# Consider a market with two firms, 1 and 2, producing an identical good. This good has market...

## Question:

Consider a market with two firms, 1 and 2, producing an identical good. This good has market demand given by the inverse demand function p(y) = 10 - 2y, where p is price, and y = y1 + y2 is the market quantity. The firms have cost functions as follows: Ci (yi ) = ci yi , where ci = 2 and yi represents the amount of output produced by firm i for i {eq}\in {/eq} {1,2}.

(a) Suppose the two firms compete by producing the identical good simultaneously. Solve for their reaction functions and find the Cournot equilibrium outputs, market price and profit per firm.

(b) Graph their reaction functions and show the equilibrium point. Include isoprofit curves through the equilibrium point for both firms.

(c) Suppose the two firms cooperate, solve for the collusive outcome determining equilibrium outputs, market price and profit per firm.

(d) Using the information from parts (a) and (c), construct a 2 2 payoff matrix where the strategies available to each of the two firms are to produce the Cournot equilibrium quantity or the collusion quantity.

## Payoff Matrix

A payoff matrix is a matrix or a table showing various payoffs or profits of players. The players can be business firms, companies or countries, or any other strategists who want to choose one strategy out of available alternatives. The matrix shows the resultant payoff for each strategy for each player.

## Answer and Explanation: 1

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**(a)**

Cournot equilibrium:

{eq}\begin{align*} p &= 10 - 2y\\ p &= 10 - 2{y_1} - 2{y_2}\\ TR &= 10y - 2{y_1}^2 - 2{y_1}{y_2}\\ MR &= 10 - 4{y_1}...

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Chapter 3 / Lesson 61Understand what is meant by the payoff matrix and learn about it with respect to economics. Discover game theory payoff matrix and explore the uses of the payoff matrix.

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