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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

Subject Economics

Paper No and Title 4: Basic Macroeconomics

Module No and Title 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

Module Tag ECO_P4_M34

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

TABLE OF CONTENTS

1. Learning Outcomes 2. Introduction

3. AD Schedule under dynamics of Inflation.

3.1 IS Curve: Goods Market Equilibrium 3.2 LM Curve: Money Market Equilibrium 3.3 Aggregate Demand Schedule

4. AS Schedule under dynamics of Inflation.

4.1 Production Function 4.2 Labor Market

4.3 Aggregate Supply Schedule

5. Overall Equilibrium under dynamics of Inflation.

6. Long – run equilibrium under dynamics of Inflation.

7. Demand Side Shocks: Aggregate Demand or AD shocks 8. Supply Side Shocks: Aggregate Supply or AS shocks 9. Summary

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

1. Learning Outcomes

After studying this module, you shall be able to

 To understand need to incorporate dynamics of inflation in AD – AS schedules.

 To understand the derivation of AD curve using Inflation modified IS-LM framework.

 To comprehend the notion of overall equilibrium in the economy under inflation.

 To understand the long – run steady state incorporating expected inflation.

 To identify the impacts of demand side shocks which affect AD curve.

 To identify the impacts of supply side shocks affecting AS curve.

2. Introduction

In the earlier module you have seen the derivation of expectation augmented aggregate demand AD and aggregate supply AS , Phillips curve and expectation augmented Phillips curve and the relationship between actual rate of unemployment , natural rate of unemployment and inflation rate .

In the real world, the prices are continuously rising therefore to study dynamics of inflation we need to generalize IS-LM model to incorporate rising inflation .As a result we need to derive Aggregate demand and aggregate supply under dynamics of inflation and then study the long-run equilibrium condition.

In the long run an economy would settle down to a specific combination of interest rate, income and inflation. The only point of argument that exists is the time it would take to obtain the equilibrium. Keynesian stream of thought would propose a long- time for economy to reach long – run equilibrium while New-Classical argue that the economy is so adjustable that it would settle to its long – run equilibrium very fast . One common factor in both the schools of thought is that they both believe in the concept of equilibrium

An unplanned movement in inventories would bring about an equilibrium in inventories, leading to changes in output and employment. This adjustment mechanism occurs whenever there is short – run equilibrium condition. In the long – run AS schedule becomes vertical as AS plays no role in determining income. This would effectively imply that fiscal or monetary policies play no role in determining income in long- run .An explanatory Monetary Policy would not be able to lower nominal interest and increase output.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

This module would incorporate the dynamics of inflation in aggregate demand AD and aggregate supply AS , thus describe the mechanism by which long run equilibrium and stability and equilibrium is attained .The module would go through the implications of demand side shocks and supply side shocks

3. AD Schedule under Dynamics of Inflation

In order to study dynamics of inflation we need to study IS – LM model which is modified to capture persistent inflation .IS curve represents the goods market equilibrium .The goods market equilibrium is represented by the situation where leakages from national income in form of Savings and Taxes are equated to injections into national expenditure in the form of Investment and Government Expenditure.

Let sum of savings and taxes i.e. ( S+T) be represented by R and sum of investment and government expenditure i.e ( I+G ) be represented by T . Also assume natural log of R be lnR and natural log of T be lnT .

Since savings depend on real income and investment depends on real income and real interest rates, their functional relationship in terms of natural log can be written as follows:

lnR = β0 + β1 lny ………Eq (1)

lnT = β2 + β3 lny – β4 ( i – πe ) ……… Eq (2)

where ( i – πe ) is in terms of levels not logs . It is the gross inflation rate of return , r is the real rate of return and πe is expected rate of return or nominal rate of interest i can be written as i = r + πe.

