Freya has preferences over bundles of leisure time (X), measured as fraction of total time [i.e. x:1 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, of 2 30, that she receives in addition to her labor income and independent of her choice to work. Freya's endowment is E : [$0, yo) = (1, 30) and her utility function is 1 any =1:. ( ) y Assume that she is absolutely free to choose the number of hours she works per week, (1 SC) - 168 E [0, 168]. 1. For xed wage rate w > 0 (per 168 hours) what is her budget? 2. Under what conditions would Freya choose not to work? That is, nd the threshold wage all such that Freya's optimal choice is (33*(w), y*(w)) = E = (1,30) for all m S if)? 3. Assume w > If), what is Fraya's optimal consumption bundle as a function of the wage rate [$*(w) , y'\" (w))? 4. Based on your previous answers determine Freya's labor supply function 3(w). That is, find the function that maps the wage rate winto the percentage of time she works, 1 17*(10). Is her optimal choice of labor supplied, is. 3(w) : 1 :1:*(w), increasing in w