In this paper we reformulate the theory of cost and production to take account of uncertain demand facing a firm. In the reformulated theory the duality between cost and production no longer obtains, and demand distribution parameters enter the cost function as well as the traditional outputs and input prices. We then estimate a short run cost function for a hospital facing uncertain demand using data from a national sample of over 5000 hospitals for the years 1983-1987. The traditional cost model is strongly rejected in favor of the reformulated model. This model is used to calculate the cost of empty hospital beds, controlling for the effect of uncertain demand on the structure of hospital costs. The cost of an empty hospital bed is calculated as $36,443 in 1987 dollars. We estimate that a one percent decrease in the number of hospital beds would decrease hospital costs by slightly over one-third of one percent. Increasing the occupancy rate from the average 1992 level (65 percent) back to the average 1980 level (76 percent) is estimated to save the average hospital over $2 million, or 9.5 percent of costs.