Optimal exploitation of common property resources: a case of groundwater mining in the Ogallala Aquifer
Water shortage is one of the most serious long-range problems for the United States, as has been witnessed in recent years. With rising energy costs and declining water tables, it appears that the U.S. agricultural sector faces the problem of how to efficiently allocate limited groundwater resources intertemporally and spacially;At first, theoretical aspects of common property resources are discussed. A model of production using common property resources is built. It focuses on factors determining intertemporal exploitation patterns of common property resources and on a comparison of a social optimal and a free market model. The theoretical analysis implies that, first, the lower the discount rate the larger the change of the exploitation rate, second, the greater the stock externality the greater the change of the exploitation rate, third, the steeper the slope of the yield function, the larger the change of the exploitation path, and fourth, the better the resource grade the more the resource will be exploited;Based on the theoretical analysis, the dynamic model is applied in the Southern Ogallala Aquifer. The solutions provide optimal rates of water use, irrigation acreages, farm income, net present values of farm income, and the levels of water tables for each of the 144 resource situations for years 1985-2005 under five alternative scenarios, with respect to energy and crop prices and discount rates. Comparing the social optimal solution with the free market solution, economic losses and excessive depletions of water due to commonality are estimated. The social optimal solution has a higher net farm income than the free market solution, and more water is conserved under the social optimal solution. With the free market policy, the region will lose 70 million in net farm income and 2.9 feet of its water table under the base scenario. Losses, however, depend on energy levels, crop prices, and the discount rate. Three alternative policies for achieving social optimal allocation of resources are examined. They are the flexible taxation in which the tax rate changes every five years, the fixed taxation which is constant over periods, and the quota policy. Examining the benefits side only, the experimental results for the Ogallala Aquifer prove that the flexible taxation is the best policy.