A tourist tax in a vertically segmented destination with congestion effects

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Abstract

We present a model of a two-segment tourist destination where there are externalities of congestion, both within and across segments. We show that when intersegment sensitivity to congestion from low to high category is sufficiently large, then a well-designed per-person tourist tax can increase local social welfare, while also increasing industry aggregate profit. In particular, it is profit maximizing to only tax the low segment, until it creates no externality on the high segment. Intervention is more likely to be optimal when the high category segment would be sufficiently more profitable (absent intersegment congestion) than the low category one. While a uniform tax on both segments may increase local welfare, it always decreases aggregate industry profits.

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Public Economics
Taxation Policy
Tourism Economics
Tourism Management
Urban Economics
Transportation Economics

1 Introduction

Since the Covid-19 pandemic ended, overtourism has returned as an important phenomenon for many destinations. In this paper, we argue that a Pigouvian tourist tax can and should be a key instrument in the toolbox of the local public authorities (LPAs) vis à vis overtourism; in fact, we show that a well-designed tourist tax may be beneficial even for the local providers, before valuing its positive effects on other stakeholders.

The tourism industry is large and growing, in terms of the number tourists, as well as in terms of its contribution to, for instance, GDP and employment. In 1995, the five main receiving countries—France, Spain, US, Italy, and Turkey—hosted a total of 189.11 million international tourists, a figure that almost doubled in 28 years, reaching 363.89 million in 2023. In particular, France, as the top host: received 60.04 million in 1995, and closed 2023 with 100 million tourists. Spain, in 1995 with 32.97 million tourists, exceeded 85 million in 2023, positioning itself as the second most visited country in the world (UNWTO, 2024). The importance in GDP has also been increasing; take Spain, where tourism represented 12.6% of GDP in (pre-pandemic) 2019, and 12.7% of employment, and it is expected to surpass this level in 2024 (Caixabank Research, 2024). Moreover, most forecasts predict that global tourism (visitors, GDP, employment) will continue to grow for the years to come. Overall, thus, we should expect that overtourism and its effects in many destinations are likely not only to persist but to increase, unless properly managed.

In particular, overtourism occurs when the impact of tourism (as measured by, say, the number of tourists, or tourist density) surpasses a destination’s physical, ecological, social, and psychological capacities, which refers to the maximum number of tourists a location can host without adverse effects on local communities or fellow visitors. Our analysis mainly focuses on the latter, on how overtourism affects the tourist experience and destination appeal, highlighting that perceived crowding often detracts from the experience. A tourist tax is thus justified because of congestion degrading the tourist experience, as overcrowding can stress resources, reduce aesthetic value, and deteriorate public services.

It is no great feat to show that Pigouvian taxes can decrease the negative externalities of overtourism.^Footnote1 The more interesting question is: at what cost to the industry? Thus, in the main, we focus attention on the bottom line of the destination’s lodging industry. Taxes reduce the—well documented—negative effect that congestion may have on the tourist experience at the destination.^Footnote2 In addition, taxes also serve as a collusion device, mitigating the tragedy of the commons, by lowering production. The taxes’ beneficial effects on other stakeholders, like local residents, are thus considered as a (positive) externality instead of drivers of our results.

As it will become clear, a key building block of our analysis is to model the industry as being composed of two vertically differentiated segments. These operate as separate markets, while capturing the phenomenon that the congestion externality exists not only within segments, but also across segments. We assume that the H-segment tourists (who value and can afford exclusivity) are affected by crowds of L-segment tourists (much) more than the other way around. An intervention, like the tax we consider, can thus have a positive effect on industry profits by changing the composition of the destination’s tourist demand, switching demand from the L segment (with lower income/willingness to pay, WTP) to the H segment (with higher income/WTP for high quality).

We start with the benchmark analysis of a LPA that sets a uniform tax on both segments, so as to maximize total local surplus: the sum of profits, tax revenue and externalities on local residents.^Footnote3 We leave out consumer surplus from the objective as tourists are not local. As expected, we find that it is optimal to set such a per person-stay uniform tourist tax, which displays the intuitive comparative statics.

Next, we turn to our main analysis, that of an LPA that has been ‘captured’ by the local industry, and thus only cares about industry aggregate profits. While in some cases, unfortunately, this is not unrealistic, we mainly think of it as a thought experiment, to evaluate whether it could be the case that the local providers should be in favor of such a tax set on both market segments. Our initial response is negative: We prove that aggregate profits are maximized when a uniform tax is zero. However, when we allow the LPA to use a differentiated tax system, setting different taxes in different segments, the result becomes markedly different: when the intersegment sensitivity to congestion is sufficiently large, it becomes aggregate profit maximizing, not only to tax, but to impose a tax sufficiently high so that the intersegment congestion externality disappears. This intervention hurts the profits of the L segment, but increases the profits of the H segment by more. Thus, in principle, adding a transfer from the H to the L segment could lead to a Pareto improvement for all providers.

It is of course well known that taxes are the typical prescription against congestion externalities (See the next section for a brief description of existing tourist tax regimes). What our analysis shows is that, while clearly beneficial at a congested tourist destination when considering all its effects (on residents, natural environment, etc.), taxes would hurt industry net profits (abstracting from spillovers from tax revenues) at a single-segment destination, that is, with a single type of tourist, or when constrained to a uniform tax.^Footnote4 What we show instead is that in a vertically segmented industry, judiciously chosen taxes may increase aggregate net industry profit at the destination.

The rest of the paper is organized as follows. We start by discussing the related literature in Sect. 2. In Sect. 3, we introduce our model, and in Sect. 4, we characterize the market equilibrium, in the absence of any intervention. Section 5 discusses the optimal tax set by an LPA maximizing local welfare. Section 6 contains the analyses of a profit maximizing LPA, first with a common tax and then with segment specific taxes. We discuss our results in Sect. 7, while Sect. 8 provides concluding remarks. Proofs not in the main body of the paper are relegated to the Appendix.

