Question

1. A monopolist faces the following demand curve:

              P = 40 - 2 Q.

His total cost curve is

              TC = 50 + 4 Q + Q².

The equilibrium quantity for this monopolist is … and the equilibrium price is …            

A. 6; $26, respectively.  

B. 9, $26, respectively.

C. 9, $28, respectively.

D. 6; $28, respectively.

E. None of the above.

2. Using the information in question #1, the monopolist’s profit is … and the Lerner index is …

A. $58; 0.75, respectively.  

B. $58; 0.4286, respectively.

C. $88, 0.4286, respectively.

D. $88; 0.75, respectively.

E. None of the above.

3. Using the information in question #1, if this monopolist were a competitive firm who faces a horizontal demand curve at P = 20 with the same cost curve. Calculate the equilibrium quantity, equilibrium price, and the profit for this competitive firm.

A. 9; $18; and $24, respectively.

B. 8; $14; and $34, respectively.

C. 9; $18; and $24, respectively.

D. 8; $20; and $14, respectively.

E. none of the above.

4. Using your answers in questions 1, 2, and 3 to compare the equilibrium quantity, equilibrium price, and the profit level of the monopolist with those of the competitive firm. The monopolist

A. produces less output, charges a lower price, and has a higher profit.

B. produces less output, charges a higher price, and has a lower profit.

C. produces less output, charges a higher price, and has a higher profit.

D. produces more output, charges a higher price, and has a higher profit.

E. None of the above.

Answer 1

Given that

Cost Function

TC = 50 + 4Q + Q2

Demand Function

P =40 - 2Q

Profit is maximized where marginal revenue and marginal cost both are equal.

Marginal revenue can be calculated from the demand function by doubling the coefficient of Q

MR = 40 - 4Q

Marginal cost can be calculated from the total cost function by differentiation.

MC = dTC / dQ

MC = 2Q + 4

Equating both MR and MC

40 - 4Q = 2Q + 4

Q = 6

To find the price we will use this quantity in demand function

P =40 - 2Q

P =40 - 2(6)

P = 28

Hence option D is correct

Total Revenue = Price x Quantity

Total Revenue = 28 x 6

Total Revenue = 168

To find the total cost we will use the total cost function

TC = 50 + 4Q + Q2

TC = 50 + 4(6) + (6)2

TC = 110

Profit = Total Revenue - Total Cost

Profit = 168 - 110

Profit = 58

Lerner Index = P - MC / P

MC = 2Q + 4

MC = 2(6) + 4

MC = 16

Lerner Index = P - MC / P

Lerner Index = 28 - 16 / 28

Lerner Index = 0.4286

Thus option B is correct

In perfect competition, P = MR and profit is maximized where MR and MC

2Q + 4 = 20

Q = 8

P = 20

Total Revenue = Price x Quantity

Total Revenue = 20 x 8

Total Revenue = 160

To find the total cost we will use the total cost function

TC = 50 + 4Q + Q2

TC = 50 + 4(8) + (8)2

TC = 146

Profit = Total Revenue - Total Cost

Profit = 160 - 146

Profit = 14

Hence option D is correct

	Price	Quantity	Profit
Monopoly	28	6	58
Perfect Competition	20	8	14

Hence option C is correct