Econ1102 Week 4

7/29/2019 Econ1102 Week 4

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Week 4

Short-run Economic Fluctuations

Reference: Bernanke, Olekalns and Frank - Chapter 4

Key Issues

• What is a recession?

• Business cycle fluctuations

• Output gaps and cyclical unemployment• Natural rate of unemployment

• Okun’s law

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Business Cycles

Economies tend to experience periods of expansion and

contraction in the level of economic activity.

If we focus on GDP as a measure or economic activity

then:

• A contraction is a period during which the level of

GDP falls.

• An expansion is a period when GDP is rising.

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Peaks and Troughs

In moving between periods of expansion and contraction

the economy will experience peaks and troughs.

• A peak is the beginning of a contraction, the high

point of GDP prior to a downturn.

• A trough is the end of a contraction, the low point of

economic activity prior to a recovery.

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Stylised Representation of a Business Cycle

Level of GDP

expansion

contraction

Peak Trough Peak Time (quarters)

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Quarterly Real GDP for Australia 1970-2011

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Early 1980s Recession in Australia

108000

110000

112000

114000

116000

118000

120000

122000

M ar - 8 1

J un- 8 1

S e p- 8 1

D e c - 8 1

M ar - 8 2

J un- 8 2

S e p- 8 2

D e c - 8 2

M ar - 8 3

J un- 8 3

S e p- 8 3

D e c - 8 3

M ar - 8 4

R e a l G D P

Melbourne Institute dates peak (Nov 1981) and trough

(May 1983), see Table 4.1

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Classical Business Cycle in Australia

Classical cycle refers to peaks and troughs in the level of

GDP Recession Dates

Peak Trough No. of Months

April 1951 September 1952 17

December 1955 December 1957 24September 1960 September 1961 13

July 1974 October 1975 15

May 1976 November 1977 18 November 1981 May 1983 18

February 1990 October 1991 20

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Characteristics

• Recessions last 18 months on average

• Expansions last 60 months on average

“Rule of Thumb” for a recession is at least two quartersof negative economic growth.

This means the level of GDP has to fall for at least twoquarters.

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Australia GDP During the GFC

Negative growth rate Dec qtr. 2008 = -0.93 percent

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12000

12500

13000

13500

14000

14500

15000

2006‐I 2006‐II 2006‐III 2006‐

IV

2007‐I 2007‐II 2007‐III 2007‐

IV

2008‐I 2008‐II 2008‐III 2008‐

IV

2009‐I 2009‐II 2009‐III 2009‐

IV

2010‐I 2010‐II 2010‐III 2010‐

IV

US GDP (Nominal, billions of $) 2006 Q1 ‐ 2010 Q4

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Potential Output

Potential output (*

y ) is the level of GDP an economy can

produce when using its resources (labour and capital) atnormal rates.

Potential output is not the same as maximum output.

Potential output grows over time with growth in labour

and capital inputs and with growth in technology. e.g.

• An ageing workforce (-)

• Development and use of new technologies (+)

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Actual Output and Potential Output

Actual output (y) can vary (expand or contract) due to:

• changes in potential output (*

y ), and

• changes in the utilisation rate of labour and capital

For example in the short-run the utilisation rate of labour

and capital can be above (or below) the normal rate.

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Output Gap

Actual output does not always equal potential output.

Difference is called output gap.

Output gap = Actual GDP less Potential GDP

Output gap =* y y −

Positive output gap* y y > : called expansionary gap

Negative output gap* y y < : called contractionary gap

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Policymakers generally view both (persistent)contractionary and expansionary as problems.

• Contractionary gaps are associated with capital and

labour not being fully utilised (cost in terms of

forgone output).

• Expansionary gaps are associated with firms operating

above normal capacity and can lead them to raise prices (inflationary)

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Natural Rate of Unemployment

The unemployment rate (u ) tends to co-move with the

output gap in an economy.

• Contractionary gaps are associated with a high

unemployment rate

• Expansionary gaps are associated with a low

unemployment rate

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3 types of unemployment: frictional, structural & cyclical

Definition

Natural rate of unemployment (*u ) is the rate of

unemployment that prevails when cyclical

unemployment is zero.

or

Natural rate of unemployment = frictional + structural.

Cyclical unemployment =*uu −

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Relationships

Contractionary Gap

Output gap Cyclical unemployment

0*<− y y 0*

>− uu negative positive

Expansionary Gap

Output gap Cyclical unemployment0*

>− y y 0*<− uu

positive negative

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Okun’s Law

Quantitative Relationship

)(100 *

*

*

uu y

y y−−=

−

× β

An additional percentage point of cyclical unemploymentis associated with a β percentage point decline in the

output gap.

(NB. BOF (page 120) say increase not decline, but I

think this is a typo from the US edition of the book,

where they define the output gap as y*- y.)

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Magnitude of β

The size of β can differ across different countries;

• For the US β is estimated to be about 2.0

• For Australia β is estimated to be about 1.5

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Numerical Example (What is the change in output gap?)

Suppose that over 2009 the actual rate of unemployment

is forecast to rise from 5% to 7%.

Assume: %5*=u and β=1.5

)(100 *

*

*

uu y

y y−−=

−

× β

0.3)57(5.1100*

*

−=−−=

−

×

y

y y

percentage points

We have a negative output gap, which is equal to

3.0 percent of potential output (or 0.03× y*).