2 Related literature: overtourism and tourist taxes

As Peeters et al. (2018) state in their Report for the European Parliament, overtourism can be defined as “the situation in which the impact of tourism, at certain times and in certain locations, exceeds physical, ecological, social, economic, psychological, and/or political capacity thresholds”. Overtourism is linked to tourist numbers, the type and time frame of their visit, and a destination’s carrying capacity, but the perspectives on overtourism may of course vary among its various stakeholders, such as residents, tourists, or businesses.^Footnote5

As stated above, the focus of our analysis of overtourism is on the negative effect that it may have on the tourist experience: on the loss it may cause in the destination’s attractiveness.^Footnote6 There is plenty of literature on the influence that tourist density/congestion/crowding at a destination has on the tourist experience (see, for example, Vaske and Shelby (2008); Yin et al. (2020).)

In our analysis, there is a rationale for a tourist tax only when the number of tourists generates congestion, namely, when a place becomes too crowded, diminishing the tourist experience. As Gago et al. (2009) explain, “mass tourism may diminish the quality of the tourist experience through congested and overcrowded facilities, psychological stress on local users and visitors, and faster deterioration of natural resources and public services, resulting in the loss of aesthetic value”.

There are several empirical studies on the impact of overtourism on the tourist experience. Jurado et al. (2013), study the Costa del Sol in Má laga (Spain), showing that 26% of its tourists interviewed view the destination as having too many tourists. This is significant proportion, especially considering that these are tourists with high income and WTP, and also that many of the tourists more negatively affected by crowding likely stopped visiting the destination. Tokarchuk et al. (2022) show that for the city of Berlin positive emotions to crowding show an inverted U shape in the number of tourists, while negative emotions show a U shape.^Footnote7

2.1 Tourist taxes

What do we mean when we talk about a tourist tax? First, it is important to point out the obvious: the tourism sector, which includes various subsectors such as transportation, accommodation, entertainment, and restaurants, is subject to the same taxes as the rest of the economy, such as corporate tax, personal income tax, and VAT. However, it is also worth noting that it is often the case that the VAT on hotels, restaurants, and domestic air transport is lower than the general one (in Spain, for instance, it is only 10%, compared to the general VAT rate of 21%).

Hence, when referring to a tourist tax, it typically means accommodation taxes, which charge an amount per person and overnight stay. This type of tax is referred to as an“occupancy tax”or “accommodation tax”in the 2017 report titled The Impact of Taxes on the Competitiveness of European Tourism by PwC for the European Commission.

In this report (PwC (2017), pp 36–37, Table 5), it is shown that these accommodation taxes range from a minimum of €0.10 (in Bulgaria) to a maximum of €7.50 (in Belgium) per person per night, with the average falling between €0.40 and €2.50. The same report notes that“these rates are low compared to hotel prices.”Since these figures date back to 2017, it is likely that the rates have increased somewhat, due both to inflation and to growing concerns about over-tourism. Current figures, while somewhat larger, lie within the same ball park. For example, the sustainable tourism tax approved in the Balearic Islands in 2017, whose initial rate was later doubled, is a maximum of €4 per person per night in 5-star hotels and up to €2 for 3-star establishments or lower. In Barcelona, the maximum rate is currently €7 for 5-star hotels and €4.25 for 3-star hotels or lower. By comparison, in Paris, the maximum rate is €14.95 per person per night for a stay in a“palace”(sic) and €2.60 in 1-star hotels.^Footnote8

While in our view tourist taxes are given too little consideration in the policy debates on how to address overtourism, there is a relatively abundant academic literature studying them (see PwC (2017), for an overview). Gago et al. (2009) explain that (indirect) tourism taxes can be justified on three grounds: (i) revenue-raising objectives, (ii) coverage of conventional costs of public services, and (iii) internalization of external costs. Our analysis shows that there may indeed be complementarity between the rationales when congestion effects are significant.

We are of course not the first ones to point out that tourism taxes can play a role in a context of congestion effects. Gago et al. (2009) themselves state that “tourism taxes could have significant direct effects on the quality of tourism demand and the magnitude of the added value generated by the sector through reduced congestion and an increased willingness to pay by tourists”. Pintassilgo and Silva (2007) even analyze formally the tragedy of the commons present in a tourism destination because of environmental externalities, and point to the potential role that taxes can play in addressing the tragedy of the commons. But neither of these papers, nor any other one to our knowledge, do what we do, a formal study of the role that a per-person tourist tax can play with regards to industry profits at a congested destination. The likely reason for this hiatus is that in a one-segment market the taxes we are considering are never optimal for the industry when abstracting away from other stakeholders, as we do.

Academic research on the tourist tax has to a large extent been empirical, analyzing for instance the effect that such a tax may have on a destination’s demand (studying the price elasticity of the destination’s demand). As an example, Aguiló et al. (2005) evaluate the effect of the tax approved in the Balearic Islands on the destination’s demand (see also Adedoyin et al. (2023); Gooroochurn and Sinclair (2005), for examples of similar analyses in other destinations). Gago et al. (2009) apply tourist taxes in a general equilibrium model of the Spanish economy, so as to study their effect and assess the relative merits of a fixed versus a value-added tax. Logar (2010) discusses the appropriateness of an eco-tax in Crikvenica (Croatia), among other policy tools, with common arguments about its usage as a way to “enhance the environmental quality of Crikvenica”. Other papers analyze the potential role that taxing tourism might play in the context of the Dutch disease attributed to a growing tourism sector (see Sheng (2011); Chang et al. (2011), for empirical analyses, and Inchausti-Sintes (2015), for a general equilibrium model analysis).

Transportation economics also provides valuable insights into the use of taxes as tools to mitigate congestion and manage the externalities associated with high volumes of activity in specific areas. Toll taxes, for instance, have long been employed to regulate traffic on highways and bridges, charging users for access and thereby incentivizing more efficient transportation behaviors. Similarly, congestion charges in city centers, such as those implemented in London or Stockholm, aim to reduce road congestion by imposing fees on vehicles entering high-traffic areas during peak times (Börjesson et al. 2012; Gibson and Carnovale 2015).

Finally, there also is a general literature on the incidence of (indirect) taxes on markets of oligopolistic competition. Particularly relevant to our study are Seade (1985); Dierickx et al. (1988). The first paper argues that due to the “overproduction” in Cournot competition a tax might increase industry profits but only if the demand function satisfies a certain condition (on the elasticity of the slope of demand) and firms are heterogeneous. The second argues that taxes shift demand between low and high cost firms, and as a result can benefit a subset of firms. They do not check the aggregate effect on the industry. We have not found any paper that addresses a two-segment market, with homogeneous cost structure, even without considering congestion externalities.

