Advanced Macroeconomics
A Summary Paper on
The effects of the economic policies in the IS-LM model and the Mundell-Fleming model
Presented By Mohammad Elius Hossain Faculty of Economics Yamaguchi University
Date: February 01, 2008
Introduction to IS-LM Model In the history of world economics, the Great Depression of 1930s was painful and intellectually significant. After 1930s the theory of Classical economists on the basis of demand and supply were questioned because of massive unemployment and reduced income of USA. In the year of 1933 it was in most unfortunate situation, one-fourth of US labor force was unemployed and GDP was 30 percent below comparing with the year 1929. So, economist could realize the development of new theory to face the sudden economic downturn. As the classical theory was seemed to explain the depression of 1930s and economist was confused to find out solution, at that time (1936) the British economist John Maynard Keynes hold the steering wheel of sank down ship with his book The General Theory of Employment, Interest, and money. He could realize the weakness of classical theory and proposed that low aggregate demand is responsible for the low income and high employment that makes the economy downturn. Economists at present reconcile the two models; aggregate demand and aggregate supply. This model is capable to determine the national income at any given price level. There are two ways to show the shocks; what happens to income in the short run when price level is fixed, or what causes the aggregate demand curve to shift.
IS-LM Curve and Fiscal Policy IS stands for “Investment” and “Saving”, whereas LM stands for “Liquidity” and “Money”. IS curve represents the condition of the market of goods and services. LM represents the situation of the supply and demand for the money. IS curve plots the relationship between interest rate and the level of income. Any change in fiscal policy changes the demand for goods and services, and thus shifts the equilibrium in a given interest rate. Since IS curve represents demand and supply for goods and services, fiscal policy shifts the IS curve; and moves economy to a new equilibrium. To clarify the impact of fiscal policy in IS curve, we have to understand the Keynesian Cross.
Keynesian Cross and Fiscal Policy In his book Keynes describes that in the short run economy’s total income is the desire to spend by households, firms and the government. He interpreted the relationship among Demand for goods and services that is known also as “Planned Expenditure”, and Supply of Goods and services that is known as “Actual Expenditure” and Income (output). Planned Expenditure is the amount households, firms and the government would like to spend on goods and services. Actual expenditure is the amount households, firms, and the government spends on goods and services that equal the economy’s gross domestic products (GDP). If we consider the economy a closed one then net export is zero. So, demand for goods and services are Consumption (C), Investment (I) and Government purchase (G). We consider the planned economy as E. So, the equation can be shown as: E = C+ I+ G Again, Consumption demand depends on disposable income that is the residual of income (Y) after paying tax (T). Thus, we can write the equation:
D= C (Y-T) + I + G
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In the Keynesian cross, the economy is in equilibrium when actual expenditure (Y) equals planned expenditure (E). Actual Expenditure (Y) = Planned Expenditure (E) It means that supply curve is 45-degree line. Now the Keynesian Cross Diagram can be shown like below:
Planned Expenditure, E
Actual expenditure, Y= E Planned expenditure, E= C + I + G A The equilibrium in the Keynesian cross at the point A, Where Y= E.
Equilibrium Income
Income, Output, Y
Fiscal Policy and the Government Purchases Multiplier Government purchase affects the economy in large scale. Higher government purchase leads the economy to higher planned expenditure for any given level of income. If government purchase is increased by ∆G, demand schedule will also go up by ∆G. With increase in government expenditure by ∆G, demand schedule shifts upward. Equilibrium point shifts from point A to B, and income rises from Y1 to Y2. Increase in income ∆Y is greater than ∆G. In this case government purchase multiplier is the ratio of ∆Y/∆G. Government-purchase multiplier depends on Marginal Propensity to Consume or MPC. The higher the MPC, the greater will be consumption, and thus the more will be multiplier effect on income.
