Output Decision Under Demand Uncertainty with Stochastic Production Function: A Contingent Claims Approach

Kee H. Chung

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Capital Investment and Risk Analysis Supply Chain and Inventory Management Management and Optimization Techniques

Abstract

This paper presents a contingent claims analysis of output decisions for the firm facing technological and demand uncertainty. The paper reveals that: (i) the optimal output level increases with the higher interest rate when the firm is subject to demand (and technological) uncertainty; (ii) the effect of demand volatility and production lead time on the optimal output level could be either positive or negative; (iii) the optimal project value decreases with the higher demand volatility; (iv) the optimal project value decreases with the longer production lead time when the firm is subject to demand uncertainty; and (v) the optimal project value decreases with the higher interest rate when the firm is subject to demand uncertainty; it increases with the higher interest rate, however, when the firm is subject to both demand and technological uncertainty. Some important managerial implications are discussed.

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References

1973The Pricing of Options and Corporate Liabilities 1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1973An Intertemporal Capital Asset Pricing Model 1966Equilibrium in a Capital Asset Market 1982The Value of Waiting to Invest 1985Evaluating Natural Resource Investments 1978THE VALUE OF AN OPTION TO EXCHANGE ONE ASSET FOR ANOTHER

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