Setup and notation: As a twenty years old high school graduate, Delkash wants plan for her college studies, her lifetime

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Setup And Notation As A Twenty Years Old High School Graduate Delkash Wants Plan For Her College Studies Her Lifetime 1 (135.42 KiB) Viewed 43 times

Setup and notation: As a twenty years old high school graduate, Delkash wants plan for her college studies, her lifetime consumption profile, and savings for her retirement. She is endowed with family financial support wo. We model her decision-making in a three periods setup. The first period represents college-going ages and includes t1 = 5 years. The second period represents working ages and includes t2 = 30 years. And the third period represents her retirement ages and includes t3 15 years. If she decides to go to college she earns no income in period one and needs to pay total tuition 11 * T for college; in sum, she earns t2 + (y + A) in terms of labor income in period two; and she earns nothing in the third period. If she does not pursue college studies she earns in sum t1 * y of labor income in period one; in sum 12 * y of labor income in period two; and again nothing in period three. De note the total consumption during period one by c1, total net borrowing during period one by b1, total consumption during period two by c2, total net saving during period two by s2, and total consumption during period three by c3. The net interest rate for borrowing/saving from period one to two is r1 and the net interest rate for borrowing/saving from period two to three is r2. We assume Delkash "prefers more to less". Part A. Write down the budget constraint for periods one, two, and three. Argue if budget constraints hold with equality. Part B. Specify the optimal choice for investment in college studies. Under what condition she goes/does not go to college? Does wo matte? Does r2 matter? Does B1 and B2 matter? More assumptions and notation: Now assume the marginal rate of substitution between total consumption in periods one and two is MRS1,2 = c2/c1 1/B1 * 11/12 and between periods two and three is MRS2,3 = c3/c2 + 1/B2 t2/13, where the factors t1/12 and 12/13 are called to scaled total consumption to per-year values and 31 s 1 and 52 s 1 are subjective time discount factors. Part C. Argue that the optimal consumption profile does not permit c1 = 0, C2 = 0 or c3 = 0. Moreover, prove that the optimal consumption path satisfies MRS1.2 = 1 + r1 MRS2,3 = 1 + r2 Part D. Analytically solve for the optimal net borrowing band net savings s in period one and two, and the optimal consumption in periods one, two and three, i.e., c1, c2 and c3. Under either scenarios of going or not going to college as the optimal choice, what happens to b and s if the initial endowment wo increases, and what happens to c1 and c2 if r2 increases? What happens to c1 If r1 increases? A numerical example: Suppose B1 = 4. B2 = 25, 11 = 1.5,r2 = 3, y = $35, 000, A = $25,000 and T = $15, 000. Set wo = 0. Part E. Show that Delkash chooses to go to college as a rational choice. Evaluate c1, c2 and c3, and b and s. Part F. Suppose because of financing frictions the interest rate on borrowing in period one goes up to rB,1 = 11 + y = 1.5 + y for some positive u. But the rate on savings remains the same rS,1 = 11 = 1.5. Argue that for p = 0.1 it is still the optimal choice for Delkash to go to college. Part G. Redo part E with MRS 1,2 = (c2/c1 ) 2 + 1/B1 * 11/12 and MRS2,3 = (c3/c2y^2 + 1/82 * 12/13. Assume p = 0 but keep all other parameter values unchanged.