Determine the profitmaximizing prices when a firm faces two

Determine the profit-maximizing prices when a firm faces two markets where the inverse demand curves are Market A: PA 100-2QA where demand is less elastic, and Market B: P 80 1QB where demand is more elastic, and Marginal Cost = m-20 for both markets. For Market A: PA (Round your response to two decimal places) For Market B: P(Round your response to two decimal places.)

Solution

For Market A: P_A = $60

For Market B: P_B = $50

Explanation:

Market A:

P_A = 100 - 2Q_A

TR_A = P_A * Q_A = 100Q_A - 2Q²_A

MR_A = 100 - 4Q_A

MC = 20

The profit maximizing condition is:

MR_A = MC

100 - 4Q_A = 20

4Q_A = 80

Q_A = 80 / 4 = 20

P_A = 100 - 2(20) = $60

Market B:

P_B = 80 - 1Q_B

TR_B = P_B * Q_B = 80Q_B - 1Q²_B

MR_B = 80 - 2Q_B

MC = 20

The profit maximizing condition is:

MR_A = MC

80 - 2Q_B = 20

2Q_B = 60

Q_B = 60 / 2 = 30

P_B = 80 - 1(30) = $50