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
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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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.
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