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Unformatted text preview: 14.01 Fall 2009: Exam 2 Solutions November 13, 2009 1. True/False/Uncertain Questions (20 points) In this section, write whether each statement is True, False or Uncertaint. You should fully explain your answer, including diagrams where appropriate. Points will be given based on your explanation. (a) (4 points) In a perfectly competitive market, price ceilings make consumers worse o . Please include a graph in your answer. Uncertain. This depends on the di erence between the loss of consumer surplus due to excess demand at the price ceiling, and the additional consumer surplus received by individuals who are able to purchase the good: (b) (4 points) A rm whose production technology exhibits constant marginal products has constant returns to scale. True. q = f ( k,l ); f l = const., f k = const. ⇒ 1 f ( λk,λl ) = λk · f k + λl · f l = λ ( k · f k + l · f l ) = λf ( k,l ) Note that this is true only if f (0 , 0) = 0 as well. Otherwise it will be uncertain. Some of you interpreted the question to mean that the production technology has non- diminishing marginal products. The correct answer for this interpretation was also ac- cepted since the question was ambiguously stated. (c) (4 points) In the short run, a perfectly competitive rm may operate even if it is earning a negative pro t. True. If the average total cost at the pro t maximizing level of output is higher than the price, the rm will make a loss. The rm will stay in operation as long as the price is greater than the average variable cost since it's minimizing its losses this way. (d) (4 pionts) In an economy with perfectly elastic demand, any positive tax on the nial good will drive the quantity demanded to zero. Uncertain. If there is a positive amount of producer surplus in equilibrium, it is possible to implement a tax and still have a positive quantity demanded (as the tax revenue come s entirely out of producer surplus). However, if the supply curve is perfectly elastic as well, any tax will prevent the market from reaching equilibrium. (e) (4 points) In an Edgeworth Box, indi erence curves are always tangent along the contract curve. False. This will be true only when both individuals are consuming a positive amount of each good. The marginal rates of substitution do not have to be equal (and hence the indi erence curves do not have to be tangent) along the boundaries of the box. 2. Production and Costs (16 points) Suppose that the production function of a rm making burritos is: q ( K,L ) = K 1 2 L 1 2 where q is the number of burritos produced, K is the machines used in production and L is labor used in production. (a) (4 points) Assume that the wage rate is w = 4 , and the rental rate on capital is r = 1 ....
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