# Ch10 - Chapter Ten Intertemporal Choice Intertemporal...

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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 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 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?...
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## 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.

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Ch10 - Chapter Ten Intertemporal Choice Intertemporal...

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