# The Solow Growth Model and Economic Growth

```Economic Growth and
The Solow Growth Model
Looks at the overall economy in the longrun, i.e. Y* = YN.
Focuses on a country’s standard of living,
measured by real per-capita GDP (income
per person).
Model is commonly used to prescribe ways
to maintain and improve a country’s longrun standard of living (economic growth), as
opposed to getting Y* to a given YN
(fluctuations).
The Solow Growth Model:
Simplifying Assumptions
No Business Saving, all saving is
Personal Saving (done by
consumers).
No government, i.e. G = T = 0
i.e. Exports = Imports = NX = 0
The Solow Growth Model:
Main Properties
Full employment, so that
labor employment = population
Equilibrium is based upon constant
per-capita levels of output and related
variables
Per-capita output = Y/N, where N is
labor employment. Other per-capita
variables are defined correspondingly.
The Solow Growth Model:
More Properties
Even at equilibrium, the levels of
output (Y) and capital stock (K) grow at
a constant rate over time.
Population (N) also grows at a constant
rate over time, given by n.
Since (Y/N)* and (K/N)* are constant, at
equilibrium Y and K also grow over
time at constant rate n.
Incorporating Dynamics:
Investment and the Capital Stock
Important identity relationship between
Investment (I) and the capital stock (K),
not accounted for in static models:
I = K + K,
where  is the rate of physical
depreciation of the capital stock.
The “Magic Equation” in
The Solow Model
The “Magic Equation”
S + (T – G) + (-NX) = I.
With G = T = NX = 0, it becomes:
S = I.
Note that the equation also holds
in per-capita terms:
(S/N) = (I/N).
Determining the Per-Capita
Saving Function (S/N)
Consider the production function for
the economy with positive and
diminishing marginal product of labor
and capital (from standard micro):
Y = A[F(K,N)],
where A is technological change.
Assume the production function
exhibits constant returns to scale
(doubling all inputs results in a
doubling of output).
Determining the Per-Capita
Saving Function, Continued
Constant returns to scale  the
production function for the economy
can be written (in per-capita terms) as:
Y/N = A[f(K/N)],
with f’ &gt; 0.
Determining the Per-Capita
Saving Function, Finally
Assume that consumers save a
constant proportion (s) of their income
 S = (s)(Y),
where s is the Average Propensity to
Save or The Saving Rate.
Multiply both sides of the per-capita
production function by s
 (s)(Y)/N = S/N = (s)(A)[f(K/N)].
Determining the Per-Capita
Investment Function (I/N)
Recall that the capital stock grows at a
constant rate n (the population growth)
 K/K = n.
Use investment-capital stock identity
to substitute for K.
 (I  K)/K = n.
Algebra  I = (n + )K.
Determining the Per-Capita
Investment Function (I/N)
Continue with this equation,
 I = (n + )K.
Divide both sides by N, in order to form
per-capita values:
 I/N = (n + )(K/N).
Equilibrium in the Economy
Equilibrium takes place where the percapita Saving and Investment functions
intersect, gives a value of equilibrium
per-capita capital stock (K/N)*.
Equilibrium can change due to shifts in
the per-capita Saving or per-capita
Investment functions.
Given changes in (K/N)* that occur, use
the per-capita production function to
infer how (Y/N)* will change as a result.
The Effect of an Increase in
Population Growth
Consider an increase in the population
growth rate (n).
Described as shifting the Per-Capita
Investment function upward  (K/N)*.
From the production function, this
implies that (Y/N)* as well.
Increased population growth lowers
the average standard of living.
The Effect of an Increase in
the Saving Rate
Consider an increase in the society’s
saving rate (s).
Described as shifting the Per-Capita
Saving function upward  (K/N)*.
From the production function, this
implies that (Y/N)* as well.
An increased saving rate raises the
average standard of living.
Per-Capita Consumption
and the Saving Rate
What is the effect of an increase in
the Saving Rate (s) on equilibrium
Per-Capita Consumption (C/N)*?
Per-Capita Consumption
and the Saving Rate
Two conflicting effects.
-- An increase in the saving rate,
ceteris paribus on (Y/N), decreases
per-capita consumption.
-- But an increase in the saving rate
also increases (Y/N)*, which in turn
increases per-capita consumption.
There exists an optimal saving rate that
maximizes (C/N)*.
Technological Change and
the Solow Model
Technological Change is given by the
variable A within the production
function.
An increase in A is referred to as
neutral technological change,
increases the efficiency of labor and
capital stock equally, leading to higher
output for given inputs.
Effect of an increase in A similar to that
of an increase in the saving rate.
Multifactor Productivity and
“The Solow Residual”
The variable A is formally known as
Multifactor Productivity, neutral
technological change that increases
output for given levels of labor and
capital stock.
The Solow Residual – seeking to come
up with a data series for the estimated
growth in A over time for a country,
based upon the properties of the percapita production function.
The Solow Model: Extensions
Endogenous Growth Theory – policies
seeking to induce continuous technological
change over time
Incorporating human capital in the
production function
Foreign Investment, technological change,
and economic growth
Infrastructure, technological change, and
economic growth
Political structures, legal determinants, and
geography in economic growth
```