Hi, please help with these questions. Thank you!

1. A household contains two individuals, with the individuals having utility functions given by 11.1 = 0.4]n11+0.5lnc v.2 = 0.61n32+0.4lnc, where c = 101 I11 +w2 hg + yl +y2, where w,- is the wage, y,- the non-labor income, I, the leisure, and he the labor supply of individual i. For each individual, T = IiiHg, 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 y1=y2=10,w1=10,w2=5,andT=2O. 1. Find the Nash equilibrium levels of labor supply in the household, .31 and 5%. Find the utility of each individual at the Nash equilibrium labor supplies. 2. Let the household agree to solve maxd X u1(h1,h2) + (1 5) X Ug(h1,h2), where Ug(h1,h2) denotes the utility of individual i 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 5 = 0.5. Find the labor supplies 11:, i = 1,2, that solve the household's maximization problem. What are the utility levels of the two individuals? 3. Assume that 181 62. wlIwz 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 problem. 2. The parent in a singleparent household has a utility function given by u = 0.2km! + 0.3lnc+ 0.5 ink1 where I is leisure, c is consumption of a good purchased in the market, and k is the cognitive ability of the child. The production function of child quality is given by k : 705,504,605 where kg is initial child quality, 6 is the money spent on investment in the child, and 'T is time spent by the mother investing in the child. Let kg = 10. The mother has a wage of w = 5, non-labor income of y = 20, and a time endowment of T = 20. 1. Find her utility-maximizing decisions h', T'\