitly consider residents’ consumption decisions, and we allow for borrowing (lending) to finance investment of local tourism firms into quality and residents’ consumption by relaxing their resource constraints. Investments in tourism quality as well as consumption expenditures are not constrained period by period by the income generated from tourism. Instead, an intertemporal budget constraint is met. Fourth, we do not restrict our attention on the regional economy’s steady state (or balanced growth path) but pay close attention on the transitional dynamics.

We analyze the spillovers from quality referenced tourism services on firms and residents and derive optimal corrective policies for a region in which tourism service quality is growing over time toward its steady-state level. We develop a simple model of a small open economy, which is completely specialized in the production of tourism services and in which residents are the owners of firms. They finance expenditures on consumption and quality investments by using firms’ profits and by borrowing funds from the rest of the world. We impose a solvency condition which rules out Ponzi schemes of unsustainable development. We would like to stress that this type of small open economy framework fits particularly well to regional economic settings. For analytical purposes and as a starting point, we focus on tourism service quantity and quality and do not consider the regional labor market. After analyzing the first-best social optimum, achieved in the centrally planned regional economy, we show that the equilibrium in the decentralized market economy is sub-optimal. Our main finding is that in a decentralized regional market economy, the quantity and quality of tourism services always move in tandem, because agents do not take the spillovers into account. However, in case of sufficiently high tourist numbers, the maximization of residents’ well-being would require that quantity and quality move in opposite directions. It can thus be optimal to reduce the number of tourists visiting a region and in order to increase the quality of tourism services offered to tourists. In other words, from a social point of view, there may exist a trade-off between tourism quantity and tourism service quality. We apply Turnovsky’s (1997) method and replicate the first-best optimum by time-variant policies, that is, taxes (or subsidies) on tourism quantity and tourism service quality that change over time. These will induce private agents to behave in a socially desirable manner and will maximize residents’ well-being.

The rest of the article is structured as follows. The following section sets up the model of a small open regional economy and describes the economic framework. In the third section, we discuss the macroeconomic equilibrium in a centrally planned regional economy and derive the first-best optimum. In the fourth section, we analyze the equilibrium in the decentralized market economy while the fifth section compares the centrally planned economy and the decentralized regional market economy. Finally, we replicate the first-best optimum for the decentralized regional economy by introducing dynamic taxes and subsidies on tourism output and quality. In the seventh section, we provide policy implications, summarize, and conclude.

The analytical framework

The small regional economy comprises a large number of identical households, who consume a traded good and who own firms, which are completely specialized in the production of tourism services.¹ For the sake of simplicity and without loss of generality, we assume that the number of households equals the number of firms, and that the number of households and firms is constant and given by N. In other words, each household owns one firm.

Each tourism firm produces tourism services, resulting in revenue, measured in terms of the traded good,

y_{i} = y (T_{i}, q_{i}, \bar{q})

Firm i’s revenue depends on the number of tourists T_i served by the firm, the quality of its services² offered, q_i, and on the average service quality $\bar{q} = \frac{1}{N} \sum_{i = 1}^{N} q_{i}$ prevailing in the region. Our form of the revenue function y_i allows for all types of market forms.³ The revenue function is assumed to have the following properties^4,5:

\begin{array}{l} y_{T} > 0, y_{T T} < 0, y_{q} > 0, y_{q q} < 0, y_{\bar{q}} ≷ 0, y_{\bar{q} \bar{q}} < 0, y_{T q} > 0, y_{T \bar{q}} ≷ 0, \\ y_{q \bar{q}} \geq 0, y_{q} + y_{\bar{q}} > 0, y_{T q} + y_{T \bar{q}} > 0, y_{q q} + y_{q \bar{q}} < 0, y_{\bar{q} \bar{q}} + y_{\bar{q} q} < 0 \end{array}

That is, the marginal revenue of selling tourism services is positive ( $y_{T} > 0$ ), but diminishing ( $y_{T T} < 0$ ).⁶ The firm’s revenue increases with the quality it offers ( $y_{q} > 0$ ), albeit at a diminishing rate ( $y_{q q} < 0$ ). The effect of a higher average regional quality on the firm’s revenues is ambiguous ( $y_{\bar{q}} ≷ 0$ ), whereas the marginal revenue of average quality is definitely decreasing ( $y_{\bar{q} \bar{q}} < 0$ ). A higher average regional quality could allow the firm, on the one hand, to charge a higher price for its own services, given its own quality; on the other hand, a higher regional quality, given the firm’s own quality, may reduce tourists’ willingness to pay for the firm’s services. Therefore, the effect of a higher average regional quality on its marginal revenue y_T from selling tourism services is ambiguous ( $y_{T \bar{q}} ≷ 0$ ), too. Increasing its own service quality, given average quality, however, will increase the firm’s marginal revenue y_T (i.e. $y_{T q} > 0$ ). We shall reasonably assume that an increase in both the firm’s quality and average quality increases both the firm’s revenue y (i.e. $y_{q} + y_{\bar{q}} > 0$ ) and its marginal revenue y_T, (i.e. $y_{T q} + y_{T \bar{q}} > 0$ ), that is, if own quality and average quality move in tandem, both revenue and marginal revenue increase. The effect of a higher average quality on the firm’s marginal revenue from increasing its on quality is assumed to be non-negative ( $y_{q \bar{q}} \geq 0$ ).⁷ Furthermore, we assume that $y_{q q} + y_{q \bar{q}} < 0$ and $y_{\bar{q} \bar{q}} + y_{\bar{q} q} < 0$ , that is, that the total effect of a joint increase in both the firm’s and the regional average quality on the firm’s marginal revenue of (i) the firm’s service quality and (ii) average quality is negative. The production of the firm’s tourism services gives rise to a convex cost function $K_{i} = K (T_{i}); K' (T_{i}) > 0, K ″ (T_{i}) > 0$ .⁸

Changing the firm’s quality of tourism services q_i is time consuming and costly. Increasing service quality typically will require investments in, for example, equipment, furniture, buildings, leisure facilities, and so on. Investments are not restricted into what traditionally is considered as the physical capital stock. Our concept of quality is a broader one, including physical, but also other types of “investments,” for example, educational expenditures to train personnel to be able to perform in qualitatively better ways. It is thus natural to model quality as a sluggish state variable. When the firm changes the quality of its services, it has to undertake “investment in quality,” I_i,

\dot{q} = I

In analogy to investment into physical capital, a change in service quality associated with convex quality adjustment costs. Total expenditure for a change in the firm’s service quality by new “investment” plus “installation cost” is denoted by $C (I_{i})$ . The investment cost function is expressed of the traded good; it has the properties $C' \geq 0, C ″ > 0, C' (0) = 1$ . Firm i’s profits in terms of the traded consumption good are thus

π_{i} = y (T_{i}, q_{i}, \bar{q}) - K (T_{i}) - C (I_{i})

The representative household owns the representative firm and receives its profits. She derives utility from consumption of a traded good, produced outside the region and thus “imported,” c_i, from the average quality of tourism services available in the region, $\bar{q}$ —for example, think about the quality of restaurants and the availability of leisure activities—, and the average number of tourists per resident, $\bar{T} = T / N$ , where the number of tourists T may be measured by the number of overnight stays, for example. Her instantaneous utility function is given by

U = U (c_{i}, \bar{q}, \bar{T})

The utility function is assumed to be concave with the following partial derivatives:

\begin{array}{l} U_{c} > 0, U_{c c} < 0, U_{\bar{q}} > 0, U_{\bar{q} \bar{q}} < 0, U_{\bar{T}} ≷ 0, U_{\bar{T} \bar{T}} < 0, U_{c \bar{q}} > 0, \\ U_{c \bar{T}} ≷ 0, U_{\bar{q} \bar{T}} ≷ 0 \end{array}

The marginal utility of consumption and of average quality is positive ( $U_{c} > 0$ and $U_{\bar{q}} > 0$ ), but diminishing ( $U_{c c} < 0$ and $U_{\bar{q} \bar{q}} < 0$ ). The utility function incorporates the possibility that tourists may reduce the resident’s well-being, that is, $U_{\bar{T}} < 0$ . We shall refer to this case as over-tourism. The critical number of tourist above which residents’ well-being starts to fall when more tourists arrive can be denoted by $\hat{T}$ .⁹ This threshold $\hat{T}$ will generally depend on the small open economy’s structural characteristics, which for the sake of simplicity we shall take as given. This assumption does not represent a strong limitation, as we do not consider economic growth, which may change the region’s structure and capacity. Tourists may reduce residents’ well-being in two ways: directly, as, for example, regional locations become crowded, waiting times increase, prices for goods residents buy rise, and indirectly, as too much tourists may negatively affect the environment, which, over time, can result in environmental degradation, which negatively affects the resident’s well-being. In our model, the impact of changes in the average number of tourists, $\bar{T}$ , includes both these direct and indirect effects. In such a scenario, the marginal utilities of consumption and of quality will be reduced when the ratio of tourists to residents rises, that is, $U_{c \bar{T}} < 0, U_{\bar{q} \bar{T}} < 0$ .¹⁰

