Subsidizing Innovation and Production - Gamal Atallah

In a three-stage game, the government chooses production and innovation subsidies in the first stage to maximize welfare in the presence of a shadow cost of public funds; two firms invest in cost-reducing R&D in the second stage; and the two firms compete in quantities in the last stage. [...] In a three-stage game, the government chooses production and innovation subsidies in the first stage to maximize welfare in the presence of a shadow cost of public funds; two firms invest in cost-reducing R&D in the second stage; and the two firms compete in quantities in the last stage. [...] Hence, the main reason the government increases the production subsidy with spillovers (for high spillovers) is to reduce the cost of the innovation subsidy. [...] As increases, the marginal benefits of sx to firms and consumers increase, and the reduction in the cost of the production subsidy increases; these benefits outweigh the steep increase in the marginal cost of the innovation subsidy with spillovers, leading to a positive relationship between sx and . [...] Moreover, the marginal benefit of su to consumers is U-shaped with spillovers: the negative slope for low mimics the decline of the marginal benefit of sc (figure 3), while the positive slope for high mimics the positive slope of the marginal benefit of sx (figure 4).