文档介绍：Chapter Ten
Intertemporal Choice
跨时期选择
Structure
Present and future values
Intertemporal budget constraint
Preferences for intertemporal consumption
Intertemporal parative statics
Valuing securities
Intertemporal Choice
Persons often receive e in “lumps”; . monthly salary.
How is a lump of e spread over the following month (saving now for consumption later)?
Or how is consumption financed by borrowing now against e to be received at the end of the month?
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.
Future Value
., if r = then $100 saved at the start of period 1 es $110 at the start of period 2.
The value next period of $1 saved now is the future value of that dollar.
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
Present Value (现值)
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.
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 es $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.
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
Present Value
., if r = then the most you should pay now for $1 available next period is
And if r = then the most you should pay now for $1 available next period is