InterChoice - Chapter Ten Intertemporal Choice...

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Chapter Ten Intertemporal Choice
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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?
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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.
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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.
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Future Value ± Given an interest rate r the future value one period from now of $m is FV mr = + () . 1
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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. $1 saved now gives $(1+r) > $1 next period.
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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 .
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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 .
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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.
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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 )?
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The Intertemporal Budget Constraint ± For an answer we need to know: the intertemporal budget constraint intertemporal consumption preferences.
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InterChoice - Chapter Ten Intertemporal Choice...

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