Optimal Subsidy Schemes and Budget Allocations for Government‐Subsidized Trade‐in Programs

Applications of government subsidies to speed up consumer trade-ins of used products can be commonly observed in practice. This study investigates the design of such trade-in subsidy programs and aims to provide implementable insights for practice. In particular, we focus on two open problems in the literature, (i) how to optimally allocate the subsidy budget among the multiple products covered by the trade-in program, and (ii) how to most effectively utilize the assigned budget to incentivize consumer trade-ins for each product. We develop a three-stage Stackelberg game model that captures the essence of the interaction between the government's subsidy decision, the manufacturer's trade-in rebate decision, and the consumer's product replacement decision. We show that a sharing subsidy scheme under which the government subsidy is proportional to the manufacturer's rebate is more effective in encouraging consumer trade-ins than fixed-amount subsidies. Moreover, a product with a higher environmental impact, a larger market size, a longer lifespan, or a lower value to consumers typically demands a larger subsidy budget allocation. We further use our results to derive a simple proportional budget allocation rule that can provide robust and near-optimal performance. We illustrate our results by a case study based on the "old-for-new" program in China that subsidizes home appliance trade-ins. Our results indicate that policy makers should pay attention to the correlation between government subsidies and manufacturer's rebate as well as key product and market characteristics when designing a subsidy scheme for trade-in programs.