An Analytical Treatment of the Economics of Soil Depletion
Three basic model of soil conservation decisions are developed with a complete analysis of their dynamic properties. The first model assumes that soil is farmers' main asset and that they recognize its influence on the production function and the effects of agricultura production on the soil. The model indicates that the steady state shadow price of the soil characteristic will increase whenever output price increases or the discount rate decreases,while a higher discount rate or soil renovation rate will lower it. The effects of these parameters on the steady state soil stock will be opposite to those on its shadow price, but an increase in the discount rate would lower both. The effects of input price changes can be signed with few additional assumptions. The monotonicity property of the solution is derived and commented upon. An expanded version of the above model is analized in chapter four, to study the case when farmers also accumulate capital and financial assets. Contrary to what would be expected, most of the steady state comparative statistics results can be signed when capital and soil stock are assumed to be complements. In this model there possibility of having increases in steady state soil stock with an increase in the interest rate. The monotonicity property of the optimal solution is maintained given the stability properties of the solution. The final chapter presents two related dynamic stochastic models of farmer's decisions to study the effects of wealth and revenue variability. The two-date.