Equilibrium Output in the Short-Run

1
Equilibrium Output in the Short-Run

• Antu Panini Murshid

2
Todays Agenda

• The components and determinants of aggregate
  demand in an open economy
• Goods market equilibrium
• Asset market equilibrium
• Short run equilibrium in an open economy

3
Components of Aggregate Demand

• It is useful to decompose aggregate demand into
  four components
• Consumption spending
• Planned investment
• Government spending
• Net exports

4
Determinants of Consumption

• Disposable income
• Income minus taxes (Y-T)
• Permanent income
• Real wealth
• Real interest rate

Typically we will assume that taxes are lump sum
5
Consumption Function

• Since consumption is a function of disposable
  income we can write C C(Yd,a), where Yd Y-T,
  and a denotes all other arguments
• A linear consumption function would take the
  following form
• C a bYd

Autonomous consumption
Marginal propensity to consume
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Autonomous Consumption

• Autonomous consumption is that part of
  consumption which is not effected by disposable
  income
• These are expenditures that would occur even if
  household disposable income was zero
• What determines autonomous consumption?
• Other determinants of consumption, e.g. wealth,
  real interest rates, etc.

7
Marginal Propensity to Consume

• The proportion of each additional dollar of
  income that is used for consumption expenditures
• The marginal propensity to consume is just the
  slope of the consumption function

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Marginal Propensity to Consume

• Normally we assume that the MPC is less than one
• Why is this a reasonable assumption?
• Because some proportion of each additional dollar
  of income is devoted to savings

9
A Linear Consumption Function Against Yd

• Autonomous consumption is just the intercept
• Note the slope of the consumption function is
  less than one

consumption
450
c a b(Y-T)

• Note also that the consumption function is drawn
  against disposable income
• What would the consumption function look like,
  if we drew it against income?

autonomous consumption
slope marginal propensity to Consume (b)
a
disposable income (Y-T)
10
A Linear Consumption Function Against Y

• If we draw consumption against income, the
  intercept becomes (a-bT1)

consumption
450
c a b(Y-T1)
c a b(Y-T2)

• What happens to the consumption function if we
  increase taxes?
• The consumption function shifts downward

a-bT1
a-bT2
income (Y)
11
Determinants of Planned Investment

• Real interest rate (cost of borrowing)
• Rate of return on capital (marginal product of
  capital)
• Risk and future expectations

12
A Linear Investment Schedule
real interest rate
2planned investment increases
5
4
1. As the real interest rate falls
Planned investment
Investment
1,000
1,500
13
Shifts in the Investment Schedule
An increase in the return to investments shifts
the schedule to the right
real interest rate
A decline in the riskiness of investments has the
same effect
5
I2
I1
1,500
Investment
1,000
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Adding Up Consumption and Investment
450
consumption

• First draw the consumption function
• Now add investment

C I1 a b(Y-T) I1
C a b(Y-T)
Investment
a-bT
income (Y)
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Impact of an Increase in Investment

• A reduction in the interest rate, change in
  expectations, etc. will raise investment and
  shift CI schedule up

450
consumption
C I2
C I1
income (Y)
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Assumption Planned Investment is Exogenous

• While there are several determinants of planned
  investment, let us assume that it is exogenously
  given
• This will make life simpler and let us focus on
  other important channels by which income is
  affected in an open economy

17
Assumption Government Savings

• As with planned investment, let us assume that
  government spending is exogenously given
• Again this is a simplification that lets us focus
  on the important open-economy channels that
  impact on income

18
What About Net Exports?

• One component of expenditure that we cannot
  simply treat as exogenous is net exports
• Net exports have an important influence on
  aggregate demand in open economies and one that
  distinguishes it from closed economies
• Below we consider the determinants of exports and
  imports separately

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Determinants of Exports

• World income
• An increase in world income, increases the demand
  for exports
• Real exchange rates
• A depreciation in the real exchange rate makes
  domestically produced goods more competitive and
  so increases the demand for our exports

20
Determinants of Imports

• Domestic income
• An increase in domestic disposable income will
  increase the demand for imports
• Real exchange rates
• A depreciation in the real exchange rate will
  have an ambiguous effect on imports
• Why?

