Sustainable development in tourism municipalities: The role of public goods

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Tourism Management 29 (2008) 883–897 www.elsevier.com/locate/tourman

Sustainable development in tourism municipalities: The role of public goods Ricard Rigall-I-Torrent Departament d’Economia, Facultat de Ciencies Economiques i Empresarials, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain Received 22 September 2006; accepted 31 October 2007

Abstract It is usually argued that, since many of the inputs used in the production function of private firms in tourism municipalities are depletable, unsustainability looms over the horizons of tourism jurisdictions. However, this reasoning forgets that public goods are an important part of tourism products. Since public goods are nonrival (and hence nondepletable), a way out of the apparent unsustainability might exist. By considering well-established growth models, this paper argues that a correct supply of public goods may contribute to achieve sustainable development throughout time in tourism municipalities. r 2007 Elsevier Ltd. All rights reserved. Keywords: Local public goods; Endogenous economic growth models; Sustainable development; Tourism jurisdictions

of open societies. The closed economy of the future might similarly be called the ‘spaceman’ economy, in which the earth has become a single spaceship, without unlimited reservoirs of anything, either for extraction or for pollution, and in which, therefore, man must find his place in a cyclical ecological system which is capable of continuous reproduction of material form even though it cannot escape having inputs of energy.

1. Introduction Many activities related to tourism intensively use the territorial and natural resources of the jurisdiction where they are located. This is the case, for instance, of the hotels located in a given tourism municipality. Economic activity in the jurisdiction is directly related to the number of tourists visiting it. Although greater numbers of tourists increase the economic activity of the jurisdiction where the tourism supply is located (thus increasing the jurisdiction’s income levels), increasing numbers of visitors also imply more pressure on the jurisdiction’s resources. For instance, as more hotels are built to accommodate increasing demand, natural and territorial resources become scarcer and, since those resources are clearly limited (a jurisdiction has fixed boundaries), a limit to growth is to be reached some time into the future. This reasoning lies at the heart of Kenneth Boulding (1966): (y) I am tempted to call the open economy the ‘cowboy economy,’ the cowboy being symbolic of the illimitable plains and also associated with reckless, exploitative, romantic, and violent behaviour, which is characteristic

Indeed, it could be argued that there is no way to escape the apparent unsustainability of development and growth in tourism municipalities. However, this paper argues that a way out of the trade-off exists for municipalities which base their tourism supply on the provision of local public goods. One should understand a jurisdiction’s ‘‘public goods’’ in a broad sense, including cultural legacy (monuments, gastronomy, traditions, etc.), preservation of the environment and landscapes, brand image (reputation, prestige) and public services and infrastructures (roads, public safety, cleanness of public places). Since public goods are nonrival, they can be enjoyed by many users (tourists) without decreasing the amount available to additional users.1 Thus, because they are not depleted by use, public goods might lay the ground for sustainable

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Although some congestion may exist.

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development in tourism municipalities. Higher quantities of inputs having public good characteristics would imply higher output for a municipality (i.e., higher income and welfare for its inhabitants). In a sort of virtuous circle, higher output would lead (by means of higher total tax revenues) to higher levels of public goods feeding back successive waves which would not stop because of (the apparently inescapable, in a traditional tourism development model) diminishing returns. Since at the end of the day the sustainability of the tourism activity at local level depends on a municipality’s ability to reproduce the inputs entering the production function of its firms, a development model based on public goods is more likely to be sustainable than one relying on depletable inputs. However, sustainability in a tourism model with public goods assumes that the public sector provides the optimal quantity of those goods.2 If the public sector fails to do so, then unsustainability looms over the horizons tourism municipalities. This paper tackles the sustainability of economic activity in tourism municipalities in five sections. Section 2 discusses what sustainable development is in a tourism setting. Section 3 reviews well-established endogenous growth models in order to identify how a correct supply of public goods may contribute to achieve a sustainable development level throughout time in tourism municipalities. Section 4 presents some implications regarding the role of the public sector in managing the provision and financing of public goods. Finally, the paper’s main conclusions are summarised in Section 5.

2. Sustainable development and tourism 2.1. The meaning of ‘sustainable development’ The term ‘sustainable development’ has been widely used, with multiple meanings, in very different settings. This paper understands ‘sustainable development’ in the terms expressed by the so-called Brundtland Report3: ‘‘Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs’’. From this definition it can be deduced that, in general, an activity is sustainable whenever it can be carried out continuously in the course of the time without diminishing either its characteristics or effects. As a matter of fact, different activities have distinct characteristics which may determine the feasibility of a development model. One of the intrinsic characteristics of tourism (which fundamentally differentiates it from other economic activities) is that in order to enjoy a tourism product it is necessary to move to the 2 Of course, the composition (type, quality and characteristics, for instance) of public goods also matters. However, for simplicity, here only total quantities of public goods have been considered. 3 World Commission on Environment and Development (1987), Our Common Future, Oxford University Press, p. 54.

physical location (municipality) where the good is ‘‘produced’’. This implies that tourism-related activities impinge several types of impact on a jurisdiction. According to the United Nations,4 there are three types of impact: 1 Impacts on the environment (both natural and manmade): Two types of impact, of opposite sign, exist. On the one hand, many tourism activities (especially those linked with the construction of general infrastructures and tourism facilities) may have a negative impact on the environmental resources on which they depend, damaging or destroying them. On the other hand, by raising financial resources and the tourists’ awareness of environmental values, tourism can increase the preservation of the environment. 2 Socio-cultural impacts: They involve the effects on host communities of direct and indirect relations with tourists, and of interaction with the tourism industry. Tourism activities may imply negative impacts when they bring about changes in value systems and behaviour threatening indigenous identity, changes in community structure, family relationships, collective traditional life styles, ceremonies and morality. However, tourism may have positive effects whenever it serves as a force for peace, it fosters pride in cultural traditions and, by creating local jobs, helps avoiding urban relocation. 3 Economic impacts: Likewise environmental and sociocultural impacts, they can be either positive or negative. Negative impacts are related to the resources required to provide the infrastructures that sustain the tourism industry, the increase in prices linked to increasing demand for basic services and goods from tourists, the emergence of economic dependence of the local community on tourism or the seasonal character of jobs, among many others. Positive impacts are related to foreign exchange earnings, the contribution to government revenues, the generation of employment, the stimulation of infrastructure investment and the contribution to local economies, for instance. In view of the impacts above, according to the World Tourism Organization5,6 to be sustainable a tourism model should: 1 Make optimal use of the environmental resources that constitute a key element in tourism development, maintaining essential ecological processes and helping to conserve natural heritage and biodiversity. 4

