(f) Find the optimal level of each firm's R&D input under collusion. Compare your answer with (d). Intuitively explain the difference.

題組內容

Now, suppose the two firms agree to collude in Stage 1 but continue to compete in a Cournot manner in Stage 2. That is, the two firms will collude with the R&D input level in Stage 1, and then individually decide the output levels in Stage 2. The two firms agree to coordinate R&D levels to maximize total joint profit.

5. (15 %) Consider a product market in which a private firm faces an inverse demand function \( p(Q) = a - b Q \) and private cost \( \frac{c}{2} Q^2 \). The environmental damage \( D(Q) = \frac{d}{2} Q^2 \), where a, b, c, d > 0.Assume that each unit of output produces one unit of carbon emissions. Firms engage in Environmental Corporate Social Responsibility (ECSR) by internalizing a fraction \( \gamma \in [0,1] \) of units of carbon emissions. The government can impose a per-unit carbon tax t on output. Derive the equilibrium price and how an increase in the degree of ECSR \( \gamma \) affects the equilibrium price.

題組內容

(f) Find the optimal level of each firm's R&D input under collusion. Compare your answer with (d). Intuitively explain the difference.

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