Economics 451 Exam 1 Fall 2007 Prof Montgomery Answer all questions. 100 points possible. 1. [30 points] Consider a household composed of a husband, wife, and child. Each member of the household allocates time to produce market goods (M) and/or household goods (H) in order to maximize household utility U(M, H). Assume that both the husband and the child have constant returns to production in each sector (with the husband having the comparative advantage at market work). Further assume that the wife has diminishing returns to production in each sector, and that her PPC is initially flat at the vertical intercept (with slope close to zero), eventually very steep at the horizontal intercept (with slope approaching -∞), and smooth (with continually changing slope and no “kink” points). Graphically, the individual PPCs are given by husband’s PPC wife’s PPC child’s PPC M M M H H H Draw the combined PPC for the household, and briefly discuss its shape. [HINT: Obviously, you don’t have numerical information about the individual PPCs. But you do have enough information to illustrate the qualitative features of the combined PPC. To receive full credit, your graph should be neat and appropriately labeled.] Then, assuming that the household is efficient, state whether each of the following outcomes is possibleor impossible. a) husband and wife work only in market; child works only in household b) husband and wife work in both sectors; child works only in household c) husband works in both sectors; wife and child work only in household d) all 3 members work in both sectors 2. [15 points] Consider a household composed of a selfish wife with utility function Uw= u(Zw) and an envious husband with utility function Uh= u(Zh) – ηu(Zw). [Following the notation from lecture, suppose that Zwand Zhare consumption levels, that u(Z) is a concave function of Z, and that η> 0 is an envy parameter.] Further suppose that husband is endowed with income Ihwhile the wife is endowed with income Iw. Either spouse can transfer income to the other, but cannot enforce negative transfers. For this household, describe the equilibrium (after-transfer) consumption levels Zh* and Zw* and illustrate by drawing an indifference-curve diagram (or diagrams). If the wife could take an action that would increase her own income (Iw) but decrease total income (Iw+Ih), would she take this action? Briefly explain.
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