Limitations of the IS-LM Model

Limitations of the IS-LM Model

There are some limitations with the IS-LM model which we have developed so far. The limitations are connected with the fact that in this model we have assumed money supply to be exogenously determined, we have also looked only at a closed economy and also assumed the price level to be fixed.

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Summary

As a quick summary, we can say that:

Fiscal policy is more effective the flatter is the LM curve and the steeper is the IS curve.

Monetary policy is more effective the steeper is the LM curve and the flatter is the IS curve.

The condition that makes monetary policy most effective makes fiscal policy least effective. The reason for the difference is the differing role of interest rate plays in transmitting the effects of
monetary and fiscal policy .

Monetary Policy

Monetary Policy

Changes in money supply shifts the LM curve. When an expansionary monetary policy is adopted, for example, the LM curve shifts right causing interest rate to fall and income to rise.

The increase in money supply, by creating an excess money supply causes interest rate to fall. The fall in interest rate stimulates investment and this therefore results in an increase in income. A new equilibrium is achieved when the fall in interest rate and the rise in income jointly increase money demand by an amount equal to the increase in money supply. This equilibrium occurs at the point where the new LM curve intersects the IS curve. A decline in money supply has the opposite effect.

Monetary policy is effective provided:

Md must be interest inelastic (insensitive to changes in interest rate- LM steep); and

Investment must be responsive to changes in interest rate (IS relatively flat)

Fiscal policy to be effective

Hence, for fiscal policy to be effective (i.e. give rise to a big change
in T):

Md must be sensitive to changes in interest rate – the responsiveness of the demand for money to interest rate determines the slope of the LM curve; and

Investment must be interest inelastic – the responsiveness of investment to a change in interest rate determines the slope of the IS curve .

Fiscal Policy

Fiscal Policy

The use of fiscal policy shifts the IS curve, thereby affecting the equilibrium income and interest rate. In the case of an expansionary fiscal (when G is increased or T is reduced) for e.g., the IS curve shifts right, resulting in an increase in the equilibrium level of income and interest rate. A contractionary fiscal policy has the opposite effect.

An expansionary fiscal policy causes interest rate to rise (to maintain equilibrium in the money market). The increase in interest rate in turn causes a decline in investment spending. The decline in investment spending will partially offset the increase in aggregate demand resulting from the increase in government spending. Consequently the increase in income less than in the simple Keynesian model which does not take the offsetting effect into account. An expansionary fiscal policy raises interest rate which therefore dampens its expansionary fiscal impact.

The Effectiveness of Fiscal and Monetary Policies

The Effectiveness of Fiscal and Monetary Policies.

Whenever the economy is not operating at full employment, the government can intervene and help bring the economy to its full employment position by adopting appropriate fiscal and monetary policies.

The effectiveness of these policies will depend on the slopes of both the IS and the LM curves. (More of this will be touched upon when we look at the open economy).

Equilibrium in the Goods and Money Market

Equilibrium in the Goods and Money Market

Simultaneous equilibrium in both the goods and money market occurs at the intersection of the IS and the LM curves. The intersection of the IS and LM can be at full-employment, above full-employment or below full-employment.

Internal balance is achieved only if the economy is equilibrium is at full-employment.

Two special cases

Two special cases for the slope of the LM curve deserves to be mentioned. One when the interest elasticity of the Md is zero and the other when it is extremely high.

When the interest elasticity of the Md is zero i.e. h = 0. When Y increases in this case there is no possible rise in interest rate that can reduce the demand for money back to the level of the fixed
money supply. Reason being that a rise in interest rate cannot cause people to reduce their speculative demand for money or to economize on transactions balances. Consequently, the money market can be at equilibrium at only one level of income. Therefore the LM curve is this case is vertical.

The other extreme case occurs when the interest elasticity of money demand becomes extremely large, approaching infinity. This occurs when there is a liquidity trap i.e. a situation when interest rate is so low relative to what is considered normal, that there is now a general consensus that interest rate will rise. In this situation, expected future losses will outweigh the interest earnings on bonds. The public would rather hold any increase in money balances (with negligible fall in interest rate). When we have the liquidity trap case, the LM curve is horizontal.

The slope of the LM curve

The slope of the LM curve:

The slope of the LM curve on the other hand, depends on (i) the responsiveness of the demand for real money balance to a change in interest rate(h); and (ii) the responsiveness of the demand for real money balance to a change in income (k).

Conclusions:
The more responsiveness is the demand for real money balance to a change in interest rate (h), i.e. the bigger is h, the flatter is the LM curve and vice versa.

The less responsiveness is the demand for real money balance to a change in income (k), the smaller is k, the flatter is the LM curve

Conclusions

The position of the LM curve:

The position of the LM curve
depends on (i) the money supply in the system; (ii) the autonomous component of the demand for real money balance; and (iii) the price level).

Conclusions:
An increase in Ms (no change in P) increases the supply of real money balance and shifts the LM curve right. Reason: at the same income level, equilibrium in the money market is restored at a
lower interest rate. Vice versa, a decrease in MS (no change in P) decreases the supply of real money balance and shifts the LM left.

