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1. Two individuals, 1 and 2, inhabit a household. The utility of individual i is given by u.- = enamel) +0.751nc, t: 1,2. where 0

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1. Two individuals, 1 and 2, inhabit a household. The utility of individual i is given by u.- = enamel) +0.751nc, t: 1,2. where 0 is total household consumption, which is given by 0:131:11 +'w-2-ll2-l-Yi and where Y is the nonlabor income of the household. Each individual has a time endowment of T : 20. The nonlabor income of the household is Y : 101}. The wage of individual 1 is 1.1!] = ll]I and the wage of individual 2 is tug = 5. 1. Determine the labor supplies of the two individuals, 311 and fig, if they behave non-cooperatively (Nash equilibrium). 2. Determine the labor supplies of the two individuals if they behave in an ei- eient manner. where labor supplies are determined by the household solving the following problem: gs: [1.51:1 + (1.5%. 3. Comment on the differences between the solutions in [1.1] and (1.2]. Is welfare higher for both individuals in part {1.2}? 2. Consider the same two-person household as in Question 1. Let the household mem- bers use a Nash bargaining protocol to determine labor supplies in the household. Namely, let the value of the \"outside option" of individual i be given by (2;. Then labor supplies are given by the solution to ggwshs he) or)\" x Walks-'12) on)\". 1. Find the labor supplies a; and it: when Q; is equal to the utility level of individual :i for the case that the household behaves noneooperatively [i.e.. in the noncooperative Nash equilibrium you solved for in Question 1.1]. 2. Let each individual have nonlabor income of Y, = 50 (so that total household nonlabor income, Y, is 50 + 50 = 100, as it was in Question 1). Find the labor supplies h, and h2 when Q; is equal to the utility level of individual i for the case in which the household members live alone (i.e., they "divorce")

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