The IS-LM ModelDuring the current period of a cyclical slowdown in economic activity, economists debate on effectiveness of macroeconomic policies. We studied goals and instruments of fiscal policy and their impact on macroeconomic variables in the real sector. On the other hand, we studied goals and instruments of monetary policy and their effectiveness in the regulation of the financial sector. In real life these two sectors are not isolated. Now we have to analyze the impact of both fiscal and monetary policy on macroeconomic activity.

Since the central economic problems at the moment are related rather to income and unemployment than to the price level, we will concentrate on changes in macroeconomic equilibrium under the assumption of constant prices. The analytical tool widely used in this analysis is the IS-LM model, developed by the British economist Sir John Hicks and the American economist Alvin Hansen.

The IS-LM model brings together the impact of fiscal and monetary policies on both the real sector and the financial sector. In addition to the assumption of

constant price level

we will assume

only two types of financial assets: money and bonds (interest bearing assets), and

a closed economy (we will ignore foreign exchange fluctuations and international capital movements)

Later we will relax some of these assumptions.1. The LM curve

a) the equilibrium in the money market as a function of income and definition of the LM curve

In order to put together the monetary and the real sector, we have to define the equilibrium in the monetary sector as a function of a income, which is a real sector variable.

The equilibrium in the monetary sector is set when MS = MD. Under a given level of income (Y1) money supply and money demand determine the equilibrium interest rate (i1), presented on the graph below (Fig. 1).

Fig. 1. Equilibrium in the money market.The increase in income from Y1 to Y2 raised the demand for real money balances and the money demand curve shifts to the right, as shown on Fig. 2 (left panel). Thus, if income rises, the equilibrium interest rate increases, other things held constant. We can build a relationship between income and the equilibrium interest rate, as shown on Fig. 2 (right panel). The point of macroeconomic equilibrium E1 under income Y1 is presented on the right panel as a function of income. It shows what the interest rate should be, in order to have equilibrium in the money market. When income rises to Y2 the equilibrium in the money market at point E2 is achieved at a higher interest rate i2 .On the left panel this equilibrium point shows what the interest rate should be under income Y2 in order to have equilibrium in the money market. When we put together the equilibrium points on the money market we derive the LM curve. It presents the relationship between the level of income and the equilibrium interest rate, as shown on Fig. 2 (left panel).

Fig. 2. Deriving the LM curve

The LM curve shows what the interest rate should be at every level of income, so that we have equilibrium in the money market.

b) analyzing the LM curveThe first point of the analysis of the LM curve is its slope. When is the LM curve shallow and when is it steep?

If money demand is highly elastic as regard income, a relatively small increase in income in percentage terms, would lead to a relatively large increase in the money demand in percentage terms. The equilibrium interest rate will increase significantly and as a result the LM curve will be very steep, as shown on Fig. 3.

If money demand is inelastic as regard income, a relatively large increase in income in percentage terms, would lead to a relatively small increase in the money demand in percentage terms. The equilibrium interest rate will increase just a little and as a result the LM curve will be very shallow, as shown on Fig. 4.

Fig. 3. Highly elastic money demand as regard income and a steep LM curve.

Fig. 4. Highly inelastic money demand as regard income and a shallow LM curve

The second factor determining the slope of LM depends on the slope of the MD curve. If the money demand is elastic as regard interest rate, the money demand curve is very shallow and this will contribute to a greater slope of the LM curve. If money demand is inelastic as regard interest rate, the MD curve is steep and this will contribute to a steeper LM curve.

Thus, the slope of the LM curve depends on

the elasticity of money demand as regard income and

the elasticity of money demand as regard interest rate.

If the money demand is elastic as regard income and inelastic as regard interest rate, the LM curve is steep.

