A monopoly firm faces two markets where the inverse demand curves are: Market A: P_A = 140 - 2.75Q_A.

Market B: P_B = 120 - Q_B.

The firm operates a single plant where total cost is C = 20Q + 0.25Q^2, and mammal cost is m = 20 + 0.5Q.

Required:

1. Suppose the firm sets a single price for both markets. Using the information above, the profit maximizing price is $86.18 and the profit maximizing quantity is 53.37 units. Given this information, you determine that the firm will earn a profit of $ .

2. Now suppose the firm is able to engage in group price discrimination. To maximize profits, the firm will produce 16.95 units for market A and charge customers in market A a price of $ 93.39 per unit. And it will produce 36.6 units for market B and change customers in market B a price of $ per unit.

3. If the firm engages in your price discrimination it will earn a profit of $ .

1. The firm will earn a profit of $2,819.94.

2. The firm will charge customers in market B a price of $83.40 per unit.

3. If the firm engages in your price discrimination it will earn a profit of $2,847.50.

Explanation:

Given:

Market A: P_A = 140 - 2.75Q_A ………………….. (1)

Market B: P_B = 120 - Q_B ……………………………(2)

C = 20Q + 0.25Q^2 ……………………………………… (3)

Marginal cost = m = 20 + 0.5Q …………………… (4)

Therefore, we have:

1. Suppose the firm sets a single price for both markets. Using the information above, the profit maximizing price is $86.18 and the profit maximizing quantity is 53.37 units. Given this information, you determine that the firm will earn a profit of $ .

P = Profit maximizing price = $86.18

Q = Profit maximizing quantity = 53.37

R = Total revenue = P * Q = $86.18 * 53.37 = $4,599.43

Substituting Q = 53.37 into equation (3), we have:

C = (20 * 53.37) + (0.25 * 53.37^2) = $1,779.49

Profit = R – C = $4,599.43 - $1,779.49 = $2,819.94

Therefore, the firm will earn a profit of $2,819.94.

2. Now suppose the firm is able to engage in group price discrimination. To maximize profits, the firm will produce 16.95 units for market A and charge customers in market A a price of $ 93.39 per unit. And it will produce 36.6 units for market B and change customers in market B a price of $ per unit.

This implies that we have:

Q_B = 36.6

Substituting Q_B = 36.6 into equation (2), we have:

P_B = 120 - 36.6 = 83.40

Therefore, the firm will charge customers in market B a price of $83.40 per unit.

3. If the firm engages in your price discrimination it will earn a profit of $ .

Q_A = 16.95

P_A = 93.39

R_A = Market A Revenue = Q_A * P_A = 16.95 * 93.39 = 1,582.96

Q_B = 36.6

P_B = 83.40

R_B = Market B Revenue = Q_B * P_B = 36.6 * 83.40 = 3,052.44

R = Total revenue = R_A + R_B = 1,582.96 + 3,052.44 = 4,635.40

Q = Q_A + Q_B = 16.95 + 36.6 = 53.55

Substituting Q = 53.55 into equation (3), we have:

C = (20 * 53.55) + (0.25 * 53.55Q^2) = 1,787.90

Profit = R - C = 4,635.40 - 1,787.90 = 2,847.50

Therefore, if the firm engages in your price discrimination it will earn a profit of $2,847.50.

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