3. Consider an agent who works for two periods and has the option to make a human capital investment in the first period. If the agent does not invest in human capital in period 1, her earnings profile will be flat: Y, = Y2 = Y, where Y, is the agent's earnings in period t. If the agent does invest in period 1, she forgoes some earnings in period 1 but reaps a return in period 2; in this case, her earnings profile is Y1 = (1 - 0)Y, Y2 = (1+ n)Y, where 0 0. The agent's lifetime utility is given by U(C1, (2) = In C1+ - . In C2, where C, is the agent's consumption in period t and p 2 0 is the agent's personal discount rate (i.e., the rate at which period 2 utility is discounted relative to period 1 utility). The agent's full utility maximization problem is to make the optimal investment decision (which is a binary choice - invest or don't invest) and to make the optimal consumption allocation across periods among all feasible allocations. This problem asks you to analyze how the presence or absence of a loan market to finance investments in human capital affects these decisions (and therefore does not assume at the outset the agent's goal is to maximize the present discounted value of earnings). a. Suppose that the agent can borrow (or save) at interest rate r > 0. In this case the agent's budget constraint is C2 = Yz + (1 + r)(Y] - C1), where first period consumption is constrained to the interval, 0