Take the first-order conditions for c1 and c2 and obtain expressions for A1 and A2.Use these expressions for A1 and A, in the first-order condition with respect to s1.This will give you a trade-off between purchasing more c1 at the expense of c2 orvice versa. Consider the problem of an individual that has Y dollars to spend on consuming overtwo periods. Let c, denote the amount of consumption that the individual would liketo purchase in period 1 and c2 denote the amount of consumption that the individualwould like to consume in period 2. The individual begins period 1 with Y dollars andcan purchase c1 units of the consumption good at a price P and can save any unspentwealth. Use sı to denote the amount of savings the individual chooses to hold at the endof period 1.Any wealth that is saved earns interest at rate r so that the amount of wealth theindividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1.This principal and interest on savings is used to finance period 2 consumption. Again,for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumptiongood in period 2.2The individual's total happiness is measured by the sum of period utility across time,u(cı) + u(c2). Let u(c) be an increasing function that is strictly concave in the amountof consumption c enjoyed by the individual. Also assume that the function u(c) satisfiesthe Inada condition lim.→0du(c) is the first-derivative of theo u'(c)utility function u(c) with respect to c.= 0 where u'(c) :dc

In period 1 : Budget Constraint : P1c1 + S1 = Y Where , S1 are savings , P1c1 is income spent on…

Consider the problem of an individual that has Y dollars to spend on consuming over 7o periods. Let c, denote the amount of consumption that the individual would like purchase in period 1 and c2 denote the amount of consumption that the individual puld like to consume in period 2. The individual begins period 1 with Y dollars and n purchase c1 units of the consumption good at a price P and can save any unspent ealth. Use s1 to denote the amount of savings the individual chooses to hold at the end

Consider the problem of an individual that has Y dollars to spend on consuming over 7o periods. Let c, denote the amount of consumption that the individual would like purchase in period 1 and c2 denote the amount of consumption that the individual puld like to consume in period 2. The individual begins period 1 with Y dollars and n purchase c1 units of the consumption good at a price P and can save any unspent ealth. Use s1 to denote the amount of savings the individual chooses to hold at the end

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.8P

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Consider the problem of an individual that has Y dollars to spend on consuming over wo periods. Let c1 denote the amount of consumption that the individual would like co purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase ci units of the consumption good at a price P and can save any unspent wealth. Use s1 to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the ndividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2.
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