Production planning and equity investment decisions in agriculture with closed membership cooperatives

This paper examines the production planning and equity investment decisions of a cash-constrained farmer who processes a raw commodity into a value-added product through a closed-membership agricultural cooperative (closed co-op). The farmer is required to purchase a certain amount of shares within specific limits to join in the co-op. The equity investment entitles the right to deliver a particular amount of qualified raw commodity in proportion, and the shares are transferable and appreciable. We consider a multi-period model in which the farmer first considers a one-time decision on participation (whether to join in the co-op). If yes, the farmer determines the production capacity and the initial equity investment in addition to the periodic production planning and equity investment adjustment when yield, spot prices, and share price are uncertain. We propose the condition under which the farmer shall participate in the co-op and characterize the optimal capacity and equity investment policies in closed form. We also investigate how the transferability of shares affects the farmer's optimal decisions and profitability by fixing the initial equity investment. Further, we examine the performance of a variety of heuristic policies when the quality requirement or the yield uncertainty is ignored. The results provide insights into a farmer's decision making, production planning, and cash management.