Input use and capacity constraint under uncertainty: The case of irrigation

In this paper we consider a two periods model of cropping using irrigation. The farmer takes two kind of decisions, one related to the level of investment in irrigation capacity and the other one to the irrigation level in each period. In the first period, decisions are taken under uncertainty on the rainfall level which is resolved at the beginning of the second period. Assuming a CARA utility function, we show that taxing the investment may entail an increase in preventive irrigation although the investment decreases. Moreover, in the case of a logistic production function, the total water use is non monotonic with respect to the price of investment. Indeed, taxing capital may induce the farmer to increase the total level of irrigation despite that the irrigation capacity decreases. Surprisingly, the impact of an increase of water price is generally ambiguous even assuming risk neutrality.