Chapter 3
Continued
•Solow Growth
Model
•Endogenous Growth
3.5 The Neoclassical Counterrevolution, or
“Market Fundamentalism”
‒ Traditional neoclassical growth theory (Solow model)
‒ Includes labor as a separate input
‒ Shows that with diminishing returns, growth cannot be
sustained by capital accumulation alone
‒ Adds separate, explicit accounting of the role of
technological change
‒ The model details are presented in Appendix 3.2
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Constant returns to scale production function (Cobb-Douglas is an
easy example)
Yt  At K t L1t 
A= TFP (Factor neutral Technological improvement will increase
this) L=Labour
K=capital
t= the time subscript
Divide across by L to get output per worker
Yt
Kt 
 AT ( )
Lt
Lt
or
y t  f ( kt )  At kt

In a stationary equilibrium (where everything is stable over time)
savings per worker must be just enough to offset any depreciation
in the capital stock and provide capital for new workers
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
From the Appendix:
Interpreting the Solow equilibrium equation
sf (k*) = (d + n)k *
(A3.2.5)
• Interpreting of the Solow Equilibrium in Equation (A3.2.5) and
the preceding figure (A3.2.1),
• sf(k*) is savings per worker, and is just equal to the sum of:
• δk*, the amount of capital (per worker) needed to replace
depreciating capital
• nk*, the amount of capital (per worker) that needs to be added
due to population (labor force) growth.
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Figure A3.2.1
Equilibrium in the Solow Growth Model
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Appendix 3.1: Components of Economic
Growth
• Capital Accumulation, investments in physical and
human capital
– Increase capital stock
• Growth in population and labor force
• Technological progress
– Neutral, labor/capital-saving, labor/capital augmenting
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Figure 2.5
The growth of real output per person since 1750
US output grew roughly
threefold between 1950-2017
Source: Data from Maddison Project Database
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Decomposing Growth in the Solow Model
y t  At kt

Take logs:
ln y t  ln At   ln kt
Derivative of log approximates percentage change
d ln y t  d ln At   d ln kt
% growth in output is a fraction of % growth in k and %
change in A.
But k does not change that much so residual is A
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Figure A3.1.3
Effect of Technological Change in the Agricultural
Sector on the Production Possibility Frontier
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Figure A3.1.4
Effect of Technological Change in the Industrial
Sector on the Production Possibility Frontier
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Figure A3.2.2
The Long-Run Effect of Changing the Saving
Rate in the Solow Model
Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Conclusions on Solow Model
• This is a neo-classical model
• In Contrast with Harrod-Domar or Lewis model an increase in
savings (Investment) leads to a once off increase in output per
head
• Increasing capital stock does not lead to a virtuous circle of
growth in this model
• Empirical analysis suggests “technology” parameter drives
growth
• Also note the model predicts “Conditional” convergence in
incomes between rich and poor countries (but not
“Unconditional” convergence)
Endogenous Growth Theory
• In the Solow Model Growth was primarily driven by
“Exogenous” technological change
• Exogeneity assumption limits the models ability to identify
underlieng reasons why some economies grow faster
• Given the low capital labour ratios in poor countries, why did
capital not flow to these economies when they liberalised
capital markets as model predicts?
• With endogenous growth theory the processes that
determine growth are determined within the model
• Allow increasing returns to scale and external effects of
investments
• we can explain why low levels of investment in Education,
infrastructure or R&D lower the rate of return
• Romer Model: each industry produces with constant returns
to scale but there are increasing returns at the aggregate
 1
Yt  At K t Lt K

• Like Solow model except for each firm part of capital is
“Knowledge capital” K
• developed by one firm but shared amongst others
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Yt  At K t   L1t 
Can think of this argument applying to:
•
•
•
•
Learning by doing at the firm level
Investment in public education or R&D
Investment in Infrastructure or Public Goods
Per capita growth can continue in the steady state
• Note that issues such as Institutional failings in developing
countries not addressed by this model
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