The change in the interest rate i is indicated by a move along the IS curve. If
other variables contained in the IS equation (T, G, I, C) change, the IS curve
shifts. This behavior will now be described in more detail.

At the initial point, with given taxes, government spending, autonomous
consumption and autonomous investment, the IS curve represents
the equilibrium income as a function of the interest rate. In the
graph, a change in the interest rate can be realized by pulling point
$i$. It can be seen that
the production level $Y$
adjusts according to the change of the interest rate.

As an example for shifts of the IS curve, a change in taxes or government
expenditure will be discussed in more detail here. First, both effects are
considered separately, and then together, as a tax- and government expenditure-
effect.

At a given interest rate, if taxes T are increased, the disposable income decreases,
which leads to a decline in consumption. The decline in consumption induces a decline
in the demand for goods and thus a decline of the equilibrium income, which falls
from $Y0$
to $Y$.
The IS curve shifts to the left and for each interest rate the corresponding
equilibrium income Y is now lower than before the tax increase. All factors that
lead to a decrease in equilibrium income at a given interest rate shift the IS curve
to the left. As in the case of a tax increase, a decrease in government spending,
autonomous consumption or autonomous investment would cause the IS curve to
shift to the left.

Conversely, all factors that increase equilibrium income at a given interest rate
shift the IS curve to the right. Examples are a tax cut or an increase
in government spending, autonomous consumption, or autonomous
investment. A rise in government spending increases the demand for
goods at a given interest rate. The equilibrium income increases from
$Y0$ to
$Y$.

In our model the effects are additive. Therefore, the simultaneous change in tax
rate and government spending can be easily analyzed. As explained in more detail
above, a tax increase results in a decrease in disposable income. This leads to a
decline in consumption and, thus, to a decline in the demand for goods. The IS
curve shifts to the left. On the other hand, an increase in government spending
increases the demand for goods and the IS curve shifts to the right – thus,
the two effects are opposing. If we now look at the tax- and government
expenditure- effect together, the increase in tax and the increase in government
expenditure almost cancel each other out and the new equilibrium income
$Y$ is
close to the original equilibrium income. The IS curve, resulting from the
combined tax- and government-expenditure- effect, is close to the original IS
curve. In marginal cases, the two effects may even cancel each other out
completely. If the increase (decrease) in government expenditure is as
large as the increase (decrease) in taxes, the new equilibrium income
$Y$ is equal to the
original income $Y0$
and the new IS curve is equal to the original IS curve.

In the case of policy measures of the same focus, the effects add up. As an
example, we will look at the effect of a tax increase with a simultaneous reduction
in government spending. As described above, the tax increase reduces the
demand for goods and the IS curve shifts to the left. As a result of the
reduction of government expenditure, the demand for goods decreases as
well and the IS curve also shifts to the left. If we look at the tax- and
government expenditure- effect together, the IS curve shifts even further to the
left than when we look at each effect individually, because the effects
add up. At the given interest rate i, the new equilibrium income is at
$Y$ and is significantly
lower than $Y0$.

(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