United Nations Environment Programme, http://www.unep.org/. World Tourism Organization (2004), Sustainable Definition of Tourism. Conceptual Definition, http://www.world-tourism.org/frameset/frame_ sustainable.html. 6 See World Tourism Organization (WTO), United Nations Environment Programme (UNEP), United Nations Educational, & Scientific and Cultural Organization (UNESCO) and European Union (1995), Lanzarote Charter for Sustainable Tourism, http://www.world-tourism.org/ sustainable/doc/Lanz-en.pdf. 5

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2 Respect the socio-cultural authenticity of host communities, conserve their built and living cultural heritage and traditional values, and contribute to inter-cultural understanding and tolerance. 3 Ensure viable, long-term economic operations, providing socio-economic benefits to all stakeholders that are fairly distributed, including stable employment and income-earning opportunities and social services to host communities, and contributing to poverty alleviation. Besides tackling the different aspects above, ‘‘sustainable tourism development requires the informed participation of all relevant stakeholders, as well as strong political leadership to ensure wide participation and consensus building. Achieving sustainable tourism is a continuous process and it requires constant monitoring of impacts, introducing the necessary preventive and/or corrective measures whenever necessary’’ (see footnote 5). Finally, ‘‘sustainable tourism should also maintain a high level of tourist satisfaction and ensure a meaningful experience to the tourists, raising their awareness about sustainability issues and promoting sustainable tourism practices amongst them’’ (see footnote 5). 2.2. (Un)sustainable tourism models A tourism municipality’s development model which is based on a tourism product obtained by intensively using exhaustible environmental and territorial resources will hardly be sustainable. This would be the case, for instance, of ‘‘mass’’ tourism, i.e., a model of activity based on low prices, seeking to attract high numbers of tourists and impinging high tensions on natural resources. This is shown in Fig. 1. The broken curve represents the stock of natural and territorial resources available in a given tourism municipality (for instance, total unbuilt surface, length and quality of beaches or surface and beauty of natural spots). It should be noted that in the long run several factors might shift that stock upwards (i.e., increase the available resources which make possible a given level of economic activity). Typically, technological progress may allow the regeneration of natural resources. For instance, new methods to regenerate beaches more efficiently may be discovered, so that beaches can accommodate more tourists without diminishing the quality of the sand or the water, or building procedures friendlier with the environment may be developed. Anyway, some resources (chiefly, a jurisdiction’s surface) are not replicable, i.e., their supply is fixed. The black curve in Fig. 1 shows a development path where economic activity (measured as tourists attracted or gross domestic product obtained, for instance) depletes all the available natural and territorial resources. Such a model of development would be unsustainable in the long run, since if resources are limited ¯ would (i.e., nonreproducible) then an upward limit ðAÞ exist from where no further increases in the jurisdiction’s economic activity would be possible.

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It is interesting to consider whether there is any way out of a development path like the one depicted in black in Fig. 1. The grey curve draws a development path for which economic activity indefinitely increases without exceeding the physical limits set by limited natural and territorial resources. It could be argued that a development path like that is not attainable in the real world, since arguably any tourism activity needs some limited physical resources. ¯ from where no further Then, sooner or later, level A, increases of economic activity are possible, would be reached. It is true that some endowments of resources are fixed and not replicable. For instance, the surface where it can be built on: once used in full no further expansions are possible (unless higher premises are built). Filling with concrete all the surface in a municipality precludes natural resources as a source of future economic growth. However, some inputs exist whose supply is more flexible: these are inputs with characteristics of public goods.7 Public goods are nonrival and nonexcludable (see, for instance, Samuelson, 1954). Nonrivalry implies that one individual’s consumption does not prevent another person’s consumption (this is the same as saying that once a public good is provided, the cost of any additional user is zero). Hence, any nonrival good can be consumed by many people without being depleted. A tourism jurisdiction basing its final product on public goods will surely have a higher scope for growth than a jurisdiction relying on intensive use of limited resources. 2.3. Local public goods in a tourism setting In a tourism setting, several goods having public good characteristics may play an important role for a municipality’s perspectives of growth. Consider, for instance, a jurisdiction’s preservation of the environment and the landscape. Once a public good is provided, every tourist is able to enjoy sightseeing a well-preserved environment. Although some degree of congestion may exist, the environment is there for everybody to admire and enjoy. Compare this with the scenario where a new hotel is built: a part of the landscape now disappears and it cannot be enjoyed by anybody in the future (unless the hotel is demolished). Another example of public goods would be a jurisdiction’s cultural legacy. A municipality’s tourism businesses profit from the jurisdiction’s monuments, gastronomy, art and traditions. All these elements build up a jurisdiction’s cultural heritage and cannot be cut off from the tourists’ experience when they visit that jurisdiction. Besides, a jurisdiction’s cultural legacy does not diminish with the number of tourists: a tourist’s enjoyment of a jurisdiction’s traditions, art or gastronomy does not preclude other tourists’ enjoyment of the same elements (remember, however, the objections in Section 2.1). Consider also a jurisdiction’s brand image (which includes 7 For a thorough treatment of public goods’ characteristics see, for instance, Cornes and Sandler (1996).

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Use of depletable resources

Depletable resources available Sustainable development path

Unsustainable development path

A

Economic activity

Fig. 1.

a municipality’s reputation and prestige): it affects all the firms located there, regardless of a particular firm’s brand image (as a matter of fact, an individual firm is likely to be too small to have any influence at all on a tourism destination’s brand image). Similar effects occur with public infrastructures and many other elements: anybody may enjoy a seafront walk without diminishing (up to a point) the quantity of the infrastructure available to others. It should be noted that all this elements are local public goods, i.e., they only influence the jurisdiction where they are provided. Therefore, they should be provided by the local authorities (see, for instance, Rubinfeld, 1987). By means of a review of endogenous growth models applied to a tourism setting, the next section addresses in detail the relationship between the supply of local public goods and development in tourism municipalities. 3. Public goods and the sustainability of the tourism activity: a review of endogenous growth models Solow (1956) was one of the pioneers in explaining economic growth rigorously. Solow argued that economic growth was the result of combining physical capital (i.e., machinery and buildings) and labour given the state of the art of technology. In Solow’s neoclassical setting economic growth was limited since, in absence of technological change, the law of diminishing returns would kick in: as the use of an input increased in equal increments (with other inputs fixed) a point would eventually be reached at which the resulting additions to output would decrease. Solow’s theory was not entirely satisfactory: only capital and labour were endogenous factors (i.e., explained by the model), since technology was like manna fallen from heaven, outside the economic agents’ will. Thus, Solow’s explanation of growth relied on an unexplained variable. In

