The IS-LM Framework - CLICK HERE - Advanced Macroeconomics

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1.2 The IS-LM Framework

Introduction

In an economy, the production of goods depends on a number of factors. But the average supply of goods in the economy is considered as the aggregate supply. Such an average supply keeps prices at a constant level. The aggregate supply of goods determines the equilibrium price. The average price level decides the aggregate demand. If prices change then the aggregate demand is affected. The aggregate demand is related to the average price and supply. If the aggregate demand rises, it reflects on the aggregate supply.

1.2.1 The goods and money markets

The economy is divided into the goods and money markets. The money and goods market have different equilibriums.

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Graph 1.1 Equilibrium of the goods and money markets in an economy

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Advanced Macroeconomics

Introduction to Macroeconomics The goods market is in equilibrium when the demand for goods is equal to the supply of goods. The price level remains in equilibrium. The prices of commodities can change if the demand for goods rises faster while the supply remains constant. This could result in a rise in the price of the commodities.

The rise in price, in turn, will have an effect on the demand for the commodity. There is an inverse relationship. When the supply of a certain good rises while demand remains constant, the price of this good declines or falls.

If we consider money market equilibrium then the demand for money is equal to the supply of money.

The interest rate remains constant in the long run. If the demand for money increases fast due to a number of reasons while the supply remains constant, then the interest rate will start rising. When the supply of money rises while demand for money declines, the interest rate declines but this is a short term adjustment.

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Figure 1.5 Flowchart of the goods and money markets Source: Dornbusch and Fischer (1994)

In the long run, the demand for and the supply of money remain equal to the supply of money and the interest rate remains unchanged. At the same time, the demand for goods is also equal to the supply of goods. Prices remain constant and the goods and money markets remain in equilibrium with stable prices and stagnant interest rates. Such equilibrium in the goods and money markets may change after an economic expansion or contraction due to monetary and fiscal policies in the short run. In the long run, both markets remain in equilibrium.

Advanced Macroeconomics

Introduction to Macroeconomics

1.2.2 The goods market equilibrium

The goods market is in equilibrium when the desired investment and the desired national savings are equal or equivalent, when the aggregate quantity of goods supplied equals the aggregate quantity of goods demanded (Bernanke, 2003). Alternatively, in the goods market, the demand for goods and supply of goods remain in equilibrium. The prices of goods remain in equilibrium. In other words, the prices of goods remain constant. The aggregate demand curve (ADC) is related to the interest rate and to the income level. As the aggregate demand curve shifts upward, the interest rate falls and the aggregate income increases. The planned investments in the economy increase with an increase in output and income.

In a closed economy, output is equal to expenditures.

Y = C+ I + G (1.45)

Now we will classify each variable into different categories.

C = c (Y, r) (1.46)

Consumption is related to income and the interest rate. As the level of income rises, the consumption expenditures increase. There is a positive relationship between consumption and income. Income is inversely related to the interest rate. As the interest rate starts rising, the consumption expenditures start declining. Income is further categorized as

Y Y= D+T^(1.47)

The consumption function can be written as follows:

( , ^e) C c Y T i π

+ −

= − − _(1.48)

The linear version of the consumption function can be written as

0 1( ) 2( ^e)

C c c Y T c i= + − − −π _(1.49) where c₀ is the autonomous consumption independent of income. c₁ is the responsiveness of consumption to a change in disposable income. c₂ is the responsiveness of consumption to a change in the ex-ante real rate of interest. The investment function can be defined as

I = a – b(i-π^e) (1.50)

where a is shorthand for business confidence and the productivity of investments. b is the parameter that explains how much investments decline in response to an increment in the ex-ante real interest rate.

The government expenditures can defined as

G G= ⁻ ^(1.51)

Advanced Macroeconomics

Introduction to Macroeconomics The government’s expenditures in the economy are considered the average expenditures. The IS curve is derived as follows:

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Figure 1.6 Derivation of the IS curve

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Advanced Macroeconomics

Introduction to Macroeconomics Figure 1.6 shows that the aggregate demand of investment is equal to the aggregate supply. The interest rate is constant. The interest rate is related to the aggregate demand. At point E, the aggregate demand curve shows the interest rate and income.

