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
• 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
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
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
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).
M = 600000
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
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
• When interest increases the budget line gets st