econ11practice1.answer

econ11practice1.answer - Answers to Selected Questions in...

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Answers to Selected Questions in Practice Problem Set 1 ECON 11 Summer Session C 2010 Microeconomic Theory Yong Yang 1. [Market equilibrium] (a) omitted. (b) Q D = Q S = 240 is the equilibrium quantity at the equilibrium price P = 90. The demand elasticity is ε D = - 3 2 , and the supply elasticity is ε S = 9 8 at the equilibrium. (c) The consumer surplus is 7,200, and the producer surplus is 9,600. The social total surplus is 16,800. (figure omitted) (d) The new equilibrium is P = 150 and Q D = Q S = 420. (e) CS increases to 44,100, and PS also increases to 29,400. The social total surplus increases to 73,500 consequently. 2. [Sales tax] (a) The equilibrium is P = 260 and Q D = Q S = 450. (b) CS is 50,625, PS is 33,750, and thus STS is 84,375. (c) When the sales tax is imposed, sellers get the market price, so P S = P , but buyers pay more than the market price, so P D = P + 25. Writing the quantities demanded and supplied in terms of the market price P , Q D =970 - 2 P D = 970 - 2( P + 25) = 920 - 2 P Q S = - 330 + 3 P S = - 330 + 3 P At the equilibrium, Q D = Q S , so we have 920 - 2 P = - 330 + 3 P and thus P = 250 at the equilibrium. From this, we get P D = 275 and P S = 250. The equilibrium quantity would be Q D = Q S = 420. The new equilibrium (market) price is lower than before the sales tax is imposed. (However, consumers pay more than the original equilibrium price $260.) The new equilibrium quantity is less than before. (d) Consumers have the demand curve Q D = 970 - 2 P D , and buy 420 units by paying P D = 275 at the equilibrium. Note that the intercept of the demand curve is 485. So the consumer surplus would be CS = 1 2 × (485 - 275) × 420 = 44 , 100 Sellers have the supply curve Q S = - 330 + 3 P S , and sell 420 units to get P S = 250 per unit at the equilibrium. Note that the intercept of the supply curve is 110. So the producer surplus is PS = 1 2 × (250 - 110) × 420 = 29 , 400 There is a government revenue from the sales tax, which amounts to 25 × 420 = 10 , 500. So the social total surplus is 44 , 100 + 29 , 400 + 10 , 500 = 84 , 000. This is less than the one in (b), so there is a deadweight loss of $375. (e) When the sales tax is imposed proportionately, buyers pay more than the market price by 10%, so P D = 1 . 1 P . So the demand curve is Q D = 970 - 2 . 2 P in terms of the market price P . There is no change to the supply curve. Solving the equilibrium equation
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