order to overcome this, economists tried to make growth an integral part of the model (i.e., endogenous). Most of their efforts were directed to identifying the factors behind technological change (see Barro & Sala-i-Martin, 1999; Jones, 2002). Thus, Romer (1986 and 1990) stressed the role of ideas in increasing labour’s productivity. Ideas refer to new perspectives in engineering, marketing, education, pricing or mathematics, for instance, which allow a given bundle of inputs to produce more (or higher quality) output. Since ideas are nonrival, they imply increasing returns to scale: a proportional increase in all inputs yields a more than proportional increase in output, since once ideas have been created anyone can profit from them without decreasing the available quantity for others. However, even without technological change, sustained growth is possible when constant returns to scale are present. Several plausible assumptions regarding the production function warrant the existence of sustainable growth. The assumptions involve the importance that learning-by-doing and knowledge spillovers (see Romer, 1986), public goods (see Barro, 1990; Barro & Sala-iMartin, 1992) and human capital (see Barro & Sala-iMartin, 1999; Rebelo, 1991) may have in economic growth. All these assumptions imply that diminishing returns to capital (in a broad sense) do not apply, so that long-term growth in output per capita is feasible in the absence of technological progress. Since the tourism industry is not intensive in technology, the role of local public goods in generating economic growth in tourism municipalities appear as a promising alternative. In order to understand the effects of public goods on the development and growth of tourism municipalities, this paper draws from both neoclassical and endogenous growth literature. The analysis that follows is based on Solow (1956) and Swan’s (1956) economic growth models

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with exogenous saving rates and the treatment by Barro (1990) and Barro and Sala-i-Martin (1992) of endogenous growth models with one sector. Although there is nothing new with respect to endogenous growth literature in Sections 3.1 and 3.2, this paper’s novelty lies in the application of well-established growth models to understanding economic growth in tourism jurisdictions. The analysis based on Solow and Swan’s developments is useful to evaluate the effects that a lack of investment in public goods may have on sustainable development for tourism municipalities. On the other hand, the setting in Barro (1990) and Barro and Sala-iMartin (1992) serves the goal of identifying how a correct supply of public goods may contribute to get a sustainable development level throughout time in tourism municipalities and lay the basis for drawing implications for the management and organisation of both private firms and the public sector. 3.1. Sustainable development and growth in a tourism municipality without investment in local public goods: the predictions from Solow-Swan’s model It is plausible to assume that the inhabitants of tourism jurisdictions are at the same time consumers (tourists) and producers (tourism firms’ owners).8 Thus, they own the inputs and arrange them as they think fit (according to the state of the technology, summarised in a production function) in order to obtain a tourism product. To make matters simple, it is assumed that only three different inputs, capital (K(t)), labour (L(t)), and public goods (Z(t)) are used to get the final output, Y(t), which is a homogeneous product that can be thought of as GDP and can be used either for consumption (C(t)) by the municipality’s inhabitants or to increase the available capital in the municipality, i.e., as investment (I(t)). It is assumed that the production function in the economy is Cobb–Douglas, Y ðtÞ  F ½AðtÞ; KðtÞ; LðtÞ; ZðtÞ; t ¼ AðtÞZðtÞK a ðtÞL1a ðtÞ, (1) where A(t)40 is the technology available at time t (say year 2007, for instance) and a, 0oao1, is a fixed parameter which characterises the production possibilities available to the firms located in a jurisdiction. Note that the form of (1) implies that all inputs are strictly necessary so as to obtain a positive quantity of output (if, for instance, no territorial surface existed in a municipality or no labour was available, the output would be zero). This seems appropriate for tourism municipalities, where all those factors play an important role. Expression (1) shows constant returns to scale (i.e., increasing both capital and labour by 8 By considering that the inhabitants are tourists and owners of the tourism firms at the same time, it is possible to understand tourism municipalities from an aggregate point of view without introducing many complications derived from open economies’ settings.

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a factor l increases total output by l), so that it is possible to write the production function in per capita terms Y 1 1  F ðA; K; L; ZÞ ¼ AZK a L1a L L   L K a ¼ AZ ! y ¼ AZka , L

ð2Þ

where y ¼ Y/L is output per capita (i.e., per capita GDP), k ¼ K/L capital per capita (i.e., units of capital per worker) and, for simplicity, references to time have been omitted. It is easy to check that marginal products for capital and labour are positive and decreasing (for instance, employing more workers in a hotel yields smaller and smaller increases in output). In a tourism municipality, capital is composed by the territory, the buildings hosting tourism firms and the machinery used to obtain the tourism output. Decreasing marginal products for capital and labour look plausible in tourism municipalities: since the territorial surface of a municipality is clearly limited, the number of buildings available is also limited, i.e., an upward limit for the quantity of available capital exists. Since population growth and capital depreciation are assumed constant, a level of capital will exist so that no further increases in capital per capita are possible: for that level of capital all output invested will be devoted in full to compensate for population growth and to replace obsolete capital. For a tourism jurisdiction, this can be understood as follows: once a municipality’s landscape is filled with concrete (with 300-storey hotels, for instance), the scope for further increases in physical capital and, correspondingly, subsequent increases in output, is severely limited. Further increases in output depend on technological improvements and on investment in public goods. Technology may be understood as the quality of capital: for given quantities of capital and labour, greater technological content results in greater tourism output. For instance, the development of computer booking systems based in yield management allows tourism firms (hotels, for instance) to increase the number of booked rooms without increasing the number of rooms available (i.e., total output in the municipality goes up with capital kept constant). So as to keep things simple, it is initially assumed, along the lines of Solow (1956) and Swan (1956), that the percentage of final output devoted to investment (s, 1XsX0) and consumption (1s) in tourism municipalities is fixed and exogenous (for simplicity, it is also assumed that no borrowing or lending is available). Besides, it is assumed that capital depreciates (by use or obsolescence, for instance, hotel buildings wreck as they get older) at a constant rate d40. In this setting the accumulation of capital throughout time can be described by means of9: _ ¼ IðtÞ  dKðtÞ ¼ sAðtÞZðtÞK a ðtÞL1a ðtÞ  dKðtÞ, KðtÞ 9

In order to simplify the analysis, continuous time is used.

