Cathy faces a two-period decision problem in which she must choose how many hours to work in each period, H1 and H2. Cathy gets utility from her free time in each period (the time she is not working), Li and L2, and from her consumption expenditures in each period, C and C2. Cathy starts the first period with no wealth, savings, or debt, and she must end the second period with no wealth, savings, or debt. Between the two periods she can borrow or save at an interest rate r. If Cathy works, she receives hourly wages of W1 in period 1 and W2 in period 2. Initially, she does not receive any other income. a. Write and explain the equations for Cathy's per-period budget constraints in periods 1 and 2 (4 points each) and her two-period budget constraint (6 points). Be sure to explain ALL the terms in each constraint. b. Let Cathy's initial optimal labor supply choices in the two periods be Hi* and H2*. Write and explain the functions (the labor supply functions) for both of her choices (3 points each). Be sure to explain ALL the terms in each function. Suppose that Cathy's second period wage is exactly twice as high as her first period wage (W2 = 2 x W1). With these wages, i. Will Cathy's second period consumption be higher than her first period C. consumption? Carefully explain and justify your answer (5 points). ii. Will Cathy's second period labor supply be higher than her first period labor supply? Carefully explain and justify your answer (5 points). Suppose now that Cathy will be receiving a gift in period 2 from her Uncle Joe of N2 dollars. d. Write and explain Cathy's new two-period budget constraint (4 points). e. How does Uncle Joe's gift change Cathy's consumption in periods 1 and 2? Carefully explain your answers. If consumption in period 1 changes, explain how this is possible (8 points). How does Uncle Joe's gift change Cathy's labor supply in periods 1 and 2? Carefully explain your answers. If labor supply in period 1 changes, explain how this is possible (8 points). f.