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equilibrium price and quantity in a market with no government intervention

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Consider a manufactured good whose production process generates pollution. The annual demand for the good is given by Qd = 100 â?" P. The annual market supply is given by
Qs = P-10. In both equations, P is the price in dollars per unit. For every unit of output produced, the industry emits one unit of pollution. The marginal damage from each unit of pollution is given by Q.
a) Find the equilibrium price and quantity in a market with no government intervention.
b) At the equilibrium you computed, calculate: (i) consumer surplus; (ii) producer surplus; (iii) total dollars of pollution damage. What are the overall social benefits in the market?
c) Find the socially optimal quantity of the good. What is the socially optimal market price?
d) At the social optimum you computed, calculate:
(i) consumer surplus; (ii) producer surplus; and (iii) total dollars of pollution damage. What are the overall social benefits in the market?
e) Suppose an emissions fee is imposed on producers. What emissions fee would induce the socially optimal quantity of the good?

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This solution analyzes equilibrium price and quantity in a market with no government intervention.

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Price in this market in the absence of government intervention

Question 4. A study by the CDC has shown that preventive care measures impose sizable positive externalities on others. To keep things simple, in this problem we will study the consumption of preventive care by a single individual.

Let q denote the consumption of preventive care by the individual. The CDC has estimated that the direct marginal benefit that the individual derives from his own consumption of preventive care is given by MBdirect = 10 - q, and that the marginal benefit that his consumption generates on everyone else in society is given by MBext = 10 - q.

Suppose that preventive care is sold on a competitive market and that it can be produced without fixed costs at a constant marginal cost of $2/unit.

a) Compute the equilibrium quantity and price in this market in the absence of government intervention.

b) Compute the socially optimal level of individual consumption of preventive care.

c) What is the size of the DWL? Provide a numerical answer and depict it in a carefully labeled diagram.

d) What is the size of the optimal corrective tax or subsidy (consider as usual a per unit tax)? Assume that the tax or subsidy is paid/received by the consumer. Please provide a numerical answer.

e) What is the change in producer profits that results from the introduction of the optimal corrective tax or subsidy?

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