Each resident household is the owner of one firm. The household receives profit income and interest income.¹¹ The representative household can lend or borrow on the financial market at a given and constant interest rate r.¹² The stock of her assets is denoted by a_i.¹³ The household’s flow budget constraint in terms of the traded good is given by

{\dot{a}}_{i} = r a_{i} + π_{i} - c_{i}

indicating that the difference between her income from earning interest $r a_{i}$ and profits $π_{i}$ and her consumption expenditures c_i is saved in the form of assets. Without loss of generality, we can consolidate the representative household and the representative firm, resulting in a representative consumer–producer. Inserting the firm’s profits (1c) into the household’s flow budget constraint gives

{\dot{a}}_{i} = r a_{i} + y (T_{i}, q_{i}, \bar{q}) - K (T_{i}) - C (I_{i}) - c_{i}

The representative agent’s intertemporal utility function is given as

W_{i} \equiv \int_{0}^{\infty} U_{i} (c_{i}, \bar{q}, \bar{T}) e^{- β t} d t,

where $β$ is her constant rate of consumer time preference. It is important to recognize that from the point of view of an individual agent there are two externalities, causing three external spillover effects. First, for the individual household and firm the average service quality is given, resulting in a positive external effect on (i) utility and an external effect on (ii) revenues and thus income. Second, the ratio of tourists to residents $\bar{T}$ is also an externality and affects the agent’s well-being.¹⁴ That is, when residents optimize their behavior, they take $\bar{q}$ and $\bar{T}$ as given, whereas in fact these two averages are determined by the market and by residents’ interactions.

As a benchmark, we first describe the socially optimal equilibrium emerging in a centrally planned economy.

Equilibrium in the centrally planned regional economy

The benevolent regional central planner, in deciding about the N consumer–producers’ rates of consumption c_i, tourism service production T_i, asset accumulation ${\dot{a}}_{i}$ , and service quality accumulation I_i, to maximize welfare W_i, see (1f), subject to the flow budget constraint (1e), the quality accumulation equation (1b) and the given initial quantities of wealth $a_{i} (0) = a_{i 0}$ and service quality $q_{i} (0) = q_{i 0}$ , takes the externalities into account by recognizing that all agents will behave in the same way (i.e. $q_{i} = q_{j}, T_{i} = T_{j}$ ), so that in equilibrium $\bar{q} = \frac{1}{N} \sum_{i = 1}^{N} q_{i} = q_{i}$ and $\bar{T} = \frac{1}{N} \sum_{i = 1}^{N} T_{i} = T_{i}$ . The present value Hamiltonian for the central planner’s optimization problem is thus given by

H \equiv U (c_{i}, q_{i}, T_{i}) + λ ([r a_{i} + y (T_{i}, q_{i}, q_{i}) - K (T_{i}) - C (I_{i}) - c_{i}]) + γ I_{i}

where $λ$ is the shadow value or the marginal utility of wealth in the form of assets, and $γ$ measures the shadow value of service quality in terms of utility. Performing the optimization gives rise to the following optimality conditions:

U_{c} (c_{i}^{*}, q_{i}^{*}, T_{i}^{*}) = λ^{*}

C' (I_{i}^{*}) = \frac{γ^{*}}{λ^{*}} \equiv v^{*}

y_{T} (T_{i}^{*}, q_{i}^{*}, q_{i}^{*}) + \frac{U_{\bar{T}} (c_{i}^{*}, q_{i}^{*}, T_{i}^{*})}{λ^{*}} = K' (T_{i}^{*})

β - \frac{{\dot{λ}}^{*}}{λ^{*}} = r

\frac{y_{q} (T_{i}^{*}, q_{i}^{*}, q_{i}^{*})}{v^{*}} + \frac{y_{\bar{q}} (T_{i}^{*}, q_{i}^{*}, q_{i}^{*})}{v^{*}} + \frac{U_{\bar{q}} (c_{i}^{*}, q_{i}^{*}, T_{i}^{*}) / λ^{*}}{v^{*}} + \frac{{\dot{v}}^{*}}{v^{*}} = r

together with the transversality conditions

lim_{t \to \infty} λ^{*} a_{i}^{*} e^{- β t} = lim_{t \to \infty} γ^{*} q_{i}^{*} e^{- β t} = lim_{t \to \infty} λ^{*} v^{*} q_{i}^{*} e^{- β t} = 0

where an asterisk denotes equilibrium in the centrally planned economy. Equation (2a) equates the marginal utility of consumption of the traded good to the marginal utility of wealth in the form of assets. Equation (2b) gives rise to a Tobin “q” theory of investment into quality. It equates the marginal cost of investment (new quality) to the social value of quality, $v^{*}$ , both expressed in terms of the traded good.¹⁵ Equation (2c) equates the social marginal value of tourism services T_i, which is the sum of the firm’s marginal revenue of T_i and the household’s marginal utility of T_i, measured in terms of the traded good, to the marginal cost of producing an additional unit of T_i. The central planner thus recognizes the effect of a change in tourism on residents well-being. Note that in case of over-tourism, $U_{\bar{T}} < 0$ , so that $U_{\bar{T}} / λ^{*}$ represents an additional marginal cost.

Equations (2d) and (2e) are dynamic no-arbitrage conditions. The former equates the rate of return on consumption to the rate of return on assets, that is, the interest rate. For an interior solution, we require $β = r$ , implying a time-constant marginal utility of wealth, $λ^{*}$ . This has an important consequence: The marginal utility of consumption, $U_{c} (c_{i}^{*}, q_{i}^{*}, T_{i}^{*})$ has to remain constant during transition, otherwise the rate of return on consumption would not equal the interest rate, and well-being would not be maximized. Equation (2e) equates the social rate of return on the firm’s quality to the given interest rate. The social rate of return on the firm’s quality comprises four elements: (i) a private “dividend yield” $y_{q} / v^{*}$ , that is, the ratio of the marginal revenue of the firm’s quality to the social value of quality, $v^{*}$ , (ii) a social “dividend yield” $y_{\bar{q}} / v^{*}$ , which takes into account that all the firms’ qualities increase, raising thus average quality $\bar{q}$ , creating an additional dividend for the firm, which may be positive or negative, depending on the sign of $y_{\bar{q}}$ , (iii) another social “dividend yield” $U_{\bar{q}} / (λ^{*} v^{*})$ , which is the ratio of residents’ marginal utility of quality, measured in terms of the traded good, $U_{\bar{q}} / λ^{*}$ , to the price of quality, and (iv) a “capital gain” ${\dot{v}}^{*} / v^{*}$ , which is the rate of change of the social value of quality.¹⁶ The central planner thus takes the two externalities of quality into account. Finally, the transversality conditions (2f) must hold to ensure that the representative consumer–producer’s intertemporal budget constraint is met.

