The Learning Curve and Optimal Production under Uncertainty

This article examines the implications of the learning curve in a world of uncertainty. We consider a competitive firm whose costs decline with cumulative output. Because the price of the firm's output evolves stochastically, future production and cumulative output are unknown and are contingent on future prices and costs. We derive an optimal decision rule that maximizes the firm's market value: produce when the price exceeds a critical level, which is a declining function of cumulative output. We show how the shadow value of cumulative production, the total value of the firm, and the decision to produce depend on the volatility of the price and other parameters. Uncertainty increases the critical price required for the firm to produce, but also increases the value of the firm. Thus, during periods of high volatility, firms facing a learning curve ought to be producing less, but are worth more.