1. Consider an individual with quasi hyperbolic discounting, the (8,6) model, who lives over threeperiods, t= 1,2,3. Let e denote consumption in period t = 1,2,3. Assume that the per-period utilityfunction is given by the natural logarithm function, for c>0,u (c₂) = Inc.There is a labor income y> 0 in period 1 but no income in subsequent periods. We assume for now thatthe individual can only save in one period financial instruments with its interest rate being normalizedto be zero.(1) Write down the lifetime discounted utilities of self 1 and self 2 and the budget constraints ineach time period.Suppose that 3= 1 and 6 = 1 in (2), (3), and (4).(2) Derive the optimal consumption/saving behavior of self 2, given a strictly positive saving inperiod 1, 81 > 0.(3) Derive the optimal consumption/saving behavior of self 1, anticipating the optimal behavior ofself 2.(4) Suppose that the individual in period 1, self 1, can commit a consumption plan that is bindingto self 2. Derive the optimal consumption/saving plan of self 1. Show if the consumption plan underperfect commitment is consistent with the consumption solutions of (2) and (3).Suppose from now on that < 1 and 6 = 1 and the individual is so sophisticated that self 1 hascorrect beliefs about the preferences of subsequent selves.(5) Derive the optimal consumption/saving behavior of self 2, given a strictly positive saving inperiod 1, $1 > 0.(6) Derive the optimal consumption/saving behavior of self 1, anticipating the optimal behavior ofself 2.(7) Suppose that the individual in period 1, self 1, can commit a consumption plan that is bindingto self 2. Derive the optimal consumption/saving plan of self 1. Show if the consumption plan underperfect commitment is consistent with the consumption solutions of (5) and (6).

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Answered: budget constraints

Business

Economics

budget constraints

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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