3 The model

We represent a tourist destination by two interconnected market segments for accommodation. In the high category (H) segment there are $n_{H}$ firms and in the low category (L) segment there are $n_{L} \geq n_{H}$ firms. For simplicity, we assume that, within a category, firms are identical, have no (binding) capacity constraints, have no fixed costs and have constant (zero) marginal cost of production. They compete à la Cournot: each firm i (in segment $j = H, L$ ) simultaneously and independently sets the quantity of tourists it is willing to serve: $q_{j}^{i}$ .^Footnote9,^Footnote10 The aggregate quantity of lodging available in segment j is then $Q_{j} = \sum_{i \in j} q_{j}^{i}$ . As the prices adjust to clear each market segment, all the lodging offered is taken and the total mass of tourists visiting the destination is $Q = Q_{H} + Q_{L}$ .

There is a continuum of consumers, divided into two groups depending on which category of lodging they wish to consume. That is, for tractability, we assume that which segment a consumer belongs to is exogenously fixed. A possible justification for this assumption is a type of income effect (after all, tourism is a luxury good): H consumers have no demand for L lodging, while the (equilibrium) price of H lodgings exceeds the valuation/budget of L consumers.^Footnote11

Each tourist visiting the destination consumes one unit of lodging. The net (quasilinear) utility potentially obtained by a segment j consumer is

(1)

where $r_{j}$ stands for the gross utility derived from a lodging of category j (assuming no other tourists present), $p_{j}$ is the market-clearing price and $b_{j}$ and $c_{j}$ measure the consumers’ sensitivity to congestion in their own segment and in the other segment, respectively. $a_{j}^{'}$ is the bliss amount of fellow tourists within the segment: they wish to have more “company” below this level, and less above it. Across segments, they are not bothered by the first $a_{- j}$ measure of tourists of the other type.^Footnote12

Obviously, $r_{H} >> r_{L}$ . It is also reasonable to assume that $c_{H} > c_{L}$ and $b_{H} > b_{L}$ : guests of high category hotels appreciate relative exclusivity more than those of low category. In order to significantly simplify the analysis, we take this observation to the limit and assume $c_{L} = 0$ (and $c_{H} = c = c_{H} - c_{L}$ ): only tourists visiting the H segment are affected by inter-segment congestion, so c actually measures the difference in inter-segment sensitivity to congestion.^Footnote13 Comparing the intra- and intersegment sensibilities to congestion, it is reasonable to assume that the fellow tourists, with whom there is more commonality of interest, create more congestion: $b_{j} > c$ , $j = 1, 2$ . Regarding the threshold quantities, it makes sense to assume that, as long as tourists would prefer to have more tourists in their own segment, tourists of the other segment are not bothered by these: $a_{j}^{'} \leq a_{j}$ .

As our focus is on a mature destination suffering from congestion, we will restrict attention to parameter configurations such that—absent any intervention—the equilibrium measure of tourists exceeds the optimal value both within and across segments: we have overtourism. Formally, we assume that $a_{H}^{'} < Q_{H}$ and $a_{L} < Q_{L}$ , and consequently, (1) can be simplified to^Footnote14

(2)

Finally, tourists have heterogeneous outside options that they value in net utility terms. The distributions of these opportunity costs are denoted by $G_{j} (u)$ , meaning that in segment j thereare $G_{j} (u)$ measure of potential tourists with outside options valued at less than u. In reality, the $G_{j} (.)$ curves are likely to be concave, growing to an asymptote (corresponding to the total amount of potential tourists in the segment). The relevant characteristic is that the two curves do not cross: there are more budget-constrained tourists with opportunity cost below any value. To capture this while maintaining tractability, we assume that the distributions are uniform: $G_{j} (u) = u / s_{j}$ .^Footnote15 Note that this implies that a higher $s_{j}$ corresponds to fewer tourists from the j segment. As in reality the budget-constrained segment tends to be larger, $s_{H} > s_{L}$ .

4 The market equilibrium

To provide a benchmark, in this section, we solve the model in the absence of any intervention. We start by deriving the number of tourists that each segment will serve in equilibrium. The outcome of the L segment corresponds to a standard independent Cournot equilibrium (modified by the intra-segment externality). The H segment, however, is affected by the congestion generated by the L segment, and thus it clears as a function of the outcome in the L segment.

The marginal tourist in each segment is indifferent between her/his outside option and visiting the tourist destination: $Q_{j} = G_{j} (u_{j}) =$ $u_{j} / s_{j}$ , and thus $u_{j} = G_{j}^{- 1} (Q_{j}) = s_{j} Q_{j}$ . Letting $R_{j} = r_{j} + a_{j}^{'} b_{j}$ , from (2), the (inverse) demand functions in the two segments are given by^Footnote16

(3)

Note that an increase in the amount of tourists in a segment decreases the equilibrium willingness to pay at two margins: the (intra-segment) externality margin, captured by $b_{j}$ , and the entry margin (for more tourists to come—that is, give up their outside options—their net utility must be higher, so ceteris paribus the price must decrease), captured by $s_{j}$ . Due to the linearity of our model, these values simply add up: the sensitivity to intra-segment congestion is a perfect substitute for the slope of the supply curve of tourists.

From (3) the following proposition can be directly obtained (see the detailed proof in the Appendix). Let $M_{j} = \frac{n_{j}}{(s_{j} + b_{j}) (n_{j} + 1)}$ , then:

Proposition 1

The equilibrium number (measure) of tourists visiting each segment is^Footnote17

As expected, both markets sell higher quantities when there are more firms, $n_{j}$ , or when their customers have higher intrinsic valuations, $r_{j}$ or higher optimal level of intra-segment congestion, $a_{j}^{'}$ (as long as it is below the actual, $Q_{j}$ , by our assumption of overtourism). We can also observe that the sensitivity to intra-segment congestion, and the slope of the (inverse) demand curve of tourists have a negative effect: both $b_{j}$ and $s_{j}$ decrease the amount of tourists willing to come to segment j, ceteris paribus.^Footnote18 In the H segment, we have the additional effect that the intrinsic valuation of tourists, $r_{H}$ , is lowered, in proportion to the equilibrium measure of “excess” L tourists weighted by the inter-segment congestion sensitivity, c.

