Exercise 1: Consumer Choice Application Labor-Leisure Choice Freya has preferences over bundles of leisure time (x), measured as fraction of total time (i.e. X=l corresponds to 100% of time - or 168 hours per week- spent on leisure) and money for consumption (y). She has an endowment consisting of both time and a dividend payment, d = 30, that she receives in addition to her labor income and independent of her choice to work. Freya's endowment is E = [1:0, yo) = (1, 30) and her utility function is 1 any =m. ( ) y Assume that she is absolutely free to choose the number of hours she works per week, [1 1:) - 168 E [0, 168]. 1. For xed wage rate to > 0 (per 168 hours) what is her budget? 2. Under what conditions would Freya choose not to work? That is, nd the threshold wage 1E! such that Freya's optimal choice is [3*(10), y* (10)) = E = (1, 30) for all to S if)? 3. Assume w > if}, what is Fraya's optimal consumption bundle as a function of the wage rate (33\" (w), y*(w))? 4. Based on your previous answers determine Freya's labor supply function 3(w). That is, nd the function that maps the wage rate winto the percentage of time she works, 1 1:*(w). ls her optimal choice of labor supplied, i.e. 3(w) = 1 33"'(w), increasing in w