Week 12 Lectures 23 & 24

The Economy in the Long Run: Economic Growth Reference: Bernanke, Olekalns and Frank – Chapters 11, 12 Key Issues

Economic Growth

Real GDP per capita

The production function – Cobb-Douglas

Growth accounting

2

Economic Growth Economic growth has delivered large increases in standard of living (at least for many people) Concerned with the long-run evolution of potential real output (y*) In AD-AS model changes in AD have no effect on long-run growth rate of GDP (need a different model)

3

Measuring Economic Growth Conventional to use real GDP per capita as a measure of a country’s living standards and stage of economic development

Real GDP per capita: 𝐺𝐷𝑃

𝑃𝑂𝑃=

𝑦

𝑃𝑂𝑃

We know from Week 1, that GDP is not a perfect measure of economic wellbeing; however it does seem to be positively related to life expectancy, infant health etc.

4

Real GDP per Capita for Australia (1973-2012)

0

10000

20000

30000

40000

50000

60000

70000Se

p-1

97

3

Oct

-19

74

No

v-1

97

5

De

c-1

97

6

Jan

-19

78

Feb

-19

79

Mar

-19

80

Ap

r-1

98

1

May

-19

82

Jun

-19

83

Jul-

19

84

Au

g-1

98

5

Sep

-19

86

Oct

-19

87

No

v-1

98

8

De

c-1

98

9

Jan

-19

91

Feb

-19

92

Mar

-19

93

Ap

r-1

99

4

May

-19

95

Jun

-19

96

Jul-

19

97

Au

g-1

99

8

Sep

-19

99

Oct

-20

00

No

v-2

00

1

De

c-2

00

2

Jan

-20

04

Feb

-20

05

Mar

-20

06

Ap

r-2

00

7

May

-20

08

Jun

-20

09

Jul-

20

10

Au

g-2

01

1

$A

, cvm

5

Growth Fact 1

There are large differences in the level of real GDP per capita across countries

$US (2005 prices)

US Japan China South Korea Chad

2010 41,376 31,453 7,746 26,614 1,332 Cross-country inequality in averages

6

Growth Fact 2

An important cause of this inequality is the fact that countries grow at different rates.

Average % per annum

US Japan China South Korea Chad 60-90 1.4 5.0 2.4 6.0 -1.7

7

Small Differences in Growth Rates Have Big Level Effects Relatively small differences in growth rates, maintained over many years, can make large differences in living standards. Country Growth Initial Income after x years Rate Income 5 25 35 A 1% 1000 1051 1284 1419 B 2% 1000 1105 1649 2013 B-A 0 54 365 594

8

Convergence and Catch-up Idea that relatively poor countries will have higher growth rates, than rich countries and eventually catch-up in terms of the level of per-capita GDP. If we look at the set of all countries in the world, then there is no evidence of convergence in per-capita GDP But, for some groups of countries there is evidence of convergence

9

Convergence in Rich Countries

JA, IT, GER, FR, UK, CA, AU, US

0

1

2

3

4

5

6

0 2000 4000 6000 8000 10000 12000 14000

An

nu

al g

row

th %

(1

95

0-2

00

0)

GDP-per capita in 1950 (1995 USD)

10

Decomposing Changes in GDP per Capita

Real GDP per capita: 𝐺𝐷𝑃

𝑃𝑂𝑃

Re-write real GDP per capita as:

POP

N

N

GDP

POP

GDP

where N is employed workers. The right-hand-side is:

Average labour productivity (GDP/N) (times)

Share of population in employment (N/POP)

11

Growth in Australian Real GDP per Capita Real GDP per capita can only grow if labour productivity grows, and/or the employment share grows From 1965 and 2006, real GDP per capita grew by 108%.

share of population working grew from 66% to 74%; as more women entered the workforce

average labour productivity increased by 87%

12

Influences on Labour Productivity (y/N) Physical Capital per worker Includes the stock of machines, tools, plant and equipment, buildings and structures Increases in quantity and quality of physical capital increase labour productivity But, there are usually diminishing marginal returns to capital.