In equilibrium, leakages are equal to injections implying savings and taxes are set equal to investment and government expenditure .This gives the relationship between income and interest rates. Therefore the IS schedule would look like:

3.1 IS Curve: Goods Market Equilibrium

lny = α0 – α1( i - πe ) ………Eq(3)

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

α0 = (β2 - β0 )/ ( β1 - β3 ) and α1 = β4 / ( β1 - β3 ) . Since the coefficient of i is – α1 , the slope of IS curve is -1/ α1 . However the IS curve is negatively sloped only if β1> β3 . This implies that the response of savings to income be larger than that of investment to income .All the points lying on the right hand side of IS curve are points representing excess supply in the goods market while points lying on left hand side are the points of excess demand in the goods market .All the points on the IS curve are the points where the goods market is in the equilibrium.

An increase in expected inflation would leave the slope of IS curve same but will shift the IS schedule outwards. This change in goods market gets reflected in Aggregate Demand schedule as the aggregate demand schedule denotes those combinations of real income and real interest rate where both goods and money market are in equilibrium.

FIG 1: Shift in IS Schedule

Let Y represent natural log of real income.

α0 : measures exogenous components of aggregate demand

Any change in α0 which means a change in exogenous variables like change in fiscal policy would bring about changes in IS schedule and further affects AD curve .This implies a rise in government expenditure will shift IS schedule outwards without changing its slope.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

3.2 LM Curve: Money Market Equilibrium

LM curve on the other hand reflects money market equilibrium. It deals with asset markets at a point in time .In money market equilibrium, demand for money is given by Md = KY – hi

Rewriting the above equation in natural log form

m-p = α2lny – α3 i ……….Eq(4) where , m : natural log of nominal supply of money

p : natural log of price level

Opportunity cost of holding real cash balances depends on nominal rate of interest i Let µ be the rate of growth of nominal money and π be the rate of inflation . Cash balances grow at the rate of µ - π

As a result LM schedule can be written as

µ - π = ( m-p ) – ( m- p )-1 ………Eq (5)

( m- p )-1 : real money demand in the last period so that right hand side of above equation denotes growth of real balances .

Substituting real demand equation in the above equation we get

µ - π = α2lny – α3i – (m-p)-1……….Eq (6)

The money market would be in the steady state where the real cash balances are constant with slope equal to di/dy = α2/ α3 . Therefore the LM curve would be positively sloped.

All the points lying above the LM curve depict points of excess supply while points lying below the LM curve represent points of excess demand. All the points on the LM curve are the points where money market clears i.e money market is in the equilibrium.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

FIG 2: Money Market Equilibrium

In order to look for the equilibrium of both goods market and money market, we plot both IS and LM schedules. Based on the Keynesian assumption that interest rates respond to money market and national income responds to goods market , one can understand the mechanism through which the economy will settle down at the equilibrium where IS and LM schedules intersect at point E in Fig 3 .Point E provides the corresponding equilibrium level of interest rates i* and income Y* .

FIG 3: General Equilibrium

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

Keeping expected rate of inflation constant the following will happen

1. An expansionary Fiscal Policy with unchanged inflationary expectations, would shift IS schedule outwards to IS’, as a result both income and interest would rise.

This is depicted by a new equilibrium E'.

2. With expansionary Monetary Policy, LM would shift outwards to LM’, leading to fall in interest and rise in income. This is depicted by a new equilibrium E’’.

Both the above impacts are only explaining the way the policy instruments are incorporated in the model and provide a misleading picture if expected rate of inflation πe is kept constant while rate of inflation π , is changing .

3.3 Aggregate Demand Schedule

We can now use the IS-LM schedules to derive an aggregate demand ( AD ) schedule. To derive AD schedule we express IS curve as interest rates in terms of real income as given below and further substitute for i in the LM equation.

IS schedule: i =α0 – Y + πe α1

LM Schedule: µ - π = α2 lny – α3 i – ( m-p )-1

Using the i from the IS schedule as above and substituting in LM schedule and rearranging we get

π = µ + ( m-p )-1 - [α2 + α3]Yd + α3 α0 + α3 πe………Eq 8 α1 α1

Yd : It is defined as natural log of real income represented by lny .It is written as Yd to indicate

Aggregate Demand AD

From the above relationship AD schedule defines a negative relation between rate of inflation π and Yd ( aggregate demand ) .An increase in rate of inflation reduces the real quantity of money in economy creating excess demand in money market . This would

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

further make nominal interest rate to rise. With expected rate of inflation held constant, real interest rate also rises reducing investment and hence aggregate demand.