Knowing the equilibrium quantities, we can read off from the “tourist-supply curves”, $G_{j}^{- 1} (Q_{j})$ , the utility obtained by a representative tourist in each segment.

Corollary 1

The equilibrium utilities obtained by the tourists are

and

By construction, the more tourists decide to visit, the higher is their utility as they have to give up higher outside options. The rest of the comparative statics coincide with those of the aggregate quantities in each segment. The negative relation between the H tourists’ well-being and the quantity of L tourists is salient. In particular, note that H tourists would benefit from a more concentrated L market (lower $n_{L}$ ).

Given the equilibrium quantities, via the demand curve (3), we can also easily obtain the equilibrium prices.

Corollary 2

The equilibrium prices in each segment are

Prices in a segment decrease in the number of firms and increase in the consumers’ valuation, as standard. The H segment’s price also decreases in $c (Q_{L}^{*} - a_{L})$ , reacting to the negative externality. Finally, prices are increasing in the intra-group sensitivity to congestion, $b_{j}$ , and in the optimal amounts of tourists, $a_{j}$ and $a_{j}^{'}$ .

Multiplying prices and quantities—recall that we assumed costs away –, we can calculate the aggregate profits that each segment makes in equilibrium.

Corollary 3

In equilibrium, per segment aggregate profits are

and

The within segment comparative statics are as expected: in the L-segment aggregate profits are increasing in the consumers’ valuation but they are decreasing in L-tourist scarcity, and in the number of competing firms. If $a_{j}^{'}$ is sufficiently low, profit is also decreasing in intra-segment sensitivity to congestion, $b_{j}$ . In the H segment we have the same effects, complemented by the negative effects of inter-segment consumer sensitivity to congestion, and the quantity of L tourists.

For the subsequent analysis it will be important that the H firms would benefit from a decrease in the L tourists’ valuation of the L firms’ product, despite the fact that we have assumed away competition between the two segments for tourists: $\frac{d Π_{H}^{*} (R_{L}, R_{H})}{d R_{L}} < 0$ . The mediator is once again congestion: if L tourists value their lodging less, fewer of them will come, $\frac{d Q_{L}^{*}}{d R_{L}} > 0$ , what will decrease (inter-segment) congestion and thus increase the H firms’ profits, $\frac{d Π_{H}^{*} (R_{L}, R_{H})}{d Q_{L}^{*}} < 0$ .

5 The local public authority’s problem

Before turning to our main contribution, relative to the tax maximizing aggregate profits, it is useful to see how a “traditional” social planner would set taxes. We model taxes as fixed amounts to be paid by each tourist in each segment (akin to ‘occupancy taxes’ in PwC (2017)) and first consider a uniform tax imposed on both segments. The usual welfare function has three components: profits, consumer surplus, and tax income (presumably converted into public goods). In our setting, this needs to be adjusted: the consumers are non-residents, and as such their welfare does not enter (at least directly) into the local authority’s objective. On the other hand, residents suffer from the externalities generated by the tourists. Consequently, we replace the traditional consumer surplus with the loss of utility caused by tourism on the residents.^Footnote19 To model this loss, we denote the coefficient multiplying the aggregate measure of tourists by z. As this section is only to provide a benchmark, for simplicity, we assume $a_{L} = 0$ .

The key observation toward finding the effects of a tourist tax in our model is that a tax of t is equivalent to a reduction of the intrinsic valuation, R, by t: valuing at $R - t$ is the same as valuing at R and having to pay t (extra). Thus, using Corollary 3 for the profits, and Proposition 1 for the quantities, our welfare function becomes

Proposition 2

The optimal uniform tax set by the LPA is strictly positive for non-negative c and z, and it is increasing in z until it leads to closing down the L segment. Moreover the higher is c, the slower the tax grows with z.

As expected, it is optimal for the local authority impose a non-negative uniform tax on both segments. Importantly, while the tax is increasing with the sensitivity of local residents, the incentives to tax are present even if they do not suffer a negative externality. Absent intersegment externalities, the tax is still positive, underlining the importance of the income generation motive. Additionally, the externalities on tourists (of the other segment) are substitutes to the externalities on residents: when the taxes are already there for one reason, they react less to the presence of the other reason.

Unsurprisingly, with the optimal tax of the LPA the service providers lose out. While this result is not obvious, due to the overproduction in Cournot competition coupled with the intersegment externalities, it holds, as a corollary of the result in our next section, where we calculate the optimal uniform tax when the LPA maximizes aggregate profits, ignoring the rest.

While it stands to reason that the LPA does not incorporate consumer surplus in its objective function, the amount and welfare of tourists are still key performance indicators. The following corollary describes the changes in these variables due to the imposition of a tax.

Corollary 4

Both the number of tourists, $Q_{j}^{*}$ , and the consumer surplus, $u_{j} Q_{j}^{*}$ , are decreasing in t in both segments.

Note that this result implies that if for some—political, legal, moral—reason the LPA decided to incorporate consumer surplus in its objective, the resulting trade-off would imply a lower tax.

Of course, if the LPA were able to set different taxes in the two segments it would still find that a positive tax is optimal (in at least one segment). While the analysis of this case would be straightforward, we do not consider it a relevant benchmark: What we wished to demonstrate in this section was that a welfare maximizing LPA would impose taxes, even if they had to be uniform.

6 A tourist tax imposed for industry profit

Having described how the local authority should tax, in this section we investigate the effects of taxes on industry profits (at the destination). As we discussed in the introduction, this could be thought of as the local authority being ‘captured’ by the hotel lobby. The question we wish to explore is: under what circumstances—if any—will such a tax benefit the industry as a whole, namely by increasing the aggregate profits across the two segments? To tilt the balance against our result, we eliminate the two main causes for the local authority to impose a tax: we suppose that the tax revenue is considered “lost” to the local industry: it is collected by the LPA and spent on unrelated issues. Similarly, the externality on the local residents is ignored. In this section we reintroduce $a_{L} > 0$ to increase the generality of our result.

Let the LPA maximize $Π (t) = Π_{L}^{*} (R_{L} - t) + Π_{H}^{*} (R_{L} - t, R_{H} - t)$ .^Footnote20

Proposition 3

When the objective is to maximize aggregate profit, it is never optimal to impose a uniform tax on both segments.

