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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(c1) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved 0 (slope of the utility function becomes vertical as consumption In order to save the individual must purchase bonds at a price 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(c1) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved 0 (slope of the utility function becomes vertical as consumption In order to save the individual must purchase bonds at a price of

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Using the first-order conditions of this problem with respect to c1, c2 and s1, (i.e. the partial derivatives that have been set equal to zero) construct the optimal intertemporal consumption trade-off condition between c1 and c2. This trade-off is executed by variation in savings.

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 q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount 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 the budget constraints of periods 1 and 2 by choice of (c1, C2, s1). Formally, the individual solves the problem = (slope of the utility function becomes vertical as consumption max {u(c) + 8и(с2)} C1,C2,81 subject to the first period budget constraint, qs1+ C1 = y1 along with the second period budget constraint, C2 = Y2 + S1.
Transcribed Image Text: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 q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount 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 the budget constraints of periods 1 and 2 by choice of (c1, C2, s1). Formally, the individual solves the problem = (slope of the utility function becomes vertical as consumption max {u(c) + 8и(с2)} C1,C2,81 subject to the first period budget constraint, qs1+ C1 = y1 along with the second period budget constraint, C2 = Y2 + S1.
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