13

Influences on Labour Productivity (y/N) Human Capital Refers to education and training, skills and talents of labour Can be formal education or schooling or on-the-job training Think of N as “basic” or unskilled labour input. Human capital accumulation raises “quality” of N

14

Influences on Labour Productivity (y/N) Land and Natural Resources Productive land, energy and mineral resources have potential to improve labour productivity e.g. Australia But,

Not essential to high labour productivity e.g Japan, Singapore

“Resource curse” Abundant natural resources impede economic growth e.g. African countries

15

Influences on Labour Productivity (y/N) Technology Stock of ideas and knowledge Development of new technologies is viewed as the primary source of economic growth Combination of: - Primary research and - Development (applied research)

16

Influences on Labour Productivity (y/N) Management and Entrepreneurs Development of new firms and the way firms are organised Bill Gates and Microsoft, e.g. Entrepreneur Just-in-time inventory, theory of management Internal to a firm

17

Influences on Labour Productivity (y/N) Political and Legal Environment External to the firm Includes the system of property rights, degree of political stability What are the incentives for people to produce goods or ideas?

18

Policies to Promote Economic Growth Are there policies that can increase a country’s rate of economic growth? - Support for (basic) human capital accumulation - Encourage saving and investment - Support for research and development (particularly

fundamental research) - Secure system of legal and property rights

19

Limits to Economic Growth Can economic growth continue indefinitely without depleting natural resources and causing massive change to the global environment? Are there limits to growth? Some possibilities:

Growth in real GDP can be in the form of new or higher quality products

Higher levels of real GDP per person are associated with lower levels of pollution

Market prices can adjust for shortages in resources

20

Aggregate Production Function Production functions will be familiar from microeconomics – where we can represent the output of an individual firm as a function of its inputs. No. of computers produced by a firm depends on:

Number of workers

Quantity of capital In macroeconomics we represent aggregate output (GDP) by a production function.

21

Aggregate Production Function Assume that level of real output (y) depends upon three things:

aggregate labour input (l)

aggregate capital stock (k)

the state of technology (A) Formally

𝑦 = 𝐴 × 𝑓(𝑘, 𝑙)

The exact form of the function (.)f is not specified

22

A Picture

Y 𝑦 = 𝐴 × 𝑓(𝑘, 𝑙)

k and A are fixed l (labour)

23

Another Picture

Y 𝑦 = 𝐴 × 𝑓(𝑘, 𝑙)

l and A are fixed k (capital)

24

Property 1: Constant Returns to Scale (CRS)

𝑦 = 𝐴 × 𝑓(𝑘, 𝑙) Suppose we simultaneously double (×2) both k and l, this leads to a doubling of output.

𝐴 × 𝑓(𝑘, 𝑙) Double

𝐴 × 𝑓(2𝑘, 2𝑙) CRS implies

2 × 𝐴 × 𝑓(𝑘, 𝑙) = 2𝑦

25

Which of the following production functions exhibits CRS?

(a) y = k + l (b) y = k×l (c) y = k/l

26

Which of the following production functions exhibits CRS?

(a) y = k + l 2k+2l = 2(k+l) = 2y Yes (b) y = k×l 2k×2l = 4×k×l = 4y No (c) y = k/l 2k/2l = k/l = y No

27

Property 2: Diminishing Marginal Product

),( lkfAy Suppose we change one input, but hold all of the others fixed. Marginal products of labour and capital are:

positive

0),(

lkfA

k

yMP kk 0),(

lkfA

l

yMP ll

28

Diminishing Marginal Product

diminishing

kMPk lMPl

29

Demand/Marginal Product for Labour

lMP

lMP l Marginal product curve gives demand for labour.

Labour will be employed up to point where: P

WMPl

30

Demand/Marginal Product for Capital

kMP

kMP k Marginal product curve gives demand for capital.