Thus, we see that the service providers’ problem is not just that the LPA sets too high a tax because of its additional taxing motives, rather that it sets a tax at all. The benefits of lower congestion and lower output do not compensate for the loss in demand. However, as we show next, the situation is markedly different when the taxes need not be homogeneous across segments.

6.1 Segment specific taxes

In the previous subsection, we have seen that when the LPA is restricted to setting a uniform tax for the segments, the service providers lose out for certain. It is therefore of interest to investigate whether this result changes if the LPA is allowed to set different taxes in each segment. As it will be clear from Proposition 4 below, if $c = 0$ , and thus the two segments operate independently, there is no room to impose a tax. The intra-segment externality, captured by $b_{j}$ , is sufficiently internalized by the hotels, so that it is too expensive to correct via a tax the revenues of which are discarded. Thus, the result below crucially depends on the existence of two interconnected market segments and two taxes.

Let the LPA choose taxes $(t_{L}, t_{H})$ that maximize^Footnote21

(4)

Let $A = \frac{R_{H}}{M_{L} R_{L} - a_{L}}$ and $B = \frac{(n_{H} + 1) (M_{L} R_{L} + a_{L})}{(n_{L} + 1) M_{H} M_{L} (M_{L} R_{L} - a_{L})}$ .

Proposition 4

It is profit maximizing not to tax the H segment, $t_{H}^{*} = 0$ , while if c is sufficiently high the L segment is taxed so that $Q_{L} = a_{L}$ , otherwise it is not taxed either,^Footnote22

It is intuitive that the H segment is not taxed as the profits of the H segment are decreasing in $t_{H}$ while those of the L segment are independent of it. This result is less obvious than it may sound at first sight. The reason is that in the non-cooperative Cournot equilibrium the firms ignore the negative externality imposed on their competitors when increasing their supply. Consequently, the equilibrium leads to oversupply from the point of view of industry (segment) profits, a typical case of the “tragedy of the commons”. Imposing a tax leads to a reduction in quantities what ceteris paribus would increase profits via higher prices. However, the taxes also impact on the prices directly, since the consumers’ valuation decreases, shifting demand downwards. The second effect outweighs the first, and $p_{H}$ actually decreases with $t_{H}$ (together with $Q_{H}$ ).

On the other hand, the optimal tax in the L segment must also consider the effect it has on the profits of the H segment. As we have seen, the H segment’s profits are decreasing in $R_{L}$ and, consequently, they are increasing in $t_{L}$ , as long as $Q_{L} > a_{L}$ . Of course, just as with the H segment above, the L segment’s profits are decreasing in $t_{L}$ . Consequently, it never pays to increase taxes above the level that would lower $Q_{L}$ to $a_{L}$ . Otherwise, the trade-off depends on the strength of the externality, c, and on the relative profitability of the two segments. If the H segment (absent inter-segment externality) would be sufficiently profitable relative to the L segment, and c is sufficiently high, then it is optimal to increase $t_{L}$ until it restricts the L segment to $Q_{L} = a_{L}$ .^Footnote23 Otherwise, no tax can increase industry profits ( $t_{L}^{*} = 0$ ). As natural, the need for the restriction is less likely, the higher the lower bound for the cross-segment congestion externality, $a_{L}$ is.

It is straightforward to establish that $c^{'}$ is decreasing in A and $- B$ . This implies the following corollary.

Corollary 5

The threshold intersegment sensitivity to congestion, $c^{'}$ , is decreasing in $r_{H}$ , $- s_{H}$ , $- b_{H}$ , $- n_{H}$ , $- r_{L}$ , $s_{L}$ , $b_{L}$ , $n_{L}$ and $a_{L}$ .

Thus, agreeing with intuition, an intervention is more ‘likely’ if the H consumers value their stay more, if there is more of them, they are less sensitive to intra segment congestion, their segment is less competitive; the L consumers value their stay less, there is less of them, they are more sensitive to intra-segment congestion, their segment is more competitive. Note that these comparative statics practically say that intervention is optimal if the H segment is sufficiently more profitable than the L segment, similarly to the observation we have made above (which only ensured that $c^{'}$ exists).

Note that we have a bang-bang solution for $t_{L}$ : either no tax or “full” tax. This is a consequence of the convexity of the profit function in the consumer’s WTP and—consequently—also of the tax, which is just a reduction of the former. This convexity comes from profits being the product of price and quantity, both of which are proportional to $R_{j} - t_{j}$ . Convexity implies that if it is a good idea to raise taxes to a certain level, it is an even better idea to increase them further. The question then boils down to the comparison of the two extreme values. This comparison is a function of c.

A key issue of concern is: What happens to the amount of tourists visiting the destination when the L segment is restricted? Does the intervention decrease the externality on other stakeholders, not incorporated into our model? It is obvious that $Q_{L}$ decreases, from $Q_{L}^{*}$ to $a_{L}$ , while $Q_{H}$ increases, but how do the magnitudes of change compare? The following corollary clarifies.

Corollary 6

When the tax intervention is implemented, the change in the measure of tourists visiting each segment is $Δ Q_{H} = c M_{H} (M_{L} R_{L} - a_{L})$ and $Δ Q_{L} = - (M_{L} R_{L} - a_{L})$ . Consequently, $| \frac{Δ Q_{H}}{Δ Q_{L}} | = c M_{H}$ .

For example, if we wish to account for carbon footprints, this means that if the carbon footprint of a tourist visiting the H segment is x times that of a tourist visiting the L segment, the tax reduces total carbon emission if and only if $x c M_{H} < 1$ . While at first it may sound surprising, a low sensitivity to congestion is “good” since the number of extra H tourists is proportional to the size of the externality that the intervention eliminates, what is proportional to c. Other than that, we need a less competitive market with high “elasticity of demand” ( $s_{H}$ ).

In a parallel manner do the utilities derived by the tourist vary, as their utility is directly proportional to their equilibrium quantity via their “supply” function $G_{j}^{- 1} (Q_{j})$ . That is, despite the price hike, H tourists are better off without the inter-segment externality (and, in addition, more of them will come who make a gain relative to the outside option they were taking beforehand). At the same time, the L tourists are hurt– as the price is lowered by less than the tax –, on two margins: first, some of them will choose their outside option instead, but these options will be lower than the utility they would have derived from visiting our destination before the tax was imposed; second, those who continue to come will derive a lower utility than before. Whether or not overall consumer surplus goes up or down depends on the parameters.