Centralized macroeconomic equilibrium

The macroeconomic equilibrium of this intertemporal general equilibrium model is defined to be a situation in which all the planned supply and demand functions are derived from optimization behavior, the economy is continually in equilibrium, and all anticipated variables are correctly forecasted. We will call this concept a “perfect foresight equilibrium.”¹⁷ From the static first-order conditions (2a)–(2c), we obtain the short-run solutions

T_{i}^{*} = T_{i}^{*} (λ^{*}, q_{i}^{*}); \frac{\partial T_{i}^{*}}{\partial λ^{*}} > 0, \frac{\partial T_{i}^{*}}{\partial q_{i}^{*}} ≷ 0

c_{i}^{*} = c_{i}^{*} (λ^{*}, q_{i}^{*}); \frac{\partial c_{i}^{*}}{\partial λ^{*}} < 0, \frac{\partial c_{i}^{*}}{\partial q_{i}^{*}} ≷ 0

I_{i}^{*} = I (v^{*}), I' = \frac{1}{C ″} > 0

Investment into quality is a function of the social value of quality, $v^{*}$ . A higher social value of quality increases investment into quality, see equation (3c). The partial derivatives of consumption c_i and tourism T_i with respect to the firm’s quality q_i are given by¹⁸

\frac{\partial T_{i}^{*}}{\partial q_{i}^{*}} \equiv T_{q}^{*} = \frac{1}{Δ} [U_{c c} ((y_{T q} + y_{T \bar{q}})) + \frac{1}{λ^{*}} ((U_{c c} U_{\bar{T} \bar{q}} - U_{\bar{T} c} U_{c \bar{q}}))]

\frac{\partial c_{i}^{*}}{\partial q_{i}^{*}} \equiv c_{q}^{*} = \frac{1}{Δ} [U_{c \bar{q}} ((y_{\bar{T} \bar{T}} - K ″ + \frac{U_{\bar{T} \bar{T}}}{λ^{*}}) - U_{c \bar{T}} ((y_{T q} + y_{T \bar{q}})) - \frac{U_{c \bar{T}} U_{\bar{q} \bar{T}}}{λ^{*}})]

Δ \equiv \frac{1}{λ^{*}} ((U_{\bar{T} c}^{2} - U_{c c} U_{\bar{T} \bar{T}})) - U_{c c} ((y_{T T} - K ″)) < 0

If tourism is below a critical value, that is $U_{c \bar{T}} > 0, U_{\bar{q} \bar{T}} > 0$ , the signs of $\partial T_{i}^{*} / \partial q_{i}^{*}$ and of $\partial c_{i}^{*} / \partial q_{i}^{*}$ are positive, and an increase in tourism quality induces the central planner to raise residents’ consumption $c_{i}^{*}$ and the number of tourists served by each firm, $T_{i}^{*}$ . Quality and the number of tourists move then in tandem. Intuitively, a higher quality increases both the marginal utilities of consumption and of tourism, and the marginal revenue of tourism services, inducing the central planner to raise production of tourism services, increasing thus the firms’ profits, leading to higher residents’ incomes, allowing the planner to increase their consumption and raising hence their well-being further and above the utility increase due to higher quality and more tourism.

However, if the region suffers from over-tourism ( $U_{\bar{T}} < 0, U_{c \bar{T}} < 0, U_{q \bar{T}} < 0$ ), the second terms in the expressions $\partial T_{i}^{*} / \partial q_{i}^{*}$ and of $\partial c_{i}^{*} / \partial q_{i}^{*}$ become positive,¹⁹ and the reaction of tourism production and consumption upon an increase in quality becomes ambiguous. On the one hand, a higher quality enhances residents’ well-being and increases firms’ marginal revenue, and augmenting tourism production rises profits and thus residents’ income, which would allow a higher rate of consumption. On the other hand, higher tourism lowers residents’ well-being and increases the social marginal cost of tourism. The central planner weights social marginal benefits and social marginal costs and increases tourism production if the former outweigh the latter. If the negative effects of over-tourism are sufficiently severe, the central planner will reduce tourism production, and an increase in tourism service quality will be accompanied by lower tourism numbers, creating thus a trade-off between quantity and quality of tourism services. The optimal reaction of consumption in case of over-tourism (i.e. where $U_{c \bar{T}} < 0$ ) can be figured out by inspecting equation (2a), which requires the marginal utility of consumption to be constant. If over-tourism is not severe, so that it is optimal to increase both tourism service quality and tourism production, the marginal utility of consumption increases on the one hand because of better quality, on the other hand the marginal utility of consumption falls because of more visitors. If the former effect outweighs the latter, the central planner increases consumption to keep its marginal utility constant; if the latter effect dominates, consumption has to be reduced, and a trade-off between quality and the resident’s consumption arises, as tourism service quality and consumption move in opposite directions. If over-tourism is sufficiently severe so that an increase in quality is accompanied by lower tourism production, the marginal utility of consumption will increase, and the central planner will raise consumption to bring marginal utility of consumption back to the constant marginal utility of wealth, $λ^{*}$ .²⁰

Denoting steady-state values with tildes, the linearized dynamics for the level of service quality $q_{i}^{*} = {\bar{q}}^{*}$ and its social value $v^{*}$ follow from (1b) together with (3c), and (2e) together with (3a), and is given by

\begin{array}{l} ((\begin{matrix} {\dot{q}}_{i}^{*} \\ {\dot{v}}^{*} \end{matrix})) = ((\begin{matrix} 0 & 1 / C ″ \\ a_{21}^{*} & r \end{matrix})) ((\begin{matrix} q_{i}^{*} - {\tilde{q}}_{i}^{*} \\ v^{*} - {\tilde{v}}^{*} \end{matrix})), \\ a_{21}^{*} \equiv - [y_{q q} + y_{\bar{q} \bar{q}} + 2 y_{q \bar{q}} + ((y_{q T} + y_{\bar{q} T} + \frac{U_{\bar{q} \bar{T}}}{λ^{*}})) \frac{\partial T_{i}^{*}}{\partial q_{i}^{*}} + \frac{1}{λ^{*}} ((U_{\bar{q} \bar{q}} + U_{\bar{q} c} \frac{\partial c_{i}^{*}}{\partial q_{i}^{*}}))] \end{array}

where all derivatives are calculated at steady state. The characteristic equation is

ϕ (μ^{*}) = (μ^{*})^{2} - r μ^{*} - \frac{a_{21}^{*}}{C ″} = 0

The dynamic system is saddle-point stable if and only if $a_{21}^{*} > 0$ , otherwise the system will be unstable. It can be shown that a mild sufficient condition for $a_{21}^{*} > 0$ is $U_{c c} U_{\bar{q} \bar{T}} - U_{c \bar{T}} U_{c \bar{q}} > 0$ , which is automatically satisfied in the case of over-tourism ( $U_{\bar{q} \bar{T}} < 0, U_{c \bar{T}} < 0$ ). In what follows, we assume that $a_{21}^{*}$ is always positive.²¹ From the characteristic equation (6), it follows then that $μ_{1}^{*} < 0$ and $μ_{2}^{*} > 0$ .²² The stable solution for the level (stock) of quality, $q_{i}^{*}$ , and its market value, $v^{*}$ , is:

q_{i}^{*} (t) - {\tilde{q}}_{i}^{*} = ((q_{i 0} - {\tilde{q}}_{i}^{*})) e^{μ_{1}^{*} t}

v^{*} (t) - {\tilde{v}}^{*} = μ_{1}^{*} C ″ ((q_{i 0} - {\tilde{q}}_{i}^{*})) e^{μ_{1}^{*} t}

As can be seen from (7), the stable saddle-path is $v {(t)}^{*} - {\tilde{v}}^{*} = μ_{1}^{*} C ″ (q_{i}^{*} (t) - {\tilde{q}}_{i}^{*})$ , which is a negatively sloped line in $(q^{*}, v^{*})$ -space. If the region is below its steady-state level of quality, the social value of quality, $v^{*}$ , will be greater than unity, indicating that the value of quality is higher than its cost, and this causes investment into quality $q_{i}^{*}$ , and quality increases over time. As quality improves, its marginal social benefits become smaller, leading to a falling social value of quality. The region’s transitions toward steady state, accumulating quality, accompanied by a falling social value $v^{*}$ .

Inserting the short-run solutions (3) into the representative resident’s flow budget constraint (1e), recalling $q_{i}^{*} = {\bar{q}}^{*}$ , yields

{\dot{a}}_{i}^{*} = r a_{i}^{*} + y (q_{i}^{*}, q_{i}^{*}, T_{i}^{*} (λ^{*}, q_{i}^{*})) - K (T_{i}^{*} (λ^{*}, q_{i}^{*})) - c_{i}^{*} (λ^{*}, q_{i}^{*}) - C (I (v^{*}))

The (linearized) asset dynamics follow from linearizing equation (8) and using the stable solutions (7) for $q_{i}^{*}$ and $v^{*}$ and is given by

{\dot{a}}_{i}^{*} = Ω^{*} (q_{i}^{*} - {\tilde{q}}_{i}^{*}) + r (a_{i}^{*} - {\tilde{a}}_{i}^{*})

where²³

Ω^{*} \equiv y_{q} + y_{\bar{q}} - μ_{1}^{*} C' (0) - ((\frac{U_{\bar{T}}}{λ^{*}} \frac{\partial T_{i}^{*}}{\partial q_{i}^{*}} + \frac{\partial c_{i}^{*}}{\partial q_{i}^{*}}))

describes the influence of an increase in quality $q_{i}^{*}$ on the change in asset accumulation ${\dot{a}}_{i}^{*}$ . The sign of $Ω^{*}$ is ambiguous. The first and the third term give rise to a positive sign, whereas the sign of $y_{\bar{q}}$ is ambiguous, and the sign of the last term in brackets depends on the signs of $U_{\bar{T}}$ and the partial derivatives of tourism production and consumption on a change in quality. For our purposes, the sign of $Ω^{*}$ is not important.²⁴ In Online Appendix A.1, we show that the stable solution for the resident’s traded asset position is

a_{i}^{*} (t) - {\tilde{a}}_{i}^{*} = \frac{Ω^{*}}{μ_{1}^{*} - r} (q_{i}^{*} (t) - {\tilde{q}}_{i}^{*})

Setting $t = 0$ in (10) yields the resident’s and thus the region’s per capita intertemporal budget constraint, which ensures that the resident and thus the region remains intertemporally solvent.