(3)

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i.e., the evolution of capital (for instance, the change in the _ 10 can be obtained number of hotels in a municipality), KðtÞ, by computing investment (new hotels built and old hotels reformed), I(t), net of depreciation (hotels wrecked) dK(t). Besides, available labour depends on the evolution of migrations, fertility and mortality in the municipality. For simplicity it is assumed that all of a jurisdiction’s inhabitants work with the same intensity and have identical ability (which imply that their work yields identical output per hour worked), so that it is possible to identify total labour available with total population. Thus, the evolution of labour (total number of workers at time t) can be described though: LðtÞ ¼ ent ,

(4)

where n is the population’s growth rate (number of people per year) and population and working intensity per capita at t ¼ 0 have been normalised to 1. In this setting it is interesting to analyse the evolution of different variables affecting the individuals’ welfare: capital used by firms, output and consumption by the inhabitants of a tourism municipality. The long run evolution of the economy of a tourism municipality can be understood by analysing capital accumulation (i.e., the variation in the number and capacity of hotel buildings, for instance), as expressed in Eq. (3) which, in per capita terms (i.e., dividing by total population at time t, L(t)), yields11 a k_ ¼ s AZk |fflffl{zfflffl} ðn þ dÞk.

(5)

f ðkÞ

Note that for the production function (2) (and for given levels of A and Z), consecutive increases in capital per capita (i.e., increases in capital which exceed labour’s growth), k, result in smaller and smaller increases in output _ _ is per capita output growth, k=k per capita, y. Thus, if y=y per capita capital growth, and c_=c per capita consumption _ _ growth, then a steady state will be reached when y=y, k=k and c_=c are constant. In a tourism municipality the steady state will occur when   dk=dt k_ sAZ 1=1a  ¼ sAZka1  ðn þ dÞ ¼ 0 ) k ¼ , k k nþd (6)

a

y ¼ AZk ¼ ðAZÞ1=1a



s nþd

a=1a (7)

10 I.e., the partial derivative of capital with respect to time, K_  ðdK=dtÞ. In general, in the sequel variables with an upper dot denote absolute _ variation with respect to time. The rate of variation is represented by K=K. 11 Where it has conveniently been used the fact that

_  K L_ K_ dðK=LÞ KL K L_ ¼ ¼  k_  2 L |{z} L dt L |{z} L k

n

and 



c ¼ ð1  sÞy ¼ ð1  sÞðAZÞ

1=1a



s nþd

a=1a .

(8)

Once k* is reached, the growth of capital, consumption and output per capita will be zero (i.e., total growth will be equal to the increases in the population). These results are shown in Fig. 2. The quantity of output obtained for different quantities of capital (per capita) is shown at the top of Fig. 2. Starting from a level of capital k(0), ¯ and saving rate (s), technology (A), public goods ðZÞ, capital per capita (and, hence, per capita output and consumption) increases to k*, the level for which the quantity of per capita output devoted to investment equals depreciation and population growth. On the other hand, if the municipality starts from a level of capital which is too high, k0 (0), then since the output obtained from that quantity of capital is too low to cover the depreciation of the capital and the growth of the population, then capital diminishes to reach the steady-state level k*. Thus, in a tourism municipality without investment in public goods, sustainable growth of the standards of living is clearly limited, since, as it has been argued above, it is plausible that diminishing productivity of capital exists. Increases in technological progress, in the working intensity of workers or the quantity of public goods would give rise to a transitory increase in the rate of growth of the jurisdiction’s economy. Thus, higher steady-state levels of capital, output and consumption per capita would be reached, since capital and labour would become temporarily more productive. However, there would not be a sustained increase in per capita terms. This is shown in Fig. 3. Besides, increases in the productivity of capital and labour due to technological progress are unlikely to be important in tourism municipalities. Indeed, in general the production technology in the tourism sector is very simple and labour-intensive, so that productivity improvements yielding continuous betterment of living conditions are likely to be exhausted soon. Furthermore, given the industry’s characteristics (type of technology, but also mean size of tourism firms), improvements in technology are usually out of the hands of individual firms and municipalities. The only input capable of generating growth which is in the hands of those municipalities (although it is not, at least directly, in the hands of individual private firms) is investment in public goods. As noted above, since they are nonrival, public goods may be consumed by several users (tourists) without getting depleted. Therefore, tourism municipalities can use investment in local public goods to foster sustainable development and growth. This is shown in the next subsection. 3.2. Sustainable development and growth in a tourism municipality without investment in local public goods: the prediction of endogenous growth models This subsection considers a setting where tourism municipalities can tax economic activity and invest the

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(n + ) k

Net disinvestment

y = AZk c(0)' sAZk

c(0)' Gross investment (negative) sAZk < (n + ) k Gross investment (positive) sAZk > (n + ) k

k(0)

Physical capital

k(0)'

k*

sAZk-1 Negative growth

n+

Positive growth

Fig. 2.

proceeds from taxation in local public goods enjoyed by tourists. The analysis follows closely that in Barro (1990) and Barro and Sala-i-Martin’s (1992) papers on endogenous growth models with one sector. In this setting, on the one hand consumers (the inhabitants of tourism municipalities, i.e., local residents) supply labour to tourism firms in exchange for a salary (i.e., they are the waiters and the cleaners at the hotels) and, at the same time, own the firms, earning a return from their investment in assets (i.e., they are the managers and shareholders of the hotels). On the other hand, local residents buy outputs (i.e., consume the tourism product elaborated by tourism firms) and save (buying assets, which can be understood as shares in tourism firms) according to their preferences. Besides, tourism firms produce outputs by means of a given technology, pay wages to local residents for their labour and interest for their capital (dividend payments). A perfect competition setting, where consumers and firms take prices as given is assumed (so that prices in a given tourism municipality are the same as in the rest of the economy).12

3.2.1. Households More to the point, a set of households exists in each municipality. The members of each household are altruistic with their descendants. Thus, households get satisfaction from their own and their descendants’ consumption of different goods.13 Therefore, the inhabitants of a tourism jurisdiction, when taking their decisions, must take into account how their consumption and production choices today may affect the consumption possibilities (i.e., the standard of living) of future generations. In other words, today’s local residents must worry, in some sense, for the sustainable development of the economic activity in their municipality, i.e., they must satisfy their current consumption needs without endangering their descendants’. Formally, households maximise an overall utility function (i.e., they wish to make their own and their descendants’ happiness as big as possible) such as Z

1

eðrnÞt

U¼ 0



 cð1yÞ  1 dt; 1y

(9)

12

It is worth realising that in Section 3.1 it is also assumed that local residents are tourists and owners of the tourism firms at the same time. See footnote 10.

13 Although they get less utility from their descendants’ consumption, whence the introduction, as it will be noticed, of a discount factor.

