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The purpose of this study is to examine effects of tourism on economic development. We build an economic growth model of a small open country with tourism in a perfectly competitive economy. The economy coists of one service sector and one industrial sector. International tourists and domestic residents coume non-traded goods and services. The land is distributed between housing and supply of services. The production side is the same as in the neoclassical growth theory, while we use an alternative utility function to determine behavior of the household. The system has a unique stable equilibrium point. We simulate the motion of the national economy and examine effects of changes in the rate of interest, the price elastity of tourism, the global economic condition, the total productivities of the industrial and service sectors, and the propeity to save. The comparative dynamic analysis provides some important iights. For itance, when the price elastity of tourism is increased, the tourist demand and the price of services are reduced; national trade balance is deteriorated; the output of the service sector is reduced and the output of the industrial sector is increased; some of labor force is shifted from the service sector to the industrial sector; the lot size fal and the land input of the service sector is reduced; and the GDP, the coumption leve of the goods and services and wealth level rise initially but fall in the long term. Keywords: tourism, price elastity of tourism, growth, capital accumulation, small open economy. 1. Introduction Tourism has grown very rapidly in recent years. Tourism goods such as monuments of national heritage, historical sites, beaches, and hot springs, are not - tradable as their coumption is at the same location. Nevertheless, people in other regio can visit the spot. Tourism converts non - traded goods into tradable ones. As reported by the World Tourism Organization (2008), over 903 million people travelled to a foreign country in 2007. The export income of international tourism is the fourth after fue, chemica, and automotive products. Tourism accounts for 6 per cent of global exports overall and thirty per cent of global exports of services (Copeland 2012). In some open economies, like Singapore and Hong Kong, foreign tourism is an important source of income and employment. Tourism affects local economies in different ways. On the one hand, tourism attracts resources such as labor, capital and housing from other sectors of the economy and, on the other hand, the income generated by tourism encourages development of other economic activities. A tourism boom may deteriorate environment and cause congestio in traportation systems and other public falities. There is a close interdependence between tourism and other economic activities. This study examines the dynamic interdependence in a general equilibrium framework. There are many studies on tourism in the literature of economi.1 As observed by Chao et al. (2009), study of tourism has been largely limited to the static framework. A main purpose of this study is to study dynamic interdependence between tourism and the rest of the economy. We are ao concerned with changes of economic structures with tourism. As tourism uses national resources, development of tourism may cause changes of economic structure. As tourism competes with the other sectors in the economy for resources and labor, it may lead de industrailization.2 On the other hand, tourism may ao stimulate industrialization as tourism brings in income and increases demands for industrial goods. It can be seen that the net effect of a tourism boom on other aspects of the economy system is situation-dependent. In fact, empirical studies in the literature demotrate an opposite For itance, Sinclair, and Stabler (1997); Luzzi, and Flücger (2003); Hazari, and Sgro (2004); and Hazari, and Lin (2011). Zeng, and Zhu (2011) examine this issue in a static equilibrium framework. This study is concerned with dynami of tourism and economic structural change in a small-open economic growth framework (see ao, Corden, and Neary, 1982; Copeland, 1991). Issue 2(6) Volume III Winter 2012 relatiohip between a tourism boom and economic development.3 Hazari, and Sgro (1995) develop a model to study the dynamic relatiohip among tourism, capital accumulation, per capita coumption and the terms of trade. According to their study an increase in the international demand for tourism leads to a positive effect on long - run economic growth. In another study by Chao et al. (2006), it is found that an expaion of tourism can result in capital decumulation in a two - sector dynamic model with a capital - generating externality. In order to fully understand possible effects of tourism on national economic development and economic structure, it is necessary to build a dynamic general equilibrium framework.4 This study studies tourism and economic growth on basis of Uzawa's twosector growth model in context of a small - open economy. There are a few dynamic economic mode which deal with the interdependence between economic growth and tourism with micro - behavioral foundation. Nevertheless capital accumulation is seldom modeled with land and land markets in the literature of tourism