06. Intertemporal Choice

# 06. Intertemporal Choice - Intertemporal Choice Professor...

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Intertemporal Choice Professor John Diamond ECON 370: Microeconomic Theory Lecture 6

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2 Intertemporal Choice: Introduction Single period consumer problem ignores saving Income can be saved now for consumption later Earnings high in middle of life cycle, lower later People often receive income in “lumps”; e.g. bonuses, windfalls, inheritances Consumption > income can be financed by borrowing from future income at rate r Previous debts must be repaid with interest ( r ) Borrowing and lending rates differ in reality
3 Background: Present and Future Values Two periods -- 1 and 2 This month and next, this year and next Life cycle model: earning years and retirement years Let r denote the interest rate per period If r = 0.1 then \$100 saved at the start of period 1 becomes \$110 at the start of period 2 Future Value : Value next period of \$1 saved today

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4 Future Value Given r, FV of \$1 one period from now is FV = 1 + r Given r, FV one period from now of \$m is FV = m(1 + r)
5 Present Value How much must be saved now to get \$1 next period? m saved now becomes, m(1+r) in the next period. So, want m such that m(1+r) = 1 Thus, m = 1/(1+r) = present-value (PV) of \$1 obtained at start of next period

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6 Present Value Present value of \$1 at start of next period is PV r = + m 1 And present value of \$m at start of next period is PV r = + 1 1
7 Present Value: Examples If r = 0.1, then PV (most you should pay now for \$1 next period) is PV = + . = . 1 1 0 1 91 \$0 PV = + . = . 1 1 0 2 83 \$0 If r = 0.2, then

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8 Present value of \$m, t periods from now t r m PV ) 1 (
9 Intertemporal Choice Problem: Variables Exogenous variables m 1 and m 2 are period 1 and 2 incomes p 1 and p 2 are period 1 and 2 consumption prices Endogenous (choice) variables c 1 = period 1 consumption c 2 = period 2 consumption

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10 The intertemporal choice problem Given incomes m 1 and m 2 Given consumption prices p 1 and p 2 What is most preferred intertemporal consumption bundle (c 1 , c 2 )? Information needed (analogous to one- period problem): the intertemporal budget constraint intertemporal consumption preferences Intertemporal Choice Problem
11 Intertemporal Budget Constraint Ignore changes in consumption prices over time (inflation): p 1 = p 2 = 1 Benchmark: Suppose consumer neither saves nor borrows (stays at “endowment point”) c 1 = m 1 c 2 = m 2

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12 Intertemporal Budget Constraint c 1 c 2 m 2 m 1 0
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## 06. Intertemporal Choice - Intertemporal Choice Professor...

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