A Two Period Model: The Consumption
Savings Decision and Credit Markets
This chapter focuses on intertemporal decisions--that is, decisions that involve
economic trade offs across periods of time. This chapter also examines the
implications of intertemporal decision making for how government deficits
affect macroeconomic activity. This model consists of many consumers, and a
government that need not balance its budget and can issue debt to finance a
The Ricardian equivalence theorem is an important of implication of this
model. The theorem states that there are conditions under which the size of a
government’s deficit is irrelevant to, in that it does not affect any
macroeconomic variables of importance or the economic welfare of any
The consumption-savings decision is an intertemporal decision in the sense
that it involves trade off between current and future consumption. Similarly,
the government’s decision to finance its expenditures is an intertemporal
decision in the sense that it involves trade off between future and current
taxes. For instance, if the government chooses to lower taxes in the present, it
must borrow from the private sector to do so, which implies that taxes will rise
in the future in order for the government to pay off its debt. Essentially, the
government’s financing decision is one about the quality of saving, or the size
of the government deficit, making it related to the consumption-savings
decisions of private consumers.
The first period is the current period, and the second period is the future
period. A key variable of interest in this model is real interest rate--that is, the
interest rate at which consumers and the government can borrow and lend.
The real interest rate determines the relative price of future consumption in
terms of present consumption.
An important point of interest with regards to consumer choice is how present
and future savings and consumption are affected by changes in the real
market interest rate and in the consumer’s present and future income.
Another important point of interest is consumption smoothing--that is, the
tendency for consumers to seek a consumption path over time that is smoother
than income. Consumption-smoothing behavior is implied by certain
properties of indifference curves. Consumption-smoothing behavior also has important implications for how consumers respond in the aggregate to
changes in government policies or other features of their external
environment that affect their income streams.
The Ricardian Equivalence Theorem establishes conditions under which the
timing of taxation does not matter for economic activity. This theorem
attaches importance to the size of the government budget deficit. A key
implication of this theorem is that a tax cut is not a free lunch. Interesting
issues arise due to frictions in the credit market that cause departures from the
Ricardian Equivalence Theorem.
A Two Period Model of the Economy:
A consumer’s consumption-saving decision (a dynamic decision, that is one
that has implications over more than one period in time) fundamentally
consists of a trade off between current and future consumption. Through
saving, a consumer gives up consumption in exchange for assets in the present
to consume more in the future. Also, a consumer can dissave by borrowing in
order to increase current consumption, and thus sacrifice future consumption
when the loan is repaid. (Borrowing/Dissaving/Negative Savings).
N is the number of consumers. Each consumer lives for two periods. Each
consumer receives exogenous income.
(Lowercase letters represent variables at individual level, and uppercase letters
represent variables at aggregate levels)
y is the consumer’s real income in the current period
y is the consumer’s real income in the future period
t is the lump-sum tax that each consumer pays in the current period
t is the lump-sum tax that each consumer pays in the future period
Suppose incomes can be different for different consumers, but all consumers
pay the same taxes.
s is the consumer’s savings in the current period
Then the consumer’s budget constraint in the current period is:
c is the current consumption
Eqn (1) states that consumption plus savings is equal to disposable income.
We assume that the consumer starts the current period with no assets.
If s>0, then the consumer is a lender on the credit market, and if s<0, then the
consumer is a borrower. We assume that the financial asset being traded in the credit market is a bond. In this model, bonds can be issued by both consumers
and the government. If a consumer lends, then he or she buys bonds, and is he
or she borrows, then there is a sale of bonds.
Two important assumptions:
I. bonds are indistinguishable because a consumer cannot default on his or
her debt, that is there is no risk associated with holding a bond.
II. Bonds are traded directly into the credit market.
In this model, the issue of a bond in the current period is a promise to pay 1+r