The aggregate demand curve remains in equilibrium with income and the interest rate. In the long run, consumption expenditures increase due to the increase in disposable income. A fall in the interest rate leads to an increase in investments and also leads to a rise in incomes and investments by the government and the private sector. The government expenditures (infrastructure projects, defense, law and order) increase every year due to the welfare state. Such developmental and social welfare expenditures raise the aggregate demand in the economy.

In figure 1.6, the rise in aggregate demand leads to a shift in equilibrium from E to E’, making the interest rate fall from i to i₁. The decrease in the interest rate leads to a rise in income. If we join points a and b, the result is a downward sloping IS curve.

Properties and shift of the IS curve

1. The IS curve is downward sloping from left to right.

2. The IS curve shows the interaction between the interest rate and income/output.

3. A change in the aggregate demand curve leads to a shift of the IS curve from left to right.

4. The IS curve is steep when there is a small change in the interest rate and a large change in income.

Shifts of the IS curve

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Figure 1.7 Shifts of the IS curve

Advanced Macroeconomics

Introduction to Macroeconomics As investments in the economy start rising, output also increases. This leads to an increase in the aggregate demand which is observed at point E. But a rise in the aggregate demand shifts the AD curve to AD₁. The new equilibrium is achieved at E₁. At this new equilibrium point, income rises from Y to Y₁. If we derive points a and b, then a shift occurs from IS to IS₁. The new IS₁ curve does not get affected by the interest rate. There is no change in the interest rate but income changes. The slope of the IS curve remains the same.

1.2.3 Derivation of the LM curve

The Liquidity preference-Money supply (LM) curve shows the relationship between money supply and demand. The interest rate remains constant when there is no change in the demand for and the supply of money. In the short run, the demand for money changes very fast but the supply of money doesn’t.

Therefore, when the demand for money rises, the interest rate rises, too. It is also possible that the demand does not rise but the supply remains high. In this case, the interest rates decline.

The demand for real balances increases with the level of real income and decreases with the interest rate.

The demand for real balances is written as

L = kY - hi k,h > 0 (1.52)

The parameters k and h reflect the sensitivity of the demand for real balances to the level of income and the interest rate.

For money market equilibrium, the demand for money should equal the supply of money.

M kY hi P

−

− = − (1.53)

If we solve the above equation for the interest rate, we can rewrite it as 1 ( M)

i kY

h P

−

= − − (1.54)

The above equation is for the LM curve. In the following figure, figure 1.8, the LM curve is derived.

Advanced Macroeconomics

Introduction to Macroeconomics

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Figure 1.8 Derivation of the LM curve

Figure 1.8 shows that the demand for money and the supply of money are in equilibrium at E. The interest rate is constant at income level Y. As the demand for money shifts from Md to Md₁, the interest rate also rises from I to I₁. At the same time, income rises from Y to Y₁. When there is more and more demand for money, income further increases. But at the same time, the interest rate also rises. This means that the LM curve shows the link between the interest rate and income. There is a positive relationship between the two variables.

Advanced Macroeconomics

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1.2.4 Shifts of the LM curve

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Figure 1.9 Shifts of the LM curve

Figure 1.9 shows that the demand for money in the short run shifts from M_d to Md₁. The supply of money also shifts from MS to MS₁. The new demand and supply of money point E1 shows an increase in the income, as shown at Y to Y₁. At point A and at point B, two separate LM curves are drawn. An expansionary monetary policy leads to an increase in the income. The interest rate remains constant at I. The LM curve shifts to LM₁.

Properties of the LM curve:

1. The LM curve is upward sloping.

2. The LM curve shows the relationship between income and the interest rate.

3. At the same level of the interest rate, the demand for money shifts the IS curve to the right.

1.2.5 Equilibrium of the IS-LM model

In the long term, the IS-LM curves intersect each other and they remain in equilibrium. The downward sloping IS curve and upward sloping LM curve always intersect with each other at different possibilities of equilibrium.