Steady state in centrally planned region

The region’s steady-state equilibrium is reached when ${\dot{q}}_{i}^{*} = {\dot{v}}^{*} = {\dot{a}}_{i}^{*} = 0$ . Hence, we get the steady-state relationships

{\tilde{v}}^{*} = 1; {\tilde{I}}_{i}^{*} = 0

11a

y_{q} ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*})) + y_{\bar{q}} ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*})) + \frac{U_{\bar{q}} (c_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*}), {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*}))}{λ^{*}} = r

11b

r {\tilde{a}}_{i}^{*} = c_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*}) + K (T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*})) - y ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*}))

11c

a_{i 0} - {\tilde{a}}_{i}^{*} = \frac{Ω^{*}}{μ_{1}^{*} - r} ((q_{i 0} - {\tilde{q}}_{i}^{*}))

11d

The steady state in the centrally planned region can be calculated in the following sequential manner. First, in steady-state investment in service quality equals zero, implying that the social value of quality, ${\tilde{v}}^{*}$ , in steady state equals unity. Hence, there are no quality investment expenditures, see (11a). Second, given a value for the constant marginal utility of wealth, $λ^{*}$ , the no-arbitrage condition (11b), equating the steady-state social rate of return of quality to the rate of return on traded assets (the given interest rate r) determines then the steady-state level of service quality ${\tilde{q}}_{i}^{*} = {\tilde{\bar{q}}}^{*}$ as a function of $λ^{*}$ , that is, ${\tilde{q}}_{i}^{*} = {\tilde{q}}_{i}^{*} (λ^{*})$ . Note that the central planner takes the effects of average quality on the firm’s marginal revenue and on residents’ well-being into account. Third, given ${\tilde{q}}_{i}^{*}$ , the steady-state quantity of traded assets as a function of $λ^{*}$ follows then from (11c) as ${\tilde{a}}_{i}^{*} = {\tilde{a}}_{i}^{*} (λ^{*})$ . This equation requires that the difference between steady-state expenditures on consumption and tourism production and revenue from tourism production has to be financed by interest income. Fourth, inserting ${\tilde{q}}_{i}^{*} (λ^{*})$ and ${\tilde{a}}_{i}^{*} (λ^{*})$ into the intertemporal budget constraint (11d) gives then the equilibrium value of the constant marginal utility of wealth, $λ^{*}$ which guarantees the region’s intertemporal solvency. Fifth, knowing the equilibrium value of $λ^{*}$ determines then immediately the steady-state values of ${\tilde{q}}_{i}^{*}$ and ${\tilde{a}}_{i}^{*}$ , and in turn steady-state consumption ${\tilde{c}}_{i}^{*}$ and steady-state tourism production ${\tilde{T}}_{i}^{*}$ . Note that via equation (11d) the steady state depends on the region’s initial levels of traded assets $a_{i 0}$ and tourism quality $q_{i 0}$ .

If, for example, the initial regional level of quality $q_{i 0}$ is below steady state, the region grows along the stable saddle-path toward the socially optimal long-run equilibrium, ${\tilde{q}}_{i}^{*}$ . The regional transitional dynamics are characterized by investment into quality, as the market value of quality $v^{*}$ is greater than unity, following thus a Tobin’s “q” theory. Depending on the type of tourism (“desirable” tourism versus over-tourism), the increasing quality level ${\bar{q}}^{*}$ is accompanied by an increasing number of tourists due to rising tourism service production, or by a reduction of tourism production and less tourists.

It is possible that in an early stage of transition, tourism is associated with positive net social benefits, and that, as a consequence, the central planner will increase quality and quantity in tandem, whereas in a latter stage, when the number of tourists has risen sufficiently, the negative social effects of tourism dominate, and the continuing increase in quality of tourism services will occur jointly with a reduction of tourism production.

Note that by taking the externalities of tourism production and service quality into account, the dynamic adjustment paths and the steady state chosen by the central planner maximize the representative resident’s well-being. Thus, the equilibrium in the centrally planned economy is the first-best optimum.

Equilibrium in the decentralized regional economy

We now turn to the representative resident operating in a decentralized market economy, where there is a regional government. Her objective is to maximize her intertemporal utility function (1f), subject to the historically given initial levels of quality $q_{i} (0) = q_{i 0}$ and traded assets $a_{i} (0) = a_{i 0}$ , the quality accumulation constraint (1b), and her flow budget constraint

{\dot{a}}_{i} = r a_{i} + y (T_{i}, q_{i}, \bar{q}) - K (T_{i}) - C (I_{i}) - c_{i} - τ_{q} q_{i} - τ_{T} T_{i} + Z_{i}

1e′

Z_i denotes a lump-sum payment from the regional government (if $Z_{i} < 0$ , the resident has to pay a lump-sum tax). The local government, being aware of externalities, can impose specific taxes (or subsidies) on tourism service quality q_i and on tourism service production T_i with tax rates $τ_{q}$ and $τ_{T}$ .^25,26 Being small, in making her decisions, the representative resident takes the average level of tourism service quality $\bar{q}$ and the ratio of tourists to residents $\bar{T}$ as given. The resident’s first-order conditions are

U_{c} (c_{i}, \bar{q}, \bar{T}) = λ

12a

C' (I_{i}) = v

12b

y_{T} (T_{i}, q_{i}, \bar{q}) = K' (T_{i}) + τ_{T}

12c

β - \frac{\dot{λ}}{λ} = r

12d

\frac{y_{q} (T_{i}, q_{i}, \bar{q}) - τ_{q}}{v} + \frac{\dot{v}}{v} = r

12e

together with the transversality conditions

lim_{t \to \infty} λ a_{i} e^{- β t} = lim_{t \to \infty} λ v q_{i} e^{- β t} = 0

12f

As in the centrally planned regional economy, equation (12a) equates the marginal utility of consumption of the traded good to the marginal utility of wealth in the form of assets, and equation (12b) equates the marginal cost of investing in quality to the market value of quality, v. Equation (12c) equates the tourism firm’s marginal revenue y_T of tourism services T_i to the marginal cost of producing an additional unit of T_i, comprising marginal production costs $K' (T_{i})$ and the specific tax $τ_{T}$ on tourism services. In contrast to the central planner, the representative resident does not take the externality of tourism on her utility into account. Equation (12d) is the same as in the centrally planned economy and equates the resident’s rate of return on consumption to the rate of return on assets, r, which again implies $β = r$ and a time-constant marginal utility of wealth. Equation (12e) equates the resident firm’s rate of return on its quality to the interest rate. The firm’s rate of return on quality now comprises two elements: (i) the net private “dividend yield” $(y_{q} - τ_{q}) / v$ , that is, the ratio of the after tax marginal revenue of the firm’s quality to the market value of quality, v, and (ii) a “capital gain” $\dot{v} / v$ .²⁷ Note that in contrast to the central planner, the resident does not take the two externalities of quality on the regional firms’ revenues and on residents’ well-being into account. Finally, the transversality conditions (12f) must hold.

