Macroeconomics Chapter 51 Conditional Convergence and Long- Run Economic Growth C h a p t e r 5.

Macroeconomics Chapter 5 1

Conditional Convergence and Long-Run Economic Growth

C h a p t e r 5


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*] (−) (+)


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



Japan and Germany after 2nd world war.

East Asia countries

African Countries


Long-Run Economic Growth

Solow model, the growth rate of capital per worker, k, is given by

∆k/k= s· (y/k) − sδ − n



A case in which capital broadly defined to include human and infrastructure capital is the only factor input to production. AK model

y= Ak



k – capital per worker

y/k= A

∆k/k= sA− sδ − n



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


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



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



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)



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]



Steady state: all variables grow at constant rates.

∆k/k is constant ∆k/k= s(y/k)− sδ − n

y/k is constant



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


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.



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)



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

)1/(gns

sAk


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)


Endogenous Growth Theory

The essential feature of knowledge or technology:

1. non-rival good2. not diminishing with the rise of A.


The basic R&D model

• Assumptions

1. The labor force is the single production factor

2. Generalized Cobb-Douglas function without capital

)()1)(()( tLatAtY L

3. The fraction of the labor force is exogenous


The basic R&D model

• The evolution function of labor

where

0)()( ntnLtL

dt

tdLtL

)()(

• The evolution function of knowledge

00)()]([)( BtAtLaBtA L

1 1 0 0


The basic R&D model

• The dynamic of knowledge accumulation

1)()]([)(

)()( tAtLaB

tA

tAtg LA

)()1()(

)(tgn

tg

tgA

A

A


The basic R&D model

•

1

* ngA

Interpretation:

• endogenous long run growth rate

• positive link with population growth


Diffusion of Technology

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 51 Conditional Convergence and Long- Run Economic Growth C h a p t e r 5.

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