Finding equilibrium i and Y in the IS LM model - FreeEconHelp.com, Learning Economics... Solved!

## 4/2/12

This post goes over some common economics problems associated with the IS-LM model.  Remember that the IS-LM model shows the relationship between real income (Y) and the real interest rate (i) using the IS (Investment and Saving equilibrium) curve along with the LM (Liquidity Preference and Money supply equilibrium) curve.

Four common policies the government can enact are:

1.  Expansionary fiscal policy (which will shift the IS curve right)
2.  Contractionary fiscal policy (which will shift the IS curve left)
3.  Expansionary monetary policy (which will shift the LM curve right)
4.  Contractionary monetary policy (which will shift the LM curve left)

Depending on the current state of the economy, the government may want to fight high inflation (through contractionary policies) or help lower unemployment (through expansionary policies).  There is tradeoff between low inflation and low unemployment so the government generally has to pick one strategy at a time.

Let’s begin with the basic IS-LM graph, and go through each of the examples above to see what the results on equilibrium real income and the real interest rate will be.

We start with the downward sloping IS curve, and the upward sloping LM curve.  We can then add in the fiscal policy choices by shifting the IS curve.  We can check to see how the IS curve will shift by reviewing the IS equation:

Y = C(Y-T(Y))+I(r)+G+NX(Y)

We can see that G (government spending – fiscal policy) is exogenous, and that an increase in G or expansionary fiscal policy will have a positive impact on the equation or increase the IS curve (shift it right).  Likewise, a decrease in G or contractionary fiscal policy will have a negative impact on the equation or decrease the IS curve (shift it left). Looking at the graph, the ISi represents expansionary fiscal policy.  The new equilibrium point results in a higher real GDP or income level Yi>Y and real interest rate ii>i.  Note that the LM curve did not change.

Similarly, the ISd curve represents contractionary fiscal policy and results in a lower equilibrium real interest rate and real GDP.

When the central bank enacts monetary policy, we will shift the LM curve.  We can figure out how the LM curve will shift by looking at its equation:

M/P = L(i,Y)

If the central bank enacts expansionary monetary policy, we will see M (the money supply) rise which has a positive impact on the equation.  This causes the LM curve to shift right (to LMi) which results in a lower real interest rate and higher real GDP.  A decrease in the money supply causes the LM curve to shift left (to LMd), which results in a higher interest rate and a lower equilibrium level real GDP.