Question

6. Assume market demand characterized by MWTP(Q)=42-Q (MWTP=marginal willingness to pay, and is another term for demand) and market supply characterized by MC(Q)=6+2Q (MC is marginal cost – recall the supply curve is also a firm’s marginal cost curve in a competitive market). Further, assume a negative externality equal to $6 per unit transacted.

a. Solve for the equilibrium quantity transacted in a market without interventions as well as the efficient (socially optimal) quantity.

b. In an appropriately labeled graph, clearly identify the deadweight loss resulting from a market without interventions.

c. Calculate the deadweight loss resulting from a market without interventions.

d. Consider using a Pigouvian tax to maximize total surplus. What would the tax be?

e. Explain how a tax increases total surplus despite (by definition) decreasing both consumer and producer surplus.

Answer 1

(a)

(i) In market equilibrium, MWTP = MC(Q)

42 - Q = 6 + 2Q

3Q = 36

Q = 12

P = 42 - 12 = $30

(ii) Marginal social cost (MSC) = MC(Q) + Externality cost = 6 + 2Q + 6 = 12 + 2Q

Social optimum is obtained by equating MWTP with MSC.

42 - Q = 12 + 2Q

3Q = 30

Q = 10

P = 42 - 10 = $32

(b)

In following graph, D, MPC and MSC are demand (MWTP), marginal cost and marginal social cost curves respectively. Market equilibrium is at point A where D intersects MPC with price P0 (= $30) and quantity Q0 (= 12). Socially optimum outcome is at point B where D intersects MSC with higher price P1 (= $32) and lower quantity Q1 (= 10). Deadweight loss is area ABC.

(c)

Deadweight loss = (1/2) x Unit externality x Difference in quantity = (1/2) x $6 x (12 - 10) = $3 x 2 = $6

(d)

The Pigouvian tax per unit is the unit Externality cost, which is $6.

Total tax revenue = Tax per unit x Efficient quantity = $6 x 10 = $60

NOTE: As per Answering Policy, 1st 4 parts are answered.