A higher Mdo (i.e. an increase in the amount of money demanded for given levels of interest rate and income e.g. if very unsettled economic conditions increases the probability of firms going
bankrupt and hence the default risk on bonds, the demand for money might increase) shifts the LM to the left and vice versa.

A decrease in price (no change in Ms) increases the supply of real money balance and shifts the LM curve down. On the other hand, an increase in P ( no change in Ms) reduces the supply of real money balance and shifts the LM curve up.

Algebraic derivation of the LM curve

Algebraic derivation of the LM curve

As mentioned before, equilibrium in the money market occurs
when

Md/P = Ms/P
Md/p = L (r, Y)

We can write an equation for the demand for real money balances,
which we shall represent by Md.

Md/P = Mdo + kY – hr

where: Mdo = autonomous money demand
k = elasticity of real money demand with respect to income
h = elasticity of real money demand with respect to interest
rates.
r = interest rate

Graphical Derivation of the LM curve

Graphical Derivation of the LM curve

The nominal quantity of money is assumed to be an exogenous variable determined by the central bank. Mathematically, this means that the supply of real money balance is a vertical line as it is independent of interest rates.

At income level Yo, the demand for real money balance is indicated by Lo (Yo). Equilibrium in the money market therefore occurs at A at interest rate ro. When income increases to Y1, the
demand for real money balance likewise increases to L1(Y1).

At this higher level of income, equilibrium in the money market occurs at a higher interest rate, r1. This relationship between income and interest rate gives us the LM curve. The LM curve is
positively sloped because when income increases, a higher interest rate is needed to bring about equilibrium in the money market.

LM curve

LM Curve

Objective:
(a) The meaning of the LM curve and how it is derived;
(b) What determines the slope of the LM curve; and
(c) What determines the position of the LM curve.

The LM curve shows the combinations of interest rate and income that brings about equilibrium in the money market. Equilibrium in the money market occurs when the demand for real money balance equals the supply of real money balance.

Recall that there are three motives for holding money – the transaction demand for money, the precautionary demand for money and the speculative demand for money. While the first two
motives for holding money are positively related to income, the speculative demand for money is inversely related to interest rate. The demand for real money balance is therefore a function of:

Md/P = L (r, Y)

What cause the IS curve to shift?

What cause the IS curve to shift?

The IS curve shifts when any of the factors which were held constant when drawing the curve changes. These are the autonomous components of expenditure i.e. Co. Io, Go (and if we have a lump sum tax it will include To).

Recall the concept of the paradox of thrift which you learnt in Introduction to Economics. What is the paradox of thrift and how does the fact that people want to save more affect the IS curve?

What determines the slope of the IS curve?

What determines the slope of the IS curve?
There are two factors, namely:

The responsive of investment to a change in interest rate; and The size of the multiplier.

Conclusions:
The more responsive investment is to a change in interest rate, the flatter is the IS curve and vice versa;

The bigger is the multiplier, the flatter is the IS curve, vice
versa.

Steps for drawing the IS curve

Steps for drawing the IS curve:

At the initial interest rate of ro, investment is Io and the planned expenditure line corresponding to this level of interest rate and investment is Eo. With planned expenditure represented by Eo(ro), equilibrium in the goods market is attained at output level Yo. As interest rate falls to r1, investment increases to I1. This in turn increases planned expenditure to E1 resulting in a higher new equilibrium level of output, Y1.

Conclusion:
A decline in interest rate results in a new equilibrium at a higher level of output. Interest rate and output are inversely related, therefore the IS curve which shows the relationship between interest rate and the equilibrium output is negatively sloped.

Drawing of IS curve

To draw the IS curve, we need to first understand the relationship between interest rate and investment. Investment is inversely related to interest rate. This inverse relationship can be expressed as:

I = Io – br

Where: Io = autonomous investment
b = elasticity of investment with respect to interest rate (b>0) It measures the responsiveness of investment to changes in interest rate.

Since the IS curve shows the combinations of interest rate and income that brings about equilibrium in the goods market (i.e. equality between demand and supply), what we will need to do in order to draw the IS curve is to change interest rate and observe the
effect on Y.

What happens when we are not at equilibrium?

What happens when we are not at equilibrium i.e. at Y1 or Y2?

When the economy is at Y1, planned expenditure (at B) is greater than output. Firms are not producing enough and this results in a rundown of inventories. The fall in inventories will induce firms to increase their output. This causes the economy to move toward the equilibrium at Yo.

At Y2, however, planned expenditure (at C) is less than output. Firms are selling less than what they are producing. The increase in inventories induces firms to cut back on production. As output and employment falls the economy moves back to the equilibrium level of output, Yo.

IS curve

The IS Curve

What you need to know about the IS curve:
(a) The meaning of the IS curve and how it is derived;
(b) What determines the slope of the IS curve; and
(c) What determines the position of the IS curve.

The meaning of the IS curve and how it is derived The IS curve shows us the interest rate and income combinations that gives equilibrium in the goods market.

Equilibrium in the goods market occurs when planned expenditure equals income or output. Remember that in Keynesian economics, total spending is the key to determining the output in the economy.