Tsinghua Micro Ch10 021011

# Tsinghua Micro Ch10 021011 - Chapter Ten Intertemporal...

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Chapter Ten Intertemporal Choice

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What Are We Doing in this Chapter? We apply our basic framework of consumer choice to study issues of choices across different time periods; Again, in terms of theoretical framework, not much is new!
What Are the Questions? 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?

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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.
Future Value Given an interest rate r the future value one period from now of \$m is FV m r = + ( ). 1

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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 .

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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.
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.

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The Intertemporal Budget Constraint To start, let’s ignore price effects by supposing that p 1 = p 2 = \$1.
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. m 2 m 1 0 0

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The Intertemporal Budget Constraint c 1 c 2 m 2 m 1 0 0 m r m 2 1 1 + + ( ) the future-value of the income endowment
c 1 c 2 m 2 m 1 0 0 is the consumption bundle when all period 1 income is saved. ( 29

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Tsinghua Micro Ch10 021011 - Chapter Ten Intertemporal...

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