The Effects of Tourism Promotion on Unemployment and Welfare in the Presence of Environmental Protection and an Agricultural Subsidy

Abstract

Tourism is an important strategy for economic development especially in many developing countries. Actually, tourism promotion has been successful in some developing countries. Thus, policymakers have a special interest in tourism promotion in the hope that it can improve welfare and decrease unemployment. However, tourism promotion has negative impacts on the economy by exacerbating the environmental situation through deforestation, ocean pollution, air contamination, and so on. Thus, introducing a pollution tax in order to mitigate these negative effects of pollution is natural. It is known in the literature that, under certain conditions, tourism promotion coupled with a pollution tax expands the tourism sector and improves welfare while increasing unemployment. This suggests that an additional policy is required in order to alleviate the problem of unemployment. Thus, in this chapter, we develop a three-good general equilibrium model with both the pollution tax and an agricultural subsidy and examine the effects of tourism promotion on production, welfare, and (un)employment.

Appendix 8.1

Herberg and Kemp (1969) have shown that the price-output response may be ambiguous in the presence of externality . Mayer (1974) has shown that the output of a given commodity responds positively to an increase in its relative price in a dynamically stable system. Following Mayer (1974), let us consider the following dynamic adjustment mechanism.

$$ {\dot{X}}_t={a}_1\left\{\left({p}_t-t\right)-\left({a}_{Lt}w+{a}_{Kt}{r}^{\ast}\right)\right\}, $$

(A8.1)

$$ {\dot{X}}_a={a}_2\left\{\left(1+s\right)-\left({a}_{La}w+{a}_{Ka}r\right)\right\}, $$

(A8.2)

$$ {\dot{p}}_t={a}_3\left\{{D}_t\left({p}_t,Z,{T}^{\ast}\right)-{X}_t\right\}, $$

(A8.3)

$$ {\dot{r}}^{\ast }={a}_4\left({a}_{Kt}{X}_t-{K}^{\ast}\right), $$

(A8.4)

$$ \dot{w}={a}_5\left\{{a}_{La}{X}_a+{a}_{Lt}{X}_t+\left(1+\lambda \right){a}_{Lm}{X}_m-L\right\}, $$

(A8.5)

$$ \dot{r}={a}_6\left\{{a}_{Ka}{X}_a+{a}_{Km}{X}_m-K\right\}, $$

(A8.6)

where “.” denotes differentiation with respect to time and a _j is the positive coefficient measuring the speed of adjustment. We assume a Marshallian adjustment process in the tourism and agricultural good production and a Walrasian adjustment mechanism in the tourism good and factor markets.³

The Jacobian matrix of the system of simultaneous Eqs. (A8.1) and (A8.6) is

$$ {\displaystyle \begin{array}{ll}& J\\ {}& =\left[\begin{array}{cccccc}-{a}_{Lt}& -{a}_{Kt}& 1& 0& 0& 0\\ {}-{a}_{La}& 0& 0& -\left(1+s\right)\left(\xi +\tau \right)/{X}_t& -s/{X}_a& 0\\ {}0& 0& \alpha {X}_t/{p}_t& -\left(1+\gamma \right){X}_t& 0& 0\\ {}{a}_{Kt}{X}_t{\theta}_{Lt}{\sigma}_t/w& -{a}_{Kt}{X}_t{\theta}_{Lt}{\sigma}_t/{r}^{\ast }& 0& {a}_{Kt}& 0& 0\\ {}-\tilde{C}& {a}_{Lt}{X}_t{\theta}_{Lt}{\sigma}_t/{r}^{\ast }& 0& \tilde{B}& {a}_{La}& \left(1+\lambda \right){a}_{Lm}\\ {}{a}_{Ka}{X}_a{\theta}_{La}{\sigma}_a/w& 0& 0& -{a}_{Ka}{X}_a{X}_t\xi & {a}_{Ka}& {a}_{Km}\end{array}\right],\end{array}} $$

(A8.7)

where

$$ \tilde{B}={a}_{Lt}-{a}_{La}{X}_a/{X}_t, $$

$$ \tilde{C}=\left\{{a}_{Lm}\left(1+\lambda \right){X}_m+{a}_{La}{X}_a{\theta}_{Ka}{\sigma}_a+{a}_{Lt}{X}_t{\theta}_{Kt}{\sigma}_t\right\}/w. $$

Thus, $J=\Pi \tilde{\Delta}\Omega$, where

$$ \Pi =\left[\begin{array}{cccccc}{p}_t-t& 0& 0& 0& 0& 0\\ {}0& 1+s& 0& 0& 0& 0\\ {}0& 0& {X}_t& 0& 0& 0\\ {}0& 0& 0& {K}^{\ast }& 0& 0\\ {}0& 0& 0& 0& L& 0\\ {}0& 0& 0& 0& 0& K\end{array}\right], $$

$$ \tilde{\Delta}=\left[\begin{array}{cccccc}-{\theta}_{Lt}& -{\theta}_{Kt}& \pi & 0& 0& 0\\ {}-{\theta}_{La}& 0& 0& \left(\xi +\tau \right)& -\tau & 0\\ {}0& 0& \alpha & -\left(1+\gamma \right)& 0& 0\\ {}{\theta}_{Lt}{\sigma}_t& -{\theta}_{Lt}{\sigma}_t& 0& 1& 0& 0\\ {}-C& {\lambda}_{Lt}{\theta}_{Kt}{\sigma}_t& 0& B& {\lambda}_{La}& \left(1+\lambda \right){\lambda}_{Lm}\\ {}{\lambda}_{Ka}{\theta}_{La}{\sigma}_a& 0& 0& -{\lambda}_{Ka}\xi & {\lambda}_{Ka}& {\lambda}_{Km}\end{array}\right], $$

$$ \Omega =\left[\begin{array}{cccccc}1/w& 0& 0& 0& 0& 0\\ {}0& 1/{r}^{\ast }& 0& 0& 0& 0\\ {}0& 0& 1/{p}_t& 0& 0& 0\\ {}0& 0& 0& 1/{X}_t& 0& 0\\ {}0& 0& 0& 0& 1/{X}_a& 0\\ {}0& 0& 0& 0& 0& 1/{X}_m\end{array}\right]. $$

Here,

$$ \left|J\right|=\left[\left(1+s\right){K}^{\ast } LK/{wr}^{\ast }{X}_a{X}_m{\left(-1\right)}^2\right]\left|\tilde{\Delta}\right|=\left[\left(1+s\right){K}^{\ast } LK/{wr}^{\ast }{X}_a{X}_m\right]\left|\Delta \right|, $$

(A8.8)

because ${\left(-1\right)}^2\left|\tilde{\Delta}\right|=\left|\Delta \right|$.

According to the Routh–Hurwitz theorem , a necessary condition for local stability of the system is that |J| > 0. Thus, if we assume that the equilibrium is stable, it can be seen that Δ > 0.