Near-Optimality of Uniform Copayments for Subsidies and Taxes Allocation Problems

We study a subsidies and taxes allocation problem with endogenous market response subject to a budget constraint. The central planner’s objective is to maximize the consumption of a good, and she allocates per-unit copayments and taxes to its producers. We show that the optimal policy taxes the more efficient firms and allocates larger copayments to less efficient firms, making it impractical. Therefore, we consider the simple and frequently implemented policy that allocates the same copayment to each firm, known as uniform copayments, and provide the first worst-case performance guarantees for it. Namely, we show that uniform copayments are guaranteed to induce a significant fraction of the consumption induced by the optimal policy in small markets for price-taking (Cournot) producers with affine increasing marginal costs facing any nonincreasing (linear) inverse demand function, even for different firms’ efficiency levels. Moreover, compared with the best policy that allocates copayments only, uniform copayments induce at least one-half of the optimal consumption. Furthermore, for Cournot competition with linear demand and constant marginal costs, the latter guarantee increases to more than 85% of the optimal consumption. Our results suggest that uniform copayments are surprisingly powerful in increasing the market consumption of a good.