Optimal strategies for a three-level contract-farming supply chain with subsidy

We consider a three-level contract-farming supply chain with a risk-averse farmer, a risk-neutral supplier and a risk-neutral distributor, in which the farmer faces a yield uncertainty and the government offers agricultural subsidy to the farmer. The CVaR criterion is used to describe the risk-averse behavior of the farmer. We derive the optimal strategies of the supply chain and perform some sensitivity analysis to investigate the effects of the government subsidy and other factors, The results indicate that, as the subsidy increases, the farmer's total target production increases. Further analysis shows that the total production increase is mainly from the increased farm size, and the farmer's endeavor actually decreases. In addition, the results indicate that the profits of the supplier and the distributor both increase with respect to the subsidy. However, the impact of the subsidy on the farmer's profit depends on the farmer's degree of risk-averse. In particular, the impact of the subsidy to the farmer's profit tends to be positive for farmers with high degree of risk-averse, and the impact tends to be negative for those with low degree of risk-averse. The sensitivity analysis is also performed for the level of yield uncertainty in term of the standard deviation.