econ 451 - exams - 2006

# econ 451 - exams - 2006 - Economics 451 Exam 1 Spring 2006...

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Economics 451 Exam 1 Spring 2006 Prof Montgomery Answer all questions. 100 points possible. Explanations can be brief. 1) [25 points] Following Becker’s analysis of the household division of labor, consider a household in which a husband and wife can produce market goods (M) and household goods (H). a) Suppose that the wife’s production is given by the equations M = 5 t M and H = 5 t H where t M = time spent in market production, t H = time spent in household production, and the wife’s time constraint is t M + t H = 40. Derive the equation for the wife’s production possibilities curve. b) Suppose the husband’s production is given by the equations M = 2 t M and H = 4 t H where t M = time spent in market production, t H = time spent in household production, and the husband’s time constraint is t M + t H = 40. Derive the equation for the husband’s production possibilities curve. c) Plot the overall household production possibilities curve. [HINT: Your graph doesn’t need to be drawn perfectly to scale, but you must label your graph carefully and give numerical coordinates of important points on the curve.] d) Suppose that the household’s utility function has the functional form U(M, H) = M + θ H where θ is a constant such that ½ < θ < 1. What level of market and household goods (M*, H*) will the household optimally choose? [HINT: What is the slope of any indifference curve?] What is the division of labor in the household? Does either household member split their time between sectors? How would your answers change if θ was lower so that 0 < θ < ½? Briefly explain. 2) [20 points] Consider a household with bilateral altruism between the husband and wife. Suppose that the utility functions for the husband (h) and wife (w) are U h = ln(Z h ) + (1/3) ln(Z w ) and U w = ln(Z w ) + (3/2) ln(Z h ) where ln( ) denotes natural log. Suppose that the husband has income I h while the wife has income I w . Each household member can transfer some of their income to the other member, but cannot enforce negative transfers. For each of the following cases, give the final consumption level of the husband and wife after any transfers have been made. [HINT: Total household income I h + I w = 300 in every case below.] a) I h = 300, I w = 0 b) I h = 0, I w = 300 c) I h = 200, I w = 100 d) I h = I w = 150

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3) [27 points] Consider a marriage market with 3 men and 3 women. Utilities generated by each possible match are given by the following matrix. The first column gives the payoff that each man would receive if he remains single; the first row gives the payoff that each female would receive if she remains single; the remaining entries give the payoff (m ij , f ji ) that would be received by male i and female j if they marry. females
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## This note was uploaded on 08/08/2008 for the course ECON 451 taught by Professor Montgomery during the Fall '07 term at Wisconsin.

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econ 451 - exams - 2006 - Economics 451 Exam 1 Spring 2006...

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