21
Real Exchange Rate and Imports

• There are two effects that a real exchange rate
  depreciation will have
• Lower the volume of imports
• Increase the price of imports
• There are therefore opposing forces at work since
  the total value of imports is just
• Value of imports price volume

?
22
The Marshall-Lerner Condition

• So what will be the overall effect of a real
  exchange rate depreciation on net exports?
• The Marshall-Lerner condition says that a real
  exchange rate depreciation will improve the trade
  balance if ?x?Mgt1, where ?X is the elasticity
  of demand for exports and ?M is the elasticity of
  demand for imports
• Can you prove this (assume NX 0)?

23
Intuition Behind the M-L Condition Elasticity of
Imports
price of imports

• If demand is inelastic a reduction an exchange
  rate depreciation and a rise in the price of
  imports has little impact on quantity of imports
  demanded, hence value of imports rises
• If demand is elastic the same change in price has
  a much larger impact on volumes and so imports
  fall

Increase in imports
Decrease in imports
p2
p1
D2
D1
q1
q2
Q2
quantity of exports
Q1
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Intuition Behind the M-L Condition Elasticity of
Exports
foreign price of exports

• When export-demand is elastic an exchange rate
  depreciation which lowers the foreign price of
  exports, has a large impact on the quantity
  demanded
• This implies that the value of exports
  necessarily rises significantly since the
  domestic price received for exports has not
  changed

Large increase in exports demand
pf1
pf2
D
Q1
Q2
quantity of exports
25
Does the Marshall-Lerner Condition Hold? The
J-Curve

• In our analysis, we will assume that the
  Marshall-Lerner condition holds
• Is this a good assumption?
• Yes and no
• Often the initial effect of a depreciation is to
  cause the trade deficit to increase, over time
  however the deficit improves. This is known as
  the J-curve effect

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Reasons for the J-Curve

• Import and export volumes are slow to adjust
  after exchange rate changes
• Most import and export orders are placed months
  in advance, hence the primary effect of a
  depreciation is to raise the value of the
  pre-contracted level of imports

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Summarizing the Determinants of AD Income

• ? disposable income ?
• ? consumption ? imports
• Net effect ? aggregate demand
• Why? Why does the increase in import demands not
  dominate the increase in consumption

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Summarizing the Determinants of AD World Income

• ? world income ?
• ? exports
• Net effect ? aggregate demand

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Summarizing the Determinants of AD Real Exchange
Rate

• We will assume that the Marshall-Lerner condition
  holds
• ? ? (real ex depreciation) ?
• Note ? ? (real ex depreciation) implies either
• ? e (nominal exchange rate)
• ? Pf (foreign price level)
• ? P (domestic price level)
• ? exports ? imports
• Net effect ? aggregate demand

All of these factors will increase ?
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Summarizing the Determinants of AD Other
Determinants

• There are several other determinants of AD
• real interest rate, productivity of capital,
  future expectations, etc.
• However in the analysis below we focus on the
  impact of disposable income and the real exchange
  rate on consumption and net exports, all other
  variables are treated as exogenous

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Equation For Aggregate Demand

• AD C(Yd) I G NX(?,Yd,Y)

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Aggregate Demand Function
450
consumption
C I G
Government spending
C I G NXaggregate expenditures
C I
Net exports
Cf(Y)

• Consumption
• Investment
• Government spending
• Net exports
• Planned aggregate expenditures
• Note in this example net exports are negative

Investment
income (Y)
33
Slope of Aggregate Demand Function in Open Economy

• Note that the slope of the aggregate demand
  function is less than the slope of the domestic
  absorption function. Why?
• Because imports increase with income
• The proportion of each additional dollar of
  household income that is used for imports is
  called the marginal propensity to import (MPM)
• The slope of the aggregate demand function is
  equal to MPC-MPM

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Illustrating Increases in Aggregate Demand
450

