Question 1 Suppose there are two firms, A and B, that produce identical goods an

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Question 1 Suppose there are two firms, A and B, that produce identical goods and have cost functions 2 Ca (Q) = 10Q + and Each firm creates pollution, but firm A uses a clean technology that creates a marginal external cost MECA 2 per unit, whereas firm B uses a dirty technology that creates a marginal external cost MECB 4. There is perfectly elastic demand for the output of the (i) How much will each firm produce in equilibrium? (ii) What is the socially efficient output for each firm? (iii) Suppose that each firm is forced to pay the same unit tax t on its output. What value of the tax t would maximize total surplus? (iv) Suppose that each firm is told that it cannot exceed a common maximum level of output Q. What value of the quota Q would maximize total surplus?

Explanation / Answer

a) For equilibrium, MR= MC,

Firm A- Revenue= pq, so MR= P, MR= 20, MC= derivative of 10Q + 1/2 Q2

= 10 + 1/2 X 2Q = 10 + Q, MR=MC, so 10+ Q= 20, Q=10 units at equilibrium

Firm B- MC= 8 + Q, 20= 8+Q, Q=16 units at equlibrium.

b) Socially efficient output= fOR FIRM A, MC + MEC= MR

10+Q+2= 20, Q= 8 units

For firm B, 8+Q+4 = 20, Q= 8 units

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