Mavis earns income in two periods, M, and M2 and buys consumption goods in two periods as well, C, and C2 (the numbers indicate the period in which the income is earned and the consumption goods are purchased). Her utility function is as follows: U= U(C, ) + , where & is the time rate of preference and 1+8 U(C, )=U(C2) when C, = C, and U(C) is well behaved. Mavis can borrow money from or save money at a local bank. The interested rate (whether saving or borrowing) is r. a. Write out Mavis' utility maximizing Lagrangian equation. No need to solve it. b. Describe the process for conducting the comparative statics necessary to determine the sign of the following change: orC. What is the significance of 8? Assuming you would graph her consumer choice model with C, on the horizontal axis, explain why a higher value for & would make her indifference curves steeper or flatter