economi. This study makes a contribution to the literature of tourism by developing an economic growth model with tourism, basing on the two key mode in the neoclassical growth theory and tourism economi within the context of growth theory of small open economies. The two mode are the Uzawa two - sector growth model in the neoclassical growth theory and the growth mode with tourism in tourism economi. Most of the mode in the neoclassical growth theory model are exteio and generalizatio of the pioneering wor of Solow (1956). The Solow model has been extended and generalized in numerous directio.5 An important exteion was initiated by Uzawa (1961), who made an exteion of Solow's one - sector economy by a breakdown of the productive system into two sectors using capital and labor, one of which produces industrial goods, the other coumption goods. Solow's one - sector growth model, Uzawa's two - sector growth model, and their various exteio and generalizatio are fundamental for the development of new economic growth theories as well.6 But all these studies do not have tourism. This study structurally generalizes the Uzawa two - sector model to include tourism. As observed by Zeng, and Zhu (2011), in the literature of tourism economi, almost all the mode are based on a small open economy. We still follow this tradition in dealing with growth and capital accumulation within the analytical framework of small open economies.7 The neoclassical growth aspects of our model are based on Zhang (2007). The introduction of tourism to growth theory is influenced by Chao et al. (2006). A main different between our approach and the model by Chao et al. is that this study is based on an alternative utility function proposed by Zhang (2005). Moreover, this model simulates the model to illustrate how the system moves over time. The rest paper is organized as follows. Section 2 denes the basic model. Section 3 shows how we solve the dynami and simulates the model. Section 4 examines effects of changes in some parameters on the economic system over time. Section 5 concludes the study. The appendix proves the main results in Section 3. 2. The growth model with tourism This section denes a small open growth model with capital accumulation. Like in Chao et al. (2009), we coider a small - open economy that produces two goods: an internationally traded good (called industrial good) and a non - traded good (called services).8 Domestic households coume both goods, while foreign tourists coume only services. It is assumed for analytical simplity that tourists do not coume traded goods. Tourism converts the non - traded good into an exportable commodity. Our model is a combination of the basic features of the well - known three mode, the Solow growth model, the Uzawa two - sector growth model, and the growth mode with tourism. An See, for itance, Balaguer, and Cantavella - Jorda (2002); Dritsas (2004); Durbarry (2004); Oh (2005), and m et al. (2006). 4 Dwyer et al. (2004) discuss the need for dynamic general equilibrium modeling when studying tourism and its interaction with the rest economy. Blake et al. (2006) ao address the issue. 5 The literature of the neoclassical growth theory is referred to Burmeister, and Dobell (1970), and Zhang (2005). 6 See, for itance, Diamond (1965): Stiglitz (1967); Benhabib et al. (2000); Drugeon, and Venditti (2001); and Ortigueira, and Santos (2002). 7 Refer to, for itance, Obstfeld, and Rogoff (1996); Lane (2001); Kollmann (2001, 2002); Benigno, and Benigno (2003); and Galí, and Monacelli (2005), for the literature on economi of open economies. It should be noted that as far as the production side and international markets are concerned, our model follows the traditional modeling framework. As these mode are analytically complicated and analyze many other aspects of international markets, our model can be further generalized or extended in some directio on the basis of the traditional literature. 8 The classication of the economic sectors is ao similar to that in a growth model of a small open economy by Brock (1988), in which goods and services are divided into traded and non-traded. Brock examines the dynamic adjustment of the relative price of non - traded and the current account following exogenous shoc, such as government purchases, changes in tax income or investment subsidy. Journal of Environmental Management and Tourism open economy can import goods and services and borrow resources from the rest of the world or exports goods and lend resources abroad. There is a single good, called industrial good, in the world economy and the price of the industrial good is unity. Capital depreates at a cotant exponential rate, k , which is independent of the manner of use. We assume that the economy is too small to affect the world interest rate. The households hold wealth and land and receive income from wages, land rent, and interest payments of wealth. Land is only for residential and service use. Technologies of the production sectors are characterized of cotant retur to scale. All markets are perfectly competitive and capital and labor are completely mobile between the two sectors. Capital is perfectly mobile in international market and we neglect possibility of emigration or/and immigration. We assume that labor is homogeneous and is