Chapters 4
& 5: Economic Growth
Goal: To understand forces causing differences in income
over time and across countries.
·
Economic
growth is based upon the production function of the economy.
·
Differences
in income and growth over time must come from differences or changes in
capital, labor, and technology
·
Changes
in the production function results in shifts in the aggregate supply curve (to
the right) so that higher output occurs for a given price level.
Our Primary Task is to develop the Solow model of economic growth.
Our Secodary Task is to examine how economic
policy can influence the level and growth in our standard of living.
Chapter 4: The Solow Growth Model without Technology
Change
1. The Supply of Goods and the Production Function
a.
The
Solow model assumes that the supply of goods and services depends upon a
production function with constant returns to scale. zY = F(zK, zL)
b.
Hence,
with substitution if z = 1/L, then Y/L = F(K/L, 1), i.e. output per worker
depends upon capital per worker.
c. With constant returns, changes in output per worker depends upon changes in capital per worker.
d.
Let
y = Y/L and k = K/L, then y = f(k)
e.
The
marginal productivity of capital MPK = f(k+1)
- f(k) will diminish if the amount of
labor and technology is fixed. (See
Figure 4-1)
Clearly
changes in the stock of capital will result in an increase in the supply of
goods and services, even with the supply of labor and technology fixed.
B. Investment, Consumption, and the Demand for Goods.
a.
The
Solow model assumes that the demand for goods depends upon consumption and
investment.
b. If expressed in terms of consumption and investment per worker,
then y = c + i
c.
Consumption
is assumed to depend upon income, ie. c = (1-s)y where s
is the marginal propensity to save (change in savings per worker for a given
change in income per worker) (1-s) is the marginal propensity to consume
if income is either consumed or saved.
d.
Hence, total desired spending (demand) is given by y = (1-s)y + i
e. Solving
this equation results in investment that is proportional to income, i = sy
The Evolution of Capital and
the Steady State
a.
We
have seen that y = f(k) and i = sy; therefore, i = s
f(k). The higher the capital stock the higher the level of output and
investment. Also, the saving rate
determines the allocation of output between consumption and savings for every
value of k.
b. Net
investment adds to the capital stock.
This occurs only if gross investment is greater than depreciation. If depreciation is given by d k, then change in the capital stock is
s f(k) - d k
Approaching the Steady State
a. The steady state occurs when investment
equals depreciation. Then no net
investment occurs. s
f(k) = d k* where k* is the steady-state level of capital.
b.
Changes
in the savings rate will increase growth until a new steady state is reached at
a higher level of output.
c. Rich
countries have higher rates of savings and investment than poor countries.
The Golden Rule Level of
Capital
a.
The
steady state that leads to the highest level of consumption per capita is
called the Golden Rule level of capital accumulation.
b.
The
steady state level of consumption c* =
f(k*) - d k* (output minus investment).
Since output is not changing investment is equal to depreciation.
c.
Consumption
is maximized when the slope of f(k*) = d
k* (the largest vertical distance between f(k*) and d k*)
d.
This occurs when the MPK = d
Transition to the Golden
Rule Steady State
a.
If more capital than the
golden rule, then
consumption can be increased with lower saving rate and rate of
investment. Over time output per capita
will fall along with investment and savings, but consumption per capita will
rise above the initial steady state.
b.
If less capital than the
golden rule, then
current consumption must be sacrificed in order to increase savings and
investment to benefit future generations.
c. The US is in this latter condition so that present consumers would have to sacrifice for future generations in order to improve the long-run rate of consumption.
Population Growth
a.
Increases
output but lower income per capita
b.
The
change in capital must now be sufficient to meet depreciation plus the erosion in
the productivity of capital due to less capital per worker as the number of
workers increase.
c. Hence, the steady state level of capital per worker falls with more population as the slope depreciation plus employment curve rotates upwards (see Fig. 4-11)
d.
The
Golden Rule level of capital accumulation also falls until the MPK equals d + n.
Less capital accumulation results in lower output and consumption
per capita in more populated countries.
Chapter 5: Technological Progress in the Solow Model
a.
Solow
explains technological progress as the residual between the rate of growth in
output and the amount explained by the rate of growth in capital and the rate
of growth in labor inputs. This is
called the “Solow Residual.”
b.
Technological progress is assumed to increase the efficiency of labor and, hence, is labor-augmenting. L x E is the
efficiency unit of labor, so that k =
K/(LxE) is the amount of capital per efficiency unit.
c. An increase in labor augmenting technology has the same influence as an increase in population. Now capital must accommodate depreciation, greater population, and labor augmenting technology.
d.
The
Golden Rule level of capital MPK - d = n
+ g where n is population growth
and g is the growth in technology.
e. Previously
we noted that capital per efficiency unit is constant in the steady state. Then, y = f(k) is also constant in the
steady state. But the number of
efficiency units per worker is increasing at a rate g. Hence, total output grows at a rate n + g.
Therefore, only technological progress can explain
persistently rising living standards.
Savings, Growth and Economic
Policy
a.
The MPK - d in the US is
presently about 8 percent per year well in excess of the current growth rate of
below 3 percent per year.
b.
Policies
to change the rate of savings
c.
Policies
to allocate investment
d.
Policies
to encourage technological progress
a.
The
basic model: Y = AK
Growth in Y = sA – d What determines A?
b. The role of knowledge (human capital) with constant or increasing returns. How are ideas tuned into innovations?
c.
“Standing
on shoulders” versus “stepping on toes”