Transcript A ∆k

Chapter5
Conditional Convergence and LongRun Economic Growth
Macroeconomics
Chapter 5
1
Conditional Convergence in Practice



Growth rate of capital per worker, ∆k/k:
 ∆k/k= ϕ[ k(0) , k*]
(−) (+)
y= A· f(k)
Growth rate of real GDP per worker is a
function of initial and steady-state real GDP
per worker
 ∆ y/y= ϕ[ y(0) , y*]
(−) (+)
Macroeconomics
Chapter 5
2
Conditional Convergence in Practice
Macroeconomics
Chapter 5
3
Conditional Convergence in Practice

Variables that influence y* that are held
constant.








A measure of the saving rate
The fertility rate
Subjective measures of maintenance of the rule
of law and democracy
The size of government
The extent of international openness, measured
by the volume of exports and imports
Changes in the terms of trade
Measures of investment in education and health
The average rate of inflation
Macroeconomics
Chapter 5
4
Conditional Convergence in Practice

Japan and Germany after 2nd world war.

East Asia countries

African Countries
Macroeconomics
Chapter 5
5
Long-Run Economic Growth

Solow model, the growth rate of
capital per worker, k, is given by
∆k/k= s· (y/k) − sδ − n
Macroeconomics
Chapter 5
6
Long-Run Economic Growth

A case in which capital broadly
defined to include human and
infrastructure capital is the only
factor input to production.


AK model
y= Ak
Macroeconomics
Chapter 5
7
Long-Run Economic Growth

k – capital per worker

y/k= A

∆k/k= sA− sδ − n
Macroeconomics
Chapter 5
8
Long-Run Economic Growth
Macroeconomics
Chapter 5
9
Long-Run Economic Growth

Conclusions


The long-run growth rate of capital per
worker, ∆k/k, is greater than zero and
equal to sA− sδ − n
Growth rates of capital and real GDP per
worker, ∆k/k and ∆y/y, do not change as
capital and real GDP per worker, k and y,
rise.

poor economies with low k and y do not
tend to grow faster than rich economies
Macroeconomics
Chapter 5
10
Long-Run Economic Growth

The regular process of improvement
in technology is called technological
progress.


exogenous technological progress the improvements in technology were not
explained within the model.
∆A/A= g
Macroeconomics
Chapter 5
11
Long-Run Economic Growth

Exogenous Technological Progress

∆Y/Y= ∆A/A+α·(∆K/K)+(1−α)·(∆L/ L)

Using ∆A/A= g and and ∆L/L = n

∆Y/Y= g+ α·(∆K/ K) + (1−α) · n

∆y/y= ∆Y/Y− ∆L/L = ∆Y/Y− n
Macroeconomics
Chapter 5
12
Long-Run Economic Growth

Exogenous Technological Progress

∆y/y= g+α·(∆K/K)+(1−α)·n − n
= g+α·(∆K/K − n)

∆ k/k= ∆ K/K − ∆L/L = ∆K/K − n


∆y/y= g+α·(∆k/k)
Macroeconomics
Chapter 5
13
Long-Run Economic Growth


Exogenous Technological Progress
∆k/k - in the Solow model


∆k/k= sA·f(k)/k− sδ − n
Growth rate of real GDP per worker
with technical progress

∆y/y= g+α·[ sA· f(k)/k− sδ−n]
Macroeconomics
Chapter 5
14
Long-Run Economic Growth


Steady state: all variables grow
at constant rates.
∆k/k is constant

∆k/k= s(y/k)− sδ − n

y/k is constant
Macroeconomics
Chapter 5
15
Long-Run Economic Growth

Exogenous Technological Progress





(∆y/y)* = (∆k/k)*
(∆y/y)* = g+ α·(∆k/k)*
(∆y/y)* = g+ α·(∆y/y)*
(∆y/y)* − α·(∆y/y)* = g
(1−α)·(∆y/y)* = g
Macroeconomics
Chapter 5
16
Long-Run Economic Growth