Capital will be employed up to point where: rMPk

31

Cobb-Douglas Production Function

),( lkfAy Specific Form

1lAky

32

Marginal Products

1lAky How does y change if we change l? Partial derivative

llAk

l

llAklAk

l

y 1)1()1()1( 1

l

yMP

l

yl )1(

Marginal product of labour

33

Marginal Products Marginal product of labour

ll APl

yMP )1()1(

Marginal product of capital

kl APk

yMP

Marginal product = Average Product × Exponent

34

A Result: Factor Incomes Exhaust Total Output Suppose labour and capital are paid their marginal products.

(Real) labour income = ll

ylMPl

P

Wl )1(

(Real) capital income = kk

ykMPkr k

labour income + capital income = y

yyy )1(

35

Contributions to Economic Growth Suppose we believe that the Cobb-Douglas function provides a good model for aggregate output in an economy.

1lAky It must be the case that all changes in Y can be accounted for by changes in labour, capital or technology. Growth accounting

36

A Result on Logarithms Suppose

axz

Take logs of both sides

xaz loglog Take the difference of both sides

xaz loglog

Note that z

zz

log

So x

xa

z

z

37

Decomposing Output Growth Production function for output in period (t):

1

tttt lkAy Use the above result to write

1

1

1

1

1

1

1

1 )1(

t

tt

t

tt

t

tt

t

tt

l

ll

k

kk

A

AA

y

yy

or

1111

)1(

t

t

t

t

t

t

t

t

l

l

k

k

A

A

y

y

38

Contributions to Output Growth

1111

)1(

t

t

t

t

t

t

t

t

l

l

k

k

A

A

y

y

In any period output growth is due to:

growth in technology; 1

t

t

A

A

growth in capital (weighted by ); 1

t

t

k

k

growth in labour (weighted by 1-); 1

)1(

t

t

l

l

39

Estimating the Growth Rate of Technology While we potentially have direct measures of output, labour and capital, this is not so for technology. However write

1111

)1(

t

t

t

t

t

t

t

t

l

l

k

k

y

y

A

A

Given data on the growth rates of ouput, labour and

capital and a value for , we can estimate the growth rate of technology (sometimes called TFP = Total Factor Productivity or MFP = Multi-Factor Productivity)

40

Estimating We showed earlier that

k

yMPk

Now re-arrange to get

y

kMPk

If capital is paid its marginal product

y

kr

so the left-hand side is just capital’s share of total output,

and we can use this figure as an estimate for .

41

Decomposition of Output Growth for Australia’s Market Sector Annual Growth Rates

Period y/y k/k + (1-) l/l A/A 1965-1970 5.1 4.0 1.1 1970-1980 2.9 1.4 1.6 1980-1990 3.2 2.4 0.8 1990-2000 3.2 1.7 1.5 2000-2005 2.8 2.2 0.6 1965-2005 3.3 2.1 1.2 Source: ABS

42

Decomposition of Output Growth for Australia’s Market Sector (Updated) Annual Growth Rates

Period y/y k/k + (1-) l/l A/A 1965-1970 5.1 3.9 1.2 1970-1980 3.1 1.6 1.5 1980-1990 3.1 2.4 0.7 1990-2000 3.4 2.1 1.3 2000-2010 3.3 3.1 0.1 1965-2010 3.4 2.4 1.0 Source: ABS

43

TFP (or MFP) Growth in Australia 1966-2011

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

Jan-1

96

6

Jan-1

96

8

Jan-1

97

0

Jan-1

97

2

Jan-1

97

4

Jan-1

97

6

Jan-1

97

8

Jan-1

98

0

Jan-1

98

2

Jan-1

98

4

Jan-1

98

6

Jan-1

98

8

Jan-1

99

0

Jan-1

99

2

Jan-1

99

4

Jan-1

99

6

Jan-1

99

8

Jan-2

00

0

Jan-2

00

2

Jan-2

00

4

Jan-2

00

6

Jan-2

00

8

Jan-2

01

0

% p

er

ann

um