The government’s optimal subsidy scheme under Manufacturers’ competition of price and product energy efficiency

As motivated by various Chinese government’s subsidy schemes (e.g., promoting energy-efficient home appliances in 2007, energy-saving automobiles in 2010, and green and efficient agricultural machinery in 2018), we study a government’s optimal subsidies for energy-efficient products in a market with two competing firms. The firms differ in their production costs and compete on their product prices and product energy efficiencies. The government subsidy scheme specifies the amount of subsidy and the certification threshold of the energy consumption level below which the product is certified for certain energy-efficiency/saving and is thus qualified for the subsidy. We first derive the subgame Nash equilibrium of the product prices and product efficiency strategies given the subsidy scheme. Interestingly, we find that if the subsidy is too low, it is possible that the low-cost firm will produce an uncertified product while the high-cost firm will produce a certified product. Furthermore, we derive the government’s endogenous optimal subsidy scheme under three different objectives, i.e., minimizing the total energy consumption, the average energy consumption per product, as well as the average energy consumption per unit of GDP. While previous studies show that minimizing the first two objectives are equivalent in a monopoly manufacturer setting, we show that they are not equivalent in our duopoly competition setting, and we demonstrate that minimizing the average energy consumption helps to sustain the product variety/duopoly outcome. Counterintuitively, when minimizing the total energy consumption, inducing the low-cost firm to produce an uncertified product and the high-cost firm to produce a certified product is optimal under some conditions. Moreover, we demonstrate that both the objectives of minimizing the average energy consumption per product and per unit of GDP result in the same equilibrium market structure.