Agricultural subsidies are crucial for food security and rural development but can cause market distortions. Current subsidy systems often prioritize quantity over quality, leading to environmental problems. China, among other nations, invests billions in agricultural subsidies, aiming for green and high-quality development. This paper focuses on edible agricultural products, where both quantity and quality (impacting safety) are critical. While various subsidy types exist (output, input, price support), hybrid subsidies, combining quantity and quality incentives, are under-researched. This study designs and evaluates a hybrid subsidy model, analyzing its feasibility under cost uncertainties and input constraints, arguing that it provides a more flexible and efficient approach to supporting edible agricultural products and promoting food security and safety. The model, while general, is particularly relevant to agriculture given the sector's unique reliance on government support. The paper's novel contributions include designing a quantity-and-quality based hybrid subsidy, analyzing the impact of cost uncertainty (separated into quantity and quality components) and input constraints on subsidy efficiency, and providing theoretical support for China's Agricultural Support and Protection Subsidy (ASPS) policy reform.

The literature highlights the controversy surrounding agricultural subsidies: their necessity for food security and rural development versus their potential for market distortion. Many countries utilize subsidies, with various types employed (input, output, price support). Recent reforms emphasize decoupled subsidies, aligning with WTO rules. While quantity and price-oriented subsidies are common, research on the impact of subsidies on quality is limited. Existing studies examine energy efficiency of different subsidy types, the effects of subsidies on product quality under monopoly, and the influence of cross-subsidies on utility service quality. Several studies have suggested that uncertainty and input constraints significantly affect the efficiency of agricultural subsidies. However, no prior research has comprehensively investigated the effects of hybrid subsidies considering both cost uncertainties and input constraints. This study aims to fill these gaps.

The study employs a theoretical model focusing on a representative food product firm operating under a monopoly structure (justified by the relatively weak impact of competition on the conclusions). The inverse demand function reflects the impact of quantity and quality on equilibrium price: p = a + βq - x, where p is price, x is quantity, q is quality, a is market capacity, and β represents the marginal price contribution of quality. The firm's profit function incorporates quantity and quality subsidies: π = (α + βq - x)x - c(x, q) + ysx + (1 - y)sq, where π is profit, s is subsidy intensity, y is the quantity-oriented subsidy ratio, and c(x, q) is the cost function. A quadratic cost function, c(x, q) = x² + q², is used for analytical tractability. The model is analyzed under three scenarios: hybrid subsidy (0 < y < 1), pure quality subsidy (y = 0), and pure quantity subsidy (y = 1). Equilibrium solutions are derived for quantity, quality, and price under each scenario. Welfare analysis considers consumer surplus (CS), producer surplus (PS), government budget (TS), and total social welfare (SW). The model is then extended to incorporate input constraints (equal priority, quantity priority, quality priority) and cost uncertainties (quantity and quality cost uncertainty). Equilibrium solutions and welfare variables are analyzed under these extended scenarios. The analysis utilizes mathematical calculations and numerical simulations.

The analysis yields several key findings. First, the hybrid subsidy policy is shown to be more flexible and efficient than pure quantity or quality subsidies, allowing for a convenient trade-off between food security and safety. Second, cost uncertainties (both quantity and quality) and input resource constraints significantly impact the efficiency of the hybrid subsidy. Third, the equilibrium quantity, quality, and price under different subsidy scenarios (hybrid, pure quality, pure quantity) are characterized. Fourth, the impact of subsidy intensity and the quantity-oriented subsidy ratio on the equilibrium values and welfare measures are analyzed. Fifth, under input constraints, equilibrium values differ based on priority (equal, quantity, quality), with quantity priority resulting in the highest output quantity but the lowest quality. Sixth, cost uncertainty (both quantity and quality) negatively impacts equilibrium quantity, quality, and profits. Seventh, quantity cost uncertainty increases price, while quality cost uncertainty decreases it. Eighth, the impact of different types of uncertainty on expected quantity, quality, profit, and profit risk are compared and contrasted.

The findings support the argument for hybrid subsidy policies as a more flexible and efficient tool for promoting both food security and safety. The significant impact of cost uncertainties and input constraints highlights the need for policymakers to consider these factors when designing and evaluating agricultural support policies. The trade-off between quantity and quality underscores the importance of carefully balancing these competing goals. The results offer valuable insights for policymakers seeking to optimize agricultural subsidies to achieve both food security and safety objectives. The model's flexibility allows for adjustments based on specific circumstances and policy priorities. The consideration of input constraints provides a more realistic portrayal of the challenges faced by agricultural producers. The results suggest that policies should aim to mitigate both quantity and quality cost uncertainties to improve overall welfare.

This study demonstrates the flexibility and efficiency of hybrid agricultural subsidies in promoting food security and safety. It highlights the crucial role of cost uncertainties and input constraints in shaping subsidy effectiveness. Future research could explore the model's application under different market structures (competitive markets), endogenize subsidy intensity and ratio for optimal policy design, incorporate interaction effects between quantity and quality in the cost function, and consider environmental externalities associated with agricultural production. Empirical validation of the model's findings is also warranted.

The study's limitations include the assumption of a monopoly market structure and the absence of empirical data to validate the theoretical conclusions. The exogenous nature of subsidy ratio and intensity also limits the analysis. Further research should relax these assumptions and incorporate a more comprehensive analysis of market dynamics and optimal subsidy determination.