FIG 4: Aggregate Demand Function

Further, a change in Fiscal Policy will shift the AD schedule without changing its slope.

(m-p)-1 i.e the real money demand in the last period will keep changing so long as rate of growth of money and rate of inflation are not equal. An increase in expected rate of inflation πe will shift AD schedule by α3 times the change in πe. At any given level of income, this will also increase π by α3 . Therefore the expected inflation pursues actual inflation.

4. AS Schedule under Dynamics of Inflation

AD alone cannot determine the optimal values of rate of inflation π and income or output Y.

Aggregate supply schedule shows the combinations of rate of inflation π and income Y appropriate with production conditions in labor market. This involves two key components like an aggregate production function indicating total output produced by labor input. Secondly, it reflects labor market supply and demand conditions relating labor supply and demand to rate of inflation.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

4.1 Production Function

It is defined as the relationship between the output produced and the inputs used . A specific form of production function can be assumed as

Ys = β5 + β6l + β7k……….Eq 9

where Ys is the natural log of the real output supplied , it is equal to lnys, n is the natural log of total labor input and k is the natural log total capital input . β5 , β6 and β7 are defined as positive parameters . The above production function is in the form of Cobb – Douglas production function.

Considering the short – run equilibrium, the amount of capital is considered to be fixed or given exogenously, as a result production function can be written as

Ys = β8 + β6 l……….Eq 10

where β8 = β5 + β7 k . Therefore production function in the short – run is a relationship between Ys and n that is a relationship between output supplied and amount of labor supplied . This relationship is represented by a straight line with intercept β8 and slope β6.

An increase in capital stock will shift the production function β7 times the increase in capital.

FIG 5: Aggregate Supply Function

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

4.2 Labor Market

The labor market again has two components demand side and supply side .The demand for labor is inversely proportional to real wage rate. The labor demanded by firms depends negatively on real wage rate.

l = β9 – β10 ( w - p )………..Eq 11

where w – p is the natural log of real wage rate while β9 and β10 are defined as positive parameters the labor demand schedule is inversely related to real wages . Since wages and prices are rising continuously, the labor demand schedule can incorporate rates of changes in form of:

l - l-1 = β10 [ w – w-1 - ( p – p-1 ) ] ………Eq 12 The above can be written as

l = l-1 - β10 ( w – π ) ………..Eq 13 l-1 is the labor demand in the previous period and w = ( w – w-1 )

The amount of labor will rise only if wages are greater than rate of inflation i.e w > π .This imply that the real wages would be falling over time .When w = π , the real wage will be constant l=l-1

4.3 Aggregate Supply Schedule:

The aggregate supply schedule which is a relationship between rate of inflation and income can be obtained by taking the difference in one lag period of the production function in Eq 10.

Ys = Ys-1 + β6 ( l – l-1 ) ………...Eq 14

Substituting change in demand for labor in two periods in the above equation that is Eq 13 we obtain

Ys = Ys-1 – β6β10 ( w – π ) ……….Eq 15

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

The above equation indicates that an increase in inflation rate with given wage rate would reduce the real wages and increase demand for labor given by the parameter β10. This demand for labor would produce more output as measured by the parameter β6 , implying more production in the current period as compared to last year .

Ys>Ys-1

This results in positive relationship between rate of growth of real output Ys and rate of inflation π .The slope of the aggregate supply curve is given by 1/α4 , where α4 = β6β10

The labor market is considered to be in the equilibrium w = π , implying that the rate of growth of real wages is equal to rate of growth of prices , then amount of labor demand in this period is same as labor demanded in the last year . This further means that the output as given by Eq 10

Ys = β8 + β6 l is independent of π or w i.e. rate of inflation and rate of growth of real wages. Therefore aggregate supply curve is vertical as shown in the figure below.

FIG 6: Long-Run Aggregate Supply

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

5. Overall Equilibrium under Dynamics of Inflation

A complete overall Equilibrium is a state when the goods market is in equilibrium, money market is also in the equilibrium thus the aggregate demand derived from this situation intersects with the aggregate supply schedule to give the equilibrium level or combination of inflation rate and real income.