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(n + ) k y = A(t1)Zk

sA(t1)Zk

y = A(t0)Zk sA(t0)Zk

k(t0)*

k(t1)*

sA(t0)*Zk-1

Physical capital sA(t1)*Zk-1

n+

Fig. 3.

which is the discounted sum (r is the discount factor, which gives less weight to future generations’ consumption) of each period’s utility from consumption of all the household’s members,14 u(c(t)), where cð1yÞ  1 . (10) 1y In (10), y (y40) is a parameter showing local residents’ preferences for a temporal consumption path (thus, the higher y the more consumers would like to enjoy a uniform, smooth consumption path). Local residents, when maximising (9), face the constraint uðcðtÞÞ ¼

_ ¼ ðrðtÞ  nÞaðtÞ þ wðtÞ  cðtÞ, aðtÞ

(11)

i.e., the variation in net assets (tourism firms’ shares) per _ person between two time periods ðaðtÞÞ depends on wages (w(t)), consumption, the increment in the members of a household (n) and the returns from the assets (r(t)).15 More to the point, expression (11) says that a tourism munici14

See, for instance, Ramsey (1928), Cass (1965) and Koopmans (1965). Remember that local residents take wages and returns on wages as given. 15

pality’s inhabitants receive, on the one hand, income from the returns on assets (r(t)a(t)), i.e., from firms’ profits, and from wages (w(t)). On the other hand, they face expenses due to their own consumption and to the diminution of the per capita returns on assets caused by the increase in population (na(t)). When this process gives rise to net savings, then local residents’ assets increase.16,17 The optimal growth rate of consumption per capita is given by (see Appendix A) c_ 1 gc ¼ ¼ ðr  rÞ. c y

(12)

Condition (12) says that the optimal rate of consumption increases with the returns on investment in tourism assets 16

Since local residents own the firms, assets become capital and are used in the production of the tourism output. 17 Finally, the transversality condition which guarantees that no Ponzi schemes exist (i.e., that all debts are settled when the municipality’s residents cease to exist) is   R1  ½rðnÞndn lim aðtÞe 0 X0,

t!1

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(since then local residents, as owners of the tourism firms, are richer for a given level of assets) and decreases with the discount rate (since then the municipality’s inhabitants prefer their own consumption instead of their descendants’) and with the local residents’ marginal propensity to smooth their consumption. 3.2.2. Tourism firms On the supply side, it is assumed that a given number of tourism firms exist in the municipality. Each firm produces its tourism product by means of a linear production function such (see Barro, 1990) Y i ¼ AL1a K ai Z 1a , i

(13)

where L is labour, K capital, Z a public good, A40 a parameter (identical for all the firms in a jurisdiction) indicating the state of technology,18 and a (0oao1) denotes the type of returns to scale and subscript i identifies the firm. It should be noted that the public good Z is pure (hence the lack of subscript), i.e., once provided, all firms can employ it as an input (nonexcludability property) and its use by each firm does not diminish the quantity of it available for other firms (nonrivalry property).19 Thanks to the introduction of an input with public good characteristics a tourism jurisdiction can enjoy constant returns to scale when capital and public goods increase at the same rate (keeping labour constant), i.e., when investment in building new hotels, for instance, is matched by investment in public infrastructures, then a tourism jurisdiction’s output increases proportionally. It is important to note that, in contrast to Solow and Swan’s setting, here the total quantity of local public goods does not directly depend on the firms’ decisions. Since public goods are nonexcludable, it is to be expected that individual firms rely on free riding on each other’s provision of public goods. Hence, the local public sector should be called upon to provide the optimal quantity of public goods.20 To make things simple, it can be assumed that the public sector runs a balanced budget, which is financed by means of a proportional tax at rate t on a P jurisdiction’s total output Y ¼ Y i . Total proceeds from i of the public good, i.e., the tax are spent in the provision Z ¼ tY. By combining (13) and Z ¼ tY an explicit equation yielding the quantity of public goods finally provided as a function of the tax rate results, the state of the technology, total labour and capital per capita results Z ¼ ðtALÞ1=a k.

(14)

18 Hence, it is assumed that all tourism firms have access to the same technology. 19 Implications for growth and development would not change a lot if congestion (i.e., some degree of rivalry) was allowed. See, for instance, Barro and Sala-i-Martin (1992). 20 Several important questions regarding the ability of a benevolent public sector to provide the quantity of public goods which maximises a municipality’s economic growth (and well-being) arise. For instance, concerns could be raised regarding the financing sources (taxes, for instance) available to municipalities. See Section 4 for more on this.

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Hence, it is possible to compute the tourism firms’ profits as output (net of taxes) minus labour and capital payments and capital depreciation,21 thus obtaining the behaviour of the variables affecting tourism firms (see Appendix B). 3.2.3. Market equilibrium in tourism municipalities From the expressions (see Appendix C) which characterise the behaviour of the different variables of interest when the tourism municipality’s market is in equilibrium (i.e., when consumers and producers’ decisions are compatible), it is possible to compute the rates of growth for consumption, capital and output per capita. These growth rates are all identical and can be characterised by i 1h c_ 1 gDecentralised  ¼ ½r  r ¼ ð1  tÞaA1=a ðtLÞ1a=a  d  r . y c y

(15) From (15) it is straightforward to conclude that in a tourism municipality public goods have two opposite effects on economic growth. On the one hand, they decrease economic growth because the marginal productivity of capital and labour diminishes when, in order to finance public goods, output is subtracted from the economy by means of the tax on tourism firms’ output (this effect is given by 1t). On the other hand, the provision of public goods increases economic growth by increasing the productivity of capital and labour (tð1aÞ=a in Eq. (15)). Since the provision and financing of public goods give rise to two effects of opposite sign, it is interesting to find the optimal tax rate, t* (and, therefore, the optimal quantity of public goods, Z*), which maximises the local economy’s growth. This results from differentiating (15) with respect to the tax rate: i qg 1h  ð1  aÞA1=a t12a=a L1a=a  A1=a L1a=a t1a=a qt y ¼ 0 ) t ¼ 1  a. ð16Þ This is shown in Fig. 4(a). Deviating greater and greater quantities of the firms’ output in order to spend in local public goods diminishes net investment in capital (too many public goods and two few hotels are provided). At the end of the day, after certain limits are reached (and since capital is essential in the tourism product’s production function), growth may decrease and, for high tax rates (and hence low capital investment), it may become negative, i.e., a tourism municipality may become poorer. If this were the case, it would be possible to increase the productivity of capital and labour by diminishing the tax rate. If, on the other hand, the tax rate were lower than optimal, then it would possible to increase growth by augmenting the tax rate (too few public goods and too many hotels would be provided). If more public goods were provided, then the increase in the productivity of capital and labour would exceed the distortions (in terms of lower 21 The tourism product can be understood as the numeraire, with its price set to 1.