• The following factors will increase aggregate
  demand
• ? taxes, ? government spending, ? planned
  investment, ? ?, ? world incomes, ? autonomous
  consumption a shift in preferences for domestic
  goods over foreign goods

aggregate expenditures
AD2
AD1
? AD
income (Y)
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Quick Quiz

• Can you illustrate the impact of the following on
  aggregate demand
• An exchange rate depreciation
• A decline in the foreign price level
• A fall in world real income
• A rise in lump sum taxes

36
Goods Market Equilibrium

• What is the equilibrium level of income in an
  economy?
• We would like to have some notion of equilibrium
  where the demand for goods and services is equal
  to the supply. Therefore we define an equilibrium
  in the goods markets as follows
• Total Output Produced Planned AE (AD)
• Y C I G NX

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Goods Market Equilibrium Graphical Illustration
450
aggregate expenditures
C I G NXaggregate expenditures
Cf(Y)

• At every point on the 450 line, income
  aggregate expenditures
• Hence the equilibrium is where the planned
  aggregate expenditures intersects the 450 line

income (Y)
Y
38
Impact of an Increase in Net Exports on
Equilibrium Output
450

• Initially suppose equilibrium income is Y1
• Now suppose net exports rise (for whatever
  reason), then AD rises and so too does
  equilibrium income

aggregate expenditures
AD2
AD1
? AD
income (Y)
Y1
Y2
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Aggregate Demand, Output and Exchange Rates

• Is aggregate demand and income related to the
  exchange rate?
• Clearly yes. What is this relationship?
• If the M-L condition holds we know that an
  increase in ? increases AD
• Hence all else equal an increase in the nominal
  exchange rate should imply an increase in AD.
  This will imply an increase in equilibrium
  income/output

40
Recap on the Intuition

• When the nominal exchange rate rises
  (depreciates), all else equal
• Exports become more competitive and thus exports
  increase
• If the M-L condition holds imports will decline
  because imports are now more expensive
• Hence AD increases
• This in turn implies an increase in income

41
The DD-Schedule

• The DD-schedule illustrates the relationship
  between the nominal exchange rate and the level
  of income or output such that the goods market is
  in equilibrium
• The DD-schedule must be positively sloped since
  an increase in the nominal exchange rate implies
  an increase in equilibrium output

42
Deriving the DD Schedule
AD2
Aggregate expenditures

• Equilibrium income is Y1 suppose the exchange
  rate is e1
• Now suppose the exchange rate rises to e2
• AD ? and Y ? to Y2
• Hence the new exchange rate-income combination is
  e2,Y2
• The locus of such points traces out the DD-curve

AD1
income
Exchange rate
Y1
Y2
DD
e2
e1
income
Y1
Y2
43
Shifts in the DD-Schedule

• What would shift the DD-schedule?
• Anything other than a change in the nominal
  exchange rate, which affects the equilibrium
  level of income
• Examples
• A change in fiscal policy
• A change in planned investment
• A change in the domestic or foreign price level
• A change in autonomous consumption
• A change in the preferences for domestic goods
  over foreign goods

44
Quick Quiz

• Which way will the DD-curve shift if
• planned investment rises
• domestic price level rises
• consumers express an increased preference for
  foreign goods

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Asset Markets

• So far our analysis has focused on the goods
  market. Now we will introduce asset markets
• We will assume that there are only two markets
• Money market
• Foreign exchange market

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Asset Markets Equilibrium

• The money market is in equilibrium if
• demand for money supply of money
• PL(y,i) Ms
• The foreign-exchange market is in equilibrium if
• domestic interest rate
• expected return on foreign assets
• i if E(?e)

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What is Determined in Asset Markets?

• What is determined in the money market?
• Equilibrium interest rate
• What is determined in the foreign exchange
  market?
• Equilibrium exchange rate

48
Exchange Rate and the Interest Rate
Money supply M1s/P

• We have already discussed the relationship
  between the exchange rate and the interest rate,
  but lets take another look
• First draw the money market graph
• The equilibrium interest rate is 10

Interest rate
Equilibrium interest rate
i110
Money demand L(i,y)
real money balances
49
Exchange Rate and the Interest Rate
Money supply M1s/P

• Now lets make everything disappear.

