Question

Suppose diesel fuel is sold in an unregulated perfectly competitive market, where the inverse market supply curve is P = 1 + 0.01QS and the inverse market demand curve is P = 8– 0.04QD where the quantity is in billions of gallons per year and the price is in dollars per gallon. Suppose that the external marginal cost of diesel fuel depends on the quantity of diesel fuel consumed as follows: EMC = 0.01Q a. What is the market equilibrium price and quantity of diesel fuel? b. What is the socially optimal level of output and price of diesel fuel? c. What is the deadweight loss in the market for diesel fuel (if any)? d. Suppose that the government imposes a $0.50 tax on each gallon of diesel fuel sold. e. With the tax, what is the market equilibrium price and quantity of diesel fuel? f. With the tax, what is the deadweight loss in the market for diesel fuel (if any)?

Answer 1

(a)

In market equilibrium, market demand equals market supply with QD = QS = Q.

1 + 0.01Q = 8 - 0.04Q

0.05Q = 7

Q = 140

P = 1 + (0.01 x 140) = 1 + 1.4 = 2.4

(b)

In social optimal outcome, Market demand = Market supply + EMC

8 - 0.04Q = 1 + 0.01Q + 0.01Q

8 - 0.04Q = 1 + 0.02Q

0.06Q = 7

Q = 116.67

P = 1 + (0.02 x 116.67) = 1 + 2.33 = 3.33

(c)

When Q = 140, EMC = 0.01 x 140 = 1.4

Deadweight loss = (1/2) x EMC x Change in quantity = (1/2) x 1.4 x (140 - 116.67) = 0.7 x 23.33 = 16.33

(d) and (e)

The $0.5 tax will shift supply curve leftward by $0.5 at every output, and new supply function becomes

P - 0.5 = 1 + 0.01Q

P = 1.5 + 0.01Q

Equating with demand,

8 - 0.04Q = 1.5 + 0.01Q

0.05Q = 6.5

Q = 130

P = 8 - (0.04 x 130) = 8 - 5.2 = 2.8 (Price paid by buyers)

Price received by sellers = 2.8 - 0.5 = 2.3

(f)

Deadweight loss = (1/2) x Unit tax x Change in quantity = (1/2) x 0.5 x (140 - 130) = 0.25 x 10 = 2.5