Decentralized macroeconomic equilibrium

From equations (12a) to (12b), we obtain the short-run solutions

T_{i} = T_{i} (q_{i}, \bar{q}, τ_{T})

3a′

c_{i} = c_{i} (λ, \bar{q}, \bar{T})

3b′

I_{i} = I (v), I' = \frac{1}{C ″} > 0

3c′

The partial derivatives of T_i and c_i are given by

\begin{array}{l} \frac{\partial T_{i}}{\partial q_{i}} = \frac{- y_{T q}}{y_{T T} - K ″} > 0, \frac{\partial T_{i}}{\partial \bar{q}} = \frac{- y_{T \bar{q}}}{y_{T T} - K ″} ≷ 0, \frac{\partial T_{i}}{\partial τ_{T}} = \frac{- 1}{y_{T T} - K ″} < 0 \\ \frac{\partial c_{i}}{\partial \bar{q}} = - \frac{U_{c \bar{q}}}{U_{c c}} > 0, \frac{\partial c_{i}}{\partial \bar{T}} = - \frac{U_{c \bar{T}}}{U_{c c}} ≷ 0 \end{array}

Differently to the centrally planned economy, the solutions for tourism production and consumption follow independently from equations (12c) and (12a), because the representative resident takes the average quality $\bar{q}$ and the average number of tourists $\bar{T}$ as given and does not internalize the external spillover effects of tourism quantity and quality. An increase in the firm’s service quality q_i increases marginal revenue, inducing the firm to raise tourism production T_i, whereas an increase in the regional average quality $\bar{q}$ may raise or reduce marginal revenue y_T, and leads to an increase or a cut-back of tourism service production. A higher tax rate on tourism production raises the firm’s marginal cost and results in lower production. Higher average regional tourism service quality increases the resident’s marginal utility of consumption, and as a consequence the agent increases her consumption of the traded goods. The effect of the average number of tourists on the resident’s consumption is ambiguous, however; it depends on the sign of $U_{c \bar{T}}$ , that is, on the regional situation; if tourism is still increasing the resident’s well-being, residents will raise consumption, if there is over-tourism, they will reduce consumption.

Note that in macroeconomic equilibrium, $q_{i} = \bar{q}$ , that is, the firm’s individual service quality coincides with the regional average quality. It follows therefore from equation (3a′) that

\frac{\partial T_{i}}{\partial q_{i}} |_{q_{i} = \bar{q}} = - \frac{y_{T q} + y_{T \bar{q}}}{y_{T T} - K ″} > 0

4a′

A region-wide increase in tourism service quality will therefore always induce firms to raise production of tourism services. In the decentralized regional market economy, tourism service quality and the number of tourists will therefore always move in tandem.

In macroeconomic equilibrium, consumption will react upon a change in tourism service quality in the following manner²⁸:

\frac{\partial c_{i}}{\partial q_{i}} |_{q_{i} = \bar{q}} = - \frac{1}{U_{c c}} [U_{c \bar{q}} - U_{c \bar{T}} ((\frac{y_{T q} + y_{T \bar{q}}}{y_{T T} - K ″}))]

4b′

If residents perceive tourism as desirable (i.e. $U_{c \bar{T}} > 0$ ), an increase in quality will induce residents to increase consumption. In case of over-tourism (i.e. $U_{c \bar{T}} < 0$ ), the consumption response is ambiguous. If the marginal utility of consumption falls a lot upon an increase in visitors (i.e. $U_{c \bar{T}} ≪ 0$ ), it is possible that residents reduce consumption.

The regional government, imposing taxes on tourism production and service quality, runs a balanced budget, that is

τ_{T} T_{i} + τ_{q} q_{i} = Z_{i}

where we note that in equilibrium individual and average quantities are equal. Assuming that tax revenues are redistributed to residents in a lump-sum fashion ensures that the use of government funds does not cause additional distortions.

Noting that in equilibrium $q_{i} = \bar{q}, T_{i} = \bar{T}$ , the linearized dynamic system of tourism quality q_i and its value, v, is given by

((\begin{matrix} {\dot{q}}_{i} \\ \dot{v} \end{matrix})) = ((\begin{matrix} 0 & 1 / C ″ \\ a_{21} & r \end{matrix})) ((\begin{matrix} q_{i} - {\tilde{q}}_{i} \\ v - \tilde{v} \end{matrix}))

5′

a_{21} \equiv - [y_{q q} + y_{q \bar{q}} + y_{q T} ((\frac{\partial T_{i}}{\partial q_{i}} + \frac{\partial T_{i}}{\partial \bar{q}}))]

where all derivatives are calculated at steady state. A mild sufficient condition for the sign of $a_{21}$ to be positive is $y_{T \bar{q}} \leq 0$ .²⁹ The dynamic system is therefore saddle-path stable, and the roots of the characteristic equation

ϕ (μ) = μ^{2} - r μ - \frac{a_{21}}{C ″} = 0

6′

have different signs, $μ_{1} < 0$ and $μ_{2} > 0$ . Tourism service quality and its value evolve over time according to

q_{i} (t) - {\tilde{q}}_{i} = (q_{i 0} - {\tilde{q}}_{i}) e^{μ_{1} t}

7a′

v (t) - \tilde{v} = μ_{1} C ″ (q_{i 0} - {\tilde{q}}_{i}) e^{μ_{1} t}

7b′

The saddle-path in the decentralized market economy and its transition dynamics toward steady state is similar to the one in the centrally planned region.

Combining the representative resident’s flow budget constraint (1e′) with the regional government’s budget constraint (13) and the short-run solutions ((3a′) to (3c′)), noting that in equilibrium $q_{i} = \bar{q}, T_{i} = \bar{T}$ , gives the regional per capita flow budget constraint

{\dot{a}}_{i} = r a_{i} + y (q_{i}, q_{i}, T_{i} (q_{i}, q_{i}, τ_{T})) - K (T_{i} (q_{i}, q_{i}, τ_{T})) - c_{i} (λ, q_{i}, T_{i} (q_{i}, q_{i}, τ_{T})) - C (I (v))

8′

Linearizing equation (8′) and solving it in the same manner as for the centrally planned regional economy, the per capita stock of traded assets follows then

a_{i} (t) - {\tilde{a}}_{i} = \frac{Ω}{μ_{1} - r} (q_{i} (t) - {\tilde{q}}_{i})

10′

where³⁰

Ω \equiv y_{q} + y_{\bar{q}} - μ_{1} - [\frac{\partial c_{i}}{\partial \bar{q}} + ((\frac{\partial c_{i}}{\partial \bar{T}} - τ_{T})) ((\frac{\partial T_{i}}{\partial q_{i}} + \frac{\partial T_{i}}{\partial \bar{q}}))]

Setting $t = 0$ gives the region’s intertemporal solvency condition in per capita terms.

Steady state in the decentralized region

The steady state in the decentralized regional economy is determined by the set of equations

\tilde{v} = 1; {\tilde{I}}_{i} = 0

14a

y_{q} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, T_{i} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, {\tilde{τ}}_{T})) - {\tilde{τ}}_{q} = r

14b

r {\tilde{a}}_{i} = c_{i} (λ, {\tilde{q}}_{i}, T_{i} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, {\tilde{τ}}_{T})) + K (T_{i} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, {\tilde{τ}}_{T})) - y ({\tilde{q}}_{i}, {\tilde{q}}_{i}, T_{i} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, {\tilde{τ}}_{T}))

14c

a_{i 0} - {\tilde{a}}_{i} = \frac{Ω}{μ_{1} - r} ((q_{i 0} - {\tilde{q}}_{i}))

14d

where we remember that in equilibrium individual and average tourism quality and quantity are equal ( $q_{i} = \bar{q}, T_{i} = \bar{T}$ ). First, steady-state investment in service quality equals zero again, and its value equals unity, see (14a). Second, the no-arbitrage condition (14b), equating the steady-state rate of return of quality $y_{q} - {\tilde{τ}}_{q}$ to the interest rate, determines then the steady-state level of quality, ${\tilde{q}}_{i} = \tilde{\bar{q}}$ . Third, having determined steady-state quality and thus the steady-state number of tourists (tourism production) ${\tilde{T}}_{i}$ , equation (14c) determines then the steady-state per capita stock of traded assets as a function of the marginal utility of wealth, ${\tilde{a}}_{i} (λ)$ . Equation (14c) says that any excess of regional expenditures on consumption and tourism production over the firms’ revenues has to be financed by interest income. Fourth, the regional intertemporal solvency condition (14d) determines then the equilibrium value of the marginal utility of wealth, from which the steady-state values of ${\tilde{a}}_{i}$ and the resident’s steady-state consumption ${\tilde{c}}_{i}$ immediately follow.

Comparison of centrally planned and decentralized regional economy

We now compare the centrally planned economy with the decentralized regional economy, in which small agents take decisions, given their circumstances, not taking into account the spillovers their decisions will cause. For reasons of comparison, we assume that the regional government does not intervene and sets the two tax rates $τ_{T}$ and $τ_{q}$ equal to zero.