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The figure drawn in the below shows the change in income due to the change in government purchase:
Expenditure, E
Actual Expenditure
Planned Expenditure
B E2
=
∆G
An increase in the G, shifts planned expenditure upward
Y2
∆Y E 1 = Y1
A
E1= Y1
E2=Y2 Income, Output Y ∆Y
Mathematically, Government Purchase Multiplier is ∆Y/ ∆G= 1/(1- MPC).
The Mechanism of Multiplier Effect G ↑→D↑→Output ↑→ Income↑→C↑ ↑← ← ← ← ← ←↓
Demand for goods Output Income
First step ∆G ∆G ∆G
Second step c∆G c∆G c∆G
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Third step c2∆G c2∆G c2∆G
… … … …
Fiscal Policy and the Tax Multiplier: The changes in taxes also change the level of equilibrium. Taxes have an impact on disposable income, a decrease in taxes can increase disposable income, and the increase of tax decreases the disposable income, and thus, effects the consumption. A decrease in taxes shifts the demand schedule upward, and increases in tax shifts the demand schedule downward. The following diagram will explain the effect of tax on equilibrium.
Expenditure, E
Actual Expenditure Planned Expenditure ∆T x MPC E 2 = Y2 B ∆Y
E1
=
Y1 A
E1= Y1
E2= Y2 Income, Output Y ∆Y
A decrease in taxes by ∆T raises disposable income by Y-T by ∆T, and increases in consumption by ∆T x MPC. This shifts the demand schedule upward, and the equilibrium point shifts from A to B. Income increases from Y1 to Y2. Increase in income ∆Y is greater than ∆T. This is due to multiplier effect of changes in taxes, known as Tax multiplier. Taxes multiplier also depends on MPC. The higher the MPC, the greater the multiplier effect on income. Tax multiplier in relation to MPC is: ∆Y/ ∆T = - MPC/ (1-MPC). Now, we saw that expansionary and contraction fiscal policy shifts the demand schedule upward and downward respectively, thus shifts the equilibrium income level.
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The effect of fiscal policy on Keynesian Cross: Policy Increase Govt. Purchase or Decrease Tax Reduce Govt. Purchase or Increase Taxes
Shift in Demand Schedule Upward
Demand for and services Increases
Downward
Decreases
goods
Income, Output Increases Decreases
The Interest Rate, Investment, and the IS Curve: The Keynesian Cross is useful to show the equilibrium of goods market. Investment and interest rate is other important factors in the good market to determine the equilibrium. In macroeconomics planned investment depends on interest rate r. Interest rate and investment is negatively correlated, i.e., if interest rate rises, investment decreases. Decreased investment shifts the demand curve downward in Keynesian Cross that reduces income. The IS curve combines the interaction between r and I expressed by the investment function. And the interaction between I and Y demonstrated by the Keynesian cross. The following figure shows the relationship: Expenditure, E
(b) The Keynesian Keynesian Cross
Actual Expenditure
Planned Expenditure
∆I
Y2
Y1
Income, Output ,Y
(a) The Investment Function (c) The IS Curve Interest Rate, r
Interest Rate, r
The IS curve summarizes these changes in the goods market equilibrium
An increase in the interest rate
r2 r1
Lowers planned investment
I (r2) I(r1)
r2 r1 IS
Y2
Investment, I
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Y1
Income, Output, Y
The above diagram shows the functional relationship between Investment Function and Keynesian Cross to derive the IS curve. Graph (a) shows the Investment function: an increase in interest rate from r1 to r2 reduces investment from I(r2) to I(r1). Graph (b) shows the Keynesian Cross: a decrease in the investment from I (r1) to I (r2) shifts the planned expenditure function downward, and thus reduces income from Y1 to Y2. Graph (c) shows the IS curve summarizing the relationship between interest rate and income: the higher the interest rate, the lower the level of income. Fiscal Policy Shifts the IS Curve: IS curve shows the combinations of the interest rate and the level of income for a particular interest rate, at which the demand of goods and services is equal to the supply of goods and services. Fiscal policy changes the demand for goods and services; thus at a given interest rate, the equilibrium income level also changes. The following figure will explain it better. (a) The Keynesian Cross Expenditure, E
Actual expenditure Planned expenditure Y2 ∆G
An increase in the G, shifts the planned expenditure upward by ∆G, which raises income by ∆G/1-MPC
Y1
Y1
Y2
Income,Output ,Y
(b) The IS Curve Interest Rate, r
r
IS2
Shifts the IS curve to the right by ∆G/1-MPC
IS1
Y1
Y2
Income, Output, Y
In this condition the national income accounts identity can be written as Y- C- G = I S= I Here, S is for national saving, and I is for Investment. National saving represents the supply of loan-able funds, and investment represents the demand for these funds.
