Solow model (for which the American economist Robert Solow was awarded
the Nobel prize in economics in 1987) ignores the temporary ups
and downs of the business cycle and explains potential income (output)
as it obtains in the long run.
The main building block is the production function. While
the 3D production function shows output to depend on the capital
stock and the labour force, the basic version of the Solow model
keeps the labour force fixed at its normal level. We may then operate
with the partial production function that keeps L fixed.
To identify the level of (potential) income (or output)
this economy generates in long-run equilibrium, we need to find
out the capital stock maintained in long-run equilibrium:
Capital is added when firms invest. Capital is lost due
to depreciation. So when investment exceeds depreciation the capital
stock grows; when investment falls short of depreciation the capital
stock shrinks. The capital stock remains unchanged, or steady, if
investment equals (offsets) depreciation. This situation is called
a steady state.
When does investment exceed depreciation, and when does
it fall short of it? This can only be answered if we know what determines
investment and depreciation:
As regards depreciation, we may safely assume that a constant fraction
of the capital stock, say 5 percent, is lost every year because
it is used up or became obsolete. Then depreciation equals 5 percent
of the current capital stock. In a Y/K diagram the depreciation
line (or, in a more general setting, the requirement line) is a
straight line with slope 0.05.
To determine investment, suppose there is no government
and no trade with other countries. Then according to the circular
flow diagram investment equals saving. Saving is a fixed share of
income. Then the amount people save and invest at different capital
stocks may be read off the red savings curve in the accompanying
Whether the capital stock grows or shrinks depends on where
it currently is. If it is at K0, firms invest and buy
more capital goods than they loose due to depreciation. Net investment
is positive. The capital stock will be higher next year. If the
capital stock is at K1, investment fails to replace all
capital that wears out. Net investment is negative. The capital
stock will be lower next year.
The crux of this is that if current capital is smaller than
K*, the capital stock grows; if it exceeds K*, the capital stock
falls. So the capital stock always moves towards K*, where it will
stay, since only there depreciation is exactly replaced by new investment.
K* is the steady-state capital stock, and Y* is steady-state income.
Further reading on pp. 228ff.
Click here for interactive applet featuring the Solow model