Now assume that the utility function takes the function form u(c) = ln(c). Note that the derivative of the natural logarthm is u'(c) = 1/c . Consider the two period consumption savings problem faced by an individual whoseutility is defined on period consumption. This utility function u(c) has the propertiesthat it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotesthe first derivative while u"(c) represents the second derivative) and satisfies the Inadacondition lim.→0 u'(c)approaches zero). The individual's lifetime utility is give by u(ci)+ Bu(c2).In the first period of life, the individual has yı units of income that can be eitherconsumed or saved. In order to save, the individual must purchase bonds at a price ofq units of the consumption good per bond. Each of these bonds returns a single unit ofthe consumption good in period 2. Total savings through bond purchases is s1 so thattotal expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumptionin period 1 chosen by the individual. In the second period of life, consumption in theamount c2 is financed out of the returns from savings and period 2 income, Y2.The problem of the individual is to maximize lifetime utility while respecting thebudget constraints of periods 1 and 2 by choice of (c1, C2, s1). Formally, the individualsolves the problem= (slope of the utility function becomes vertical as consumptionmax {u(c) + 8и(с2)}C1,C2,81subject to the first period budget constraint,qs1+ C1 = y1along with the second period budget constraint,C2 = Y2 + S1.

For the above question let us firstly derive the lifetime budget constraint : In period 1 : Budget…

Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim→0 u'(c) approaches zero). The individual's lifetime utility is give by u(ci) + Bu(c2). In the first period of life, the individual has yı units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of = 0 (slope of the utility function becomes vertical as consumption TOod nor hond Foch of thogo bonds roturng o ginglo unit of

Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim→0 u'(c) approaches zero). The individual's lifetime utility is give by u(ci) + Bu(c2). In the first period of life, the individual has yı units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of = 0 (slope of the utility function becomes vertical as consumption TOod nor hond Foch of thogo bonds roturng o ginglo unit of

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(J)
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