Question

Suppose two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve. P= 30 – Q, where Q = Q1 + Q2. Both firms have a marginal cost of $9.

1. Suppose that the two firms compete by simultaneously setting PRICES? What will the price be? How much will each firm produce? What will each firm’s profits be?

2. Now, continue with the price-setting assumption in (1), and assuming the costs changed from $9 to $18. Will Firm 1 become a monopoly? What will the market price be and what will each firm’s production be? What will each firm’s profits be?

Answer 1

Solution -

Given the demand curve is P=30-Q, the marginal revenue curve is MR=30-2Q.
Profit will be maximized by finding the level of output such that marginal revenue is
equal to marginal cost:
30-2Q=$9
Q=$18
When output is equal to 27, price will be equal to $18, based on the demand curve.
Since both firms have the same marginal cost, they will split the total output evenly
between themselves so they each produce 9 units. Profit for each firm is:
π = 18(9)-9($9)=$162
Note that the other way to solve this problem, and arrive at the same solution is to
use the profit function for either firm from part a above and let

Q =Q1= Q2
.