xed. Industrial sector The industrial sector uses capital and labor as inputs. We use subscript index, i and s , to denote respectively the industrial and service sectors. Let K j t and N j t stand for the capital stoc and labor force employed by sector j , j i, s , at time t . We use F j t to represent the output level of sector j . The production function of the industrial sector is t Ai i t Nii t , i , i 0 , i i 1, (1) products, and rms earn zero prots. The rate of interest, r * , is xed in international market. The wage rate, wt , industrial sector chooses t and Ni t to maximize prots. The marginal conditio are where Ai , i , and i are parameters. Markets are competitive; thus labor and capital earn their marginal is determined in domestic market. Hence, for any individual rm, r * and wt are given at any point of time. The r i Ai i t , wt i Ai i t , (2) where t K i t / N i t and r r * k . As r * is xed, from (2) we have A i i r 1 / i , w i Ai i . (3) Hence, we can treat and w as functio of r * . Service sector The service sector uses three inputs, capital K s t , labor force N s t , and land t , to supply services. The production function of the service sector is (4) t As K s s t N ss t s t , s , s , s 0 , s s s 1, where As , s , s , and s are parameters. Let pt and Rt stand respectively for the price of the service and the land rent. The marginal conditio are r s As pt s 1 t s t , w s As pt s t s t , Rt s As pt s t s 1 t , (5) where k s t K s t L t , t s . N s t N s t From (5) we solve s w . s r (6) Hence, we can treat k s as a function of r * . Issue 2(6) Volume III Winter 2012 Full employment of capital and labor The total capital stoc employed by the country, K t , is used by the two sectors. The capital stock is owned either by domestic residents and the rest of the world. As full employment of labor and capital is assumed, we have K i t K s t K t , N i t N s t N , where N is the xed population. We rewrite the above equatio as N i t k s N s t K t , N i t N s t N . (7) The capital inteities, and k s , are uniquely determined by the xed rate of interest in international market. Solve (7) N i t K t k s N k0 , N s t N K t k0 , (8) where k0 k s . We assume that k0 0. The labor distribution is a unique function of the total capital used by the country. Demand function of foreign tourists Let y f t stand for the disposable income of foreign countries. According to Schubert, and Brida (2009), we assume the following iso-elastic tourism demand function t at y t p t , f (9) where and are respectively the income and price elastities of tourism demand. The variable, at , is dependent on many conditio, such as infrastructures (airports and traportation systems) and environment (like criminal rates, pollutants and congestio). Behavior of domestic households We now describe behavior of households. We use L and Rt to denote the land and land rent. Each household gets income from land ownership, wealth and wage. In order to dene income, it is necessary to determine land ownership structure. Land properties may be distributed in multiple ways under various ititutio. To simplify the model, we assume the land is equally owned by the population. This implies that the revenue from land is equally shared among the population.9 The total land revenue is L Rt . The income from land per household, r t , is r t L R(t ) / N . Coumers make desio on choice of lot size, coumption leve of industrial goods and services as well as on how much to save. This study uses the approach to coumers' behavior proposed by Zhang in the early 1990s. The implicatio of this approach are similar to those in the Keynesian coumption function and mode based on the permanent income hypothesis, which are empirically much more valid than the approaches in the Solow model or the in Ramsey model. The approach to household behavior in this study is discussed at length by Zhang (2005, 2008).10 The current income is y t r * k t w r t , (10) where r *k is the interest payment, w the wage payment, and r the land rent income. We call y t the current income in the see that it comes from coumers' wages and current earnings from ownership of wealth. The sum of income that coumers are using for couming and saving are not necessarily equal to the current income Another two popular assumptio in the literature of urban economi are the absentee landownership and the public ownership. In the former, land is owned by absentee landlords who spend their land incomes outside the economic system. In the latter, for itance as accepted in Kanemoto (1980), the ty government rents the land from the landowners at certain rent and sublets it to households at the market rent, using the net revenue to subsidize ty residents equally. 