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This paper studies the role of the yield-dependent trading cost structure influencing the optimal choice of the selling price and production quantity for a firm that operates under supply uncertainty in the agricultural industry. The firm initially leases farm space, but its realized amount of fruit supply fluctuates because of 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. We consider the problem both from a risk-neutral and a risk-averse perspective with varying degrees of risk aversion. The paper offers three sets of contributions: (1) 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. (2) It proves that although the risk-neutral firm does not benefit from fruit futures, a sufficiently risk-averse firm can benefit from the presence of a fruit futures market. The same risk-averse firm does not purchase fruit futures when it operates under static costs. Thus, fruit futures can only add value under yield-dependent trading costs. (3) Contrary to the results presented for the newsvendor problem under demand uncertainty, the firm does not always commit to a lower initial quantity (leased farm space) under risk aversion. Rather, the firm might lease a larger farm space under risk aversion.
Kazaz et al. (Thu,) studied this question.