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c



c* (t)

cs (t)

* s

c0 (t)

c(0)

0 0

cn (t)

n *

s

Tax / Public goods

Time

n

Fig. 4.

output) caused by higher taxes. From the result in (16) it can be shown (see Barro & Sala-i-Martin, 1999) that the public sector in a free market tourism municipality maximises social welfare by setting the optimal tax t ¼ 1a. The effect of four different tax rates t (for different growth rates. optimal (g*), suboptimal (gs), suboptimal and zero (g0), and suboptimal and negative (gn)) on a municipality’s consumption is shown in Fig. 4(b). 3.3. Corollary: the sustainability of tourism and the preservation of the environment The effects on the sustainability of economic growth emerging from the insufficient provision of public goods are straightforward: economic growth is lower and, in some circumstances, the sustainability of the tourism activity may be in danger. It should be noted that these results have dramatic consequences for the so-called tradeoff between tourism development and the environment’s preservation. Preservation of the environment can be understood as a kind of public good. Since it is plausible that a positive relationship exists between public goods and private tourism supply, then tourism development and the preservation of the environment would not be conflicting objectives, but rather complements (see, for instance, Rigall-I-Torrent & Fluvia`, 2007): an adequate preservation of the environment (which requires optimal Z) would allow sustained (and sustainable) economic growth throughout time in tourism municipalities. All things considered, in a tourism development model based on the supply of public goods the pronounced (and apparently inescapable) tradeoff between growth and the environment’s preservation would vanish. In traditional ‘‘beach-and-sun’’ tourism

models, based on the intensive use of natural resources, no apparent way out exists: higher economic growth is only possible by destroying (through intensive use) natural and environmental resources. This growth model is doomed, unless technological innovations occur.22 This is shown in Fig. 5. The path depicted in black, which represents a growth model based on the consumption of depletable natural resources, reaches a maximum level of output, y¯ , when all available natural resources are depleted. If no technological innovations increasing the endowment of natural resources occur, then output would progressively decrease: the tourism municipality would become gradually poorer. However, in a model based on the supply of public goods complementing private goods, higher (sustainable) economic growth in the long run is solely possible if natural resources are preserved. In such a development model the vicious circle of ‘destroying in order to grow’ becomes the virtuous circle of ‘preserving to grow’. In this setting the scope for achieving a development path like the one depicted in dark grey in Fig. 5, where output per capita increases throughout the path, is greatly increased. 4. Some implications 4.1. Public goods and growth The gist of the implications from the analysis above is that because they are not depleted by use, public goods lay 22 The capacity of technological innovations to preserve and/or regenerate the environment, and thus increase the scope for sustainable growth, should not, unlike it has frequently happened in the past, be underestimated.

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Use of depletable resources

Depletable resources available Sustainable development path Unsustainable development path

y

Output per capita

Fig. 5.

the foundations for sustainable development in tourism municipalities. Since higher quantities of inputs having public good characteristics imply higher output for that municipality, a sort of virtuous circle emerges: higher output leads to higher levels of public goods which could in turn lead to higher output, feeding back successive waves which would not stop because of diminishing returns. Thus, a development model based on public goods is more likely to be sustainable than one relying on depletable inputs. Although the setting above is quite stylised, the analysis has important implications for the role of the public sector in guaranteeing the optimal provision of public goods in tourism municipalities and for local public finance. It also suggests that joint initiatives between the public and the private sectors could be in order. A simple numeric example will make clear how the quantity of public goods affects a tourism municipality’s economic growth. Assuming the following values for the parameters in expression (16) a ¼ 0.5 (parameter characterising the production possibilities of the economy), y ¼ 0.5 (parameter characterising consumers’ consumption path), t ¼ 0.5 (tax rate on output), d ¼ 0.06 (depreciation rate), r ¼ 0.05 (discount factor), A ¼ 1 (state of technology), k(0) ¼ 1 and L(0) ¼ 1 (initial capital and labour endowments), then the optimal tax rate (which completely determines the quantity of public goods) is t ¼ 1a ¼ 0.5. This yields a growth rate of 3% a year for output, capital and consumption per capita. Therefore, output, capital and consumption available per person would take 23 years to double. On the other hand, if the public sector was unable to invest the optimal quantity of private output (by means of taxes) then economic growth would suffer. For instance, if the tax rate was 0.4 (i.e., 40% of total output was invested in local public goods), the economy would rise at a

rate of 2% a year. This would have dramatic effects for the municipality’s economy, since now output, capital and consumption per capita would take 34 years to double. Something similar would happen if investment in public goods were excessive. Furthermore, if the tax rate was 0.25 (and hence the quantity of public goods provided was much lower than what would otherwise be optimal), then the municipality’s economy would shrink at a rate of 3.25% a year. This would imply that output, capital and consumption per capita in the municipality would be halved every 21 years approximately. 4.2. Private firms and the public sector The production function in (1) can be understood as a stylised representation of the hypothesis that individuals obtain satisfaction from a tourism product which combines public and private attributes. For instance, a tourist’s enjoyment of a stay in a hotel during her holidays is affected not only by the specific characteristics of the hotel finally chosen (its number of rooms, category, discotheque, swimming pool size, activities for children or food type and quality, to name only a few). The characteristics of the municipality or region where the hotel is located also play an important role in that tourist’s final experience and satisfaction: the cleanness of the swimming waters, the public safety, the approaches to the resort (roads, airports, railways, ports, etc.) or the preservation of the environment, although being out of the hands of a particular hotel, also matter (see, for instance, Rigall-I-Torrent & Fluvia`, 2007). When public and private characteristics are complements, firms should realise that their offer of private attributes should match the supply of public attributes in their location. Otherwise, two few (or too many) private

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characteristics would be offered relative to the firms location’s public characteristics, so that firms would be offering a product variety which would not fulfil their customer’s expectations. This would have undesired consequences on a municipality’s economic growth. Nevertheless, since firms are not able to control the supply of public attributes which surround them, then the public sector should also provide the quantity of public goods which yields the optimal rate of economic growth. Otherwise, their product variety will hardly match their customers’ desires and, as a result, economic growth would be again lower than expected. 4.3. Local public finance It could be argued that it is in tourism municipalities’ self-interest to provide the optimal quantity of public goods. However, the local public sector may prove unable to do so. In Section 3 it has been assumed that the local public sector is responsible for the provision and financing of public goods. As a matter of fact, several levels of government exist. Each level collects taxes and provides some goods and services. It is important to remark that it will be seldom the case that a municipality’s local public sector receives from higher government levels the very same quantity of tax proceeds which have been collected in its jurisdiction. Consider, for instance, tourism municipalities. It is usually the case that these municipalities enjoy higher incomes per head. Therefore if progressive taxation is in place, then the inhabitants of tourism municipalities would surely pay more to higher government levels than what they receive. In Section’s 3 setting, this would have negative consequences for economic growth. To see this, assume that the total tax burden for the firms in a tourism municipality is given by t ¼ tiL þ tF ,

