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Problem 3 Alan's utility function for consumption (C) and leisure time (I) is U(C,l) = 20/2 + I . Each week, Alan has a time endowment of 120 hours that he can devote to work (N) or leisure time @- The unit price of C is $1 while the unit wage rate is w. Alan also earns A dollars per week of non-labor income. a) Write the expression of Alan's budget constraint. b) Find Alan's optimal combination of consumption and leisure time as a function of the wage rate w and of his non-labor income A. c) Does a higher wage push Alan to work longer hours or shorter hours? Show your work. d) Why do different workers respond differently to wage raises with some increasing their hours worked and others cutting hours worked? Suppose Alan won the Mega Million Lottery and his non-labor income increased. e) After winning the lottery, would he work longer or shorter hours? Justify your answer. f) After winning the lottery, would he decide to drop out of the labor force? Clearly explain? g) After winning the lottery, would Alan consumption (C) increase, stay the same or drop? Justify your answer. h) Does Alan consider leisure time a normal good or an inferior good? Justify your answer. h..-l..'l..._. A