The first thing to note is that the optimally chosen number of tourism services T_i and thus the number of tourists fundamentally differ. By comparing equations (2c) and (12c), one immediately sees that in the centralized economy, the effect of increasing the number of tourists on residents’ well-being is taken into account. In case that this spillover affects residents’ well-being positively, the decentralized market solution will produce too little tourism services; on the other hand, in case of a negative effect on residents’ well-being, too much tourism will be supplied, leading to the phenomenon of over-tourism.

Second, by comparing the no-arbitrage conditions (2e) and (12e), which equate the rate of return on quality to the interest rate, one sees that the central planner takes the spillover effects of quality on (i) other firms and on (ii) residents’ well-being into account, whereas in the market economy these “dividend yields” for the externalities of quality are not considered. Thus, in general, the social value of quality, $v^{*}$ , will differ from the private value of quality, v. As long as the externalities of quality constitute a net benefit, $v^{*}$ will in general larger than v,³¹ which in turn implies that investment into quality in the market economy will be lower than socially desirable.

Third, in market equilibrium, $q_{i} = \bar{q}$ . As shown in expression (4a′), in the decentralized economy tourism quality q_i and tourism quantity T_i always move in tandem, because the external spillover effects of service quality are not internalized. A higher quality increases firms’ marginal revenue, given the level of tourism production, inducing thus firms to raise the production of tourism services provided and sold to tourists. This result stands in sharp contrast to the centrally planned regional economy, where in case of sufficiently severe over-tourism quality and quantity are related by a trade-off and will move in opposite directions, see equation (4a). In this case, the positive effect of increasing tourism services together with the effect of higher quality on firms’ revenues and residents’ well-being does not outweigh the negative effect of higher tourism production on welfare. The reaction of residents’ consumption upon an increase in quality in case of severe over-tourism in the centrally planned economy (equation (4b)) also differs from its response in the decentralized market economy (equation (4b′)). Whereas in the centrally planned economy consumption increases with quality, the market economy consumption will fall. The reason is the different responses of tourism production (trade-off versus tandem).

Turning to the steady states of the centralized and the market economy, comparing the steady-state no-arbitrage conditions (11b) and (14b) shows that because in the market economy the effects of quality spillovers to firms’ revenues and residents’ preferences (i.e. the two “external dividend yields”) are not considered, the steady-state levels of quality in the decentralized economy and in the centrally planned region will differ in general, and in case that $y_{\bar{q}} + U_{\bar{q}} / λ^{*} > 0$ , which is automatically satisfied if $y_{\bar{q}} \geq 0$ , the decentralized market economy will operate at a lower than socially optimal level of quality, that is, ${\tilde{q}}_{i} < {\tilde{q}}_{i}^{*}$ .

Finally, the social value of quality, $v^{*}$ , will in general differ from the market value of quality, v, giving rise to different rates of investment into quality and therefore to a different evolution of quality and hence to different time paths the centralized and the market economy will follow. Therefore, in general $μ_{1}^{*} \neq μ_{1}$ . The speed of adjustment in the two regional economies is not the same, and the centralized regional economy and the market economy converge at different rates toward their steady states.

Because the central planner maximizes residents’ well-being by definition, well-being in the market economy will typically be lower than in the centrally planned region, because agents do not take spillover effects into account, implying that the government can improve residents’ well-being by introducing taxes or subsidies. In fact, the first-best optimum achieved in the centrally planned regional economy can be replicated in the market economy by appropriate taxation of tourism services and tourism quality. This is the task of the next section.

Replication of first-best optimum

The equilibrium corresponding to that of the centrally planned regional economy, derived in the third section, represents the welfare-maximizing first-best optimum, because the three spillover effects of the two externalities are fully taken into account. We now determine the specific taxes (subsidies) on tourism services, $τ_{T}$ , and quality, $τ_{q}$ , that will affect residents’ decisions in a way that the first-best optimum will be replicated. There are two general requirements to be met. The first is that the market economy must ultimately attain the steady state of the centrally planned regional economy. Second, having replicated the steady state, the transitional dynamic adjustment paths in the two economies must also coincide. In general, to achieve these two objectives, the optimal tax (subsidy) rates $τ_{T}$ and $τ_{q}$ must be time-varying (see Turnovsky, 1997).

Replication of steady state

We first consider the steady state. In order for the steady state in the two economies to coincide, the levels of tourism quantity and quality and the marginal utility of wealth in the two economies must be equal, that is, ${\tilde{q}}_{i} = {\tilde{q}}_{i}^{*}$ , $T_{i} = T_{i}^{*}$ , and $λ = λ^{*}$ . Given the socially optimal level of quality, the quantity of tourism services in steady state of the market economy is socially optimal if and only if equations (2c) and (12c) result in the same quantities of $T_{i}^{*}$ and T_i, that is

\begin{array}{l} y_{T} ({\tilde{T}}_{i}^{*}, {\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}) - K' ({\tilde{T}}_{i}^{*}) + \frac{U_{\bar{T}} ({\tilde{c}}_{i}^{*}, {\tilde{q}}_{i}^{*}, {\tilde{T}}_{i}^{*})}{λ^{*}} = y_{T} ({\tilde{T}}_{i}, {\tilde{q}}_{i}, \tilde{\bar{q}}) - K' ({\tilde{T}}_{i}) - {\hat{τ}}_{T} \end{array}

But this, in turn, requires to set the steady-state specific tax rate on tourism production ${\hat{τ}}_{T}$ equal to

{\hat{τ}}_{T} = - \frac{U_{\bar{T}} ({\tilde{c}}_{i}^{*}, {\tilde{\bar{q}}}^{*}, {\tilde{\bar{T}}}^{*})}{λ^{*}}

The optimal tourism tax rate equals the negative of the marginal utility of tourism production, measured in terms of the traded good. If tourism increases residents’ well-being, that is, $U_{\bar{T}} > 0$ , the steady-state tax rate on tourism production has to be negative, and tourism services have to be subsidized rather than taxed. In the case of over-tourism, tourism contributes negatively to residents’ well-being, and the steady-state tourism tax rate has to be positive.

Given that tourism production is at its socially optimal quantity $T_{i}^{*}$ , the market economy’s equilibrium level ${\tilde{q}}_{i}$ will be socially optimal if and only if the private and the social rate of return on quality are equalized. Given equal marginal utilities of wealth and tourism production rates, setting equations (2e) and (12e) equal gives

\begin{array}{l} y_{q} ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*})) + y_{\bar{q}} ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*})) + \frac{U_{\bar{q}} (c (λ^{*}, {\tilde{q}}_{i}^{*}), {\tilde{q}}_{i}^{*}, T_{i}^{*} (λ^{*}, {\tilde{q}}_{i}^{*}))}{λ^{*}} = \\ y_{q} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, T_{i} ({\tilde{q}}_{i}, {\tilde{q}}_{i}, {\tilde{τ}}_{T})) - {\hat{τ}}_{q} \end{array}

Solving for ${\hat{τ}}_{q}$ , the two quality levels will coincide if and only if the steady-state tax rate on quality is set equal to

{\hat{τ}}_{q} = - ((y_{\bar{q}} ({\tilde{q}}_{i}^{*}, {\tilde{q}}_{i}^{*}, T (λ^{*}, {\tilde{q}}_{i}^{*})) + \frac{U_{\bar{q}} ({\tilde{c}}_{i}^{*}, {\tilde{\bar{q}}}^{*}, {\tilde{\bar{T}}}^{*})}{λ^{*}}))

The optimal tax on tourism quality incorporates the two external spillover effects of average quality on firms’ revenues and residents’ well-being. It is equal to the negative of the two “external dividend yields” in steady state, caused by the externality, and results in an equalization of the market and the socially optimal steady-state rates of return on quality. In case that the sum of these two dividend yields is positive (i.e. $y_{\bar{q}} + U_{\bar{q}} / λ^{*} > 0$ ), tourism service quality has to subsidized in steady state; otherwise it has to be taxed.

Given both tourism service quality and the quantity of tourism production, replication the steady-state levels of consumption in the two economies requires that $λ^{*} = λ$ (see equations (2a) and (12a)). But this is only possible if the steady-state levels of traded assets ${\tilde{a}}_{i}$ are equal, too; otherwise the two consumption rates would have to differ (compare equations (11c) and (14c)). However, the two steady-state stocks of traded assets can be equal if and only if the intertemporal budget constrains of the two economies, (11d) and (14d), coincide, otherwise at least in one of the two economies the intertemporal solvency condition would be violated. This in turn requires the stable root of the two dynamic systems (5) and (5′) to coincide, too.

