Using this functional form in the intertemporal trade-off condition that you previ- ously derived, do some algebra to obtain an equation that specifies how much the individual would save as a function of q, β, y1 and y2. 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 atility is defined on period consumption. This utility function u(c) has the properties hat it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes he first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.0 u'(c) = ∞ (slope of the utility function becomes vertical as consumption pproaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has yı units of income that can be either !c→0 ngumod or sovod In ordor to govo the individuel must purchoso bonds ot o prieo of

Consider the two period consumption savings problem faced by an individual whose atility is defined on period consumption. This utility function u(c) has the properties hat it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes he first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.0 u'(c) = ∞ (slope of the utility function becomes vertical as consumption pproaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has yı units of income that can be either !c→0 ngumod or sovod In ordor to govo the individuel must purchoso bonds ot o prieo of

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

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Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ). Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock price is uncertain. There is a 10 % chance the stock price increases to $4 per share, a 50 % chance the stock price increases to $2.25 per share, and a 40 % chance the company B goes bankrupt and the stock price falls to $0 per share. Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back). 1. Assume without proof that at t=1 , she still consumes…
Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ). Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock price is uncertain. There is a 10 % chance the stock price increases to $4 per share, a 50 % chance the stock price increases to $2.25 per share, and a 40 % chance the company B goes bankrupt and the stock price falls to $0 per share. Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back). 1. If Amy invests $ 100 in stocks at t=1 , what is the…
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