If money demand is inelastic as regard income and elastic as regard interest rate, the LM curve is shallow. Such an LM curve is usually observed during recessions.If the money market is in disequilibrium, at a given level of income the interest rate is either lower, or greater than the equilibrium interest rate. Lets take the case when the level of the interest rate is below the equilibrium, as shown on Fig. 5. At point A at a lower interest rate the opportunity cost of holding money is lower. The public will prefer more liquidity. MD > MS. How can the public have more liquidity? They will start selling their interest bearing assets (bonds). The excess supply of bonds will drive their price down and the interest rate will increase until it gets to its equilibrium point A on the LM curve.

Fig. 5. MD>MS and a move to equilibrium interest rate.If the LM curve is very steep, the achievement of the equilibrium interest rate assumes a significant reduction in the prices of financial assets and a respective significant increase in the interest rate. If the LM curve is shallow, small activities in the bonds market lead to equilibrium in the money market. The second point of the analysis of the LM curve is its location. Thus, we have to analyze factors, determining the shifts in the LM curve.

Changes in money supply

If MS increases at the same level of income, the equilibrium interest rate falls. The equilibrium in the money market shifts from E1 to E2, as shown on Fig. 6 (left panel). Respectively, point E1 shifts to point E2, at the same level of income (right panel). The LM curve shifts to the right.

Fig. 6. Increase in money supply and a shift in the LM curve to the right

If MS falls, the LM curve shifts leftwards.Autonomous changes in money demand

Autonomous increase in money demand means that it rises not because of the increase in income, in the interest rate or in the price level, but because of a change in an exogenous variable. For example, if holding bonds becomes more risky, the public prefers liquidity as a less risky asset and money demand rises. At the same level of income the equilibrium interest rate increases (Fig. 7 left panel) and respectively, the LM curve shifts leftwards (Fig. 7 right panel).

Fig. 7. An increase in autonomous money demand and a leftward shift in LM

If autonomous money demand falls, LM shifts rightwards.

2. The IS curvea) the equilibrium in the real sector as a function of the interest rate and the IS curve

In the analysis of the LM curve we studied the impact of income as a real sector variable on the equilibrium in the monetary sector. Now we will shift our attention to the impact of the interest rate as a monetary sector variable on the equilibrium in the real sector.

Under the assumption of a constant price level the equilibrium in the real sector is best presented on the AE-Y diagram. On Fig. 8. AE1 = Y1 under a given price level.

Fig. 8 AE Y diagram

AE = C + I + G + X M. Investment spending depends on the interest rate. If the interest rate falls, investment spending rises. Since investment spending is a component of AE, aggregate expenditures increase with the reduction in the interest rate. As a result, the equilibrium income rises from Y1 to Y2, as shown on the upper panel of Fig. 9. Thus, we found a relationship between the interest rate and the equilibrium income. We can develop in on a graphical model as shown on the lower panel of Fig. 8. At the higher interest rate i1 the equilibrium income (AE + Y) is Y 1. At a lower interest rate i2, the equilibrium income rises to Y2 . When we put together all equilibrium points E as a function of the interest rate we derive the IS curve, as shown on Fig. 8.The IS curve shows what should be the equilibrium income at every level of the interest rate.

Fig. 8. Deriving the IS curve

c) analyzing the IS curveThe slope of the IS curve depends on the elasticity of investment demand as regard the interest rate.

If the investment demand is highly elastic as regard the interest rate, small changes in the interest rate in percentage terms cause large changes in investment in percentage terms. Respectively, AE changes significantly and the IS curve is shallow, as shown on Fig. 9. If the investment demand is highly inelastic as regard the interest rate, significant changes in the interest rate in percentage terms cause small changes in investment demand in percentage terms and respectively in the AE. As a result, the IS curve is steep, as shown on Fig. 10.

Fig. 9. Elastic investment demand as a shallow IS curve

Fig. 10. Inelastic investment demand and a steep ISThe economy is in disequilibrium when AE are larger or smaller than income for a given interest rate. If, for instance income is at a lower level for a given interest rate (at point A on Fig. 11), investment demand is motivated by this the low interest rate and AE > Y. As you remember, in this case inventories fall, production rises, unemployment falls and income increases. This process of increase in income will take place until it grows to its equilibrium point A.

