Solow Model Develompent Economics
THE SOLOW MODEL
Standard neoclassical model of economic growth (1956).
It was developed by Robert Solow and it has three basic sources: Labor (L), Capital (K),
The Solow model retains the assumption of Diminishing returns, but explores another property of
the neoclassical production function: the property of Constant Returns to Scale: if capital is set to
expand at the same rate as population, then total output will grow at the very same rate and per
capita income will remain constant, rather than declining towards a low level subsistence trap.
In general, production functions may also exhibit decreasing returns to scale (in which case output
grows less than proportionally than inputs) and increasing returns to scale (when output grows
more than proportionally than inputs).
The key assumption of the neoclassical growth model is that of constant returns to scale (CRS).
CRS means that if one increases the use of all inputs by a positive proportional factor, output will
rise in the same proportion.
The Law of Diminishing Returns states that increasing the use of one input while holding the
other input constant, output will grow less than proportionally.
Consider a closed economy with no government with a large number of small firms producing a
single homogeneous good, Y, using two inputs: labour (N), and capital (K), which can be
produced and accumulated.
Population and the labour force are the same.
Inputs are hired from households, who are also the owners of the firms and the consumers in this
Households spend a fraction (1-s) of their income on consumptions, and save the remaining, to
buy new capital.
The capital stock depreciates at a constant rate,
In this model, the ability to accumulate capital (via savings) prevents output per capita from
declining when population increases.
Output is produced by neoclassical production function Y = F(K,L) that has usual properties
1. (diminishing marginal product, constant returns to scale).
The economy is closed, savings are equal to investments, S I.
Population growth is given exogenously (outside of the model).
3. The production function has diminishing return
to per capita capital.
As capital increases, output falls because of
shortage of labor.
It represents the technical knowledge of the
Net national product Y is a function of capital K
and labor L, Y =F(K,L).
This aggregate production function is fixed; how
the product depends on capital and labor does
not change as time passes.
The production function exhibits constant
returns to scale; doubling the capital and labor
doubles the output.
Depreciation increases at a constant rate as the
capital stock increases. —> the more capital you
have, the more capital depreciation you have.
Where does money for capital accumulation
came from? from saving and investments.
Depreciation is growing at the same rate as the
capital stock grows.
Each unit of capital creates creates an equal
amount of depreciation.
When I > depreciation:
Capital stock is growing, as the capital stock
grows, investment and depreciation intersect at
one point, the steady state level of capital
where I = depreciation.
When I < depreciation: some of the capital
stock needs repair but there isn’t enough
investments to do all the needed repairs and
capital stock shrinks, pushing back to the steady
In words, since the economy generates savings (and hence new investment) larger than the
amount needed to keep the amount of capital per worker constant, the capital-labour ratio will
The figure displays the production function in the intensive form, per capita savings and the break
even investment line.
The steady state occurs when the break even investment line crosses the schedule of per capita
If the economy starts out on the left (right) of the steady state, per capita savings will exceed (be
less than) the required to keep the capital labour ratio constant, so the capital will increase
If the economy starts out on the right of the steady state, per capita savings will be less than the
required to keep the capital labour ratio constant, so the capital will decrease.
An important feature of the Solow model is that, if the economy is not in the steady state, it will
converge to the steady state.
But the economy will not jump instantaneously from one steady state to the other: since capital
accumulation is bounded by the availability of savings, there will be an adjustment period, during
which the economy approaches the new steady state.
HOW PARAMETERS AFFECT THE STEADY STATE
Although the saving rate s does raise the rate of economic growth in the short run, it has no effect
on the rate of growth in the long run.
A higher value s does raise the steady-state capital/labor ratio k.
Hence the steady-state output per capita rises.
K*/ Y* = S / n+d
The Figure shows how the steady state in the
Solow model changes with an exogenous
increase in the saving rate.
In the new steady state (point 1), the capital
labour ratio and per capita output are higher than
before, but the average product of capital (Y/K) is
lower, due to diminishing returns.
In the long term, per capita income is again
constant (the increase in the saving rate
produced a “level effect”).
The rate of population growth sets the long-run growth rate of the economy.
If the population growth rate n rises, the capital-widening term nk rises.
Consequently the steady-state capital/labor ratio k falls and the steady-state output per capita falls.
In the steady state, the real interest rate is now higher, and the real wage is lower.
A fall in the population growth rate has a similar effect to that of a rise in the savings rate.
The difference is that the change in the steady state will be caused by a downward shift of the
break-even investment line.
Thus, both output per worker and capital per worker will increase, but this will happen only during
the transition from one steady state to the other.
In the new steady state, the average product of capital - and interest rate - will be lower than in the
initial steady state.
Suppose population growth changes from n1 to n2.
This shifts the line representing population growth and depreciation upward.
At the new steady state k*2 capital per worker and output per worker are lower
The model predicts that economies with higher rates of population growth will have lower levels of
capital per worker and lower levels of income.
Population growth has two effects:
effect: leaves the rate of growth unchanged, while
shifting up or down the entire path traced out by the variable
over time. effect: effect that change the rate of growth of a
variable, typically income or per capita income.
SOLOW WITH TECHNICAL PROGRESS
In the absence of technical progress, a country cannot sustain per capita income growth
For this to happen, capital must grow faster than population, but then diminishing return implies
that the marginal contribution of capital to output must decline, which forces a decline in the growth
rate of output and, therefore, of capital.
+1 anno fa
I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Shiva_1993 di informazioni apprese con la frequenza delle lezioni di Development economics and emerging market e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Ferrara - Unife o del prof Di Tommaso Marco Rodolfo.
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