Replication of dynamic adjustment

This brings us to the second general requirement that the transitional dynamics need to be replicated. In general, if during transition the taxes on tourism quantity and quality in the decentralized economy are set according to (16) and (18), the adjustment path followed by the decentralized economy will fail to mimic that of the centrally planned regional economy.

The decentralized economy’s speed of adjustment can be modified by introducing a time-varying component to the two tax rates, based on the average level of service quality $\bar{q}$

τ_{T} (t) = {\hat{τ}}_{T} + θ_{T} (\bar{q} (t) - \tilde{\bar{q}})

19a

τ_{q} (t) = {\hat{τ}}_{q} + θ_{q} (\bar{q} (t) - \tilde{\bar{q}})

19b

where we again stress the fact that in equilibrium $\bar{q} (t) = q_{i} (t)$ . These time varying tax rates leave the steady-state taxes ${\hat{τ}}_{q}$ and ${\hat{τ}}_{T}$ , necessary to implement the socially optimal steady state, unchanged.³²

We first turn to the tax rate on tourism production $τ_{T}$ . As shown in Online Appendix A.2, $τ_{T}$ has to be time variant because the marginal utility of tourism in terms of output, $U_{\bar{T}} / λ$ changes over time. In Online Appendix, we derive

θ_{T} \equiv - \frac{1}{Δ λ^{*}} ((U_{\bar{T} \bar{T}} U_{c c} - U_{\bar{T} c}^{2}) (y_{T q} + y_{T \bar{q}}) - (y_{T T} - K ″) (U_{c c} U_{\bar{T} \bar{q}} - U_{\bar{T} c} U_{c \bar{q}}))

The sign of $θ_{T}$ is generally ambiguous. The first term in brackets, $(U_{\bar{T} \bar{T}} U_{c c} - U_{\bar{T} c}^{2}) (y_{T q} + y_{T \bar{q}})$ , is always positive. In case that $U_{c c} U_{\bar{T} \bar{q}} - U_{\bar{T} c} U_{c \bar{q}} > 0$ , which holds in case of over-tourism, the second term in brackets, recognizing the minus sign, is positive, too, and $θ_{T} > 0$ .³³ If $θ_{T} > 0$ , the tax rate on tourism services $τ_{T}$ has to be raised when the region’s average service quality $\bar{q}$ increases. On the other hand, if $θ_{T} < 0$ , the tax rate $τ_{T}$ has to be reduced when average quality $\bar{q}$ rises. If tourism creates a negative externality, the market would result in a too large number of tourists, and in steady-state tourism has to be taxed at rate ${\hat{τ}}_{T}$ . Suppose that quality is rising over time, and that the region suffers from over-tourism. In this case, the initial tax rate will be lower than in steady state and will thus have to be increased over time. Intuitively, when average quality increases over time, the negative spillover effect of tourism on residents’ well-being is reinforced, as in this case $U_{\bar{T} \bar{q}} < 0$ and $U_{\bar{T} c} < 0$ , causing a higher marginal social cost of tourism. To be internalized, the tax rate on tourism services has to be raised over time, reflecting the increasing social marginal cost of tourism.

The case $θ_{T} < 0$ can only arise if tourism causes a sufficiently strong positive externality on residents’ well-being. In this case, tourism will be subsidized in steady state, that is, ${\hat{τ}}_{T} < 0$ , and during transition the subsidy rate has to be lowered along with quality improvements, as the positive externality becomes smaller.³⁴ Note that in this scenario it is also possible that during transition the subsidy switches to a tax. This will be the case when albeit tourism will cause a negative externality in steady state, initially the number of tourists is so small that in a first stage of transition the externality is a positive one, calling for subsidizing tourism services.

Second, we consider the time varying tax rate on quality $τ_{q}$ . Inserting equation (19b) into the no-arbitrage condition (12e), changes the dynamics of the value of quality v in the following way:

\dot{v} = r v - y_{q} (T_{i}, q_{i}, \bar{q}) + {\hat{τ}}_{q} + θ_{q} (\bar{q} - \tilde{\bar{q}})

The market economy’s linearized dynamic system (5′) becomes then

((\begin{matrix} {\dot{q}}_{i} \\ \dot{v} \end{matrix})) = ((\begin{matrix} 0 & 1 / C ″ \\ b_{21} & r \end{matrix})) ((\begin{matrix} q_{i} - {\tilde{q}}_{i} \\ v - \tilde{v} \end{matrix}))

5″

where

b_{21} \equiv - [y_{q q} + y_{q \bar{q}} + y_{q T} \frac{\partial T_{i}^{*}}{\partial q_{i}} - θ_{q}]

The characteristic equation is

χ (μ) = μ^{2} - r μ + \frac{b_{21}}{C ″} = 0

6″

The speed of adjustment (i.e. the negative root of (6″)) is the same as the socially optimal value $μ_{1}^{*}$ if and only if the characteristic equation (6″) equals the centrally planned region’s characteristic equation (6). This is the case if and only if $a_{21}^{*} = b_{21}$ . As shown in Online Appendix A.3, this requires to set the tax rate’s speed of adjustment $θ_{q}$ equal to³⁵

\begin{array}{l} θ_{q} \equiv & - \frac{1}{Δ} [Δ (y_{q \bar{q}} + y_{\bar{q} \bar{q}}) - \frac{1}{λ^{*}} (y_{T T} - K ″) (U_{c c} U_{\bar{q} \bar{q}} - U_{c \bar{q}}^{2}) - \frac{Det [U_{i j}]}{{(λ^{*})}^{2}} \\ + (y_{T q} + y_{T \bar{q}}) \frac{1}{λ^{*}} (U_{c c} U_{\bar{q} \bar{T}} - U_{c \bar{T}} U_{c \bar{q}}) + U_{c c} (y_{T q} + y_{T \bar{q}}) y_{T \bar{q}}] \end{array}

A mild sufficient condition for $θ_{q} > 0$ is $U_{c c} U_{\bar{q} \bar{T}} - U_{c \bar{T}} U_{c \bar{q}} > 0$ , which holds in case of over-tourism. As this is a mild sufficient condition, it is highly likely that in general $θ_{q} > 0$ , which requires the tax (subsidy) rate on quality to be increased (reduced) when the region’s average quality $\bar{q}$ rises. In Online Appendix A.3, we also establish that the speed of adjustment in the centralized economy is larger than in the market economy with a time-invariant tax on tourism quality. Intuitively, if the market economy’s steady-state quality is too low compared to the centrally planned region, the steady-state tax rate ${\hat{τ}}_{q}$ has to be negative, and quality has to be subsidized. In addition, private agents do not take the spillover effects of quality on production and well-being during transition into account. Hence, in the market economy quality is accumulated too slowly. To correct for that, the regional government has to subsidize quality accumulation, but at a decreasing rate, with the subsidy becoming the smaller the closer quality is to its socially optimal steady state. The subsidy provides an additional benefit for firms investing in quality. If the subsidy is chosen optimally, the market economy will replicate the dynamics the centrally planned economy follows.

Policy implications, applications, and conclusion

Policy implications

The model derived in this article leads to several important policy implications. In the centrally planned regional economy, residents’ well-being is maximized by taking the various spillovers into account. With large tourism numbers (i.e. over-tourism), there is a trade-off between tourism quantity and quality, which requires that increases in the quality of tourism services must be accompanied by lower tourism production and hence a reduction in the number of tourists visiting the region. In a decentralized market economy however, agents rationally do not take the spillovers into account. Independent of how tourism is perceived by residents, tourism quantity and quality always move in tandem, and in general, the resulting market equilibrium will be sub-optimal as residents’ well-being is not maximized. This would justify an active role for regional governments attempting to improve their residents’ well-being.

Our general lesson is that the regional government may be able to replicate the dynamic adjustment and the steady state of the centrally planned regional economy and thus maximize residents’ well-being by imposing and adjusting the tax rates on tourism services and on tourism quality according to equations (19). In the likely case that the “multiple externality” caused by quality is positive, quality should be subsidized, inducing private firms to boost investment into quality. To cope with the changing dynamic environment, the subsidy should be reduced as quality improves over time.

