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Chapter 5 Econ2GG3) Intertemporal choice-1May 25.doc

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Hannah Holmes

Econ 2GG3 Fred Aswani Chapter 5 Section 5.4 Edited July 11 2011 INTERTEMPORAL CHOICE MODEL (aka Life cycle model) • In previous analysis we considered the case where individuals allocate income in a single period across different goods. We now consider the case of consumption decisions over time and thus allocation of income across periods. • We consider the special case where individuals choose consumption in two periods. • How does the individual's budget line look like? M -0ncome in period 0 M 1Income in period 1 C 0Consumption in period 0 C -Consumption in period 1 1 Further assume that prices of the composite goods are 1. • Now suppose the rate of interest is i. The amount available to the consumer for consumption in period 1 if he saves in period 0 will be given by: C = M + (M -C )(1+i) 1 1 0 0 Period 1 consumption equals income in period 1 plus future value of savings in period 0. This BL is depicted in Fig. 5.5 and passes through the endowment point (I .I ) and0 1 a slope a slope of -(1+i). Note: (I 0I1) is equivalent to (M ,0 ).1he slope shows that the opportunity cost of a dollar consumed in period 0 is 1+i dollars in period 1 Horizontal intercept is the Present Value (PV) of the endowment while vertical intercept is future value of the endowment. The BL always passes through (I ,I ). 0 1 Why? Suppose i increases the BL will rotate around the endowment point. It rotates clock wise PV of endowment declined. i.e.The price of current consumption increased. See Fig. 5.6. The consumer will select a point where his MRS=(1+i). Figure 5.7 M = 600000 0 M =1200000 C 1800000 C 0800000 i=1 Harold borrows in period 0 against I . He i1 a borrower in period 0. Borrows 200000 and pays 400000 i.e. 200000 plus interest. He could have been a saver in period 0 or just consumed his endowment depending on the endowment and preferences between current to future consumption Comparative statics Exogenous variables income and i Endogenous –C and0C 1 Changes in Income shifts BL to the right. See figure 5.8 Increasing I by 0hange in I0or I1by Change in I (O+i) gives same budget line. Consumption increases from E to E’ (C0 and C1 are both normal goods) Change in interest rates We need first to distinguish whether the consumer is a saver or borrower in period 0. See Fig.5.9 • When interest increases the budget line gets st
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