Fig. 11. AE > Y and a move to equilibrium income

If the economy is at a disequilibrium above the IS curve, AE < Y. Inventories increase, production falls, unemployment rises and income falls until it achieves its equilibrium point on the IS curve.Thus, the IS curve shows what should be the level of income at every level of the interest rate so that AE = Y.

Factors, determining the location of the IS curve:

Injections

Injections are assumed to be autonomous, which means that they do not depend on the interest rate, or income. These could be government spending, autonomous investment and exports.

If for instance government spending rises at the same level of the interest rate, AE increases and the equilibrium income increases. The equilibrium point A shifts to point A. As a result, the IS curve shifts to the right as shown on Fig. 12.

Fig. 12. An increase in injections and a shift in the IS curve to the right.

If injections fall the IS curve shifts leftwards.

leakagesLeakages are assumed to be autonomous as regard interest rate. These are autonomous savings, taxes and imports. If leakages increase, equilibrium income falls and the IS curve shifts to the left.

If leakages fall the IS curve shifts rightwards.

3. Macroeconomic equilibrium in the real sector and in the monetary sectorThe LM curve shows what should be the equilibrium interest rate at every level of income. In other words, it shows the equilibrium in the monetary sector as a function of income.

The IS curve shows what should be the equilibrium income at every level of the interest rate. In other words, it shows the equilibrium in the real sector as a function of the interest rate.

Macroeconomic equilibrium is achieved when there is an equilibrium in the monetary sector and at the same interest rate there is an equilibrium in the real sector. Graphically it is presented by the intersection of the IS and the LM curve. Fig. 13

Fig. 13. Macroeconomic equilibrium in the real and in the monetary sector the IS-LM equilibrium

The IS-LM equilibrium could be easily destroyed by any changes in the real or in the monetary sector. Changes in the real sector and macroeconomic equilibrium

Lets assume that exports increase. This injection will increase equilibrium income and shift the IS curve to the right. The equilibrium in the real sector will be presented by IS2. (Fig. 14) Point E1 shifts to point R. This destroys the equilibrium in the monetary sector. At the higher income level Y2 i1 is lower than the equilibrium i. MD > MS. The public starts selling bonds, because they prefer more liquidity. PV of bonds falls and the interest rate rises. However, the increase in the interest rate affects the real sector, as well. At the higher interest rate investment falls and as a result income falls. This is why the move is along the new IS curve instead of being straight upwards to point K. The new equilibrium is achieved at E2.

Thus, the increase of injections raises the equilibrium income, but it raises the equilibrium interest rate as well.

Fig. 14. The impact of an increase in injections on the IS-LM equilibrium

We can draw a conclusion that expansionary fiscal policy leads to an increase in equilibrium income but to a rise in the equilibrium interest rate, as well.

Restrictive fiscal policy (a leftward shift in the IS curve) would reduce both equilibrium income and equilibrium interest rate.

Changes in the monetary sector and macroeconomic equilibrium

Lets assume that money supply rises at the same income. As a result, the equilibrium interest rate falls and the LM curve shifts rightwards, as shown on Fig. 15. The equilibrium point E1 shifts to point T. There is an equilibrium in the monetary sector, but in the real sector the new low interest rate raises investment and AE > Y. Inventories fall and income rises. However, the increase in income affects money demand and it increase as well. This is why the move is along the new LM curve instead of being straight rightwards to point P. The new equilibrium is achieved at E2.Thus, the increase in money supply reduces the equilibrium interest rate and raises the equilibrium income.

Fig. 15. The impact of the increase in money supply on the IS-LM equilibriumExpansionary monetary policy reduces the interest rate and at the same time raises the equilibrium income.

Monetary restriction ( a leftward shift in the LM curve) raises the equilibrium interest rate and reduces the equilibrium income.