5. Tosca has preferences over bundles of leisure (x) and money for consumption of all other goods at fixed prices (y), and is free to choose the number of hours she works. Her utility function is u(x,y) =x -(1/y). Her endowment, (1, 1), consists of both leisure time and a dividend payment. Note time is being measured as the fraction of total time, so leisure level 1 corresponds to 100% of time spent in leisure (e.g., 168 hours per week). a. Given wage rate w >0, what is her budget? [Be careful. What is special about leisure?] b. Given wage rate w > 1, what is her optimal consumption bundle? C. Given wage rate w - 1, what is her optimal consumption bundle? [Be careful.] d. If she chooses to use fraction x of her time as leisure, then her time working (labor time) is 1-x. Use your answers to Parts (b) and (c) to find her supply function for labor as a function of the wage rate. e. Is the amount of labor she supplies always non-decreasing in the wage rate or does it have a backward-bending portion