The complete macro-economic model can be represented by the following set of equations.

1. Goods market is in equilibrium as reflected by IS curve IS Schedule : Yd = α0 – α1 ( i - πe )

2. Money market equilibrium as reflected by LM curve .

LM Schedule: µ - π = α2 lny – α3 i – ( m-p )-1

3. Aggregate supply as given by

AS Schedule: Ys = Ye - α4 ( πe – π )

4. Equilibrium Conditions

Y = Ys = Yd ………Eq 16

The above overall system of equilibrium is depicted in the graph as below

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

FIG : 7 (a)Overall Equilibrium

FIG: 7 (b) Equilibrium through AD & AS

The intersection of IS – LM curve determine equilibrium level of income y and nominal interest rate i , this is shown in Fig 7 part a .On the other hand the final intersection of AD and AS schedules can easily be observed in Fig 7 part b . The equilibrium income so derived by the connection established between the two graphs implies that it is same.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

From IS schedule indicating goods market equilibrium we can read real interest rate. As a result we would be able to derive an overall equilibrium, from demand side which includes both goods market equilibrium and money market and from the supply side.

Thus, an intersection of aggregate demand AD curve and aggregate supply or AS curve at point E results in equilibrium values of 0 (inflation) and (real income) y0which reflects overall equilibrium of the economy.

6. Long – run Equilibrium under Dynamics of Inflation

In the long – run, an economy is left to itself would settle down with a specific combination of interest rate, real income and rate of inflation. . Both the schools of thought New classical and Keynesian agree on notion of equilibrium but differ in their opinion when it comes to the point of time taken in adjustment. Keynesians argue that it takes long time for adjustments and reach a long – run equilibrium therefore it is necessary intervene using fiscal and monetary policies.

While New Classical economists argue that the economy is quite adjusting and it will attain a long-run equilibrium. In the short – run, the economy attains an equilibrium given by the following equation.

y = yd = ys

Long run equilibrium is attained where , π = πe or y = ye

If there arises discrepancy between output demanded and supplied then an undesired movement in the inventories will take place bringing about further changes in the output and employment .This process is assumed to be completed every time there exists short – run equilibrium.

Labor market may not be in the equilibrium in the short – run but in the long –run, it definitely attains equilibrium .The equilibrium is attained at real wage constant where labor supply is equal to demand .When expectations of inflation are fulfilled, there is no incentive to make any further adjustments in the economy, the economy will attain a stationary state.

In the long –run equilibrium π = πe , stating that expected inflation is same as current inflation .AS schedule becomes vertical implying output is determined independent of demand as shown in Fig 8 .In the long –run , given y or the real income ,

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

IS schedule is given by : i = α0 – y + πe

α1

LM schedule is given by : µ = π = πe

From the above we get real money supply ( m-p ) and a real rate of interest is obtained

i - πe = ( α0 – ye ) / α1 ………..Eq 17

In the above equilibrium optimal levels of y,π, i are obtained sequentially .Therefore we observe that

1. Output is determined by AS schedule.

2. Inflation is equal to given rate of growth.

3. Money supply and interest is determined by location of IS curve.

4. AD curve intersects with AS curve at µ = π

As a result long –run equilibrium values of y, π , i are given by

Y = Yd = Ys = Ye……….Eq 18

π = µ = πe ………Eq 19

i = ( α0 – ye ) / α1 + µ ………...Eq 20

Fig 8 (a ) Long Run Equilibrium

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

Fig 8 (b) Long Run Aggregate Supply

It should be noticed that aggregate demand AD plays no role in determining income in the long –run as shown by part b of Fig 8. It further indicates that the stabilizing policies of demand management like fiscal or monetary policies play no role in determining output or income in long –run .This equilibrium condition can only be affected if there are shocks either from demand side or supply side .Let us now consider the situations of demand side shocks in the economy as well as supply side shocks.

