The IS curve is a model of the market for goods and services in an
economy. We first consider a closed economy, i.e. without exports and
imports.

In the upper graph we look briefly at the supply and demand or the production
and use of the gross national product. A detailed description can be found in the
corresponding chapters of basic textbooks on macroeconomics. In a closed economy,
GDP is used for three areas: private consumption C, corporate investment I, and
government consumption G. Private consumption depends positively on disposable
income $Y-T$
i.e. produced GDP minus taxes. Investments depend positively on income and
negatively on interest rates. The demand curve is designated ZZ and the following
applies

$$\mathit{ZZ}=C\left(Y-T\right)+I\left(Y,i\right)+G.$$ |

The supply of goods corresponds obviously to the produced goods
$Y$.
Therefore, the supply curve is the angle bisector
$Y$ =
$Y$.

In equilibrium supply = demand or production = consumption, i.e.

$$Y=C\left(Y-T\right)+I\left(Y,i\right)+G.$$ |

The point of equilibrium is the point of intersection of the ZZ curve with the
angle bisector. The IS curve represents the function of i and Y, which is implicitly
defined by this equation.

Now, the question arises, what happens when the interest rate changes. The lower
graph shows the change of the income depending on the change of the interest
rate.

Let us assume that the interest rate increases from
$i0$ to a higher
value $i$.
For each level of production, the higher interest rate leads to a decrease in
investment, which in turn leads to a decrease in income. This causes a decrease in
consumption and investment. Ultimately, this leads to a decrease in demand. Thus,
the demand curve ZZ (green) shifts downwards. For each level of production, overall
economic demand is now less. The new equilibrium is at GG, the intersection of
the lower demand curve ZZ and the 45 degree line. The new equilibrium income is
at $Y$.

Because of the multiplier effect, the total decline in production is greater
than the original decline in investment triggered by the rise in interest
rates.

In the graph, the equilibrium income Y is plotted on the horizontal axis
and the interest rate i on the vertical axis. Point GG in the upper graph
corresponds to point GG in the lower graph. Thus, the graph shows that,
because of the equilibrium on the goods market, the higher the interest
rate, the lower the equilibrium income. This relationship between interest
rate and income is described by the falling curve in the graph, which
is called the IS curve. The resulting IS curve is highlighted by the red
dots.

When the interest rate falls, the opposite effects can be
seen for all variables. Thus, a fall in the interest rate from
$i0$ to
$i$ leads
to an increase in investment at each level of production. The increase
in investment induces an increase in income. This, in turn, triggers an
increase in consumption and investment, and overall economic demand
increases. Therefore, the ZZ curve shifts upwards. The new, higher
equilibrium income is at Y and the new, lower equilibrium interest rate is
$i$.

(c) by Christian Bauer

Prof. Dr. Christian Bauer

Chair of monetary economics

Trier University

D-54296 Trier

Tel.: +49 (0)651/201-2743

E-mail: Bauer@uni-trier.de

URL: https://www.cbauer.de