Assume Zo's utility function is U(C, L) = CL where C is consumption measured by her total income and L is leisure. Total income is labour income and non-labour income. She has y = $400 non-labour income and a total of 150 hours to allocate between work (consumption) and leisure at the market wage rate of w = $10 per hour. a) Write down the budget constraint and the slope of the budget constraint. Solve the optimal desired hours of leisure (L) and work (h). Suppose a company makes a job offer to Zo. However, this company needs to design a system that motivates her to work more hours. The following two scenarios are suggested. Scenario I) Straight-time equivalent Suppose the company increases the hourly wage to w = $16 per hour. b) Solve the new optimal leisure-work choice (L and h). Scenario II) Overtime premium Suppose the job offer requires her to work h = 70 hours per month at $10/h and double pay for every hour beyond 70. The alternative, for her, is not to work at all. c) Show that Zo is better off accepting the offer than the alternative. d) Write down the equation of the kinked budget constraint. (Hint: The budget line is kinked so you need to define two parts: one equation for hours of work up to 70 and one equation for hours of work above 70) e) Find the optimal hours of work after accepting the offer. (Hint: Given that the offer is accepted, you should find how many hours of the remaining available time (150-70-80) is allocated between work and leisure. Then, you can calculate the total hours of work and leisure.) f) Use the appropriate budget constraint and indifference curves and show the following on one graph. The optimal point in the original case. a. b. The offered hours in scenario II. C. The optimal choice in scenario II. g) Compare the two scenarios and briefly, explain which scenario suits the company's needs better? Is this also the preferred scenario for Zo?