Equilibrium Interest Rate

For a given level of income, the intersection of the money supply and the liquidity preference curve will determine the equilibrium interest rate. It follows that for any given level of income, a curve can be drawn showing the interest rate that will result from any given level of income. This is called the liquidity and money (LM) curve. This curve is valid for a constant money supply. If the government expands or restricts the money supply, the result will be a shift to the right or left of the LM curve.

For a given level of income, the amount of savings conducted by households is determined by the marginal propensity to consume, MPC. The marginal propensity to save is equal to 1-MPC: S=(1-MPC)Y is the same as S=Y*MPS. For equilibrium in the private, real goods sector, planned savings must equal planned investment. Therefore I=Y*MPS. Investment must also fall on the marginal efficiency of invesment (MEI) curve, which is given by the investment function I=f(R). A simple investment function would be I=kR, which gives the relationship Y*MPS=kR or Y=R(k/MPS). This function gives the investment-savings (IS) curve.

When the LM and IS curves are drawn together, the point at which they intersect represents the point of simultaneous equilibrium for output (and hence investment and savings) and interest rates (and hence money supply and demand), as shown here:

The IS schedule above only includes the private sector. Of course, our expanded model includes government expenditures. Instead of achieving equilibrium when I=S, we now achieve equilibrium when I=S-G. This simply shifts the IS curve up by an amount such that the change in interest rates reduces I by the value of G. If we add trade surplus or defecit, again the IS curve is simply shifted up or down by an appropriate amount.

IS/LM: The Keynesian Liquidity Trap

Suppose that the economy is in equilibrium in the state shown by IS₁ and LM₁. The economy is severely depressed and unemployment is rampant. The government wants to take action to restore the situation to an equilibrium value where full employment (or close to it) again prevails. However, it cannot do so through monetary policy alone. No matter how aggressively the government expands the money supply, it cannot cause interest rates to fall below the horizontal portion of the LM curve. Only by shifting the IS curve  to IS₂, for example by increasing government expenditure, can full employment be restored. Notice that if fiscal policy is aided by a simultaneous expansion of the money supply resulting in LM₂, then the required increase in government expenditure and the resulting increase in interest rates are both lower.

Faced with the opposite problem, Y_E > Y_F (an inflationary gap), either fiscal or monetary policy can reduce Y_E to bring it back into equality with Y_F. If the gap is reduced using monetary policy alone, by restricting the money supply, then Y_F will be achieved but interest rates will be higher. If the gap is reduced using fiscal policy alone, then Y_F will also be achieved but this time interest rates will be lower. It would be possible through a carefully coordinated application of both fiscal and monetary policy to close the inflationary gap while leaving interest rates unchanged. Which of these three outcomes is desirable depends entirely on policy objectives outside the analytical range of economics. The relative effectiveness of fiscal and monetary policies will depend entirely on where the orginal equilibrium position lies and on the shapes of the LM and IS curves.