The Derived Demand with Hedging Cost Uncertainty in the Futures Markets: Note and Extensions

Paroush and Wolf (1992) investigated a perfectly competitive firm which faces input price uncertainty in one input of its two-input production function. The main purpose of their study was to determine the impact of the technological relationship on the derived demand when the input is hedged in a forward or futures market. They found that the partial cross derivatives of the production function and the market structure of the futures price (upward or downward bias) affect the derived demand. This note provides two extensions. First, it generalises Paroush and Wolf's theorem by using general utility function (Theorem 1). Second, it adds a new theorem (Theorem 2) that shows the impact of adding basis risk on the optimal hedging. This theorem is equally important since hedging is a decision variable. Below is a description of Paroush and Wolf's model.