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,: An individual lives for three periods. In period 1, she earns income yl, saves or borrows .91, and consumes cl. Ci + 81 = 241 In period 2, she earns income yg, pays back her loan at interest rate R if 51 0), saves or borrows 32, and consumes 02. C2+82=y2+(1+R)81 In period 3, she earngs income :93, pays back her loan at interest rate R if 32 0), and consumes C3. 63 = 3J3 + (1 + Rlsz (a) Reduce the individual's three budget constraints into a single present value budget con- straint. (b) The individual's preferences can be represented by the following utility function: \"(01) + {31402) + anks), [3 6 (0,1) Use the rst order conditions of the maximization problem to derive a condition relat ing u'(cl) to u'(cz); and another condition relating u'(C2) to u'(03). Combine the two equations to derive a third equation relating u' (c1) to u' (C3). (0) Suppose that u(c) = log c. What condition for [3 and R is necessary for CI = 02 = C3? Under this condition, what is (:1 in terms of W, the present value of the agent's earnings? ((1) Impose the condition that you derived in part (c). Suppose that 3y1 = y2 = 3y3. What is 31? What is 32