Consider a duopoly, i.e., an industry with only two firms: firm A and firm B, making the same product. The industry’s inverse demand is P(Q)=320−(1/5)Q, where P is the market price and Q is the total industry output. Each firm has a marginal cost MC of $20. There are no fixed costs and no barriers to exit the market. a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?
Consider a duopoly, i.e., an industry with only two firms: firm A and firm B, making the same product. The industry’s inverse demand is P(Q)=320−(1/5)Q, where P is the market
a) Suppose that the two firms engage in Cournot competition. Find the
b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm.
c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?
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