10 Zhang (2005) has ao examined the relatio between his approach and the Solow growth theory, the Ramsey growth theory, the permanent income hypothesis, and the Keynesian coumption function in detai. It can be shown that the behavior generated by the traditional approaches can ao be observed in Zhang's approach by spefying certain patter of preference changes. Journal of Environmental Management and Tourism because coumers can sell wealth to pay, for itance, the current coumption if the current income is not sufent for couming. The total value of the wealth that a coumer can sell to purchase goods and to save is equal to pi t k t , with pi t 1 at any t , where pi t is the price of the industrial good. Here, we assume that selling and buying wealth can be conducted itantaneously without any traaction cost. The disposable income at any point of time is ^ y t y t k t . (11) The disposable income is used for saving and coumption. At time t the coumer has the total amount of ^ income equaling y to distribute between couming and saving. In the growth literature, for itance, in the Solow model, the saving is out of the current income, y , while in this study the saving is out of the disposable income which is dependent both on the current income and wealth. At each point of time, a coumer distributes the total available budget among the lot size, coumption of services, coumption of industrial goods, and saving. The budget cotraint is ^ Rt l t pt t t st y t . (12) Equation (12) mea that the coumption and saving exhaust the coumers' disposable personal income. We assume that utility level, U t , of the household is dependent on l t , t , t and st as follows U t l0 t 0 t 0 t s 0 t , 0 , 0 , 0 , 0 0 , in which 0 , 0 , 0 , and 0 are a typical person's elastity of utility with regard to lot size, services, industrial goods, and saving. We call 0 , 0 , 0 , and 0 propeities to coume the lot size, to coume services, to coume industrial goods, and to hold wealth, respectively. Maximizing U t subject to the budget cotraint yields l t where ^ yt Rt , t ^ yt pt ^ ^ , t yt , st yt , (13) 0 , 0 , 0 , 0 , According to the denition of s t , the wealth accumulation for the household is k t st k t . Full use of land and demand of and supply for services Land is used for the residential use and service production (14) l t N t L . (15) (16) The equilibrium condition for services is t N t t . Trade balance We use Bt to denote the balance of trade. We have E t r * K t K t pt t . (17) We have thus built the dynamic growth model with endogenous wealth, coumption, and tourism. Issue 2(6) Volume III Winter 2012 3. The dynami of the national economy We now show that the motion of the economic system is determined by a single differential equation. The following lemma shows how we can determine the motion of all the variables in the dynamic system. Lemma 1 The variables, , k s , and w are uniquely determined as functio of r * . The motion of the land rent is determine by R R , (18) in which is a function of R dened in the appendix. We determine all the other variables as functio of R as follows: k by (A12) K k N K by (A11) p by (A9) K i and K s by (A1) N i and ^ N s by (A1) by (8) y by (A4) l , c , , and s by (13) by (15) by (A1) by (A4). Lemma 1 tel that for given rate of interest in the global market, the economic system at any point of time can be uniquely described as functio of the land rent and the other exogenous variables (the rate of interest, land resource, technology, and preference). Hence, if we know the motion of land rent, we can determine the motion of the whole system. It should be remarked that in a model of a small open economy by Turnovsky (1996), domestic capital accumulation involves convex costs of adjustment. The equilibrium growth rates of domestic capital and coumption are determined largely independent. The former is determined by production conditio,11 the latter is determined primarily by tastes. In our model, the capital inteities and the wag rate are determined by the internationally xed rate of interest and production conditio. Nevertheless, the total output leve, the capital stoc employed by the economy, and economic production structure are not only determined by the production conditio and the international rate of interest, but ao by tastes.12 Moreover, coumption is not only determined by preferences but ao related to the rate of interest and the production conditio. As the expressio of the analytical result are tedious, it is difcult to get explit conclusio. For interpretation, we simulate the model. We spefy parameter values as follows r * 0.06 , k 0.05 , N 10 , L 1, Ai 1.5 , As 1, i 0.3 , s 0.2 , s 0.6 , 0 0.8 , 0 0.15 , 0 0.06 , 0 0.06 , a 1, y f 4 , 1.8 , 1.2 . (19) The rate of interest is xed at 6 per cent and the population is 10. The land is unity. It should be remarked that although the speed values are not based on empirical observatio, the choice does not seem to be unrealistic. For itance, some empirical studies on the US economy demotrate that the value of the parameter, , in the Cobb-Douglas production is approximately equal to 0.3 (for itance, Abel, and Bernanke 1998). Some empirical studies show that income elastity of tourism demand is well above unity (Syriopoulos 1995; Lanza et al. 2003). According to Lanza et al. (2003), the price elastity is in the range between 1.03 and 1.82 and income elastities are in the range between 1.75 and 7.36. Refer to, for itance, Gain-Mnos (2007) for other studies on elastities. Following Lemma 1, we determine the variables. We calculate the time-independent variables 4.19 , k s 3.26 , w 1.08 . (25) The initial condition is R0 10 . We plot the motion of the dynamic system in gure 1. As the initial value of the land is xed lower that its long-term equilibrium value, the land rent rises over time. As the land rent rises, demand for services tend to fall. The price of services rises over time and the number of tourists rises. The lot size rises and the land used by the service sector fal. The coumption leve of the goods and services are increased. The output of the industrial sector fal, while the output of the service sector rises. The labor force is shifted from the industrial sector to the service sector. The capital stoc employed by the economy and the industrial sector are reduced, while the capital stock employed by the service sector is increased. This conclusion is observed in the traditional mode of small open economies with perfect capital mobility and perfect substitutability between home capital and foreign bonds (see, for itance, Zeira 1987). 