Question

The inverse demand that the duopoly quantity-setting firms face is p=240−2q1 −2q2 . Firm 1 has no marginal cost of production, but Firm 2 has a marginal cost of $18. How much does each firm produce if they move simultaneously? What is the equilibrium price? The Cournot-Nash equilibrium occurs where q1 equals and q2 equals (Enter numeric responses using integers.) Furthermore, the equilibrium occurs at a price of $....... (round your answer to the nearest penny)

Answer 1

To find the Cournot-Nash equilibrium in a duopoly, we need to calculate the quantities produced by both firms simultaneously. Firm 1 maximizes profit by setting its marginal revenue equal to zero, while Firm 2 maximizes profit by setting its marginal cost equal to its marginal revenue. The equilibrium price is determined by substituting the equilibrium quantities into the inverse demand function.

Step-by-step explanation:

To determine the Cournot-Nash equilibrium in a duopoly, we need to find the quantities produced by both firms simultaneously. Firm 1 has no marginal cost, so it will maximize its profit by setting its marginal revenue equal to zero. The inverse demand function is given by p = 240 - 2q1 - 2q2. We can substitute the marginal revenue of firm 1 into the inverse demand function to find q1. Firm 2 has a marginal cost of $18, so it will maximize its profit by setting its marginal cost equal to its marginal revenue. We can set the marginal cost equal to the inverse demand function and solve for q2. The equilibrium price can be found by substituting the equilibrium quantities into the inverse demand function.