Government’s optimal inter-temporal subsidy and manufacturer’s dynamic pricing in the presence of strategic consumers

• Published in: European journal of operational research
• Main Authors: Chen, Weichun, Mantin, Benny, Li, Bo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2025
• Subjects: Cost uncertainty; Dynamic pricing; OR in government; Strategic consumers; Subsidies; Dynamic pricing; Subsidies; Cost uncertainty; Strategic consumers; OR in government
• ISSN: 0377-2217
• DOI: 10.1016/j.ejor.2025.05.027

•We model government’s inter-temporal subsidy considering strategic consumers.•Manufacturer prices dynamically facing learning-by-doing and cost uncertainty.•The two policies we study: commitment and dynamic, result in different subsidy paths.•The dynamic policy yields higher social welfare than the commitment policy.•Products with higher initial production costs do not deserve higher subsidies. Governments in many countries offer fiscal incentives—such as subsidies or tax breaks—to consumers to encourage the purchase of environmentally-friendly products like solar panels and electric vehicles. Early adoption by consumers facilitates manufacturers’ learning-by-doing and reduces production cost over time, although the cost reduction itself is subject to uncertainty. Governments face a challenge: should they commit to a multi-period subsidy path (commitment policy) or adjust the subsidy contingent on the realized production cost reduction (dynamic policy)? What are the implications for manufacturers and consumers? We consider a two-period monopoly setting to study these policies. Given the subsidy policy, the manufacturer sets its prices, whereas consumers strategically decide when to purchase the product, if at all. Naturally, the two policies result in different subsidy paths. We find that products with higher initial unit cost (implying higher prices) do not deserve higher subsidies. Our key result is that governments, who seek to maximize expected social welfare, should adopt the dynamic policy. Insightfully, the four components of social welfare—consumer surplus, manufacturer’s profit, environmental benefit and subsidy expenditure—may all be realized higher under the commitment policy than under the dynamic policy when the realized cost reduction falls short of its expected value. This is because the second-period effective price (price minus subsidy) is more sensitive to cost uncertainty under the dynamic policy. Nevertheless, the dominance of the dynamic policy persists also when considering the realized social welfare. We study several extensions demonstrating the robustness of our results, while highlighting certain exceptions.