Question

1. Assume that the market for steel in a country is perfectly competitive. The demand for steel is P = 14 - Q and the industry supply (marginal cost) curve is P = Q + 2, where P is price and Q is quantity. There are no imports or exports.
2. 1. Depict the above demand and supply curves in a diagram and use algebra to calculate the market equilibrium price, P*, and quantity, Q*.
3. 2. Now assume that the process of steel production uses coal and pollutes the environment. The marginal external cost of steel production is MEC = 4. Calculate the socially optimal level of steel production, Q^s, and illustrate its determination in your diagram for part (a) by using any additional curve that may be needed.   
4. 3. Compute the value of social welfare at Q^s? Also, what would be the loss in social welfare if the market ignores external costs and continues to produce at Q*?   
5. 4. A per unit tax is proposed to correct the market failure in part (c). At what value should the tax be set, and would you recommend use of this tax if its implementation cost is 10? Explain.  

Answer 1

(a)

Setting demand = supply,

14 - Q = Q + 2

2Q = 12

Q = 6

P = 6 + 2 = 8

In following graph, market outcome is at point A where PMB (demand = private marginal benefit) intersects PMC (supply = private marginal cost) with market price P* (= 8) and market output Q* (= 6).

(b)

Marginal social cost (MSC) = PMC + MEC = Q + 2 + 4 = Q + 6

In efficient outcome, Demand = MSC

14 - Q = Q + 6

2Q = 8

Q = 4

P = 4 + 6 = 10

In the graph, efficient outcome is at point B where PMB intersects MSC with higher efficient price Ps (= 10) and lower efficient output Qs (= 4).

(c)

From demand function, when Q = 0, P = 14

Consumer surplus (CS) = (1/2) x (14 - 10) x 4 = 2 x 4 = 8

From MSC function, when Q = 0, MSC = 6

Producer surplus (PS) = (1/2) x (10 - 6) x 4 = 2 x 4 = 8

Total social welfare (TS) = CS + PS = 8 + 8 = 16

The negative externality, if not considered, cauwill lead to a welafre loss of area ABC.

Welfare loss = (1/2) x MEC x Change in Q = (1/2) x 4 x (6 - 4) = 1 x 2 = 3

(d)

The welfare loss can be eliminated by a Pigouvian tax of BD per unit.

Unit tax = MEC = 4

Total tax revenue = Unit tax x Efficient output = 4 x 4 = 16

If implementation cost is 10, it is lower than the Pigouvian tax revenue. So the tax can be implemented.