We develop a two sector dynamic model of a less developed economy with intertemporal utility maximizing behaviour of the household. The model consists of an imported traded good sector and a non-traded tourism service sector serving international tourists. Revenue earned from tourism finances imports. The model takes care of the negative effect of tourism development on environmental pollution. Environmental quality and capital stock accumulate over time. We analyse properties of the long-run equilibrium and show that the unique long-run equilibrium point satisfies saddle point stability.