Risk Aversion and Optimal Input Utilization under State Contingent Technology

The theory of production under uncertainty predicts that, in a single input case, a risk-averse farmer with fair insurance increases fertilizer and decreases pesticide. However, empirical studies do not always support the theoretical predictions. Chambers and Quiggin presented state contingent technology and a method to decompose the difference of optimal revenues between farmers with different risk attitudes to the pure-risk effect and the expansion effect. The theory has potential to explain the ambiguous results in the empirical studies. However, because their analyses only considered risk-averse vs. risk-neutral farmers and assumed some restrictive conditions on the technology, the implication was limited. This paper aims to address these weaknesses. An alternative method of decomposition is introduced to consider the degree of risk-aversion. Local property of marginal revenue-cost function is discussed to examine the sign of expansion effect under more general conditions of technology. This paper provides a theoretical basis for the ambiguity in the empirical studies.