The zero discounting and maximin optimal paths in a simple model of global warming

Following Stollery (1998), we extend the Solow–Dasgupta–Heal model to analyze the effects of global warming. The rise in temperature is caused by the use of fossil resources so that the temperature level can be linked to the remaining stock of these resources. The rise in temperature affects both productivity and utility. We characterize optimal solutions for the maximin and zero discounting cases and present closed-form solutions for the case where the production and utility functions are Cobb–Douglas, and the temperature level is an exponential function of the remaining stock of resources. We show that a greater weight on temperature in intratemporal preferences and a larger intertemporal elasticity of substitution both lead to postponing resource use.