The Role of Tourism in Sustainable Communities

Abstract

This chapter develops a model through which a dynamic analysis of tourism sustainability can be implemented within the context of broader community development goals. The model focuses on the relationship between tourism and quality-of-life as influenced by impacts on economic, sociocultural, and environmental outcomes. This perspective is similar to triple bottom line (TBL) assessments that add sociocultural and environmental dimensions to the traditional economic bottom line. The role of tourism is first analyzed in a stylized but formal dynamic model that equates the quest for sustainability with the quest for an optimal path to long-term stability where a visitation variable is used to control a single community quality-of-life asset. Principle results of this analysis are then further explored using mathematical planning exercise for a community with explicit sustainability goals and the recognition of its triple bottom line of environmental, social, and economic assets. By combining a TBL approach with a formal dynamic approach toward tourism sustainability, the model provides insights into trade-offs implied in sustainable tourism and suggests general principles for tourism planning.

Appendix

$$ {\displaystyle \underset{0}{\overset{\infty }{\int }}[L(V,A)]{e}^{-rt}dt}$$

$$ A=XSE$$

$$ L=L(V,A)={V}^{b}A={V}^{b}XSE$$

$$ H={V}^{b}A{e}^{-rt}+{l}_{X}\left({g}_{X}A\left(1-\frac{X}{\overline{X}}\right)+{d}_{X}V\right)+{l}_{S}\left({g}_{S}A\left(1-\frac{S}{\overline{S}}\right)+{d}_{S}V\right)+{l}_{E}\left({g}_{E}A\left(1-\frac{E}{\overline{E}}\right)+{d}_{E}V\right) $$

$$ \dot{X}=\frac{\partial X}{\partial t}={h}_{X}-{g}_{X}(V)={g}_{X}A\left(1-\frac{X}{\overline{X}}\right)+{d}_{X}{V}_{t}$$

$$ \dot{S}=\frac{\partial S}{\partial t}={g}_{S}A\left(1-\frac{S}{\overline{S}}\right)+{d}_{S}{V}_{t}$$

$$ \dot{E}=\frac{\partial E}{\partial t}={g}_{E}A\left(1-\frac{E}{\overline{E}}\right)+{d}_{E}{V}_{t}$$

$$ \begin{array}{l}{\dot{l}}_{X}=-\frac{\partial H}{\partial X}=\left[-{L}_{X}{e}^{-rt}-{l}_{X}\left(\frac{\partial {h}_{X}}{\partial X}\right)-{l}_{S}\left(\frac{\partial {h}_{S}}{\partial X}\right)-{l}_{V}\left(\frac{\partial {h}_{E}}{\partial X}\right)\right]\\ \text{}=-\left[{V}^{b}\frac{A}{X}{e}^{-rt}+{l}_{X}{g}_{X}\left(A\left(-\frac{1}{\overline{X}}\right)+\frac{A}{X}\left(1-\frac{X}{\overline{X}}\right)\right)+{l}_{S}{g}_{S}\frac{A}{X}\left(1-\frac{S}{\overline{S}}\right)+{l}_{E}{g}_{E}\frac{A}{X}\left(1-\frac{E}{\overline{E}}\right)\right]\\ \text{}=-\frac{A}{X}\left[{V}^{b}{e}^{-rt}+{l}_{X}{g}_{X}\left(-\frac{X}{\overline{X}}\right)+{l}_{X}{g}_{X}\left(1-\frac{X}{\overline{X}}\right)+{l}_{S}{g}_{S}\left(1-\frac{S}{\overline{S}}\right)+{l}_{E}{g}_{E}\left(1-\frac{E}{\overline{E}}\right)\right]\\ \text{}=-\frac{A}{X}\left[{V}^{b}{e}^{-rt}-{l}_{X}{g}_{X}\frac{X}{\overline{X}}+\Phi \right]=-\frac{L{e}^{-rt}}{X}+{l}_{X}{g}_{X}\frac{A}{\overline{X}}-\Phi \frac{A}{X},\end{array}$$

where $\Phi ={l}_{X}{g}_{X}\left(1-\frac{X}{\overline{X}}\right)+{l}_{S}{g}_{S}\left(1-\frac{S}{\overline{S}}\right)+{l}_{E}{g}_{E}\left(1-\frac{E}{\overline{E}}\right)$

$$ {\dot{l}}_{S}=-\frac{\partial H}{\partial S}=-\frac{A}{S}\left[{V}^{b}{e}^{-rt}-{l}_{S}{g}_{S}\frac{S}{\overline{S}}+\Phi \right]$$

$$ {\dot{l}}_{E}=-\frac{\partial H}{\partial E}=-\frac{A}{E}\left[{V}^{b}{e}^{-rt}-{l}_{E}{g}_{E}\frac{E}{\overline{E}}+\Phi \right]$$

$$ \frac{{\partial H}}{{\partial V}} = \beta A{V^{{\beta - 1}}}{e^{{ - rt}}} + {\delta_X}{\lambda_X} + {\delta_S}{\lambda_S} + {\delta_E}{\lambda_E} = 0 $$