Pricing and Safety Investment Decisions in Food Supply Chains with Government Subsidy

As the demand for safe food has been rapidly increasing these years, more and more stakeholders are dedicated to the safety of the food in the supply chain of this sector. To expand the market share of safe food, governments of some countries also provide subsidies to encourage food processors to invest in better food safety efforts. This paper establishes a three-stage game model between the government and a two-stage food supply chain that consists of one supplier and one processor, where the government subsidizes processors to invest in food safety efforts; furthermore, this paper determines the optimal wholesale price, marginal profit, food safety investment, and government subsidies. This paper analyzes the effects of the government subsidies and risk aversion of the food processor and introduces the mode of order quantity-based payment and demand-based payment; moreover, it also analyzes the impacts of subsidies and different payment methods on demands. The results show that suppliers can increase the market share of products by adopting the demand-based payment, but this method does not always benefit the members of the supply chain. As the processor is more risk-averse, the optimal subsidy is higher, encouraging the processor to invest in more efforts. Finally, the supplier's profit increases with the processor's risk aversion indicator.