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Labor Economics Assignment 9 Fall 2020 Due Date: Thursday, December 10, uploaded to N YU classes prior to the beginning of the lecture. I. A household contains two individuals, with the individuals having utility functions given by in = 0.4lnl1+0.6lnc uz = 0.6lnl2+0.4lnc, where c = wlhl +w2h2 +y1 +312, where w,- is the wage, yi the nonlabor income, l, the leisure, and h,- the labor supply of individual i. For each individual, T = h,- +li, where T is the time endowment. All consumption is public, so that all sources of income are pooled to purchase c in the market. Let yl =92 = 10, ml = 10,102 =5, andT=20. 1. Find the Nash equilibrium levels of labor supply in the household, Ill and lag. Find the utility of each individual at the Nash equilibrium labor supplies. 2. Let the household agree to solve maxd X \"1(h1,h2) + (1 6) X \"2(h1,h2), where ui(h1,h2) denotes the utility of individual 2' if individual 1 works hl hours and individual 2 works hg hours and 6 is the Pareto weight attached to individual 1's utility. Let 6 = 0.5. Find the labor supplies hr, 2' = 1,2, that solve the household's maximization problem. What are the utility levels of the two individuals? 3. Assume that 6 \"'1 _ wl + 102 I Now nd the labor supplies that solve the household maximization problem. What are the utility levels of the two individuals? 4. Explain the differences in the household members' utilities across the three parts of the