The Solow Growth Model and Economic Growth
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Transcript 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
No international trade,
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’ > 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)*?
Not a trivial answer
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