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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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