12 This is reflected in the parameter, . 0 Journal of Environmental Management and Tourism gure 1 shows the motion of the variables over time. It shows how the system approaches its equilibrium point. We calculate the equilibrium values of the variables as follows p 4.04 , R 11.93 , Y 38.36 , E 11.96 , K 65.69 , K 112.21, 2.27 , N i 4.51, N s 5.49 , K i 33.71, K s 31.98 , 0.295 , 12.36 , 4.35 , 2.10 , 0.208 , l 0.071. The eigenvalue at equilibrium is 0.15. This conrms that the unique equilibrium point is stable. gure 1. The motion of the national economy 4. Comparative dynamic analysis The previous section plots the motion of the variables. This section examines how changes in some parameters may affect the national economy. As we have shown how to simulate the motion of the system, it is straightforward to make comparative dynamic analysis. rst, we examine the case that all the parameters, except the rate of interest, r * , are the same as in (19). We study what will happen to the dynami of the economic system if the rate of interest is changed as follows13: r * 0.06 0.07 . The rate rises from 6 % to 7 % in the international market. We introduce a variable, xt , to stand for the change rate of the variable, xt , in percentage due to changes in the parameter value. As 11.69 , w 3.66. the cost of capital is increased, the capital inteities and wage rate are reduced as follows The changes in the time-dependent variables are plotted in gure 2. The rise in the cost of capital causes the two sectors to use less capital. The capital stock employed by the national economy is thus reduced. As the rate of interest is increased, the wealth owned by the country as well as the household is increased. The price of services is reduced and the land rent is increased over time till they approach their equilibrium values. The fall in the price attracts As we have explitly solved the dynami, we can ao carry out comparative dynamic analysis by assuming that the rate of interest varies in time, r * t . Issue 2(6) Volume III Winter 2012 more tourists. The output of the industrial sector is reduced as a coequence of the increased production cost, while the output level of the service sector is increased as a net result of increased demand and production cost. Some of the labor force is shifted from the industrial sector to the service sector. The GDP fal over time. The lot size is increased, while the land used for the service sector is reduced. The output of the service sector fal as a net coequence of the rise in the labor force and the reduction in the land and capital inputs. gure 2. A rise in the rate of interest As the country under coideration is open and small and is dependent on tourism, global economic conditio should have strong impact on the national economy. We now study what will happen to the national economy when the foreign income is changed as follows: y f 4 4.1. The capital inteities and wage rate are not affected w 0. A rise in the foreign income increases the number of tourists. As more foreigners visit the country, the price of services and output of the service sector are increased. The labor, capital, and land inputs employed by the service sector are all increased. As the price and land rent are increased, the income of the household is initially reduced but increased later on. The coumption leve of goods and services, wealth level, and lot size are all reduced initially but increased in the long time. More foreign visitors improve the trade balance. In sum, an improvement in the global income reduces the living conditio and wealth of the domestic household in short term but improves these variables in the long term. It should be noted that according to Harzri, and Sgro (1995) an increase in the international tourism leads to a positive effect on long-run economic growth. Our result shows that this conclusion is true in the long term, but not necessarily true in the short term. Similarly, their model shows that for a small open economy the growth in tourist coumption of services increases the welfare. Our simulation demotrates that this conclusion is valid in the long term, but not necessarily true in the short term. We get this "new iight" because our model explitly shows traitional processes of the economic dynami. It should be ao noted that the study by Chao et al. (2006) shows that an expaion of tourism can result in capital decumulation in a two-sector dynamic model with a capital-generating externality. Our simulation demotrates the same conclusion without any externality. There are factors which may the price elastity of tourism. A famous tourist spot may have low