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Output gap and cyclical unemployment in Australia(2000-10)

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

M a r - 0

0

S e p - 0 0

M a r - 0

1

S e p - 0 1

M a r - 0

2

S e p - 0 2

M a r - 0 3

S e p - 0

3

M a r - 0

4

S e p - 0 4

M a r - 0 5

S e p - 0

5

M a r - 0

6

S e p - 0 6

M a r - 0

7

S e p - 0 7

M a r - 0

8

S e p - 0 8

M a r - 0 9

S e p - 0

9

M a r - 1

0

p e r c e n t

u-u* (y-y*)/y*

u* and y* are based on linear time trends

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Estimate of Okun’s Law for Australia (2000-2010)

y = -0.89x

R2 = 0.38

-1.5000

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

-1.00 -0.50 0.00 0.50 1.00 1.50

u-u*

( y -

y * ) / y *

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Spending and Output in the Short-Run

Reference: Bernanke, Olekalns and Frank - Chapter 5

Key Issues

• A model of output determination – Keynesian Model

• Planned verses actual expenditure• A consumption function

• Equilibrium output in the short-run

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Background

We have defined aggregate output or GDP and now we

want a model of how it is determined. E.g. Why is

GDP equal to 500 billion in a given period, rather than

550 billion?

Model is based on the ideas of John Maynard Keynes.

Classic book called The General Theory of Employment,

Interest and Money (1936)

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Keynesian Model

Key Assumption

Prices of goods are fixed (common to say sticky) in the

short-run

• Firms do not change prices in response to a changein demand for their product

• Instead they fix their price and then meet thedemand by varying their level of production

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In the short-run firms will:

• accommodate a cut in demand by reducing output

and employment, not by reducing prices.

• accommodate a rise in demand by increasing output

and employment, not by increasing prices.

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Assumptions (Micro-economic Foundations)

• Firms have some ability to set prices (not perfectly

competitive world)

• Firms face some cost to changing prices – these are

called menu costs

In the long-run:

• sustained changes in demand will eventually leadfirms to change their prices and cause production to

return to normal capacity.

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Non-Keynesian View of the World (Classical point of view)

• There will never be excess production because firms

will cut prices to sell it. (Perfect competition)

• There will never be persistent unemployment because

workers will cut their wages to keep and get jobs. (Market clear

• Fluctuations in demand will be accommodated by

flexible prices and wages without changes in output

and employment (Price mechanism)

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Aggregate Expenditure

Given the assumption that firms meet demand in the

Keynesian model, aggregate output will be determined

by the total level of desired spending.

Define: Planned aggregate expenditure (PAE) as the

total planned spending on final goods and services.

4 components of aggregate expenditure

AE = C + I + G + NX

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Planned verses Actual Expenditure

Suppose aggregate production (GDP) = 100

• We know from Week 1 that actual expenditure must

equal 100?

• However planned expenditure can differ from 100.

Why is actual expenditure not always equal to planned

expenditure?

(Unplanned) Inventories

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Reconciliation

Suppose PAE = 90, Y = 100

AE = PAE + ΔInventories = 100

100 = 90 + 10 = 100

Planned spending equals 90 but firms produced 100, theextra 10 units is assumed to be “purchased” by firms

and becomes an inventory of unsold goods.

The firms did not plan to “buy” the 10 units of goods

and so it is called unplanned inventory investment.

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Define

Actual Aggregate Expenditure (AE)

NX G I C AE +++=

Planned Aggregate Expenditure (PAE)

NX G I C PAE P

+++=

I = actual investment (includes unplanned inventoryinvestmentP

I = planned investment

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A Model of Consumption Expenditure

So far we have defined PAE, but now we need an

economic model of the determinants of PAE.

To begin we will focus on what determines consumption

expenditure.

Hypothesize that an important influence on consumption

spending by households is current disposable income.

Disposable income = income less (net) taxes

= Y – T

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Consumption Function

)( T Y cC C −+=

C is exogenous (or autonomous) consumption.• Factors (other than disposable income) that could

affect consumption, e.g. wealth, real interest rates

• The value of an exogenous variable is determined

outside of the model under consideration

)( T Y c − captures the effect of disposable income on

consumption (sometimes called induced consumption)c = marginal propensity to consume (parameter).

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Marginal Propensity to Consume (MPC)

MPC is the change in consumption when disposable

income changes by a dollar.

)( T Y cC C −+=

cT Y

C

MPC =

−Δ

Δ=

)( Assume: 0 < c < 1

A dollar increase in disposable income raisesconsumption by less than one dollar

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C

)( T Y cC C −+=

C slope = c

0 (Y-T)

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PAE and Output

Given our definition of PAE and model of consumption

expenditure we can re-write PAE as follows

NX G I C PAE P+++= )( T Y cC C −+=

NX G I T Y cC PAE P +++−+= )( cY NX G I cT C PAE

P++++−= ][

• The first terms is independent of output and is called

exogenous expenditure• The second term is called induced expenditure since

it depends on output

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Short-Run Equilibrium Output

We define equilibrium as being when firms produce a

level of output that equals planned aggregate expenditure

PAE Y =

Using the equation for PAE,

cY NX G I cT C PAE P++++−= ][

and the above definition of equilibrium it is

straightforward to solve for equilibrium output.

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Equilibrium OutputPAE Y =

cY NX G I cT C PAE P

++++−= ][ Substituting

cY NX G I cT C Y P

++++−= ][ Collect terms in Y

][)1( NX G I cT C cY P

+++−=− ][

)1(

1 NX G I cT C

cY

Pe+++−

−=

eY is short-run equilibrium output

Econ1102 Week 4

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