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Problem 2 Suppose that an economy consists of two individuals at and j, whose disposable income is given by x,- and xj, respectively. Individual i's utility function is u,-(x,-,xj) = x,- a: max{xj xi,0} B max{x,- xi, 0} with a 2 [5' 2 0 and B S 1. a) Describe the economic intuition behind i's utility function. (5 points) b) Analyze analytically how i's utility level depends on a. Briey explain the economic intuition for your result. (2 points) cl Analyze analytically how i's utility level depends on xi. Briefly explain the economic intuition for your result. (4 points) The two individuals participate in an allocation game in which individual i chooses an allocation, while individual j remains passive. The set of feasible allocations is A: (x,- = 15:39- = 0); B: (10; 7.5); C: (5; 15); and D: (0; 22.5). Assume thata = 1 3 and B = Zhold. d) Analyze which allocation individual i will choose if she is a utility maximizer. (4 points) e) Describe the trade-offs individual i faces. (5 points) Problem 3 Consider the following lottery: If the participant wins the lottery, which happens with probability 0.5, she will earn 9 = 100. If she loses, she will payl = 50to the lottery. a) Mary's indirect utility function is 11M = , where y denotes her total wealth level after playing the lottery (measured in euros). Her initial wealth level is 151000 and she maximizes her expected utility. Show that Mary will participate in the lottery. (3 points) I \\ J P I I I x n I l