Question

A monopolist operates under two plants, 1 and 2. The marginal costs of the two plants

are given by

MC1 = 20 + 2Q1 and MC2 = 10 + 5Q2

where Q1 and Q2 represent units of output produced by plant 1 and 2 respectively. If the

price of this product is given by 20 – 3(Q1 + Q2), how much should the firm plan to

produce in each plant, and at what price should it plan to sell the product?

Answer 1

This means that the demand curve becomes P =20 -3Q2. With an inverse linear demand curve, we

know that the marginal revenue curve has the same vertical intercept but twice the slope, or MR=

20- 6Q2. To determine the profit-maximizing level of output, equate MR and MC2:

$20 - 6Q2 = 10 + 5Q2$

$Q2 = 0.91.$

Also, Q1 = 0, and therefore the total output is Q =0.91. Price is determined by substituting the profit-maximizing quantity into the demand equation.

$P =20 -3(0.91) =\$17.27$