(17)

where tiL is the tax rate set by municipality i’s local government23 and tF is the tax rate set by, say, the federal government (the same for all municipalities). Additionally, assume that although the taxes collected by the local government are assigned in full to the provision of local public goods, taxes collected by the federal government may not be earmarked for the provision of public goods where they have been collected. Therefore, the quantity of public goods finally supplied will be given by Z ¼ ðtiL þ ii tF ÞY ,

(18)

23 Local governments should be aware that the introduction of a tax at a local level might affect the competitiveness of the local economy through its effect on the price system. The sign of the effect on competitiveness is, however, unclear. Unless supply is perfectly inelastic, higher taxes would mean higher prices, which might diminish the competitiveness of local tourism firms. Nevertheless, if the revenue raised through taxes is used to provide public goods and public goods, and private supply are complements, then the competitiveness of local tourism firms might increase (see Rigall-I-Torrent & Fluvia`, 2007).

where li (liX0) is the percentage of federal taxes invested in public goods in the municipality where they have been collected.24 Now, the economy’s growth rate in the municipality (15) becomes (see Appendix D) gDecentralised ¼

i 1h ð1  tiL  tF ÞaA1=a ð½tiL þ ii tF LÞ1a=a  d  r . y

(19) It should be noticed that growth in the jurisdiction depends now on the tax rate set by the local government, tiL , as well as on the federal tax rate, tF, and the federal investment rate in the municipality, ii. By differentiating (19) with respect to tiL it is possible to compute the tax rate,  tiL , which should be set by the local public sector so as to maximise economic growth in the municipality25 qg  ¼ 0 ) tiL ¼ ð1  aÞð1  tF Þ  aii tF . qtiL

(20)

Now the optimal local tax rate is negatively related to the federal tax and investment rates. This can be seen under four representative scenarios. If the federal government did not exist (which would imply tF ¼ 0 and ii ¼ 0), then the  local government would set the optimal tax rate tiL ¼ 0:5,26 and the economy’s growth rate would then be 3%. However, if tF40 and ii ¼ 0 then, although the local public sector would optimally lower its tax rate, federal taxes would diminish the municipality’s growth rate (which becomes negative for any tF40.061).27 Something similar would happen when tF40 and ii ¼ 0.5. With tF40 and ii ¼ 1, then the optimal local tax rate would diminish as the federal tax rate increased, since both taxes are complements. The growth rate would be constant (at 3%) so long as tF+tL ¼ 0.5 and would decrease when tF+tL40.5, since too much output would be taken away from the economy (and insufficient investment in public goods would result). Indeed, the optimal local tax rate would be negative (i.e., a subsidy should be given to the firms in the municipality) when tF40.5. Finally, for tE40 and ii ¼ 1.25 the growth rate would increase with the federal tax rate as the optimal local tax rate shifted downwards. This is because, although the federal government would invest locally (in public goods) a higher amount of the revenues collected, once a certain tax burden was reached (tF ¼ 0.5, for which a maximum growth rate exceeding 9% 24 Thus if ii ¼ 0, then no investment would take place in municipality i, if 0oiio1 investment would be lower (but positive) with respect to the total taxes collected, if ii ¼ 1 investment in public goods would match the resources collected, and if ii41 investment would exceed the federal government’s tax revenues in the municipality. 25 It is assumed that the local government sets its tax rates optimally after observing both the federal tax and investment rates. 26 For parameter values a ¼ 0.5, y ¼ 0.5, t ¼ 0.5, d ¼ 0.06, r ¼ 0.05, A ¼ 1 and L ¼ 1. 27 In all four scenarios it is assumed that federal and local tax rates are between 0 and 1. With regard to the local public sector, this implies that it is not possible to give subsidies (which would mean tLo0) or to collect an amount in taxes greater than total local output (which would imply tL41).

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would be achieved), the federal tax rate would become too high and (since it is assumed that it would not be possible for the local public sector to give subsidies to firms, so that the overall tax burden decreased) economic growth would eventually decrease. To sum up, although public goods may lead to a sustainable development pattern in tourism municipalities, if the local public sector is unable to finance the local public goods required in order to sustain the economic activity in the municipality, then a vicious circle may emerge. A lack of public good provision would diminish the municipality’s output, so that lower taxes would be collected and invested in public goods, which, in turn, would cause output to shrink, and so forth. 5. Conclusions Long-run sustainable development in jurisdictions whose main economic activity is tourism is only possible if the inputs entering the tourism firms’ production functions are incessantly replicated without incurring in diminishing productivity. Some inputs, such as physical capital and labour may be replicated without problems, but they are subject to diminishing marginal productivity when increasing quantities of them are used without increasing other inputs. Besides, in the tourism sector (with respect to other industries), physical capital has strong linkages with a municipality’s territorial surface. This implies that restrictions in the available territorial surface limit in turn the scope for capital generated growth. Apart from capital and labour, public goods are important inputs for the tourism industry. Owing to their nonrivalry property, because of which they may be consumed by many tourists without depleting a municipality’s available endowments of them, public goods might be a source for sustainable development and growth. Indeed, public good provision influences tourism municipalities’ growth in two (opposite) ways. On the one hand, public good provision diminishes economic growth by means of decreasing capital and labour’s marginal productivity when, in order to finance the provision, output is taken away from the economy. On the other hand, public goods boost growth by increasing the productivity of capital and labour. From this point of view, tourism and the environment’s preservation might be complementary activities. The latter can be understood as a kind of public good, so that it allows economic growth in tourism municipalities to be sustained and sustainable throughout time. Therefore, a tourism model based on the supply of public goods may escape form the apparently unavoidable trade-off between economic development and preservation of the environment. However, if investment in public goods were lower than optimal, then economic growth in tourism municipalities would be lower than what would be socially optimal and, in some circumstances, the sustainability of development

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might be in danger. This is likely to happen when higher levels of government can set taxes (without links to local taxes) on the municipalities’ economic activity, since then excessive tax burdens may fall on the tourism municipalities’ inhabitants, so that the local public sector may be unable to finance the necessary quantities of public goods. Acknowledgement The author wishes to thank the helpful advice of three anonymous referees. Appendix A Consumers need to solve  ð1yÞ  Z 1 c 1 Max U ¼ eðrnÞt dt, fc;ag 1y 0 s:a: a_ ¼ ðr  nÞa þ w  c,   Rt  ½rðnÞndn lim aðtÞe 0 X0, t!1

að0Þ ¼ a¯ ,

ðA:1Þ

where the last constraint denotes the initial endowment of assets available for the inhabitants of a tourism municipality (mainly, territorial and landscape resources given away by Nature). To solve problem (A.1), it is useful to resort to the present value Hamiltonian  ð1yÞ  c  1 ðrnÞt H^ ¼ þ u½w þ ðr  nÞa  c. (A.2) e 1y The first-order conditions for (A.2) (note that local residents must decide which proportion of output they consume and save) are qH^  cy eðrnÞt  u ¼ 0 ) u ¼ cy eðrnÞt , qc

