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Exercise 1: LaborLeisure Choice Jennie has preferences over bundles of leisure time (X), measured as fraction of total time [i.e. x=1 corre sponds to 100% of time 1 or 168 hours per week spent 011 leisure) and money for consumption (3'). She has an endowment consisting of both time and a dividend payment, (1 : 50 per week, that she receives in addition to her labor income and independent of her choice to work. Jennie's endowment is E = (3:0. yo) = (1. 50) and her utility function is May) 2 E3: 7 _. Assume that she is absolutely free to choose the number of hours she works per week, {1 i I) - 168 E [0, 168]. 1. For xed wage rate to > 0 (per 168 hours), nd her budget equation and explain how her budget set relates to w. 2. Under what conditions would Jennie choose not to work? That is, find the threshold wage if; such that Jennie's optimal choice is (a:*(u'), y*(w)) = E = (1= 50) for all u! S if}. 3. Assume w > 73: what is J ennie's optimal consumption bundle as a function of the wage rate (56*(10), y\" (1.0))? 4. Based on your previous answers determine Jelmie's labor supply function 5(a)). That is. nd the function that maps the wage rate in into the percentage of time she works. 1 i a:*(w). ls her optimal choice of labor, i.e. 8(a)) : 1 .r\"'[w), increasing in w"