Answer to Question #223902 in Microeconomics for Raksha

Question

Which of the following is true of two firms in a duopoly market that are in a Nash equilibrium?


Both firms are producing at a level that maximizes profits
Both firms are producing at a level that minimizes average total costs
Both firms are receiving the maximum payoff available in their payoff matrix
Together the firms have chosen a level of supply equal to the level of aggregate demand
Neither firm has an incentive to deviate from its strategy

Answer 1

Correct answer : Both firms are producing at a level that maximizes profits

Explanation :

Consider an industry with two firms. Firms are identical and produce an homogenous product. Firms have to select outputs (capacity) in order to maximize profits. Each firm knows its own total cost of production, the total cost of production of the competitor and the industry demand.

We analyze two different scenarios:

(i) one-shot scenario, i.e., the life of the industry lasts one period

(ii) repeated scenario, i.e., the life of the industry lasts several periods.

The following data are known by both firms and describe the industry situation:

1) p = 140 - (Q1+Q2) (industry demand)

2) TC1 = 20Q1 (total cost of firm 1),

3) TC2 = 20Q2 (total cost of firm 2).

Observe that the industry price, equation 1, depends on the output of both firms. This feature has two implications: a) since the profits of each firm depend on the price, they depend on the choice of the competitor (strategic interaction), b) in order to establish profit maximizing decisions, each firm has to guess what the competitor will do.