Acapacity market is a business-to-business exchange in which equally capable suppliers compete with one another to satisfy generic orders from diverse buyers. The market is asymmetric because the buyers can carry inventory of the products ordered but the suppliers cannot store their capacity. In such a market, we might expect to see something like a price for capacity emerge to equilibrate demand and supply. The financial risk of participating in such a market will be driven by the volatility of the capacity price. In this paper we develop a model to explore the behavior of such a market and demonstrate, for example, that volatility of the price for capacity increases, to a point, when inflexibility of the capacity increases. We can also make statements about how the resolution of price uncertainty in the capacity market is related to the resolution of demand uncertainty faced by the buyers. Another contribution of the paper is to explain the role of market characteristics in how the market acts to minimize shortages caused by consumer demand uncertainty. We use continuous time stochastic optimal control techniques and numerical experiments to demonstrate these insights.