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

.

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