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The Money Market and the LM Curve: The LM curve plots the relationship between the interest rate and the level of income that arises in the market for money balances. For more clarification we can look into the theory of interest rate that is called the theory of liquidity preference. The theory of liquidity preference From the Keynesian point of view this theory is about how the interest rate is determined in the short run. It’s very important to say that the interest rate adjusts to balance the demand and supply for the most liquid things in the economy- money. For this theory we need to discuss what is real money balance? Here M stands for the supply of money and P stands for the price level, then M/P is supply of real money balances. _ _ (M/P)s = M/P. This relationship of interest rate and real money balances can be shown as follow:
Interest rate, r
Supply
LM Curve
Equilibrium interest rate Demand, L(r) M/P
Real money balances
In the above diagram, the supply and demand for real money balances determine the interest rate. The supply curve for M/P is vertical, because the supply of money does not depend on interest rate. The demand curve is downward sloping because the higher the interest rate, the higher the cost of holding money, and thus, lowers the quantity demanded for money. At the equilibrium interest rate , the quantity of M/P equals the quantity supplied.
A Reduction in Money Supply Reduces the Real Money Balances When the price level in the money market remains unchanged, the change in money supply then changes the equilibrium interest rate which is shown in the following figure:
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Interest rate
supply
A fall in the money supply ‌
r2
r1 Demand, L(r) M2/P
M1/P
Real money balances, M/P
In the above diagram, we see that, if price level is fixed, a reduction in the money supply from M1 to M2 reduces the supply of real money balances. Therefore, the equilibrium interest rate rises from r1 to r2. Monetary Policy Shifts the LM Curve Interest rate is equilibrates the money market at any level of income. The equilibrium of interest rate also depends on the supply of real money balances. The following diagram shows the relationship between the market for real money balances to income and interest rate. An increase in income from Y1 to Y2, raises the demand for money that raises the interest rate from r1 to r2. LM curve summarizes the relationship between interest rate and income. (a) The Market for Real Money Balances
(b) LM Curve interest rate, r
Interest rate, r
The LM curve summarizes these changes in the money market
An increase in income raises money demand and increasing the interest rate
r2
r2 L(r, Y2)
r1
r1 L(r, Y1)
M/P
Real Money Balances (M/P)
Y1
Y2 Income, output, Y
Again we can analyze how a reduction in the money supply shifts LM curve upward. The diagrams drawn in the next page clarify the matter.
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Interest rate, r
Interest rate, r
LM2 LM1
r2
r2
r1
r1
M2/P
M1/P
Real money Balances, M/P
Y Income,output,Y
The figures (a) show that for any given level of income Y, a reduction in the money supply raises the interest rate that equilibrates the money market. As a result, the LM curve in the figure (b) shifts upward. Thus, the effect on both expansionary and contractionary monetary policy, LM curve shifts. If Central Bank increases money, LM curve shifts to the right. That is known as expansionary policy. If Central Bank reduces money supply, LM curve will shift to the left. That is known as contractionary policy.