7 Discussion

Let us ponder the practical implications of our results. While the point of view of a captured LPA unfortunately makes a lot of sense, the idea that it would simply concentrate on profits is perhaps exaggerated. However, the actual discussion out there is not about optimality rather whether tourist taxes of significant size should be levied at all. In this sense, based on our model and results, we have a significant contribution to make. Suppose the intersegment sensitivity to congestion is high enough, so that the tax intervention is warranted when maximizing aggregate profit. Note that by our assumptions $M_{H} < M_{L} < 1 / c$ , and consequently, by Corollary 6, at the profit maximizing tax schedule the overall quantity of tourists is lower than in the absence of the tax. Since obviously profits and tax revenue are higher, the profit maximizing tax improves on welfare: $W (0) < W (t_{H} = 0, t_{L} = t_{L}^{*})$ . Therefore, even if the LPA wishing to improve on W were constrained to either impose the profit maximizing tax or none, it would be happy to implement a significant (recall that the optimal tax restricts the L segment so as it generates no intersegment externality) tourist tax.

A stand out feature of the optimal tax schedule is that the H segment is taxed less than the L segment, in contrast to what we observe in reality. Of course, a simple explanation can be that the other motives for taxation lead to that. In any case, the question arises whether a tax scheme satisfying $t_{L} < t_{H}$ could be beneficial to the service providers. The answer is a rotund no. Note that—as it is shown it the proof of Proposition 4—aggregate profits are decreasing in $t_{H}$ . As we have seen (Proposition 3) that any uniform tax decreases aggregate profits, increasing $t_{H}$ starting from a uniform tax will further lower aggregate profits.

If the profit motive were not the objective, but a constraint on the LPA’s optimization problem, so that the latter cannot decrease it, then we would have even higher constrained optimal taxes. However, by the above discussion, the scheme would have the feature that $t_{L} > t_{H}$ .

Finally: in the absence of action by the LPA, would the local industry be able to self regulate? Setting taxes does not sound realistic. However, note that the outcome of the profit maximizing tax scheme could be replicated by setting a minimum price, binding only in the L segment. It is not unheard of that professional colleges set such prices.

8 Concluding remarks

Pigouvian taxes are the typical economist’s prescription for addressing congestion. Nonetheless, they are underutilized, and even when tourist taxes are imposed, their size—as shown in Sect. 2—is way too low to affect congestion.^Footnote24 When comparing them to accommodation prices, it becomes clear that a tourist tax should be significantly higher than its current levels, in order to have measurable effects on congested European destinations.

In other words, the use of Pigouvian taxes to deal with overtourism is to our knowledge practically non-existent. This, together with their absence, or at least the little attention they are paid to, in the public debate about the overtourism occurring in many destinations is somewhat of a mystery to us. Our analysis thus pretends to bring them to the fore when discussing the way to manage congestion. Our results might be especially helpful, since they show that a tourist tax in a congested destination might even pay off for the hospitality industry, providing reasons for it not to lobby against it, as it is usually the case.

At the same time, though, a tourist tax—whether exclusively targeting the L-segment or applied uniformly to all tourists—may raise equity concerns among stakeholders beyond the tourism industry, such as tourists themselves. While we have shown that a tourist tax can be an effective tool to combat congestion, potentially yielding positive distributional effects for the industry, its broader equity implications could challenge its political acceptability, similar to the debates surrounding toll taxes for road congestion (see, for instance, Eliasson (2016)). This issue falls outside the scope of our paper, as we have assumed that tourists are outsiders with no political influence. However, this assumption does not always hold, particularly when tourists are also residents of the same country or when equity considerations extend across national boundaries.

The key observation in our paper is that the tourism industry consists of vertically differentiated segments. While they operate semi-independently, the effects of congestion are felt across segments and in an asymmetric way. A tourist tax then can affect the composition of the aggregate demand (and supply). We have found that this does not work well if the LPA is restricted to imposing a uniform tax scheme, the same tax on both segments. On the other hand, when it can use a differentiated tax scheme, we have shown that, in the face of high congestion externalities, it is profit maximizing to tax the tourist segment of a destination that creates a larger externality on other tourists (the low income/WTP tourists), so as to eliminate such congestion and, therefore, make the destination more attractive for high WTP tourists. Such a tax policy is more likely to be optimal when the H(L) customers value their stay more (less), the H(L) tourists are more tolerant of their peers, H(L) segment is less (more) competitive, the supply of H(L) tourists is lower (higher) and finally if the threshold quantity of L tourists for no intersegment externality is higher.

For tractability we have restricted our model to two segments with identical firms in each. In principle, one could extend the model to a series of segments and then study the choice of which segments are tax free, which are taxed partially and which are taxed till they create no externality. Finally, it would be interesting to analyze a framework with a more dynamic flavor by considering exit, entry or even category change as a result of the taxes, endogenizing the number of firms and capacity in each segment.

