The Welfare Effects of Intermittent Interruptions of Trade - Loury, Glenn C. (American Economic Review, 1983)
Consider the problem of a buyer purchasing a (costlessly) storable good at a fixed price under threat of interruption of trade. Suppose there are two distinct and exhaustive regimes: either one can buy as much as desired at the going price, or one can purchase nothing at all and must rely accumulated stocks for consumption. The market moves randomly over time between these two states, which will be referred to here as on and off, respectively. Given the stochastic process governing the evolution of market regimes, the price faced when the market is on, and the intertemporal preferences of the buyer, one may inquire as to the optimal acquisition rate for storage and consumption when the market is on, and the optimal usage of accumulated stocks when the market is off. Solutions for these problems could then be used to ascertain the degree to which buyer (and seller) welfare is affected by the probabilistic curtailment of trading opportunities, and the willingness to pay of the buyer for greater security of supply. As well, the possibility of inferring from purchase and storage behavior the buyer's perception of the likelihood and duration of trade interruptions may be explored. This paper presents a general solution to this problem for stationary environments. That is, assuming intertemporal preferences to be representable by the expected present value of a uniformly discounted, time-independent flow utility function, and taking the stochastic process governing change in regimes to be stationary Markov, optimal behavior and associated expected discounted utility are derived. The method employed adapts to this context the dynamic programming arguments of my 1981 paper, and is similar in structure to that employed in the analysis of resource depletion with technological uncertainty in Partha Dasgupta and Geoffrey Heal (1974) and Dasgupta and Joseph Stiglitz (1981). There are many industrial markets in which these considerations are important. Recent events in the world oil market have stimulated much interest in the study of strategic mineral reserves (see, for example, Thomas Teisberg, 1981). In markets where demand fluctuates randomly and prices are inflexible (for example, the industrial market for natural gas), the possibility of stochastic rationing has important implications for firm behavior (see Dennis Carleton, 1978). The prospect of strike upstream, or lag in the delivery of goods order has significant implications for inventory holdings in some industries. The framework of this paper may even be adapted to the study of labor supply and savings behavior over the life cycle for a worker facing intermittent and uncertain unemployment.