Demographic and technological growth in tourism market

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Demographic and technological growth in tourism
market

• João Ricardo FariaDepartment of Economics and
  Finance University of Texas Pan American

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Abstract

• This paper examines, in a differential game
  framework, demographic and technological growth
  in tourism market. The number of tourists is
  assumed to follow a logistic growth being
  influenced by demographic and technological
  factors as well as the size of the market and
  investment in the tourism industry. The market
  for tourism is an oligopoly with differentiated
  products.
• In the steady state equilibrium, the optimal
  population level of tourists is directly
  proportional to optimal investments in
  infra-structure and they increase with
  demographic-technological factors, and the size
  of the market and decrease with the number and
  less differentiation of destinations, production
  costs for tourism service and investment, and the
  impatience of tourism authority.

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Introduction

• The evolution of the number of tourists of
  destination i over time is assumed to follow a
  logistic growth function defined as
• This function has the following properties
• 1) when the number of tourists is small in
  proportion to environmental carrying capacity ,
  increases exponentially at the rate
• 2) As becomes larger in proportion to , the
  resources become relatively more scarce affecting
  negatively the population growth rate.

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• The model presented in this paper analyses how
  the tourism authority in a given destination
  controls investment in infra-structure aiming at
  maximizing the profits of the tourism industry
  taking into account how the number of tourists
  evolves over time as well as the strategies of
  other competing destinations.
• The market structure of the tourism industry is
  assumed to be an oligopoly with differentiated
  products as in Candela and Cellini (2006).
  Tourism products are clearly differentiated. The
  market is an oligopoly because the number of
  tourist destinations is limited, tour operators
  and intermediaries are concentrated (Aguilo et
  al., 2003) and the entry of new suppliers is
  costly. In addition, there is strategic
  interdependency among destinations.

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The Model

• The tourism market is an oligopoly with
  differentiated products. At any time t each
  destination i (i1, 2, , n) offers a
  differentiated product with respect to any other
  destination. The demand side is given by the
  following inverse demand function e.g., Spence,
  1976
• (1)
• Where p denotes the price of the product supplied
  by destination i, is the number of tourists in
  destination i at time t. Parameter Bgt0 gives the
  sensitivity of the price of variety i to the
  quantity i. Parameter D, indicates the degree of
  substitutability between any pair of varieties
  the higher D, the more substitutable i.e., less
  differentiated. If D0, the differentiation is
  the largest, if DB, varieties are perfectly
  substitutable. The parameter A captures the
  market size of destination i.

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• The evolution of the number of tourists of
  destination i over time follows a logistic
  growth
• (2)
• We assume that the carrying capacity of
  environment in destination i , is affected by the
  size of the market, A, and by the investment of
  tourism authorities in infra-structure, k. For
  simplicity we assume
• (3)

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• We assume quadratic costs for the investment
  aimed at enhancing infra-structure, and
  production cost for tourism service
• The instantaneous profit for destination i at
  time t is

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• The tourism authority of destination i aims at
  maximizing the present value of the flows of its
  profits over time
• Where rgt0 is the discount rate the impatience of
  the tourism authority.

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The dynamic problem

• Formally the problem is
• s.t.

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• Fortunately in this differential game, the state
  variable pertaining to any given player does not
  affect the optimal choice of different players.
  Thus the open-loop Nash equilibrium coincides
  with the closed-loop solution see Dockner et
  al., 2000 and it is therefore strongly
  time-consistent.

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The symmetry condition

• The symmetry condition
• so that
• Similarly we assume

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The steady-state equilibrium

• The optimal value of investment in
  infra-structure, k
• (9)
• The equilibrium number of tourists, x
• (6)
• Equation (6) shows an important result the
  optimal population level of tourists is directly
  proportional to optimal investments in
  infra-structure, taking into account the size of
  the market.

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• Using equation (9) into (6), we have
• (10)
• Equations (9) and (10) are the focus of this
  paper. They show the optimal values of investment
  and tourist population that solves the
  differential game.

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The comparative statics analysis

• The comparative statics analysis shows that the
  optimal investment and tourist population
  decrease with D, n, z, B, c, r, and increase with
  g and A.
• Recall that a higher D, the more substitutable
  i.e., less differentiated are the destinations,
  the optimal investment and tourist population
  decrease. When the number of destinations, n,
  increases this leads to a fall in optimal
  investment and tourist population.
• In the same vein, when the sensitivity of the
  price of variety i to the quantity i, given by B,
  and investment and tourism services costs, given
  by z and c respectively, rise, optimal investment
  and tourist population fall.

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• As expected, when the impatience of the tourism
  authority, r, increases, this leads to a
  reduction in optimal investment and tourist
  population indicating that myopia in planning
  investments in infra-structure do not pay off.
• As regards to the rate of tourist population
  growth, g, that captures demographic and
  technological forces, an increase in it leads to
  an increase in the optimal investment and tourist
  population. Finally, any exogenous increase in
  the size of the market A, will increase optimal
  investment and tourist population as well.