econ 451 - exams - 2007

econ 451 - exams - 2007 - Economics 451 Exam 1 Spring 2007...

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Economics 451 Exam 1 Spring 2007 Prof Montgomery Answer all questions. 100 points possible. 1) [10 points] Briefly evaluate and discuss the following claim: Economic models of the family cannot adequately address “power differentials” between family members. 2) [30 points] Consider a household composed of a husband and a wife. Each member of the household allocates his/her time to produce market goods (M) and household goods (H), and time inputs are chosen to maximize overall household utility (which depends on total M and total H produced by the household members). Assuming that the husband has increasing returns to production in each sector, while the wife has constant returns to production in each sector, their individual production possibilities curves (PPCs) are given below. Further assume that the horizontal intercepts (labeled a) and the vertical intercepts (labeled b) are the same on both diagrams. M husband’s PPC M wife’s PPC (convex) (linear) b b a H a H a) In Chapter 2 of Becker’s Treatise , he considers the case where both members of the household have constant returns to production in both sectors. Given this assumption, what result does he state regarding the optimal division of labor within households? [NOTE: I’m asking about his initial result, where coefficients of production are taken as given, not his subsequent result when individuals choose to invest in human capital.] b) Will Becker’s result (discussed in part a) still hold given the individual PPCs shown above? If you answered no, what result does hold? If you answered yes, can you state a stronger result than Becker’s? In either case, explain your answer. [HINT: Consider a potential outcome where both members allocate time to both sectors. Is the household behaving efficiently?] c) Draw the household’s overall PPC. Then, for each segment of this curve, indicate which members of the household are working in which sector(s). [HINT: Your graph doesn’t need to be perfect, but should be properly labeled, and the overall PPC must have the correct shape.]
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3) [30 points] Consider a marriage market with 4 men and 4 women. The following matrix gives the payoffs received by each man and woman in each potential match. [The matrix specifies the payoffs (m ij , f ji ) given a match between man i and woman j. The first column gives payoffs if each man remains single; the first row gives payoffs if each woman remains single.] Assume that utility is not transferable. w o m e n 1 2 3 4 men 4 3 2 1 ) 6 , 4 ( ) 2 , 9 ( ) 5 , 5 ( ) 6 , 3 ( 1 ) 2 , 5 ( ) 3 , 7 ( ) 2 , 6 ( ) 3 , 8 ( 4 ) 1 , 9 ( ) 5 , 4 ( ) 1 , 5 ( ) 4 , 6 ( 2 ) 4 , 7 ( ) 7 , 2 ( ) 9 , 6 ( ) 5 , 4 ( 5 3 4 3 2 . a) Is the match structure {M1-F4, M2-F3, M3-F1, M4-F2} stable?
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econ 451 - exams - 2007 - Economics 451 Exam 1 Spring 2007...

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