(A.3)

qH^ ¼ u_ ) u_ ¼ ðr  nÞu, (A.4) qa where (A.4) is Euler’s equation, which characterises the optimal consumption path through time. By differentiating (A.3) with respect to time, it results



qcy ðrnÞt e  ðr  nÞcy eðrnÞt . qt The substitution of (A.3) in (A.4) yields

u_ ¼

(A.5)

u_ ¼ ðr  nÞcy eðrnÞt

(A.6)

and setting (A.5) and (A.6) equal, the condition yielding the optimal consumption path throughout time, and therefore the growth rate of consumption per capita (gc) c_ 1 (A.7) gc ¼ ¼ ðr  rÞ, c y results, where ðdu0 =dtÞ=u0 ¼ ½u00 ðcÞc=u0 ðcÞð_c=cÞ has been used.

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Appendix B

Appendix D

Firms’ net profits are pi ¼ ð1  tÞY i  wLi  ðr þ dÞK i ¼ ð1  tÞAL1a K ai Z1a  wLi  ðr þ dÞK i i

¼ Li ð1  tÞAkai Z1a  w  ðr þ dÞki ,

ðB:1Þ

where kiKi/Li (i.e., capital per capita at firm i), d is the capital’s depreciation rate and the rest of the variables have already been defined. As explained above, because Z is a public good, individual firms are not able to decide on the quantity of Z finally provided. Hence, a firms’ choice is restricted to the quantities of capital and labour to be employed. Then, first-order conditions for profit maximisation are: qpi  ð1  tÞð1  aÞAkai Z1a  w ¼ 0 ) w qLi . ¼ ð1  tÞ ð1  aÞAkai Z 1a |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}

Expression (14) becomes

1=a k. Z ¼ ðtiL þ ii tF ÞAL

(D.1)

Besides, firms’ profits are (see (B.1))

pi ¼ Li ð1  tiL  tF ÞAkai Z 1a  w  ðr þ dÞki

(D.2)

and thus first-order conditions for profit maximisation are qpi  ð1  tiL  tF Þð1  aÞAkai Z 1a  w ¼ 0 qLi ) w ¼ ð1  tiL  tF Þð1  aÞAkai Z 1a

ðD:3Þ

and qpi  ð1  tiL  tF ÞaAkið1aÞ Z1a  r  d ¼ 0 qK i ) r þ d ¼ ð1  tiL  tF ÞaAkið1aÞ Z 1a .

ðD:4Þ

ðB:2Þ

Labour0 s net marginal product

References qpi  ð1  tÞaAkið1aÞ Z 1a  r  d ¼ 0 ) r þ d qK i ¼ ð1  tÞ

aAkið1aÞ Z1a |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

.

ðB:3Þ

Capital0 s net marginal product

Substituting (B.1) in (B.3) and setting ki ¼ k (remember: all firms are identical, so that they all use the same quantity of capital) yields r þ d ¼ ð1  tÞaAkð1aÞ ðtALÞ1a=a k1a ¼ ð1  tÞaA1=a ðtLÞ1a=a

ðB:4Þ

Appendix C The expressions which characterise the behaviour of the different variables of interest when the tourism municipality’s market is in equilibrium are 1 gc ¼ ðr  rÞ, y

(C.1)

k_ ¼ ðr  nÞk þ w  c,

(C.2)

  Rt  ½rðnÞn dn lim kðtÞe 0 ,

(C.3)

Z ¼ ðtALÞ1=a k,

(C.4)

w ¼ ð1  tÞð1  aÞAkai Z1a ,

(C.5)

r þ d ¼ ð1  tÞaA1=a ðtLÞ1a=a .

(C.6)

t!1

Barro, R. J. (1990). Government spending in a simple model of endogenous growth. Journal of Political Economy, 98(5, Part II), S103–S125. Barro, R., & Sala-i-Martin, X. (1992). Public finance in models of economic growth. Review of Economic Studies, 59(4), 645–661. Barro, R., & Sala-i-Martin, X. (1999). Economic growth. Cambridge, MA: MIT Press. Boulding, K. E. (1966). The economics of the coming spaceship earth. In H. Jarrett (Ed.), Environmental quality in a growing economy. Essays from de Sixth RFF Forum. Cass, D. (1965). Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32, 233–240. Cornes, R., & Sandler, T. (1996). The theory of externalities, public goods and club goods. Cambridge: Cambridge University Press. Jones, C. I. (2002). Introduction to economic growth. W.W. Norton. Koopmans, T. C. (1965). On the concept of optimal economic growth. In The econometric approach to to development planning. Amsterdam: North-Holland. Ramsey, F. (1928). A mathematical theory of saving. Economic Journal, 38, 543–559. Rebelo, S. (1991). Long-run policy analysis and long-run growth. Journal of Political Economy, 99, 500–521. Rigall-I-Torrent, R., & Fluvia`, M. (2007). Public goods in tourism municipalities: Formal analysis, empirical evidence and some implications for sustainable development. Tourism Economics, 13, 361–378. Romer, P. (1986). Increasing returns and long-run growth. Journal of Political Economy, 94, 1002–1037. Romer, P. (1990). Endogenous technological change. Journal of Political Economy, 98, S71–S102. Rubinfeld, D. L. (1987). The economics of the local public sector. In A. J. Auerbach, & M. Feldstein (Eds.), Handbook of public economics (II). Amsterdam: North-Holland. Samuelson, P. (1954). The pure theory of public expenditure. Review of Economics and Statistics, 36, 1243–1259. Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65–94. Swan, T. W. (1956). Economic growth and capital accumulation. Economic Record, 32, 334–361. United Nations Environment Programme /http://www.unep.org/S.

ARTICLE IN PRESS R. Rigall-I-Torrent / Tourism Management 29 (2008) 883–897 World Commission on Environment and Development. (1987). Our common future. Oxford: Oxford University Press. World Tourism Organization (WTO), United Nations Environment Programme (UNEP), United Nations Educational, Scientific and Cultural Organization (UNESCO) and European Union. (1995).

897

Lanzarote charter for sustainable tourism /http://www.world-tourism. org/sustainable/doc/Lanz-en.pdfS. World Tourism Organization. (2004). Sustainable definition of tourism. Conceptual definition /http://www.world-tourism.org/frameset/ frame_sustainable.htmlS.