Question

1) (Ch. 1 Assume you have $10,000 in income in each of two periods (TI & T2). a) If you can lend and borrow at 7%, what is your opportunity set algebraically (show steps) and graphically? b) If your utility curve is U ACIC -0.8cIc: (where A - 0.8), what are your optimal consumptions for TI and T2? Show your answer algebraically (with calculations) and graphically c) Are you a lender or borrower? Briefly explain d) i) At what ''A,, value in the utility curve (U-AC1C2) will you behavior differently than c) and become neither a borrower nor a lender? ii) What are your optimal consumptions for Tl and T2 with the new utility curve in d) (0? ii) Show your answer graphically e) Briefly explain why you change your behavior in (d) above

Answer 1

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Intertemporal B.C y_1 = 10000 Y_2 = 10000 Now, S_1 = y_1 - C_1 r = 0.7 = 79_0 C_2 = (1 + r)s_1 notequalto y_2 = (1.07) (y_1 - c_1) + y_2 thus opportunity set C_2 = (1 + r) y_1 - (1 + r) c_1 + y_2 c_1 (1 + r) + c_2 = (1 + r) y_2 + y_2 1.07 c_1 + c_2 = (1.07)/100 times 10000 + 10000 this 1.07 c_1 + c_2 = 10700 + 10000 = 20700 so Max u st. Intertemporal B.C {= .8 c_1 . c_2 + lambda [20700 - 1.07 c_1 - c_2] for partial differential L/partial differential C_1 = .8 C_2 - 1.07 lambda = 0, partial differential L/partial differential C_2 = .8C_1 - lambda = 0 .8 C_1 = lambda thus (.8C_2 = (1.07) . 8 C_1 thus c_2/C_1 = 1.07 thus c_2 = 1.07 C_1 form B.C 1.07 C_1 + 1.07 C_1 = 20700 = > 2.14 C_1 = 20700 C*_1 = 9672.8972 C*_2 = 10350 Since y_1 > C_1 so individual is net