© Sanjay K. Chugh
The Consumption-Savings Model
We just studied the consumption-leisure model as a “one-shot” model in which
individuals had no regard for the future:
they simply worked to earn income, all of which
they then spent on consumption right away, putting away none of it for the future.
Individuals do, of course, consider their future prospects when making economic
decisions about the present.
When an individual makes his optimal choice about
consumption and leisure in the current period, he usually recognizes that he will make a
similar consumption-leisure choice in the future.
In effect, then, it seems there are
multiple consumption-leisure choices an individual makes over the course of his lifetime.
However, these choices are not independent of each other because consumers can save
for the future (or borrow against future income, which is simply negative saving, also
known as dissaving).
That is, current choices affect future choices, and, conversely,
expectations of future choices affect current choices.
In this section, we will focus on the study of intertemporal (literally, “across time”)
choices of individuals by ignoring leisure altogether.
That is, we will revert to our
assumption that an individual has no control over his income.
But we will enrich our
model of consumer theory by now supposing that each individual lives for two time
periods – the “present” period and the “future” period. We will designate the present
period as “period 1” and the future period as “period 2.”
There is no “period 3,” and
every individual knows there is no period 3.
Think of this as meaning that the world (and
hence the economy) ends with certainty after two periods.
This stark division of all time
into just two periods will serve to illustrate the basic principles of (macro)economic
events unfolding as a sequence over time; after mastering the basics of
by using the two-period model, we will eventually extend ourselves to
consideration of an infinite-period model, which arguably may be more realistic because,
after all, when does time “end?”
But let’s build up that slowly.
In the two-period model, our stylized (that is, representative) individual will receive labor
income (over which he has no control) in each of the two periods and have to make a
choice about consumption in each of the two periods, and we will allow him to save or
borrow in period 1.
The notation we will use here, indeed the entire method of analysis,
should remind you of our initial study of consumer theory.
A Simple Intertemporal Utility Function
As always, in order to study consumer choice, we need to first specify the individual’s
In our present intertemporal context, the two arguments to the utility
function are consumption in period 1 and consumption in period 2, which we will denote