pro nas Y UGlars tO sper UP JO two periods. Let c denote the amount of consumption that the individual would like to 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 cı units of the consumption good at a price P and can save any unspent wealth. Use sı 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 individual 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.
pro nas Y UGlars tO sper UP JO two periods. Let c denote the amount of consumption that the individual would like to 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 cı units of the consumption good at a price P and can save any unspent wealth. Use sı 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 individual 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Consider the problem of an individual that has Y dollars to spend on consuming over
two periods. Let c, denote the amount of consumption that the individual would like
to 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 c1 units of the consumption good at a price P and can save any unspent
wealth. Use sı 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
individual 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.
2
The 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 amount
of consumption c enjoyed by the individual. Also assume that the function u(c) satisfies
the Inada condition lim.→0
du(c) is the first-derivative of the
o u'(c)
utility function u(c) with respect to c.
= 0 where u'(c) :
dc](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b714a0e-b01f-49d4-9d2a-b07b3adf1f36%2Fcfe9b55a-362e-4087-b8b9-8ceeab2bf2d7%2Ft0m60t_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the problem of an individual that has Y dollars to spend on consuming over
two periods. Let c, denote the amount of consumption that the individual would like
to 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 c1 units of the consumption good at a price P and can save any unspent
wealth. Use sı 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
individual 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.
2
The 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 amount
of consumption c enjoyed by the individual. Also assume that the function u(c) satisfies
the Inada condition lim.→0
du(c) is the first-derivative of the
o u'(c)
utility function u(c) with respect to c.
= 0 where u'(c) :
dc
![In words, interpret the economic trade-off between good one and good two that
you obtained in the previous step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b714a0e-b01f-49d4-9d2a-b07b3adf1f36%2Fcfe9b55a-362e-4087-b8b9-8ceeab2bf2d7%2Fx0vw7qc_processed.png&w=3840&q=75)
Transcribed Image Text:In words, interpret the economic trade-off between good one and good two that
you obtained in the previous step.
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