Optimal Monopoly Investment and Capacity Utilization under Random Demand

Unique value-maximizing programs of irreversible capacity investment and capacity utilization are described and shown to exist under general conditions for monopolist exhibiting capital adjustment costs and serving random consumer demand for a nondurable good over an infinite horizon. Stationary properties of these programs are then fully characterized under the assumption of serially independent demand disturbances. Optimal monopoly behavior in this case includes acquisition of a constant and positive level of capacity, the maintenance of a positive expected value of excess capacity in each period, and an asymmetrical response of price to unanticipated fluctuations in consumer demand. Under a general form of Markovian demand, the effect of uncertainty on irreversible capacity investment is also described in terms of the discounted flow of expected revenue accruing to the marginal unit of existing capacity and the option value of deferring the acquisition of additional capital. The option value of deferring such acquisition, created by the irreversibility of capacity investment, is characterized directly in terms of the value function of the firm, and is then shown to be zero in a stationary equilibrium with serially independent demand disturbances. The response of investment to increase demand uncertainty depends, as a result, directly on the properties of the marginal revenue product of capital. A non-negative response of optimal capacity to increased uncertainty in market demand is demonstrated for a general class of aggregate consumerpreferences. David B. Nickerson Stanley S. Reynolds University of British Columbia University of Arizona and Visiting Scholar, Federal Reserve Bank of St. Louis We would like to thank Lanny Aryan, David Backus, Mukesh Eswaran, RobertPindyck, Neil Ramon, Pat Reagan, Todd Sandier, Bill Schworm and seminar participants at the 1988 Meetings of the Society for Economic Dynamics and Controi, the Federal Reserve Banks of New York and St. Louis, North Carolina State University, the University of Waterloo and the University of British Columbia for their helpful comments, correspondence, and discussion regarding an earlier version of this paper. Partial research support for David Nickerson was provided by UBC-HSS Research Grant 5-57899. The usual disclaimer applies.