This preview shows pages 1–14. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter Ten Intertemporal Choice 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? 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 ◆ 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. 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 . FV m r = + ( ). 1 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. 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 presentvalue 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 PV r = + 1 1 . PV m r = + 1 . 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 1 0 1 91 $0 . PV = + ⋅ = ⋅ 1 1 2 83 $0 . 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. 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. The Intertemporal Budget Constraint ◆ To start, let’s ignore price effects by supposing that p 1 = p 2 = $1. The Intertemporal Budget Constraint ◆ Suppose that the consumer chooses not to save or to borrow. ◆ Q: What will be consumed in period 1?...
View
Full
Document
This note was uploaded on 01/06/2012 for the course ECON 102 taught by Professor Goodhart during the Spring '11 term at Abu Dhabi University.
 Spring '11
 GOODHART

Click to edit the document details