Varian_Chapter10_Intertemporal_Choice

Varian_Chapter10_Intertemporal_Choice - Chapter Ten...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter Ten Intertemporal Choice
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Intertemporal Choice ± Persons often receive income in “lumps”; e.g. monthly salary. ± How is a lump of income spread over the following month (saving now for consumption later)? ± Or how is consumption financed by borrowing now against income to be received at the end of the month?
Background image of page 2
Present and Future Values ± Begin with some simple financial arithmetic. ± Take just two periods; 1 and 2. ± Let r denote the interest rate per period.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Future Value ± E.g., if r = 0.1 then $100 saved at the start of period 1 becomes $110 at the start of period 2. ± The value next period of $1 saved now is the future value of that dollar.
Background image of page 4
Future Value ± Given an interest rate r the future value one period from now of $1 is ± Given an interest rate r the future value one period from now of $m is FV r = + 1. m r = + () . 1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Present Value ± Suppose you can pay now to obtain $1 at the start of next period. ± What is the most you should pay? ± $1? ± No. If you kept your $1 now and saved it then at the start of next period you would have $(1+r) > $1, so paying $1 now for $1 next period is a bad deal.
Background image of page 6
Present Value ± Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? ± A: $m saved now becomes $m(1+r) at the start of next period, so we want the value of m for which m(1+r) = 1 That is, m = 1/(1+r), the present-value of $1 obtained at the start of next period.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Present Value ± The present value of $1 available at the start of the next period is ± And the present value of $m available at the start of the next period is PV r = + 1 1 . m r = + 1 .
Background image of page 8
Present Value ± E.g., if r = 0.1 then the most you should pay now for $1 available next period is ± And if r = 0.2 then the most you should pay now for $1 available next period is PV = + =⋅ 1 10 1 91 $0 . = + 1 2 83 .
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Intertemporal Choice Problem ± Let m 1 and m 2 be incomes received in periods 1 and 2. ± Let c 1 and c 2 be consumptions in periods 1 and 2. ± Let p 1 and p 2 be the prices of consumption in periods 1 and 2.
Background image of page 10
The Intertemporal Choice Problem ± The intertemporal choice problem: Given incomes m 1 and m 2 , and given consumption prices p 1 and p 2 , what is the most preferred intertemporal consumption bundle (c 1 , c 2 )? ± For an answer we need to know: the intertemporal budget constraint intertemporal consumption preferences.
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Intertemporal Budget Constraint ± To start, let’s ignore price effects by supposing that p 1 = p 2 = $1.
Background image of page 12
The Intertemporal Budget Constraint ± Suppose that the consumer chooses not to save or to borrow. ± Q: What will be consumed in period 1? ± A: c 1 = m 1 . ± Q: What will be consumed in period 2? ± A: c 2 = m 2 .
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Intertemporal Budget Constraint c 1 c 2 m 2 m 1 0 0
Background image of page 14
The Intertemporal Budget Constraint c 1 c 2 So (c 1 , c 2 ) = (m 1 , m 2 ) is the consumption bundle if the consumer chooses neither to save nor to borrow.
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/28/2010 for the course ECON 301 taught by Professor Hansen during the Fall '08 term at University of Wisconsin.

Page1 / 69

Varian_Chapter10_Intertemporal_Choice - Chapter Ten...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online