price elastity. Development of other countries' tourist industries may ao make the home country more elastic. We now study what will happen to the national economy when the price elastity is changed as follows: 1.2 1.3. The capital inteities and wage rate are not affected, i.e., w 0. The changes in the other variables are plotted in gure 4. A rise in the price elastity reduces the tourist demand and the price of services. The national trade balance is deteriorated as a coequence of decreased number of tourists. The output of the service sector is reduced as the demand fal, while the output of the industrial sector is increased as some of labor force is shifted Journal of Environmental Management and Tourism from the service sector to the industrial sector. The lot size fal, while the land input of the service sector is reduced. The GDP rises initially but fal in the long term. Similarly, the coumption leve of the goods and services and wealth level rise initially but fall in the long term. gure 3. An Improvement in Economic Conditio of the Global Economy 5 0 5 4.5 5.75 N 7. 3 25F K t t gure 4. A rise in the price elastity of tourism Issue 2(6) Volume III Winter 2012 We now allow the total productivity of the service sector to be increased as follows: As 1 1.1. The capital inteities and wage rate are not affected, i.e., w 0. The changes in the other variables are plotted in gure 5. The increased productivity of the service sector raises the output level of services. The price of services fal in assoation with increases in the output level of the service sector. As some of labor force is shifted from the industrial sector to the service sector, the output level of the industrial sector fal. The GDP rises over time. The lot size is reduced, while the land input employed by the service sector is increased. The coumption level of services is increased in assoation with the fall in the price. The coumption level of goods is slightly affected. The trade balance is improved as the technology is improved. The wealth fal initially but rises in the long term. The capital stock employed by the service sector rises, while the capital stock employed by the industrial sector fal. gure 5. A rise in the total productivity of the service sector We now examine what will happen to the national economy when the total productivity of the industrial sector is increased as follows: Ai 1.5 1.6 . The capital inteities and wage rate are increased in the same rate, i.e., w 9.66. The changes in the other variables are plotted in gure 6. As the wage rate is increased, the GDP is increased. The price of services and the land rent are reduced. The demand for goods is increased. As a coequence of the falling price and increasing GDP, the coumption level of services fal initially but rises in the long term. The falling price of services results in decreases in the number of tourists. The trade balance is deteriorated initially but improved in the long term. The lot size is increased, while the land input employed by the service sector is reduced. Some of labor force is shifted from the service sector to the industrial sector. Journal of Environmental Management and Tourism p R 9. 8.25 t 7.5 1.4 0.95 0.5 t gure 6. A rise in the total productivity of the industrial sector We now examine what will happen to the national economy when the propeity to save is increased as follows: 0 0.8 0.81. The capital inteities and wage rate are not affected w 0. The changes in the other variables are plotted in gure 7. As the propeity to save is increased, the wealth is increased. As the disposable income is increased, the lot size and the coumption leve of goods and services are increased. The price and land rent fall in assoation of increases in the disposable income. The increasing price results in decreases in the number of tourists. The land input of the service sector is reduced. As the propeity to save is increased, the trade balance is improved. The total capital stock employed by the country is slightly changed. The output level of the industrial sector is reduced, while the output level of the service sector is increased. R p 50 L gure 7. A rise in the propeity to save Issue 2(6) Volume III Winter 2012 Conclusio This paper proposed an economic growth model of a small open economy with tourism in a perfectly competitive economy. The national economy coists of one service sector and one industrial sector. Following the traditional literature of small open economies, we assume that the rate of interest is xed in international market. The production side is the same as in the neoclassical growth theory. We used a utility function, which determines saving and coumption with utility optimization without leading to a higher dimeional dynamic system like by the traditional approaches. The system has a unique stable equilibrium point. We simulated the motion of the model and examined effects of changes in the rate of interest, the price elastity of tourism, the total productivities of the industrial and service sectors, and the propeity to save. The comparative dynamic analysis provides some important iights. 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Journal of Environmental Management and Tourism – de Gruyter
Published: Dec 1, 2012
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