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Figure 1.10 Equilibrium of the IS-LM model

Advanced Macroeconomics

Introduction to Macroeconomics Figure 1.10 shows the intersection point of the IS and LM curves at point E, where it is always at long-term equilibrium. This means that the interest rate and income remain constant. It is possible that in the short run, due to expansionary and contractionary fiscal and monetary policies, the shift can either be backward or forward. The interest rate and income can either decrease or increase. The arrows in the diagram show the movements of the original equilibrium point. The following adjustments are shown in the table 1.2.

Quadrants Income Interest rate

I Increase Decrease

II Increase Increase

III Decrease Increase

IV Decrease Decrease

Table 1.2 Adjustments in the IS-LM model

It is not advisable to follow any particular monetary or fiscal policy. This is because following one policy may have an effect on the income and on the interest rate. In the long run, either policy is ineffective.

1.2.6 Effects of fiscal policies on the IS-LM model

If the government has an expansionary fiscal policy such a policy leads to a rise in income and the interest rate.

With an expansionary fiscal policy, the government’s objective is to increase the disposable income of people.

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Figure 1.11 Effects of fiscal policies on the IS-LM model

Effects of fiscal policies on the IS-LM model

A government can help to increase the income of people by conducting an expansionary fiscal policy, like when a government reduces direct and indirect taxes. Lower taxes to pay means people have more disposable income. Lower taxes on various commodities means that there is an increase in the disposable incomes of people.

Advanced Macroeconomics

Introduction to Macroeconomics Figure 1.11 shows that an expansionary fiscal policy leads to an increase in disposable incomes. A government’s expansionary fiscal policy will result in an increase in income from Y to Y_1. But an increase in disposable incomes could also lead to people saving and keeping their money in banks to take advantage of the rise in the interest rates. In the figure, the interest rate increases from I to I₁. The increase in incomes was expected at Y₁ but they increase further to Y₂. The crowding out occurs in the expansionary fiscal policy. It is shown at Y₁ to Y₂. The increase in the interest rate wipes out the increase in the total income. Therefore, at a higher level of income and higher interest rates, industrialists do not find it easy to invest money and their investments in firms start declining. As investments decline, the generation of employment also starts declining. Workers will not be able to find jobs and their incomes will also decline. The figure shows that an increase in the interest rate reduces investments made by industrialists leading to changes in the level of employment and income in the economy. In the long run, the economy is in equilibrium at point E. Short-term expansionary fiscal policies have no effect on incomes and the interest rate.

1.2.7 Effects of monetary policies on the IS-LM model

The objective of each monetary authority is to stimulate economic growth in the country. The monetary authority therefore, always tries to increase the money supply and reduce the interest rate. At lower interest rates, increased investments are possible.

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Figure.1.12 Effects of monetary policies on the IS-LM model

A monetary policy, by reducing the interest rate, always improves the income of people. The reduction in the interest rate helps increase investments in the economy. Figure 1.12 shows that the monetary authority reduces the interest rate, and so, I declines to I₁. The level of income increases from Y to Y₁. But in the long run, the reduction in the interest rate and the increase in incomes lead to more investments.

Production increases due to higher capital investments. But higher production could also lead to lower demand, and to prices declining. This is because every firm tries to sell their products in the national and international markets. They may sell at lower prices just to cover the fixed costs of production. The decline in prices due to competition reduces the profit margin. The investments made and profits gained do not match. Future investments are affected. A recession occurs. A decline in investments reduces the employment opportunities, which reduces the income levels. Incomes decline further and go back to the original level. In the long run, an expansionary monetary policy is ineffective. The interest rate (I) and incomes (Y) remain unaffected in the long run.

1.2.8 Conclusion

The goods market is in equilibrium when the demand for goods and services equals the supply of goods and services. Prices are constant. The money market is in equilibrium when the demand for money equals the supply of money. Both the goods and money markets are in equilibrium with the interest rate and income. Expansionary fiscal and monetary policies lead to increases and decreases in the interest rate and incomes, but only in the short term. In the long term, both monetary and fiscal policies are ineffective.

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