Exercise 7 (Labor-Leisure Choice) Freya has preferences over bundles of leisure (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 of all other goods (y). She has an endowment consisting of both leisure time and a dividend payment. Freya's endowment is E = (1, 1) and her utility function is u(x,y) = x - 1. Assume that she is absolutely free to choose the number of hours she works, 1 - re [0, 1]. 1. For fixed wage rate w > 0 (per 168 hours) what is her budget? 2. Assume w > 1, what is her optimal consumption bundle (*, y* )? 3. Assume w E (0, 1], what is her optimal consumption bundle (a*, y*)? 4. Find her labor supply function, i.e. how does the amount of time she works, 1-, depend on the wage rate w? Is her optimal choice of labor, 1 -r* (w) increasing in w