professor k.d. hoover, econ 210d topic4 spring 2015 1 econ 210d intermediate macroeconomics spring...

Professor K.D. Hoover, Econ 210D Topic4 Spring 2015 1

Econ 210D Intermediate Macroeconomics

Spring 2015

Professor Kevin D. Hoover

Topic 4Long-term Economic Growth


Illustrative Growth Questions

Why does GDP rise over time? Why is GDP and GDP per capita higher

in some countries than others How is GDP affected by increases in

population from immigration or from population growth?

How are GDP and labor related: how much does unemployment fall in the slump?


Aggregate Supply and Demand

Y = C + I + G + NX

Production = Expenditure

Aggregate Supply = Aggregate Demand


Production Function – 1

y = f(k, l)

o y = outputo k = capital service inputo l = labor service input


The Production Function – 2


Properties of Production Functions – 1 the production function: y = f(k, l) no free lunch : y = f(0, l) = 0; y = f(k,

0) = 0 effort pays:

dy/dk = fk(k, l) > 0; dy/dl = fl(k, l) > 0


Properties of Production Functions – 2 diminishing returns to a factor of

production:o d2y/dk2 = fkk(k, l) < 0

o d2y/dl2 = fll(k, l) < 0

an increase in one factor raises the productivity of the other: d2y/dkdl = fkl(k, l) > 0;


Choosing the Technological Mix Profits = Revenue – Cost Add labor until marginal unit (l) leads

to more costs (wl) than revenues (py) Add capital until marginal unit (k)

leads to more costs (k) than revenues (py)

Profit maximization: Marginal Cost = Marginal

Revenue


Rules of Profit Maximization

Add labor until:o marginal product of labor (mpl) = real wageo mpl = y/l = w/p

Add capital until:o marginal product of capital (mpk) =

(implicit) real rental rateo mpk = y/k = /p


Aggregate Production Function Y = F(L, K)

Cobb-Douglas Production Function:

Y = ALK1-


Creators of the Cobb-Douglas Production Function

Paul H. Douglas (1892-1976)o labor economisto later U.S. Senator

from Illinois Charles W. Cobb

o mathematician, Amherst College

Created production function in 1928


Properties of the Cobb-Douglas Production Function Y = ALK1-

mpL = mpK = (1- Diminishing returns to capital and

labor Constant returns to scale Labor share in GDP = Capital share in GDP = 1–


Why is the Cobb-Douglas a Good Production Function? – 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006

Per

cent

age

of G

DP

Figure 9.10 U.S. Labor and Capital Shares

Labor Share

Capital Share

mean = 0.67

mean = 0.33

The labor share in GDP is the proportion of GDP earned directly or indirectly by labor. The remainder is earned by capital. Both shares vary from year to year around a nearly constant mean. The mean labor share is used as an estimate of , a key parameter of the Cobb-Douglas production function.


U.S. Aggregate Production Function, 2008

63.9)10173,40($)hours/yearworker10011,263(

10312,13$33.0967.06

9

10808

0808

KL

YA

33.067.063.9 KLY

933.0967.0608 10756,13$)10173,40($)hours/yearworker10162,276(63.9 Y

108080808 KLAY


Concepts of Productivity

Labor productivity: = Y/L

Capital productivity: = Y/K

Total-factor productivity: 1A


Short-run Production Function - Labor Figure 9.15

Short-run Adjustment to a Fall in Aggregate Demand: Labor Productivity and Unemployment

Y

L L2

* 1

Y0

Y1

1),( KALKLF

L1 LF

2

A

B C

D

labor hoarding or

unemployment


Short-run Production Function - Capital Figure 9.16

Short-run Adjustment to a Fall in Aggregate Demand: Capital Productivity and Capacity Utilization

Y

L * 1

Y0

Y1

1),( KLAKLF

K1 K

A

B

unused capacity


Measures of Capacity - Labor

LF = labor force EMP = employment rate = L/LF U = unemployment rate =

EMPLF

L

LF

LLF

11


Measures of Capacity - Capital CU= capacity utilization rate

= indexcapacity

productionindustrialofindex


Potential Output

potential output

scaled output

scaled output

1KLFAY pot

potY

YY ~

11 ~~)/(

~KLCULFLY


80.0

82.0

84.0

86.0

88.0

90.0

92.0

94.0

96.0

98.0

100.0

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008

Fra

ctio

n of

Pot

enti

al O

utpu

t (p

erce

nt)

1992

Con

stan

t D

olla

rs (

billi

ons)

Figure 9.18Output, Potential Output, and Scaled Output

Shaded areas indicate recessions.

