Transcript Lecture Notes 7

Chapter 7
Income Disparity
Among Countries
and Endogenous
Growth
Convergence of Growth
Experiences
• Prediction of the Solow model: Given
the same n,s, and z, y converges
among countries
• It is not entirely consistent with the data
• Question: Why?
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-2
• Maybe z is different across countries.
• Maybe different countries can have
different growth rate, i.e., the growth
rate can be endogenously determined.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-3
Convergence: Theory and
Evidence
• Unconditional convergence in Solow model.
• Data show convergence only in rich
countries.
• Suppose that the countries do not have
access to the same technology. There exists
significant barriers to the adoption of new
technology.
– Labor Unions
– Trade restrictions
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-4
• The barriers to the adoption of new
technology differ across countries imply
differences in z across countries
• Differences in z imply differences in y
• Policy Implications
– Promote greater competition
– Promote free trade
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-5
Figure 7.1 Rich and Poor Countries
and the Steady State
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-6
Figure 7.2 Convergence in Income per
Worker Across Countries in the Solow
Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-7
Figure 7.3 Convergence in Aggregate
Output Across Countries in the Solow
Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-8
Figure 7.4 Differences in Total Factor
Productivity Can Explain Disparity in Income
per Worker Across Countries
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-9
An Alternative: Endogenous
Growth with Human Capital
Accumulation
• Solow model is an exogenous growth
model. It does not explain the growth
itself!
• We need an endogenous growth model.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-10
• Why we cannot generate the
unbounded growth in Solow model?
• The key is diminishing marginal return
to capital stock (from concavity of
production function)
• To have an unbounded growth, we need
to break this trap.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-11
• Human Capital: stock of skills and
education embodied in people.
• The acquisition of human capital is
nonrivalrous. It has positive externality.
• It does not have the diminishing return.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-12
The Representative Consumer
• The economy only has one representative
consumer (per capita=aggregate) who does
not value leisure
• Assume he cannot save
C=wuHs
u is the fraction of time devoted to working, Hs
is the current stock of human capital
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-13
• The accumulation of human capital
H  b(1  u ) H
s'
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
s
7-14
The Representative Firm
• Production function
Y  zuH
d
• Firm’s problem
max   Y  wuH  ( z  w)uH
d
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
d
7-15
Figure 7.5 Determination of the
Equilibrium Real Wage in the
Endogenous Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-16
Competitive Equilibrium
• The equilibrium wage is w=z.
• Labor market clears
H H H
s
d
• We have
C  zuH , H '  b(1  u ) H
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-17
• The growth rate of human capital is
H ' H
 b(1  u )  1
H
• It’s easy to show same holds true for C and
Y.
• This model economy does not grow because
of any exogenous forces. n=0, b and z are
fixed.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-18
Figure 7.6 Human Capital Accumulation
in the Endogenous Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-19
Economic Policy and Growth
• Change u through taxes or subsidies to
education.
• The welfare effect depends on the
trade-off b\w current consumption and
future consumption.
• Government could also increase b by
education policy
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-20
Figure 7.7 Effect of a Decrease in u on
the Consumption Path in the Endogenous
Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-21
Convergence in Endogenous
Growth Model
• Convergence does not occur even if
countries are identical in all respects
except that there are differences in the
initial level of human capital.
• Higher (1-u) means higher growth rate,
hence implies higher y over time.
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-22
Figure 7.8 No Convergence in the
Endogenous Growth Model
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-23
Figure 7.9 Growth and Education
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-24
Figure 7.10 Income per Worker and
Education
Copyright © 2005 Pearson Addison-Wesley. All rights reserved.
7-25