Interest rate
Equilibrium interest rate
i110
Money demand L(i,y)
real money balances
50
Exchange Rate and the Interest Rate

• and reappear but rotated clockwise by 90 degrees

i110
Interest rate
Money supply M1s/P
Equilibrium interest rate
real money balances
Money demand L(i,y)
51
Exchange Rate and the Interest Rate
return on assets
/

• Now lets add the foreign exchange market graph

Expected return on assets
e11.00
i110
Interest rate
Money supply M1s/P
Equilibrium interest rate
real money balances
Money demand L(i,y)
52
Implications of an Increase in Income for Asset
Markets

• What are the implications of an increase in
  income for the interest rate and exchange rate
• ?Y ? ?Md ? ?i ? ?e
• Hence an increase in income will cause the
  currency to appreciate by causing the interest
  rate to rise

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Graphical Illustration
equilibrium exchange rate
/
e1
and a new equilibrium exchange rate
e2
i2
i1
Interest rate
M1/P
equilibrium interest rate
demand for money rises and we have a new
equilibrium interest rate
real money balances
L(i,y2)
L(i,y1)
54
The AA-Schedule

• The AA-schedule illustrates the relationship
  between the nominal exchange rate and level of
  income or output such that asset markets are in
  equilibrium
• The AA-schedule must be negatively sloped since
  an increase in income will cause the interest
  rate to rise, which will in turn cause the
  currency to appreciate in value

55
Graphical Illustration
/
/
e1
i1
i
income
y1
Ms/P

• Suppose equilibrium income is Y1
• Corresponding money demand function is L(I,y1)
• The corresponding interest rate and exchange rate
  is i1, e1 respectively

real money balances
L(i,y2)
L(i,y1)
56
Graphical Illustration
/
/
e1
e2
i2
i1
i
income
y1
y2
Ms/P

• This gives us the first point on the AA-schedule
  (e1,y1)
• Now suppose income ? to y2 ? money demand ? as
  does the interest rate and the exchange rate falls

real money balances
L(i,y2)
L(i,y1)
57
Graphical Illustration
/
/
e1
e2
i2
i1
AA
i
income
y1
y2
Ms/P

• Hence the new exchange rate-income combination is
  e2,y2
• The locus of all such points traces out the
  AA-curve

real money balances
L(i,y2)
L(i,y1)
58
Shifts in the AA-Schedule

• What would shift the AA-schedule?
• Any change other than a change in income, which
  affects the exchange rate
• Examples
• A change in the nominal money supply
• A change in the price level
• A change in future expectations regarding the
  exchange rate
• A change in the foreign interest rate

59
Quick Quiz

• Which way will the AA-curve shift if
• real money supply increases
• expected future exchange rate falls
• the foreign interest rate falls

60
Asset Markets ? Goods Markets

• It should be clear that the level of income in an
  economy is determined by developments in both
  asset markets and goods markets?
• Asset markets determine important
  variablesinterest rate and exchange ratethat
  impact on the goods market
• At the same time developments in the goods market
  can affect asset markets

61
Equilibrium

• An economy is only in equilibrium if it is on
  both the AA- and DD-curves
• If for instance an increase in e forced the
  economy off the DD-curve then income would have
  to rise to bring the goods market back to
  equilibrium as net exports increased
• If on the other hand the economy were forced off
  the AA-curve by an increase in output then the
  exchange rate would necessarily have to fall as
  interest rates rose
• It is to be expected that asset markets would
  clear more quickly than goods markets

62
Equilibrium Graphical Illustration

• At point 1 the exchange rate is too high and
  UCIP does not hold, hence the exchange rate
  appreciates immediately to return the foreign
  exchange market to equilibrium at point 2
• At point 2, the goods market is not in
  equilibrium, so output increases
• As output increases the interest rate rises and
  the exchange rate falls and we move along the AA
  schedule to point 3

exchange rate
1
e1
DD
2
3equilibrium
AA
income (Y)
Y
Y1