7. Demand Side Shocks: Aggregate Demand or AD Shocks

A demand shock occurs when factors influence the aggregate demand curve .An expansionary Monetary Policy in IS –LM framework would lower nominal rate of interest and increase output, but this will not occur in the long –run equilibrium .An increase in rate of growth of money from µ0 to µ1 will shift LM curve outwards to LM' as shown in Fig. 9 but in long- run equilibrium the rate of inflation must equal higher money supply growth rate, µ1. Hence the IS curve must shift to intersect the new LM curve and attain Ye as the equilibrium. As a result interest rates should be higher by the amount of increase in rate of growth of money supply.

However we observe that IS curve with πe = 0 does not change, this would imply real interest rate will not change. The real money supply initially increased as µ1> π but Lm curve starts retreating as rate of inflation exceeds the rate of growth in money supply .Therefore the central banks started with larger growth of money supply but the economy ended with lower value of cash balances . This is the only real variable that has been affected by growth rate of money supply.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

FIG 9: Long Run Equilibrium: IS-LM

In the long – run equilibrium rate of inflation must be equal to higher money supply µ1 . IS curve would therefore shift since πe = µ1inorder to attain equilibrium at ye . Interest is higher by the amount of increase in rate of growth of money supply. The real money supply increases initially when since µ1> π but as LM curve starts shifting back as a result rate of inflation exceeds rate of growth of money supply .

Finally one can conclude that initially Central Bank started with larger growth of money but the economy ended with lower value of real cash balances.

8. Supply Side Shocks: Aggregate Supply or AS Shocks

A supply shock occurs when at every wage rate the supply of labor falls. This can occur due to the factors like increase in non- wage income or an increase in preference for leisure. This shock shifts AS schedule to AS ' that is towards left hand side .The output would consequently fall to y1e

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

Fig 9(b): Aggregate Supply Shock

FIG 10: Aggregate Demand Shift

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

If AD curve does not shift or reduces then this would lead to excess demand and further increasing the rate of inflation. However rate of money supply has not changed , rate of inflation must remain same as before and as a result AD will shift towards left to AD ' .This new aggregate demand curve AD ' intersects with AS ' schedule leading to new equilibrium E'' as shown in fig 10 . As a result of this AS shock, LM curve is also affected. The supply shock of reduced labor supply, output or income would be lower and this will result in fall in transactional demand for money .This means for some time rate of inflation remains higher than rate of growth of money in order to reduce the value of money .The final equilibrium E'is achieved, both and i-πe will be higher .This higher real interest rate will reduce some amount of aggregate demand resulting in lower equilibrium output.

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 34: Dynamics in AD -AS Model: Stability and Convergence to Long Run Steady State

9. Summary

1. AD schedule defines a negative relation between rate of inflation π and yd (aggregate demand) .An increase in rate of inflation reduces the real quantity of money in economy creating excess demand in money market. This would further make nominal interest rate to rise. With expected rate of inflation held constant, real interest rate also rises reducing investment and aggregate demand.

5. Aggregate supply schedule shows the combinations of rate of inflation π and income ys appropriate with production conditions in labor market. This involves two key components like an aggregate production function indicating total output produced by labor and capital input. Secondly, it reflects labor market supply and demand conditions relating labor supply and demand to rate of inflation.

6. An intersection of aggregate demand AD curve and aggregate supply or AS curve results in equilibrium values of (inflation) and (real income) y .which reflects overall equilibrium of the economy.

4 In the long – run, an economy is left to itself would settle down with a specific combination of interest rate, real income and rate of inflation. Both the schools of thoughts New classical and Keynesian agree on notion of equilibrium but differ in their opinion when it comes to the point of time taken in adjustment.

5 In the long –run equilibrium rate of inflation is equal to expected rate of inflation π = πe AS schedule becomes vertical implying output is determined independent of demand. AD plays no role in determining real income y .Therefore the demand management policies namely fiscal and monetary policies play no role in determining income in long – run.

6. Supply shock occurs when at every wage rate the supply of labor falls. This can occur due to the factors like increase in non- wage income or an increase in preference for leisure. This shock shifts AS schedule to AS ' that is towards left hand side .The output would consequently fall to y1e

References

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