Technical change and irreversible investment under risk

A stochastic dynamic model was constructed to analyze investment decisions of an individual farmer under risk in the presence of irreversibilities, embedded technical change and indivisible capital. An analytical solution was obtained and its local behavior studied by numerical methods. Optimal investment is obtained by regulating the difference between the desired and actual capital stocks between two barriers that define an inaction interval. While the desired capital drifts between the barriers, no action is taken. If the desired capital touches the upper barrier, the farmer invests pushing the average efficiency of the actual capital stock up. This in turn raises the desired capital even higher and contracts the inaction interval. If these effects are strong enough, the farmer will invest again until the potential gains of the technological package are exhausted. If the desired capital falls enough, the farmer disinvests, pushing down the average productivity and expanding the inaction interval. Disinvestment continues until it stops either because the inaction interval becomes so wide that it is no longer optimal to disinvest or because the actual capital stock is so small that it is no longer profitable to produce. © 1997 Elsevier Science B.V. All rights reserved