Notes

Of course, we do not wish to minimize Arthur Pigou’s original contribution, more than a century ago.
Note that we use the term congestion as equivalent to ‘negative crowding’, a term more commonly used in the leisure literature; see Shelby et al. (1989).
We do not analyze the case of differentiated taxes across segments for our benchmark analysis, as it would not contribute to putting our main results into context.
In our model, such a tax would correspond to a parallel downward shift in demand.
A definition of carrying capacity of tourism has been developed referring to the maximum quantity of tourists being present in a destination without their activities becoming intolerable to host communities, and without preventing fellow tourists from appreciating the destination (McCool and Lime 2001; Saveriades 2000).
This is not immediately obvious: Research has shown that (perceived) crowding is a psychological construct, and that while people might consider crowds stressful in specific contexts, they may appreciate in a positive light social density in other environments, for instance at mass events such as festivals (Jacobsen et al. 2019).
Other studies’ findings are less clear cut on whether crowding should be considered negative. Neuts and Nijkamp (2012) for instance, find that in Bruges ‘only’ 18% of the interviewed gave a negative opinion. However, these are mostly one (or two) day visitors, and the study also likely faces a bias in the sample as in the other cases: those tourists more negatively affected by the overtourism of the destination will likely not be visiting it.
See https://atc.gencat.cat/ca/tributs/ieet/quota-tributaria/ and https://parisjetaime.com/eng/article/tourist-tax-a616.
We assume competition in quantities instead of prices to ensure that the firms have positive profits. As shown by Kreps and Scheinkman (1983)—and later generalized by Burguet and Sákovics (2017) –, Cournot competition is equivalent to a two-stage model where firms first invest in capacity and then compete in price. Consequently, Cournot competition is justified, if we think of firms first building capacity and subsequently competing in price.
To avoid clutter, in the rest of the paper we drop $j = H, L$ , whenever we use the j subinndex, we mean $j = H, L$ .
It is important to note that what is driving our results is that the L and H firms are competing in different markets, not that the consumers are preselected. The crucial issue is which congestion cost do the firms internalize. With separate segments (for firms) they only care about the congestion within but not across segments. Whether or not consumers self select is of second order relevance, having only quantitative effects.
Note that, if $a_{j}^{'} = a_{- j} = 0$ , then the utility function simplifies to
The unilateral inter-market externality avoids having to look for a fixed point, what in turn would lead to very complicated expressions (solutions to a system of two cubic equations). Again, this assumption works against our main result, since if there were congestion in the other direction the value of the unsatisfied L demand would be lower, lowering the cost of losing it due to the tax levied. Keeping both $b_{j}$ does not complicate the analysis.
Note that, due to $c_{L} = 0$ , $a_{H}$ does not play a role, while $a_{L}^{'} < Q_{L}$ is implied by $a_{L} < Q_{L}$ .
The fact that we ignore the asymptotes does not matter: it will never be the case that all the potential tourists visit the destination. In fact, due to the upper bound on the utilities achievable, $r_{j}$ , the maximum measure of tourists considered will be $\frac{r_{j}}{s_{j}}$ .
Please note that all upper case variables are composite objects of the underlying parameters. We use them to make it easier to parse the formulas.
We assume that $r_{H}$ is high enough so that $Q_{H}^{*} > 0$ : congestion does not “kill” the H segment. Note also that our overtourism assumption boils down to $a_{L} < M_{L} R_{L}$ and $a_{H}^{'} (1 - M_{H} b_{H}) < M_{H} (r_{H} - c (Q_{L}^{*} - a_{L}))$ .
Note that our overtourism assumption ensures that the positive effect of $b_{j}$ in $R_{j}$ is more than compensated by the negative effect in $M_{j}$ .
Of course, residents also benefit from tourism, but beyond a point the aggregate effect on them is negative. In any case, our analysis applies to positive externalities too.
We again evaluate the profit functions of Corollary 3 substituting $R_{j} - t$ for $R_{j}$ .
We again evaluate the profit functions of Corollary 3 substituting $R_{j} - t_{j}$ for $R_{j}$ .
If $A^{2} < B$ then a real lower bound on c does not exist, so $t_{L} = 0$ .
It is easy to see that $A^{2} > B$ is equivalent to $Π_{H}^{*} > Π_{L}^{*} - \frac{a_{L}^{2}}{(n_{L} + 1) M_{L}}$ , when $c = 0$ .
As it is said in PwC (2017), “the stakeholders interviewed stated that the tourist tax does not have a noticeable effect on the number of tourist arrivals or seasonality issues” Logar (2010).
The second-order condition is also satisfied.
Recall that, since we assumed overtourism in the absence of taxes, this value is positive.

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Acknowledgements

We are grateful for suggestions by the Editor and two anonymous referees as well as for comments at the Simposio de Análisis Económico (Palma, 2024) and a seminar at the Universitat de les Illes Balears. Calveras and Sákovics both thank grant PID2020-115018RB-C33 funded by MICIU/AEI/ 10.13039/501100011033. Furthermore, Sákovics thanks the Spanish government for support through a Beatriz Galindo grant (BG20/00079). This work has been partially sponsored by the Comunitat Autonoma de les Illes Balears through the Direcció General de Política Universitaria i Recerca with funds from the Tourist Stay Tax Law ITS 2017-006 (PRD2018/43).

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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.

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Authors and Affiliations

Universitat de les Illes Balears, Palma, Spain

Aleix Calveras & József Sákovics

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Correspondence to József Sákovics.

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József Sákovics and his family own shares in a company that has shares in a company that operates hotels. We have collected no unpublished data.

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Appendix

Proof of Proposition 1

From (3), in a symmetric equilibrium each firm in segment L maximizes (in q)

This leads to the first-order condition^Footnote25

leading to

In turn, each firm in segment H maximizes

leading to

Multiplying the per-firm quantities by the number of firms in each segment, we obtain the result. $◻$

Proof of Proposition 2

The maximand is

We can rewrite this as

Differentiating with respect to t, we obtain

Calculating the second derivative

This is negative if and only if $c^{2} + c \frac{n_{H} - 1}{M_{L}} - \frac{M_{H} n_{H} (1 + n_{L}) + M_{L} n_{L} (1 + n_{H})}{M_{H} M_{L}^{2} (1 + n_{L})} < 0$ . That is, between the two roots of

The roots are $c = \frac{1 - n_{H}}{2 M_{L}} \pm \sqrt{{(\frac{1 - n_{H}}{2 M_{L}})}^{2} + \frac{M_{H} n_{H} (1 + n_{L}) + M_{L} n_{L} (1 + n_{H})}{M_{H} M_{L}^{2} (1 + n_{L})}}$ . Note that there is one root on each side of zero. Consequently, since $c \geq 0$ , we have that the second-order condition is satisfied if and only if

We can rewrite the term under the square root as ${(\frac{1 + n_{H}}{2 M_{L}})}^{2} + \frac{M_{L} n_{L} (1 + n_{H})}{M_{H} M_{L}^{2} (1 + n_{L})}$ , so that the upper limit is more than (we ignore the second, positive term under the root) $\frac{1 - n_{H}}{2 M_{L}} + \frac{1 + n_{H}}{2 M_{L}} = \frac{1}{M_{L}}$ . Now recall that $M_{L} = \frac{n_{L}}{(s_{L} + b_{L}) (1 + n_{L})}$ , so $\frac{1}{M_{L}} = \frac{(s_{L} + b_{L}) (1 + n_{L})}{n_{L}} > \frac{c (1 + n_{L})}{n_{L}}$ implying that $c < \frac{1}{M_{L}} \frac{n_{L}}{1 + n_{L}} < \frac{1}{M_{L}}$ . Thus, the second-order condition is satisfied in the entire range.

