# PS9Answers - – 3(Ps 10 = 2Ps Then the new equilibrium is...

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Problem Set 9 - Solutions 1) a) First, we have that P = Mg. C., i.e., P = q + 5. Finally, it follows that q = P 5. b) From a), the short-run supply curve is Q S = 200(P 5). c) In equilibrium, Q S = Q D , or equivalently, 1000 50P* = 200(P* 5). Then, P* = 8 and Q* = 600. 2) a) For consumers of type 1 x(P X ,P Y ,I) = 0.5*I/P X , and for consumers of type 2 we have x(P X ,P Y ,I) = 0.3*I/P X . b) X(P X ,P Y ,I) = 55*I/ P X . No, P Y does not affect X(P X ,P Y ,I). c) First, we have that 55*2/ P X = 55 + 55P X , or equivalently, 2 = P X + P X 2 . Then, P x = 1, and X = 55. 3) a) First, we set 150 3P* = 2P*. Then, it follows that P* = 30, whereas Q* = 60. In addition, the consumer surplus is (50-30)*60/2 = 600, whereas the producer surplus is 60*30/2 = 900 (Note that you have to use the demand and supply functions to find the surpluses. But before you can do that you have to solve for the price as a function of quantity.) b) First, we set 150
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Unformatted text preview: – 3(Ps* + 10) = 2Ps*. Then, the new equilibrium is Ps*=24, Pd*=34 and Q*=48. Moreover, the new consumer surplus is (50-34)*48/2 = 384 and now the producer surplus is 24*48/2 = 576. Finally, the deadweight loss is (60-48)*10/2 = 60. 4) a) True. When the demand curve is perfectly inelastic, after the imposition of a tax, the equilibrium quantity does not change, as a result, the deadweight loss is zero b) True. Analogously, when the supply curve is perfectly inelastic, after the imposition of a tax, the equilibrium quantity does not change, as a result, the deadweight loss is zero. c) False. As long as the ceiling price is above the equilibrium price, this policy will not affect the equilibrium price-quantity combination. Counter example: suppose that the supply and demand curves are the same as in Ex. 3), and that the government set the ceiling price at \$1000....
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