2.2 The shift of the IS curve in a closed economy

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 $Y0$.