The Short Run Equilibrium IS-LM: From the previous discussion we can have all pieces of the IS-LM model. The two equations of this model are: Y= C (Y-T)+ I (r)+ G IS, M/P= L(r, Y)
LM
The model takes fiscal policy, G and T, monetary policy M, and the price level P as exogenous. Given these exogenous the IS curve provides the combinations of r and Y that satisfy the equation representing the goods market and LM curve provides the combinations of r and Y that satisfy the equation representing the money market. The following figure shows the two curves together at their equilibrium point: Interest rate,r
LM
The intersection of IS and LM curves represents the equilibrium in the market for goods and services and in the market of real money balances for given values of government spending, taxes, the money supply, and the price level.
Equilibrium Interest Rate
IS Equilibrium level of income
Income,Output, Y
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IS-LM Model and Shocks in the Economy: Fiscal Policy and the IS-LM Model: In the national economy, fiscal policy is two types: 1. fiscal expansion i.e. increase of government purchase or decrease of taxes 2. fiscal contraction i.e. decrease of government purchase or increase of taxes. These two types of fiscal policies are described below with the diagram. Fiscal Expansionary Policy (Increase in the Govt. Purchase or decrease of tax)
Interest Rate, r
LM
r2
B
A
r2
Y2
Y1
IS2 the IS curve shifts to the right by ∆G/(1-MPC) IS1 Income, output, Y
The figure shows first equilibrium at point A, where income Y1 and r1. With expansionary fiscal policy an increase in the government purchase shifts the IS curve to the right by ∆G/(1-MPC). The new equilibrium point then moves to point B. Income rises from Y1 to Y2, and the interest rate rise from r1 to r2. In case of tax decrease IS curve shifts by ∆T x
MPC/(1-MPC).
Contractionary Policy (Decrease in Government Purchase or Increase in Tax) Fiscal contraction policy just has the opposite impact in the monetary policy. With decrease in government purchase or increase in taxes, IS curve shifts to the left by ∆G/(1-MPC) . It reduces the equilibrium income and interest rate. In case of tax increase IS curve shift by ∆T x MPC/(1MPC).
Interest Rate, r
LM
r1 r2 IS2 Y2
Y1
IS1 Income, output,Y
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The Interaction Between Monetary and Fiscal Policy At the time of holding both monetary and fiscal policy, it is very important to know what the other policy makers are doing. A change in other policy may have the influence and this can alter the impact of the new policy. So, in this model policy maker has to consider the policy of others. This can be discussed by the three possible alternatives when tax increases and (a) Central Bank holds the money supply constant (b) the Central Bank holds the interest rate constant and (c) the Central Bank holds income constant. The effect of these policies mix will be different in IS-LM model which are shown below.
(a) Central Bank holds money supply constant: A tax increase shifts the IS curve
Interest rate, r
When tax increases, IS curve shifts to the left due to the Central Bank holds money supply constant. Income also reduces interest rate also reduces.
LM r1 r2 IS1 IS2 Y2 Y1
Income, output,Y
(b) Central Bank holds interest rate constant: A tax increase shifts the IS curve
Interest rate, r
LM2 LM1
r
When tax increases and Central Bank holds interest constant, IS curve shifts to the left, and the Central Bank reduces money supply by shifting the LM curve upward and thus interest rate will return to the initial level. Income decreases.
IS1 IS2 Y2
Y1
Income, output,Y
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(c) Central bank holds income Constant: A tax increase shifts the IS curve
Interest rate, r
When tax increases and the Central Bank holds income constant, IS curve shifts left but to keep the income constant Central Bank expands money supply. Interest rate reduces and thus bring income back to the initial level..
