The Impact of Yield-Dependent Trading Costs on Pricing and Production Planning under Supply and Demand Uncertainty

This paper studies the role of the yield-dependent cost structure influencing the optimal choice of the selling price and production quantity for a firm that operates under supply and demand uncertainty. The problem is commonly observed in the agricultural industry. We consider a firm that initially leases farm space in order to grow fruit. The realized amount of fruit supply fluctuates due to weather conditions, diseases, etc. At the end of the growing season, the firm has three options: convert its crop supply to the final product, purchase additional supplies from other growers, and sell some (or all) of its crop supply in the open market without converting to the finished product. Earlier literature considers the unit purchasing cost and the unit revenue from selling the fruit supply in the open market as static cost parameters. However in agricultural settings, these two trading cost parameters change with the realized yield. Considering a price-setting agricultural firm, we investigate the impact of the yield-dependent cost structure present in the secondary options of purchasing and selling fruit in the open market. Our work makes four sets of contributions: 1) It determines the optimal selling price, production, purchasing, and selling quantity decisions under supply and demand uncertainty; 2) It shows that the use of a static cost exaggerates the initial investment in the farm space and the expected profit significantly, and the actual value gained from a secondary (emergency) option for an agricultural firm is lower under the yield-dependent cost structure; 3) It proves that the risk neutral firm does not benefit from fruit futures, which may help explain the lack of such markets fo