CHAPTER 12

REGULATION AND ANTITRUST: THE ROLE OF

GOVERNMENT IN THE ECONOMY

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

QD = 40 − 2P and QS = 15 + 3P

(i) What is the equilibrium price and quantity on this market?

(ii) If the production of each unit of this good gives rise to a social cost of $1, what is the socially optimal equilibrium quantity and price? Assume that producers pay a tax of $1 per unit.

(iii) If the production of each unit of this good gives rise to a social benefit of $5, what is the socially optimal equilibrium quantity and price? Assume that producers receive a subsidy of $5 per unit.

Solution:

(i)                P = 5 and Q = 30

(ii) Supply becomes QS = 12 + 3P so P = 5.6 and Q = 28.8

(iii) Supply becomes QS = 30 + 3P so P = 2 and Q = 36

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

QD = 50 − 0.5P and QS = 10 + 1.5P

(i) What is the equilibrium price and quantity on this market?

(ii) If the production of each unit of this good gives rise to a social cost of $4, what is the socially optimal equilibrium quantity and price? Assume that producers pay a tax of $4 per unit.

(iii) If the production of each unit of this good gives rise to a social benefit of $8, what is the socially optimal equilibrium quantity and price? Assume that producers receive a subsidy of $8 per unit.

Solution:

(i) P = 20 and Q = 40

(ii) Supply becomes QS = 4 + 1.5P so P = 23 and Q = 38.5

(iii) Supply becomes QS = 22 + 1.5P so P = 14 and Q = 43

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

QD = 75 − 1.5P and QS = 21 + 0.5P

(i) What is the equilibrium price and quantity on this market?

(ii) If the consumption of each unit of this good gives rise to a social cost of $4, what is the socially optimal equilibrium quantity and price? Assume that consumers pay a tax of $4 per unit.

(iii) If the consumption of each unit of this good gives rise to a social benefit of $8, what is the socially optimal equilibrium quantity and price? Assume that

consumers receive a subsidy of $8 per unit.

Solution:

(i) P = 27 and Q = 34.5

(ii) Demand becomes QD = 69 − 1.5P so P = 24 and Q = 33

(iii) Demand becomes QD = 87 − 1.5P so P = 33 and Q = 37.5

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

QD = 70 − 2P and QS = 20 + 3P

(i) What is the equilibrium price and quantity on this market?

(ii) If the consumption of each unit of this good gives rise to a social cost of $5, what is the socially optimal equilibrium quantity and price? Assume that consumers pay a tax of $5 per unit.

(iii) If the consumption of each unit of this good gives rise to a social benefit of $10, what is the socially optimal equilibrium quantity and price? Assume that

consumers receive a subsidy of $10 per unit.

Solution:

(i) P = 10 and Q = 50

(ii) Demand becomes QD = 50 − 2P so P = 6 and Q = 38

(iii) Demand becomes QD = 90 − 2P so P = 14 and Q = 62

5. The market demand for the output of a public utility is:

QD = 250 − 2P

The firm's long-run average cost and long-run marginal cost functions are:

LAC = 50 − 0.125Q and LMC = 35 − 0.10Q

(i) What price and quantity combination would result if the firm was not regulated? How much profit would the firm earn?

(ii) What price and quantity combination would result if the firm was regulated at a price that resulted in an economic profit of zero?

(iii) What price and quantity combination would result if the firm was regulated at a price that resulted in the socially optimal level of output? How much profit would the firm earn?

Solution:

(i) MR = 125 − Q = 35 − 0.10Q = LMC so Q = 100, P = 75, and profit is equal to

(75)(100) − (100)(50 − {0.125}{100}) = 3,750

(ii) P = 125 − 0.50Q = 50 − 0.125Q = LAC so Q = 200 and P = 25

(iii) P = 125 − 0.50Q = 35 − 0.10Q = LMC so Q = 225, P = 12.50, and profit is equal to (12.50)(225) − (225)(50 − {0.125}{225}) = −2,109.375

6. The market demand for the output of a public utility is:

QD = 500 − P

The firm's long-run average cost and long-run marginal cost functions are:

LAC = 400 − 0.60Q and LMC = 140 − 0.20Q

(i) What price and quantity combination would result if the firm was not regulated? How much profit would the firm earn?

(ii) What price and quantity combination would result if the firm was regulated at a price that resulted in an economic profit of zero?

(iii) What price and quantity combination would result if the firm was regulated at a price that resulted in the socially optimal level of output? How much profit would the firm earn?

Solution:

(i) MR = 500 − 2Q = 140 − 0.20Q = LMC so Q = 200, P = 300, and profit is equal to (300)(200) − (200)(400 − {0.60}{200}) = 4,000

(ii) P = 500 − Q = 400 − 0.60Q = LAC so Q = 250 and P = 250

(iii) P = 500 − Q = 140 − 0.20Q = LMC so Q = 450, P = 50, and profit is equal to

(50)(450) − (450)(400 − {0.60}{450}) = −36,000

7. The domestic supply and demand functions for a good traded on a perfectly competitive market are:

QD = 700 − 8P and QS = 200 + 2P

(i) What is the equilibrium price and quantity on this market?

(ii) Assume that a foreign supplier exports a comparable good and is willing to sell all that domestic consumers want to purchase at a unit price of $35. What is the new equilibrium price and quantity on the market, and how many units of the good will be imported?

(iii) Now suppose that a tariff of $10 per unit is imposed on the imports. What is the new equilibrium price and quantity, how many units will be imported, how much revenue will be generated by the tariff, and how much revenue will the foreign firms receive?

(iv) Now suppose that, instead of a tariff, the foreign firms agree to a voluntary export quota. Assume that the quota results in the same equilibrium quantity as the $10 tariff. How many units will be imported, and how much revenue will the foreign firms receive?

Solution:

(i) P = 50 and Q = 300

(ii) P = 35 and Q = 420, of which 270 units are supplied by domestic firms and 150 by foreign firms.

(iii) P = 45 and Q = 340, of which 290 are supplied by domestic firms and 50 by

foreign firms. The tariff will generate $500 and the foreign firms will receive

(50)(35) = $1,750.

(iv) The foreign firms will sell 50 units at $45 so their revenue will be $2,250.

8. The domestic supply and demand functions for a good traded on a perfectly competitive market are:

QD = 500 − P and QS = 200 + 4P

(i) What is the equilibrium price and quantity on this market?

(ii) Assume that a foreign supplier exports a comparable good and is willing to sell all that domestic consumers want to purchase at a unit price of $40. What is the new equilibrium price and quantity on the market, and how many units of the good will be imported?

(iii) Now suppose that a tariff of $10 per unit is imposed on the imports. What is the new equilibrium price and quantity, how many units will be imported, how much revenue will be generated by the tariff, and how much revenue will the foreign firms receive?

(iv) Now suppose that, instead of a tariff, the foreign firms agree to a voluntary export quota. Assume that the quota results in the same equilibrium quantity as the $10 tariff. How many units will be imported, and how much revenue will the foreign firms receive?

Solution:

(i) P = 60 and Q = 440

(ii) P = 40 and Q = 460, of which 360 units are supplied by domestic firms and 100 by foreign firms.

(iii) P = 50 and Q = 450, of which 400 are supplied by domestic firms and 50 by

foreign firms. The tariff will generate $500 and the foreign firms will receive

(50)(40) = $2,000.

(iv) The foreign firms will sell 50 units at $50 so their revenue will be $2,500.