Olivia gets an allowance of $50 this week, but it will have to last her for two weeks, since Mom pays her every other week. Let c be her consumption this week (measured in units of stuff), and let cz be her consumption next week (measured in the same units). The price of one unit of stuff this week is $1. Next week the price will be higher, because of inflation. Assume the inflation rate is 1 percent per week, or 0.01 per week when expressed as a decimal. Therefore, the price of one unit of stuff next week will be $1(1+z) = $1.01. Olivia can borrow or lend at the local bank, and, whether she's borrowing or lending, the interest rate i is 1 percent per week, or 0.01 when expressed as a decimal. Olivia's utility function is u(C, C) = ln(c) + In(C). (a) Write down Olivia's budget constraint, first in the abstract (with M, , and i), and then with the given values incorporated. (b) Find her optimal consumption bundle (c, c). (c) Assume the inflation rate rises to 10 percent, and the interest rate drops to 0. Find her new optimal consumption bundle.