Exogenous Technological Progress

Steady-state growth rate with
technological progress


(∆y/y) * =
g/(1 − α)
Since 0 < α < 1 the steady-state growth
rate of real GDP per worker, (∆y/y)∗, is
greater than the rate of technological
progress, g.
Macroeconomics
Chapter 5
17
Long-Run Economic Growth

Exogenous Technological Progress



(∆k/k)* = (∆y/y)*
(∆k/k)* = g/(1−α)
Exogenous technological progress at
the rate ∆A/A= g leads to long-term
growth in real GDP and capital per
worker, k and y, at the rate g/(1−α)
Macroeconomics
Chapter 5
18
Long-Run Economic Growth

Exogenous Technological Progress






∆k/k= s·(y/k) − sδ − n
(∆k/k)* = g/(1 − α)
g/(1−α) = s·(y/ k)* − sδ − n
s·[(y/k)*−δ] = n+g/(1−α)
(y/k)*= δ+(1/s)·[n+g/(1−α)]
For Cobb-Douglas function
1
1

sA
k 

s


n

g
/(
1


)



Macroeconomics
Chapter 5
19
Long-Run Economic Growth
Macroeconomics
Chapter 5
20
Long-Run Economic Growth
Macroeconomics
Chapter 5
21
Long-Run Economic Growth
Macroeconomics
Chapter 5
22
Endogenous Growth Theory


Extend the model to explain why
technological progress occurs.
Most endogenous growth models focus
on investments in research and
development (R&D)
Macroeconomics
Chapter 5
23
Endogenous Growth Theory


The essential feature of knowledge or
technology:
non-rival good

MC is zero
Production function of A: ∆A =f(A,K,L)
Is the marginal product of A decreasing, increasing,
or constant?

Human capital
Macroeconomics
Chapter 5
24
Endogenous Growth Theory
The determinants of the allocation of
resources to R&D

Support for basic scientific research

Private incentives for R&D and innovation


Alternative opportunities for talented individuals:
rent-seeking
Learning-by-doing:
Macroeconomics
Chapter 5
25
Endogenous Growth Theory

Optimal intellectual property rights

The Diffusion of Technology


The imitation and adaptation of one country’s
technology by another country.
The rate of technological diffusion to a developing
country is high when the country trades a lot with
rich countries, has high education levels, and has
well functioning legal and political systems.
Macroeconomics
Chapter 5
26
Endogenous Growth Theory
Macroeconomics
Chapter 5
27
The basic R&D model
• Assumptions
1. The labor force is the single production
factor
2. Generalized Cobb-Douglas function
without capital
Y (t )  A(t )(1  aL ) L(t )
3. The fraction of the labor force is exogenous
Macroeconomics
Chapter 5
28
The basic R&D model
• The evolution function of labor
L (t )  nL(t ) n  0
where
dL (t )

L(t ) 
dt
• The evolution function of knowledge
A (t )  B[aL L(t )] A(t )
 1
 1
Macroeconomics
B0
 0
Chapter 5
 0
 0
29
The basic R&D model
• The dynamic of knowledge accumulation
A (t )
g A (t ) 
 B[aL L(t )] A(t ) 1
A(t )
g A (t )
 n  (  1) g A (t )
g A (t )
Macroeconomics
Chapter 5
30
The basic R&D model
• Case 1:   1
g *A 
Macroeconomics
n
1
Chapter 5
31
The basic R&D model
• Case 1:   1
g *A 
n
1
Interpretation:
• endogenous long run growth rate
1. positive link with population growth
2. a L has a level effect but not a growth effect
Macroeconomics
Chapter 5
32
The basic R&D model
• Case 2:   1
aL
ever-increasing growth
has a growth effect
g A
gA
Macroeconomics
Chapter 5
33
The basic R&D model
• Case 3:   1
linear growth model
aL
has a growth effect
g A
gA
Macroeconomics
Chapter 5
34