关键词: 农产品供应链, 农业补贴, 小农户, 产能限制, 产出不确定性

Abstract: Agricultural production is characterized by uncertain yields, which not only cause serious losses in farmers’ incomes, but also pose a threat to the supply of grain. In addition, it would discourage farmers from planting, resulting in the abandonment of land and a reduction in production. As a large agricultural country, China’s government has been providing a variety of subsidy policies for decades to protect farmers’ incomes from fluctuations in output and market prices, the most common of which are cost and target price subsidies. Cost subsidies can help farmers to reduce production costs and alleviate financial shortages in planting. However, it may lead to phenomena such as farmers receiving subsidies but not planting, or blindly expanding their planting area. Price subsidies are less disruptive to market prices and can be used directly to protect farmers’ incomes. The selection of appropriate and effective subsidies is important for agricultural development. Thus, the mechanism of each subsidy policy and how to choose an appropriate subsidy strategy are the subjects of this paper.
In China, agricultural production is still dominated by a smallholder economy. Farming households are characterized by large numbers, small scales and low levels of mechanization. Therefore, a game model of agricultural production decision-making that is consistent with the conditions of China’s smallholder economy has been innovatively constructed. We study a single-level agricultural supply chain of n small farmers facing the market directly, in which farmers have capacity constraints and heterogeneous production costs. First, considering the random yields of agriculture, we develop a Cournot game model for n farmers, where farmers make decisions on production with the optimization objective of maximizing their own profit, which is constrained by the production capacity A. The KKT condition is used to solve for the optimal decision input of each farmer, whereby the farmers are divided into three clusters. Supply chain performances such as total output, farmers’ surplus and consumers’ surplus are also calculated to analyze the impact of output uncertainty on agricultural supply chains. It is shown that, under capacity constraints, heterogeneous farmers with different unit production costs will make different cultivation decisions: high-cost farmers will choose to abandon cultivation; lower-cost farmers will participate in cultivation, and the lower the cost, the more they will put into production; and those with very low costs will produce in full capacity.
Then, a cost subsidy policy (reimbursing farmers for a portion of their costs) and a target price subsidy policy (compensating for the difference between the current market price and the target price, which is the historical average market price) are introduced in separate chapters, and their impact on supply chain performance is explored mathematically. Finally, the differences between cost subsidy policy and target price subsidy policy are compared. The result shows that, compared with the situation before the introduction of subsidies, (1)both cost subsidies and target price subsidies can increase the quantity of participating farmers, total production and consumer surplus. Moreover, cost subsidies are effective in achieving better results with less expenditure; (2)cost subsidies only increase the profits of high-cost farmers and reduce farmers’ total surplus. This is because subsidy policy incentivizes too many farmers to produce a particular crop, thus hurting prices and marginal profitability. In contrast, under the target price subsidy, each farmer’s profit will increase, and the total surplus of farmers will also increase. It can be verified that the target price subsidy policy reduces the impact of price volatility on farmers and has a direct effect on safeguarding their income.
These conclusions can provide a reference for the design of government subsidy mechanisms, and the government should choose appropriate strategies based on fiscal budget, purpose and the characteristics of different policies. If the government’s subsidy objective is to increase the cultivation rate of arable land, reduce land abandonment, or increase total production and consumer welfare, it should choose the cost subsidy, which is more economical and efficient. If the subsidy objective is to improve the total welfare of farmers, it should choose the target price subsidy. And if the subsidy objective is to reduce the income gap among heterogeneous farmers, a cost subsidy should be chosen.

Key words: agricultural product supply chain, agricultural subsidy, smallholder, capacity constraints, yield uncertainty