Scaled Output(right axis)

Potential GDP(left axis)

Real GDP(left axis)

Scaled output is the ratio of real GDP to potential GDP. Scaled output is a leading indicator of the business cycle at the peak and a coincident indicator at the trough.


Growth Over Time

U.S. GNP per capita:o 1790: $500o 2000: $40,000o Increase: 80 times

Chad GDP per capita, 2000: $500


The Power of Growth Rates

$1 at 1.5%/year for 2000 years = $8.5 billion o < less than U.S. GDP

$1 at 2.0%/year for 2000 years = $158,614 trilliono 2,638 times world GDP

2.91%/year = best U.S. 30-year average growth (1940-1970): 1790-1990 at that rate = $171,600 per capitao 6 times actual U.S. per capita income 1990


Divergence of Growth Experience

1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

GD

P p

er

ca

pit

a (

19

90

US

do

lla

rs)

Figure 10.2World Growth Since the Industrial Revolution

250

500

1,000

5,000

10,000

15,000

20,000log scale Western Offshoots

Western Europe

Southern Europe

Latin America

Eastern Europe Asia and Oceania

Africa

Africa (56 countries); Asia and Oceana (56 countries) Eastern Europe (9 countries); Latin America (44 countries); Southern Europe (7 countries); Western Europe (23 countries); Western Offshoots (Australia, Canada, New Zealand, and the United States).


Production Functions: 1948 & 1998 1948: Y = ALK1- = 4.60L0.69K0.31

2008: Y = ALK1- = 9.63L0.69K0.31


Production Functions: Counterfactual Interpretation – 1 Figure 10.3

A Cobb-Douglas Production Function for the United States, 2008

(A) Labor Production Function

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 100 200 300 400

(B) Capital Production Function

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 10,000 20,000 30,000 40,000 50,000 60,000

Bil

lion

s 20

05 C

onst

ant

Dol

lars

33.01367.00 )1002.4(63.9),( LKLF

Actual production point: Y =$0513,312 billion

L=263 million worker-hours

Labor (worker-hours per year (millions) Capital (billions 2005 constant dollars)

Actual production point: Y=$0513,312 billion K=$0540,173 billion

33.067.0110 )1063.2(63.9),( KKLF

The labor production function shows the actual levels of GDP and labor in the United States in 2008 and what different levels of labor could have produced with the actual 2008 capital stock.

The capital production function shows the actual levels of GDP and capital in the United States in 2008 and what different levels of capital could have produced with the labor actually available in 2008.

Source: Bureau of Economic Analysis and author’s calculations.


Production Functions: Counterfactual Interpretation – 2 Figure 10.5

The Sources of Economic Growth

(A) Labor Production Function

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 50,000 100,000 150,000 200,000 250,000 300,000

(B) Capital Production Function

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 10,000 20,000 30,000 40,000

Using the technology and capital of 2008

Using the technology of 1948 and capital of 2008

Using the technology and capital of 1948

Using the technology and labor of 2008

Using the technology of 1948 and labor of 2008

Using the technology and labor of 1948

A A

C

B

D D

C

How much growth in GDP is due to growth in the factors of production and how much to changes in technology? The lower curves represent the actual production functions of 1948; while the upper curves represent the actual production of 2008 The middle two curves in each panel are drawn with the technology (A) of 1948. The movement from point A to point B shows how much additional GDP is due to the increase in labor (L); from point B to C, the additional amount due to capital. The distance between points C and D shows how much technology has added to GDP once changes in labor and capital are accounted for.