LM1 LM2
r1 r2 IS1 IS2
Y
Income, output,Y
The Mundell-Fleming Model: The Mundell-Fleming model is an economic model first set forth by Robert Mundell and Marcus Fleming. The model is an extension of the IS-LM model. Whereas IS-LM deals with economy under autarky, the Mundell-Fleming model tries to describe a small open economy.The MundellFleming model portrays the relationship between the nominal exchange rate and the economy output (unlike the relationship between interest rate and the output in the IS-LM model) in the short run. The Mundell-Fleming model has been used to argue that an economy cannot simultaneously maintain a fixed exchange rate, free capital movement, and an independent monetary policy. In the Mundell-Fleming model the interest rate in the economy r is determined by the world interest rate r*. Mathematically, r= r* Nominal and Real Exchange Rate Nominal Exchange rate is that rate at which the currency of one country trades for another country’s currency. Real Exchange rate is that rate at which the goods of one country trades for another country’s goods. Real Exchange Rate= Nominal Exchange Rate x Ratio of Price Levels = e x (P/P*) The Goods Market and IS*Curve: In Mundell-Fleming Model goods market and services are described as much as IS-LM model. In addition to that it adds a new term for net export. The goods market is represented with the following equation: Y = C (Y-T) + I (r*) + G + NX (e)
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The Money Market and LM* Curve In Mundell-Fleming model money market is described as IS-LM model. In addition to this assumption it represents the equation with that the domestic interest rate equals the world interest rate : M/P= L (r*, Y) The following graph shows the goods market equilibrium condition IS* and the money market equilibrium condition LM*. Both curves are drawn holding the interest rate constant at the world interest rate. The intersection shows the equilibrium income and equilibrium exchange rate.
Exchange Rate, e LM*
Equilibrium exchange rate IS* equilibrium income Income, output, Y Economic Policy under Mundell-Fleming Model In the Mundell-Fleming model we will discuss the effect of Fiscal Policy, Monetary Policy and Trade policy. These three policies varies one from another in the change of floating to fixed exchange rate system. The Small Open Economy Under Floating Exchange Rates To analyze the policies we have to consider the poly adopted by any country that they have chosen to operate. Under floating exchange rates, the exchange rate is allowed to fluctuate in response to changing economic condition.
LM* Exchange Rate, e
Fiscal Policy
e2
IS2*
e1 IS1* Y
Income, output, Y
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When government take fiscal expansionary policy, an increase in the government purchases or decreases in taxes, the IS* curve shifts to the right. This rises the exchange rate but no effect on income. Contractionary fiscal policy will give the opposite result shifting IS* curve to the left.
Monetary Policy In the expansionary monitory policy under floating exchange rate, an increase in the money supply shifts the LM* curve to the right. Exchange rate reduces, and net export increases but it gives rise to income. In case of Contractionary monetary policy, it increases exchange rate; and decreases net export and income. The following two diagram shows the effect:
Expansionary Policy exchange rate, e
LM1*
Contractionary Policy LM1* LM2* LM2* exchange rate, e
e2 e1 e2
e1 IS* IS*
Y1
Y2 Income, output,Y
Y2
Y1 Income, output, Y
Trade Policy In the trade policy, the mechanism is import restriction which raises the net export (NX). In trade restriction, as import reduces the NX increases because, NX= X- M ( X for export and M for import). The following figures shows how trade restriction effect the net export and exchange rate.
(a) The Shift in the Net Export Schedule
(b) The Change in the Economy’s Equilibrium LM*
exchange rate, e
exchange rate, e
e2
e1 NX2
IS*2 IS*1
NX1 Net Export
Y Income, output, Y
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In the graph (a) restricted trade policy by imposing tariff or import quota, shifts the net-export schedule to the right. Graph (b) shows the effect as a result of graph (a) shifting the IS* curve to the right, that raises the exchange rate and keeps the income unchanged.
The Small Open Economy Under Fixed Exchange Rate Under a system of fixed exchange rates, the central bank is ready to buy or sell the domestic currency for foreign currencies at a pre determined price. This policy dictates the country’s monetary policy to the single goal of keeping the exchange rate at the announced level. It is the commitment of central bank to keep the exchange rate at equilibrium point. How the Fiscal Exchange rate system works can be shown below drawing the diagram.
