# 03_Oheads - Lecture Notes 3 Intertemporal Resource...

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1 Lecture Notes 3 Intertemporal Resource Allocation The source of “investment funds” • Most consumers prefer to spread their consumption over time and investment by firms provides a major way they can do so. • Other ways include: i. Direct lending and borrowing between consumers. ii. Direct investment in physical and human capital. iii. Government spending and taxing policies. • Financial intermediaries and capital markets channel net savings from households to firms and governments. The consumption-saving decision • Consider a simple two period model with period 1 “the present” and period 2 “the future.” Incomes are y 1 and y 2 , consumptions are c 1 and c 2 and the borrowing or lending interest rate is r. • If period 1 borrowing is b , period 1 consumption will be

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2 (1) • The maximum amount of borrowing is (2) • From (1) and (2), maximum first period consumption is: (3) • Maximum consumption in period 2, when all of y 1 is saved, is: (4) • Also, the individual can always choose c 1 = y 1 and c 2 = y 2 . • These consumption pairs define an intertemporal budget con- straint as drawn in Figure 1. Slope of constraint = (5) • The consumer can choose c 1 and c 2 anywhere inside the budget set to maximize intertemporal utility U ( c 1 , c 2 ). c 1 y 1 b + = b 1 r + () y 2 = c 1 y 1 y 2 1 r + ----------- + = c 2 y 2 y 1 1 r + + = y 2 y 1 1 r + + y 1 y 2 1 r + + --------------------------------- –1 r + =
3 Figure 1: The intertemporal budget constraint Figure 2: Intertemporal indifference curves c 1 c 2 y 1 y 2 y 2 y 1 1 r + () + y 1 y 2 1 r + ----------- + c 1 c 2 U 0 U 1 U 2 increasing utility

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4 Intertemporal indifference curves will be as in Figure 2. • The impatient person in Figure 3 chooses c 1 > y 1 and borrows in period 1. Figure 3: The choices of an impatient individual • The patient individual in Figure 4 chooses c 1 < y 1 and lends in period 1. c 1 c 2 y 1 y 2 c 2 e c 1 e y 2 y 1 1 r + () + y 1 y 2 1 r + ----------- +
5 Figure 4: The choices of a patient individual • Now suppose the interest rate increases as in Figure 5. Figure 5: An increase in the interest rate c 1 c 2 y 1 y 2 c 2 e c 1 e y 2 y 1 1 r + () + y 1 y 2 1 r + ----------- + c 1 c 2 y 1 y 2 y 2 y 1 1 r + + y 1 y 2 1 r + +

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6 • A rise in interest rates makes a borrower worse off: Figure 6: The effect of higher interest rates on a borrower Figure 7: The effect of higher interest rates on a lender c 1 c 2 y 1 y 2 U 0 U 1 c 1 c 2 y 1 y 2 U 0 U 1
7 • An increase in interest rates makes a lender better off. Figure 8: The income and substitution effects of the increase in r for a borrower • The move from A to B in Figure 8 is the substitution effect – the individual substitutes c 2 , which has become relatively less ex- pensive, for c 1 , which has become relatively more expensive.

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## This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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03_Oheads - Lecture Notes 3 Intertemporal Resource...

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