B

Y

L

Y

K

Worker-hours per Year (millions) Constant 2005 Dollars (billions)

Con

stan

t 2

005

Dol

lars

(bi

llio

ns)


Thought Experiment – 1

What would GDP be in 1948 if ceteris paribus 1998 labor were available:

bil$13,3121998 actualbil.276,3$

).bil382,5($)hours

workermil.011,263(60.4 33.067.0

33.048

67.0084848

KLAY



What would GDP be in 1948 if ceteris paribus 2008 capital were available:

homework problem



What would GDP be in 1948 if ceteris paribus 1998 labor were available:

o difference = $13,312 – $6.360 = $6,952 bil. (effect of A)

bil$13,3121998 actualbil.360,6$

).bil173,40($)hours

workermil.011,263(60.4 33.067.0

33.008

67.0084848

KLAY


Algebra of Growth Rates

if z = xy

if z = x/y

if z = xy

if z = x1/y

or if

yxz ˆˆˆ

yxz ˆˆˆ

yxz ˆˆ

yxz /ˆˆ

yxz /ˆˆ y xz


Growth Accounting – 1

Y = ALK 1-

KLAY ˆ)1(ˆˆˆ

Y

K

Y

L

Y

Aˆ

ˆ)1(ˆ

ˆ

ˆ

ˆ1


Growth Accounting – 2

Percentage of Growth Attributable to:

Labor:

Capital:

Total Factor Productivity:

Y

Lˆ

ˆ

Y

Kˆ

ˆ)1(

Y

Aˆ

ˆ


Sources of U.S. Growth

Table 10.3 Data for Growth Accounting

Variable 1948 2008 Rate of Growth:

1948-2008 Y (billions 2005 constant dollars per year) 1,854 13,312 3.34% A 4.60 9.63 1.24% L (millions of worker-hours per year) 112,356 263,011 1.43% K (billions 2005 constant dollars) 5,382 40,173 3.41% 0.67

Source: Bureau of Economic Analysis and author’s calculations. Note: Growth rates are calculated as average continuously compounded annual rates (see the

Guide, section G.10.1).

Table 10.4 Accounting for Real GDP Growth, 1948-2008

Contributing Factor Contribution to GDP Growth Percentage

Points Fraction of Overall

Growth Rate (percent) Technological change 1.24 37 Growth in labor inputs 0.96 29 Growth in capital inputs 1.12 34 Total 3.341 100

Source: Table 10.3 and author’s calculations. 1Column does not sum to total because of rounding.


The Growth Process: Rising Total Factor Productivity Product Innovation

Process Innovation

Research and Development


Product Innovation – 1


Product Innovation – 2


Product Innovation – 3: recorded music



?


Process Innovation - 1


Process Innovation - 2


Research and Development -1


The Growth Process: Labor

Law of motion for labor:

Lt = (1 + n)Lt-1

Solution:

Lt = L0(1 + n)t

o n = growth rate of labor


The Growth Process: Capital – 1 Law of motion:

Kt = Kt-1 + It-1 – depreciationt-1

o It = gross investment

o It – depreciationt = net investment

Kt = Kt – Kt-1 = It-1 – depreciationt-1

= net investmentt-1


The Growth Process: Capital – 2 Kt = net investmentt-1

1

1

1

ˆ

t

t

t

t

K

Inet

K

KK

111

1

1

1

1

1

1

1ˆ

ttt

t

t

t

t

t

t

t shareinvestmentnetY

Inet

K

Y

K

Inet

Y

YK


Balanced and Unbalanced Growth capital widening = more workers with

same K/L capital deepening = more capital per

worker (K/L ) balanced growth = all inputs and

outputs grow at same rate – i.e., capital widening, no capital deepening

unbalanced growth = inputs and output grow at different rates – capital widening and deepening


Balanced Growth


Unbalanced Growth


Technical Progress

Recall:

labor-augmenting technical progress = as if more workers ( )

capital-augmenting technical progress = as if more capital ( )

1A


Balanced Growth with Technical Progress Replace with

Replace with

Balanced growth condition with technical progress:

=

nL ˆ LL ˆˆ)(^

K KK ˆˆ)( ^

Lˆ Kˆ


Balanced Growth for the U.S.

and

Therefore, =

= speed limit for the economy

0ˆ 0ˆ

n K

n


END of Topic 4

Next Topic: 5. Labor and Unemployment

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