ADVANCED QUESTIONS 11. Warrenia has two regions. In Oliviland, the mar- ginal be

Question

ADVANCED QUESTIONS 11. Warrenia has two regions. In Oliviland, the mar- ginal benefit associated with pollution cleanup is MB = 300-10Q, while in Linne!and, the mar- ginal benefit associated with pollution cleanup is MB 200-4Q Suppose that the marginal cost of cleanup is constant at $12 per unit. What is the optimal level of pollution cleanup in each of the two regions? 12. The private marginal benefit associated with a product's consumption is PMB 360-4Q and the private marginal cost associated with its pro duction is PMC = 6P. Furthermore, the marginal external damage associated with this good's pro- duction is MD 2P. To correct the externality. the government decides to impose a tax of T per unit sold. What tax T should it set to achieve the social optimum? 13. Suppose that demand for a product is Q = 1200-4P and supply is Q-_200 + 2P. Furthermore, suppose that the marginal external damage of this product is $8 per unit. How many more units of this product will the free market produce than is socially optimal? Calculate the deadweight loss associated with the externaliny

Explanation / Answer

(12) PMC: Q = 6P, therefore P = Q/6

In private market equilibrium, PMB = PMC.

360 - 4Q = Q/6

2160 - 24Q = Q

25Q = 2160

Q = 86.4

P = 86.4/6 = 14.4

Marginal damage function: Q = 2P, or P = Q/2

Social marginal cost (SMC) = PMC + MD = (Q/6) + (Q/2) = 4Q/6 = 2Q/3

Efficient outcome is obtained by equating PMB and SMC.

360 - 4Q = 2Q/3

1080 - 12Q = 2Q

14Q = 1080

Q = 77.14

When Q = 77.14,

PMC = Q/6 = 77.14/6 = 12.86

SMC = Q/2 = 77.14/2 = 38.57

Pigouvian tax per unit (T) = (SMC - PMC) at efficient output level = 38.57 - 12.86 = 25.71

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