M Inbox (24) - KOE X M Adventis Certifi X Gi Handshake X Adventis X NYU Classes : L X ug_labor_20_a9 x Golden Kamuy X (4) YouTube * *Homework Hel X + X > C A newclasses.nyu.edu/access/content/attachment/f49eOcdb-599f-4522-a80e-343b378678d1/Assignments/49691244-134f-41f6-9ef4-45eaea41adb6/ug_labor_20_a9.pdf ABP To D ug_labor_20_a9.dvi 1 / 2 C: 1. A household contains two individuals, with the individuals having utility functions given by U1 = 0.41n/ + 0.6Inc u2 = 0.6 In /2 + 0.4 Inc, where c = wih1 + wah2 + y1 + 92, where w; is the wage, y; the non-labor income, li the leisure, and h; the labor supply of individual i. For each individual, T = hitli, 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, and T = 20. 1. Find the Nash equilibrium levels of labor supply in the household, h, and h2. Find the utility of each individual at the Nash equilibrium labor supplies. 2. Let the household agree to solve max o x u1 (h1, h2) + (1 -6) x u2(h1, hz), where ui(h1, h2) denotes the utility of individual i if individual 1 works hi hours and individual 2 works h2 hours and o is the Pareto weight attached to individual 1's utility. Let 6 = 0.5. Find the labor supplies hy, i = 1, 2, that solve the household's maximization problem. What are the utility levels of the two individuals? 3. Assume that 6 = W1 W1 + w2 Now find 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. PDF ug_labor_20_a9.pdf Show all X Type here to search O Ei 9 3 0 WA 97% 6:56 PM 12/8/2020 EM Inbox (24) - kot X M Adventis Certifi X Gi Handshake X Adventis X NYU Classes : L X ug_labor_20_a9 x Golden Kamuy X (4) YouTube * *Homework Hel X + X C A newclasses.nyu.edu/access/content/attachment/f49eOcdb-599f-4522-a80e-3436378678d1/Assignments/49691244-134f-41f6-9ef4-45eaea41adb6/ug_labor_20_a9.pdf ABP To ES D ug_labor_20_a9.dvi 2 / 2 2. The parent in a single-parent household has a utility function given by u = 0.2 In/ + 0.3 Inc + 0.5 Ink, 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 = 10.520.418-6, where ko is initial child quality, e is the money spent on investment in the child, and T is time spent by the mother investing in the child. Let ko = 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*, 7*, and e*. What is final child qual- ity k? What is the mother's utility? 2. The government sends all households with a young child a check for 40 dollars. What is the effect on k and the mother's utility? 3. The government sends all households with a young child investment goods for the child that have a value of 40. These goods can only be used for child investment, meaning that e 2 40. Find the mother's utility-maximizing choices in this case, and find the child's cognitive ability value, k. Find the mother's utility level in this case. 4. Compare the answers to parts 2 and 3. Explain the difference in the results. PDF ug_labor_20_a9.pdf Show all X Type here to search 97% 6:56 PM 12/8/2020