The externality caused by tourism production, that is, the number of visitors, may be a positive or a negative one. In case that residents’ view tourism as a positive thing, improving their well-being, the market provides too little incentives for the right quantity of tourism production. The government should therefore subsidize tourism production. This lowers firms’ production costs and induces them to produce more services supplied to tourists and locals. However, the government must consider that more and more tourists will lower the improvements in residents’ well-being, and thus it is necessary to reduce the subsidy on tourism production over time. In case that the externality is extremely positive, it may be necessary to increase the subsidy as quality improves during transition. In case that residents feel harmed by tourism, that is if the region suffers from ever-larger tourist numbers (i.e. over-tourism), the government has to tax tourism. This increases the costs of tourism production. In this way, the negative spillover of tourism production to residents is internalized. As quality improves during transition, the tax on tourism should be raised over time. It may also happen that the regional economy is initially in a state with both a low number of tourists and low tourism service quality. In such a situation, residents would benefit from more tourism. This calls for a subsidy on tourism production. But as the region evolves and tourism service quantity and quality both increase, the marginal benefits of more visitors will become smaller and smaller and my turn into a marginal cost, and the externality caused by visitors switches then from being positive to being negative. Thus, the government should lower the tourism subsidy over time, as quality improves, and in an advanced stage of quality the subsidy should be converted into a tax, which increases together with quality.

Of course, “multiple externalities” are a complex issue, and implementing first-best policies is a difficult task. The regional government not only would have to know the economy’s socially optimal steady state, but also would need a lot of both scientific and private information to calculate the socially optimal speed of adjustment and to adjust the tax (subsidy) rates on tourism production and on service quality accordingly over time. Continuous monitoring and adjustments would be necessary. One may thus doubt if it is possible to install such a complex system of time-varying tax rates and could suggest that a direct control of tourism production and its quality may be preferable. However, this would require limiting the number of visitors and set quality standards not only once, but to adjust them continuously. Changes in regulations and standards would require a lot of bureaucratic effort, and their fulfillment by firms would have to be continuously monitored, which seems to be much more difficult to accomplish than to simply adjust tax rates, granting firms their freedom of choice. Finally, setting adequate incentives via a taxation scheme seems to be a better way than a direct interference into managerial decisions of tourism firms, which often results in other inefficiencies.

Applications

In this article, we develop a theoretical dynamic model of sustainable tourism development which considers the well-being of residents and external effects and trade-offs with external effects stemming from less sustainable tourism development. The concept of tourism quality is important for the underlying theory to be developed. Further research is needed to operationalize this concept in empirical analysis and applications. Uysal and Sirgy (2019) provide a series of examples for performance indicators of well-being in host communities including the multiple externality aspects outlined earlier. Any empirical application of our model would need to construct an index of these indicators modeling both the number of visitors and tourism quality aspects of destination development. These indicators could be modeled empirically using vector autoregressive VAR models as well as through a simulation analysis based on reasonable assumptions for a tourism quality indicator following form case studies. These case studies would apply the QOL indicators outlined by Uysal and Sirgy (2019) capturing resident well-being and the hospitality and tourism impact on community well-being as well as indicators of well-being for tourism and hospitality employees.

Conclusion

This article addresses the important issue of sustainable tourism development. It is well documented that tourism may be associated with multiple and often significant externalities, both positive and negative. These “multiple externalities” derive from tourism production and its service quality to firms and residents. We discussed how a benevolent central planner would govern a regional economy over time, taking into account the spillovers and possible trade-offs of quantity and quality. This is done by employing a model of a small open regional economy in which residents own tourism firms and have access to financial markets where they can borrow or lend at a given interest rate and where firms decide on tourism service production and on investments into service quality. In an economy, where quality is growing over time toward steady state, tourism production and service quality may move in tandem or in opposite directions, depending on the magnitude and sign of the spillovers. In case of large tourism numbers (e.g. severe over-tourism), quantity and quality should move in opposite directions.

A decentralized market economy, however, does not consider spillovers, as agents rationally do not take external effects into account when making their decisions. The resulting laissez-faire equilibrium is thus suboptimal from a social point of view, as residents’ well-being is not maximized. A regional government can improve residents’ well-being by introducing a time-varying system of taxes or subsidies. These taxes, if appropriately set, change the incentives of firms in a way that they behave in a socially optimal way, resulting in a more sustainable tourism development. When looking at the initially cited examples of cities experiencing over-tourism (e.g. Venice, Dubrovnik), important lessons can be observed. While taxation of visitors may reduce tourist numbers, an appropriate policy response may require additional investments in quality, satisfying remaining visitors and residents.

One might argue that theoretical models like this one are little more than complex mathematical abstractions. But such an abstract view of a regional economy provides important insights which are often unavailable through alternative approaches (Tyrrell and Johnston, 2008: 15). Our model shows that the externality spillovers caused by visitors and by quality investments are complex and that, depending on the concrete economic situation, particular policy combinations should be implemented and adjusted over time. We view our model as an important contribution to the ongoing debate on sustainable tourism development and over-tourism, providing valuable insights and suggesting appropriate policy responses.

Of course, the case of a small regional economy completely specialized in tourism production is an extreme one. A natural extension of the model would be to add a second sector which produces a traded or non-traded good, which may be consumed and/or invested.

Despite it is plausible to assume that higher tourism revenues y imply more employment, as either more tourists are served or/and better quality is produced, augmenting the model by explicitly including a labor market would be a possible extension. In such an extended model, the representative resident derives utility from leisure (disutility from labor), and offers labor to firms, which employ labor in the service production and probably also for changing service quality q.³⁶ One could also include “imported” labor, which foreigners or seasonal workers offer. One also might add capital as another input and introduce a tourism service production function. While we view the inclusion of labor or capital as an interesting extension, the model would become more complex without adding much to our results. As a starting point, it is thus convenient to use tourism services y as a proxy for employment and to abstract from capital formation.

One could also allow non-residents to own regional tourism firms, which hire residents’ labor to produce tourism services. In such a model, the resident would own traded bonds and would offer her labor, whereas the owners of firms would extract profits, affecting thus the current account.

With such extensions, the model would become more realistic but its complexity would substantially increase. However, our basic insight that at a system of time-varying taxes (subsidies) is necessary to maximize residents’ well-being would not be affected in a qualitative manner. Hence, our parsimonious model is a natural starting point for further research in the area of sustainable tourism development employing a dynamic general equilibrium framework.

Supplemental material

Supplemental Material, sj-pdf-1-teu-10.1177_1354816620934552 - Sustainable tourism development: A dynamic model incorporating resident spillovers

Supplemental Material, sj-pdf-1-teu-10.1177_1354816620934552 for Sustainable tourism development: A dynamic model incorporating resident spillovers by Stefan F Schubert and Günter Schamel in Tourism Economics

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are grateful for financial support from the Free University of Bozen.

ORCID iD

Stefan F Schubert

Notes

Supplemental material

Supplemental material for this article is available online.

Author biographies

Stefan F Schubert started his appointment as an associate professor of Economics at the Faculty of Economics and Management of the Free University of Bozen - Bolzano in January 1st 2011. From November 2005 to December 2010 he was assistant professor of Economics. Formerly he was an assistant professor at Ludwig-Maximilians-University Munich, Germany (LMU), where he received his PhD in Economics in 2002. Schubert’s research interests comprise macroeconomic dynamics with a particular focus on the open economy and tourism economics. Currently he works, inter alia, on economic growth and unemployment. In 2013, Schubert received the “2013 Thea Sinclair Award for Journal Article Excellence” for the paper: Schubert S., Matias Á. and Costa C. (2012): A General Equilibrium Analysis of Casino Taxation in Portugal, Tourism Economics, Vol. 18, No. 3, 475–494.

Günter Schamel is an agricultural/applied economist with research interests related to wine, tourism and cooperatives. He received his PhD from the Dyson School of Applied Economics and Management at Cornell University and an MSc from UC Davis. Prior to joining unibz, he was professor at Humboldt University Berlin, had visiting appointments at Iowa State and Adelaide University, taught at Cornell, TUM, BSB Dijon and worked for the World Bank. He is a Fellow of the American Association of Wine Economist (AAWE) and affiliated with the Wine Economics Research Centre at Adelaide University, the Robert Mondavi Institute Center for Wine Economics at UC Davis and Bordeaux Wine Economics. He is a Board Member for AAWE, the Journal of Wine Economics (JWE) and Wine Economics and Policy (WEP).

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