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 cı 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)81.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→0 u'(c)utility function u(c) with respect to c.= o where u'(c) = au) is the first-derivative of thedc The individual's total happiness is measured by the sum of period utility across time,u(c1) + 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→0 u' (c)utility function u(c) with respect to c.= ∞ where u'(c)du(c)is the first-derivative of thedc1. The individual faces a budget constraint in period 1 of Pcı+s1 = Y and a period2 budget constraint of P2C2 = (1+r)s1. Interpret each of these two constraints inwords.

In period 1 : Consumption = c1 Income = Y Budget Constraint : P1c1 + s = Y Y - P1c1 = s Income in…

Consider the problem of an individual that has Y dollars to spend on consuming over o 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 ould like to consume in period 2. The individual begins period 1 with Y dollars and n purchase c 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 period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the dividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. nis principal and interest on savings is used to finance period 2 consumption. Again, r simplicity, we can assume that it costs P, dollars to buy a unit of the consumption od in period 2.

Consider the problem of an individual that has Y dollars to spend on consuming over o 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 ould like to consume in period 2. The individual begins period 1 with Y dollars and n purchase c 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 period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the dividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. nis principal and interest on savings is used to finance period 2 consumption. Again, r simplicity, we can assume that it costs P, dollars to buy a unit of the consumption od in period 2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.8P

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