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equilibrium quantity and price in this market in the absence of government intervention

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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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This solution clearly computes both the equilibrium quantity and price in this market in the absence of government intervention.

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