CHAPTER 8

MARKET STRUCTURE: PERFECT COMPETITION, MONOPOLY, AND

MONOPOLISTIC COMPETITION

1. The market supply and demand functions for a product traded on a perfectly competitive market are given below:

QD = 25 − P

QS = −5 + 4P

Calculate the equilibrium price and quantity.

Solution:

P = 6 and Q = 19

2. The market supply and demand functions for a product traded on a perfectly competitive market are given below:

QD = 50 − 2P

QS = 3P

Calculate the equilibrium price and quantity.

Solution:

P = 10 and Q = 30

3. The market supply and demand functions for a product traded on a perfectly competitive market are given below:

QD = 36 − P

QS = 4 + 3P

Calculate the equilibrium price and quantity.

Solution:

P = 8 and Q = 28

4. The market supply and demand functions for a product traded on a perfectly competitive market are given below:

QD = 28 − 2P

QS = 8 + 3P

Calculate the equilibrium price and quantity.

Solution:

P = 4 and Q = 20

5. The market demand function for a product sold by a monopolist is given below:

QD = 120 − 4P

The monopolist's marginal cost function is given below:

MC = 1.5Q

Calculate the equilibrium price and quantity.

Solution:

P = 30 − 0.25Q so TR = 30Q − 0.25Q2 and MR = 30 − 0.50Q

MR = 30 − 0.50Q = 1.5Q = MC so Q = 15 and P = 22.5

6. The market demand function for a product sold by a monopolist is given below:

QD = 270 − 5P

The monopolist's marginal cost function is given below:

MC = 6 + 2Q

Calculate the equilibrium price and quantity.

Solution:

P = 54 − 0.20Q so TR = 54Q − 0.20Q2 and MR = 54 − 0.40Q

MR = 54 − 0.40Q = 6 + 2Q = MC so Q = 20 and P = 50

7. The market demand function for a product sold by a monopolist is given below:

QD = 20 − P

The monopolist's marginal cost function is given below:

MC = −10 + 3Q

Calculate the equilibrium price and quantity.

Solution:

P = 20 − Q so TR = 20Q − Q2 and MR = 20 − 2Q

MR = 20 − 2Q = −10 + 3Q = MC so Q = 6 and P = 24

8. The market demand function for a product sold by a monopolist is given below:

QD = 2500 − 10P

The monopolist's marginal cost function is given below:

MC = 10 + Q

Calculate the equilibrium price and quantity.

Solution:

P = 250 − 0.10Q so TR = 250Q − 0.10Q2 and MR = 250 − 0.20Q

MR = 250 − 0.20Q = 10 + Q = MC so Q = 200 and P = 230

9. The market demand curve for a product is given below:

QD = 250 − 0.5P

(i) Assume that the market is supplied by a monopolist with a constant unit cost

equal to $100. Calculate the equilibrium price and quantity.

(ii) Now assume that the market is supplied by perfectly competitive firms and that the market supply curve is perfectly elastic at a price equal to $100. Calculate the equilibrium price and quantity.

Solution:

(i) P = 500 − 2Q so TR = 500Q − 2Q2 and MR = 500 − 4Q

MR = 500 − 4Q = 100 = MC so Q = 100 and P = 300

(ii) P = 100 and Q = 200

10. The market demand curve for a product is given below:

QD = 50 − 0.5P

(i) Assume that the market is supplied by a monopolist with a constant unit cost

equal to $40. Calculate the equilibrium price and quantity.

(ii) Now assume that the market is supplied by perfectly competitive firms and that the market supply curve is perfectly elastic at a price equal to $40. Calculate the equilibrium price and quantity.

Solution:

(i) P = 100 − 2Q so TR = 100Q − 2Q2 and MR = 100 − 4Q

MR = 100 − 4Q = 40 = MC so Q = 15 and P = 70

(ii) P = 40 and Q = 20

11. The demand function for a product sold by a monopolistically competitive firm is given below:

QD = 250 − P

The firm’s marginal cost function is given below:

MC = 10 +2Q

Calculate the equilibrium price and quantity.

Solution:

P = 250 − Q so TR = 250Q − Q2 and MR = 250 − 2Q

MR = 250 − 2Q = 10 + 2Q = MC so Q = 60 and P = 190

12. The demand function for a product sold by a monopolistically competitive firm is given below:

QD = 210 − P

The firm’s marginal cost function is given below:

MC = 10 +2Q

Calculate the equilibrium price and quantity.

Solution:

P = 210 − Q so TR = 210Q − Q2 and MR = 210 − 2Q

MR = 210 − 2Q = 10 + 2Q = MC so Q = 50 and P = 160