Suppose Irene lives for two periods, today (young) and tomorrow (old). Let c1 denote her consumption today and c2 denote her consumption tomorrow. Also, let m1 denote her income today and m2 denote her income tomorrow. (a) Suppose that the interest rate for savings is given by rS (i.e., if she saves $x today then she will get back $(1 + rS )x tomorrow). Compute the maximum amount Irene can consume tomorrow. (b) Suppose that the interest rate for borrowing is given by rB (i.e., if she borrows $x today then she has to pay back $(1 + rB )x tomorrow). Compute the maximum amount Irene can consume today. (c) Suppose rS rB (as is typically the case). In this case, Irene's budget (or choice) set can be represented by two mathematical inequalities. Find those two inequalities. Note that the budget line crosses the points in (a) and (b) as well as the endowment (m1, m2). (It will help if you draw the budget line to understand the structure of the budget set.) (d) Suppose Irene's preferences for consumption plans (bundles) can be represented by the utility function u(c1, c2) = c1c2, rS = rB = 0.2, m1 = 100, and m2 = 144. Find Irene's optimal consumption bundle. Will she save or borrow today?