The futures price of a commodity in fixed supply

This letter shows that in a general equilibrium model of homogeneous population with production risk, the futures price of a commodity which is in fixed supply is always below the expected futures spot price (e.g., normal backwardation). It also shows that the difference between the futures price and the expected spot price increases as the representative individual's risk aversion rises. An important application of this model is to the housing market since houses are in fixed supply in the short run and buying a house is like holding a long position in a forward contract. Therefore, if population is homogeneous, houses are not a good consumption hedge and the prices of houses are below their expected rental prices.