Solving the first-order condition

we obtain

Of course, at some level of $z$ we hit the constraint $t \leq R_{L}$ , but it is reasonable to assume that z is not that high.

The sign of derivative with respect to z is the same as the sign of (we ignore the denominator, that is independent of z)

where we have used $c < \frac{1}{M_{L}}$ again.

Finally, evaluating the objective at $z = 0$

Proof of Corollay 4

By Proposition 1,

The derivative of the first quantity with respect to t is $- M_{L}$ , while of the second it is $- M_{H} (1 - c M_{L})$ . As $c M_{L} = \frac{c n_{L}}{(s_{L} + b_{L}) (n_{L} + 1)}$ and $c < b_{L} < s_{L} + b_{L}$ , $c M_{L} < 1$ , so both derivatives are negative. Since the utility obtained by the tourists in each segment is by construction increasing in their quantity, $Q_{j}^{*} = u_{j} / s_{j}$ , $u_{j}$ is also decreasing in t. Consequently, consumer surplus, given by $u_{j} Q_{j}^{*}$ , is decreasing in t in each segment. $◻$

Proof of Proposition 3

We proceed in two steps. First we identify a lower bound on c for setting a tax to be optimal. Second we show that this lower bound is above the maximum c allowed, which as we have shown in the proof of Proposition 6 is $1 / M_{L}$ .

We start by noting that since firm revenues are lost (and nothing is gained), it never makes sense to reduce the tourist measures below $a_{j}^{'}$ . Substituting from Corollary 3 into (4), denoting the common tax by t, and taking into account that it might make sense to reduce $Q_{L}$ below $a_{L}$ , the maximand becomes

subject to $t \in [0, R_{L}]$ and $t \in [0, R_{H} - c {[M_{L} (R_{L} - t) - a_{L}]}^{+}]$ .

Suppose ${[M_{L} (R_{L} - t) - a_{L}]}^{+} > 0$ . Then

By the convexity of the objective, the optimal solution must be a corner: either $t = 0$ or, since ${[M_{L} (R_{L} - t) - a_{L}]}^{+} > 0$ implies $t < R_{L}$ , the other corner would have to be $t = R_{H} - c [M_{L} (R_{L} - t) - a_{L}] \Rightarrow$ $t = \frac{R_{H} - c (M_{L} R_{L} - a_{L})}{1 - c M_{L}} > R_{L}$ , contradiction. So only zero is possible.

Suppose ${[M_{L} (R_{L} - t) - a_{L}]}^{+} = 0$ . Then

so we must have the lowest tax that leads to ${[M_{L} (R_{L} - t) - a_{L}]}^{+} = 0 :$ $t = R_{L} - \frac{a_{L}}{M_{L}}$ .

Comparing the values of the objective at the two candidate solutions:

The first value is decreasing in $c$ , while the second is independent of it. When $c = 0$ , comparing term by term, it is straightforward to see that it is better not to tax. The two values are equal when

where we substituted A for $\frac{R_{H}}{M_{L} R_{L} - a_{L}}$ , and B for $\frac{(M_{L} R_{L} + a_{L}) (n_{H} + 1)}{M_{L} M_{H} (n_{L} + 1) (M_{L} R_{L} - a_{L})}$ . We now show that

what holds for $a_{L} < M_{L} R_{L}$ , a condition that follows from the necessary condition for a positive tax be optimal identified above: $M_{L} (R_{L} - t) = a_{L}$ .

Proof of Proposition 4

First, note that since revenues are lost (and nothing is gained), it never makes sense to reduce the tourist measures below $a_{j}^{'}$ . Substituting from Corollary 3 into (4)—and taking into account that it might make sense to reduce $Q_{L}$ below $a_{L}$ – the maximand becomes

(6a)

subject to $t_{L} \in [0, R_{L}]$ and $t_{H} \in [0, R_{H} - c {[M_{L} (R_{L} - t_{L}) - a_{L}]}^{+}]$ .

Let us first calculate the optimal $t_{H}$ given an arbitrary $t_{L}$ . The derivative of (6a) is

Consequently, the optimal tax in the H segment is zero. Substituting $t_{H} = 0$ into (6a) we obtain the objective function

(7)

If ${[M_{L} (R_{L} - t_{L}) - a_{L}]}^{+} > 0$ , the first derivative of (7) with respect to $t_{L}$ is (we divide through by $2 M_{L} > 0$ )

(8)

while the second-order condition is

This is never satisfied, the objective function is convex. Then the optimal solution must be a corner: either $t_{L} = 0$ or ${[M_{L} (R_{L} - t_{L}) - a_{L}]}^{+} = 0$ .

When ${[M_{L} (R_{L} - t_{L}) - a_{L}]}^{+} = 0$ , the derivative of the objective function is negative, so we must have the lowest tax that leads to ${[M_{L} (R_{L} - t_{L}) - a_{L}]}^{+} = 0 :$ $t_{L} = R_{L} - \frac{a_{L}}{M_{L}}$ .^Footnote26 This implies $Q_{L}^{'} = M_{L} (R_{L} - t_{L}) = a_{L}$ . Comparing (7) evaluated at the two possible values, we see that it is optimal to keep the L segment to its maximal size such that it does not impact on the H segment, if and only if

(9)

Note that (9) can be rewritten as,

This is satisfied in between the roots (in c) of

or equivalently

The roots are

Since B is positive, the lower root is positive as well. The higher root is irrelevant, too high sensitivity to congestion cannot lead to less tax on the market creating the negative externality. $◻$

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Calveras, A., Sákovics, J. A tourist tax in a vertically segmented destination with congestion effects. SERIEs (2025). https://doi.org/10.1007/s13209-025-00303-2

Received 24 July 2024
Accepted 26 January 2025
Published 21 February 2025
DOI https://doi.org/10.1007/s13209-025-00303-2

Keywords

Congestion
Industry profits
Overtourism
Pigouvian tax