The Dynamic Impact of Technical Progress on Common-pool Groundwater Use and Depletion.

A class of dynamic models is developed to assess potential gains from management of groundwater in arid and semi-arid regions in the presence of technical change. The aquifer is a common-pool resource (CPR) because users typically hold the right to pump groundwater but do not own the water contained in the aquifer and since groundwater is a fugitive resource, the stock available to an irrigator depends dynamically on the levels of extraction by neighboring irrigators. Allocations result from profit maximizing behavior of irrigating farmers. Competitive outcomes are obtained from periodic profit maximization while planning, or management, outcomes result from maximization of the net present value of the stream of profits over the lifetime of the aquifer. The divergence between these two outcomes over time indicates the magnitude of the common-pool resource externality. Dynamical systems govern the evolution of the aquifer, the climate, and the rate of technical progress. These dynamical systems may be dependent upon periodic allocations, as in the case of the aquifer, or independent of the periodic allocations, as in the case of precipitation. A simplified example of the model incorporating only deterministic aquifer and technical change dynamics is presented as a linear-quadratic optimal control problem.