Consider a market consisting of two firms where the inverse demand curve is given by P = 500 − 2Q₁ − 2Q₂.Each firm has a marginal cost of $50.Based on this information,we can conclude that aggregate profits in the different equilibrium oligopoly models will follow which of the following orderings? A)  ^Bertand  ^Collusion  ^Stackelberg  ^Cournot B)  ^Collusion  ^Cournot  ^Stackelberg  ^Bertand C)  ^Collusion  ^Stackelberg  ^Cournot  ^Bertand D) None of the preceding answers is correct.

Question

Consider a market consisting of two firms where the inverse demand curve is given by P = 500 − 2Q₁ − 2Q₂.Each firm has a marginal cost of $50.Based on this information,we can conclude that aggregate profits in the different equilibrium oligopoly models will follow which of the following orderings? A)  ^Bertand >  ^Collusion >  ^Stackelberg >  ^Cournot B)  ^Collusion >  ^Cournot >  ^Stackelberg >  ^Bertand C)  ^Collusion >  ^Stackelberg >  ^Cournot >  ^Bertand D) None of the preceding answers is correct.

Quizplus · Accepted Answer

In this question, we need to compare profits in different oligopoly models. The given inverse demand function implies that the market quantity demanded is Q = 250 − 0.5P. We can use the marginal cost, MC = $50, to derive the reaction functions for each firm. We get:
Q1 = 125 − 0.25Q2 for Firm 1
Q2 = 125 − 0.25Q1 for Firm 2
Now we can solve for the profit of each firm in each oligopoly model:

Bertand: In this case, each firm assumes that the other will keep its output fixed, so both firms end up choosing the same quantity. If both firms choose Q = 62.5, then P = $187.5, and each firm's profit is $4,687.50. Therefore, total profit is $9,375.

Collusion: In this case, both firms act as a monopolist and choose the monopoly quantity of Q = 125. Then, P = $187.50, and each firm's profit is $7,812.50. Therefore, total profit is $15,625.

Stackelberg: In this case, one firm (the leader) chooses its quantity first, anticipating the reaction of the other firm (the follower). Let's assume that Firm 1 is the leader and chooses Q1 = 77. Then, Q2 = 69.25, P = $153.50, and each firm's profit is $6,791.13. Therefore, total profit is $13,582.25.

Cournot: In this case, each firm chooses its quantity simultaneously, taking the other firm's output as given. If both firms choose Q = 83.33, then P = $166.67, and each firm's profit is $6,944.44. Therefore, total profit is $13,888.88.

Comparing these results, we can see that the ordering from highest to lowest aggregate profits is: Collusion, Cournot, Stackelberg, Bertand. Therefore, the correct choice is B.

Consider a Market Consisting of Two Firms Where the Inverse