(a) The equilibrium Exchange rate is Greater Than the Fixed Exchange Rates LM*1
LM*2
LM*2
exchange rate, e
LM*1
exchange rate, e
equilibrium exchange rate Fixed exchange rate
(b) The Equilibrium Exchange Rate is Less Than the Fixed Exchange Rates
IS*
fixed exchange rate equilibrium exchange rate
Income, output, Y
IS*
Income, output, Y
In the graph (a) the equilibrium exchange rate initially exceeds the fixed level. People will buy foreign currency and will sell to the central bank for profit. These process automatically increases the money supply, shifting LM* curve to the right and lowering the exchange rate. In graph (b) the equilibrium exchange rate is initially below the fixed level. People will buy dollars in foreign exchange markets and use them to buy foreign currency from the central bank. This process automatically reduces the money supply, shifting the LM* curve to the left and raising the exchange rate.
Fiscal Policy: Fiscal policy can be taken in two ways; Expansionary fiscal policy and contractionary fiscal policy. In expansionary fiscal policy the IS* curve shifts to the right. To maintain the fixed exchange rate the central bank must increase the money supply shifting the LM* curve to the right. Hence, in contrast to the case of floating exchange rates, under fixed exchange rates a fiscal expansion raises income. The cotractionary fiscal policy will shift the IS* curve to the left. To maintain the fixed exchange rate the central bank must reduce the money supply shifting the LM* curve to the left. It decreases income. The both policy are shown in the next page graphically:
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(a) Expansionary Policy
(b) Contractionary Policy
LM1* LM1*
LM2*
LM2*
exchange rate,e
exchange rate, e
fixed, e Fixed, e IS1* IS2* IS1*
Y1
Y2
Income,output,Y
IS2*
Y2
Y1
Income, Y
Monetary Policy: In small open economy the fixed exchange rate system cannot use monetary policy effectively; however, it can use devaluation (a reduction in the value of domestic currency against other currencies) or revaluation (an increase in the value of domestic currency against other currencies) as an alternative to monetary expansion or contraction. A devaluation shifts the LM* curve to the right and a revaluation shifts it to the left. Devaluation makes exported goods cheaper and imported goods more expensive and hence increases net exports and income. An increase in income increases the demand for real money balances. In the short run the price level is fixed. Therefore, the central bank must purchase foreign currencies to keep the money market in equilibrium. This increases the money supply and shifts LM* right. The following diagram explains the situation:
Exchange Rate, e
LM*
Fixed exchange rate IS*
Income, output, Y
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Under fixed exchange rate if monetary expansion policy is hold, the central bank will increase the money supply by buying bonds from the public which will put the downward pressure on the exchange rate. To maintain the fixed exchange rate, the money supply and the LM* curve must return to the initial positions. Thus, under fixed exchange rates, normal monetary policy is ineffective
Trade Policy: Trade policy is effective for a small open economy under fixed exchange rates. Imposing an import quota or a tariff increases net exports and shifts the IS* curve to the right. The shift in the IS* curve tends to raise the exchange rate. To prevent appreciation and keep the exchange rate fixed, the central bank must purchase foreign currencies. This increases the money supply and shifts LM* curve to the right. Income also increases from Y1 to Y2. The following diagram shows the effect.
LM1*
LM2*
Exchange rate, e
Fixed exchange rate IS2* IS1* Y1
Y2
Income, output, Y
The Mundell- Fleming Model : Summary of Policy Effects Exchange-Rate Regime Floating Exchange Rate Policy Income (Y)
Fixed Exchange Rate
IMPACT ON
Fiscal Expansion
Constant
Exchange Rate (e) Increase
Net Export (NX) decrease
Income (Y) Increase
Exchange Rate (e) Constant
Net Export (NX) Constant
Monetary Expansion
Increase
Decrease
Increase
Constant
Constant
Constant
Import Restriction
Constant
Increase
Constant
Increase
Constant
increase
Conclusion: The Mundell-Fleming model extends the IS-LM model to incorporate the balance of payments consideration which is very useful in macro economics analysis. In the IS-LM model, interest rate is the key component to the both money market and goods market equilibrium. Under the Mundell-Fleming framework of small economy, interest rate is fixed and equilibrium in both market can only be achieved by a change of nominal exchange rate.
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