CHAPTER 9
Economic Growth II: Technology,
Empirics and Policy
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MACROECONOMICS, 8th Edition
N. Gregory Mankiw
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The Solow model does not explain technological progress but, instead, takes it as given and shows how it interacts with other variables in the process of economic growth.
To examine how a nation’s public policies can influence the level and growth of the citizens’ standard of living, we must ask five questions.
1) Should our society save more or less?
2) How can policy influence the rate of saving?
3) Are there some types of investment that policy should encourage? 4) What institutions ensure that the economy’s resources are put
to their best use?
5) How can policy increase the rate of technological progress?
To incorporate technological progress, the Production Function is now written as:
Y = F (K, L E)
The term L
E measures the number of workers.This takes into account the number of workers L and the efficiency of each worker, E. It states that total output Y depends on capital K
and workers L E. The essence of this model is that increases in E (efficiency) are analogous to increases in L (number of workers). In
other words, a single worker (if twice as productive)
The Steady State
Investment, sf(k)
n + g)k
Technological progress causes E to grow at the rate g, and L grows at rate n so the number of workers L E is growing at rate n + g.
Now, the change in the capital stock per worker is: k = i –(n g)k, where i is equal to s f(k).
Technological progress causes E to grow at the rate g, and L grows at rate n so the number of workers L E is growing at rate n + g.
Now, the change in the capital stock per worker is:
k = i –(n g)k, where i is equal to s f(k).
Note: k = K/LE and y=Y/(L So, y = f(k) is now different. Also, when the g term is added, gk is needed to provided capital
to new “effective workers”
created by technological progress.
Note: k = K/LE and y=Y/(L
So, y = f(k) is now different. Also, when the g term is added, gk is needed to provided capital
to new “effective workers”
created by technological progress.
Labor-augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k. In the steady state, investment sf(k)
exactly offsets the reductions in k because of depreciation, population growth, and technological progress.
Important…
Capital per effective worker is constant in the steady state.
Because y = f(k), output per effective worker is also constant. But the efficiency of each actual worker is growing at rate g. So,
output per worker, (Y/L = y E) also grows at rate g. Total output Y = y (E L) grows at rate n + g.
Capital per effective worker is constant in the steady state.
Because y = f(k), output per effective worker is also constant. But the efficiency of each actual worker is growing at rate g. So,
Steady-state consumption is maximized if MPK = n + g,
rearranging, MPK - n + g.
That is, at the Golden Rule level of capital, the net marginal product of capital, MPK - equals the rate of growth of total output, n + g. Because actual economies experience both
population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than they would at the Golden Rule steady state.
The introduction of technological progress also modifies the
criterion for the Golden Rule. The Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker. So, we can show that steady-state consumption per effective worker is:
c*= f (k*) - ( n + g k*
Capital per effective worker k = K/(E L) 0 Output per effective worker y = Y/ (E L) = f(k) 0 Output per worker Y/L = y g
So far we have introduced technological progress into the
According to the Solow model, technological progress causes the values of many variables to rise together in the steady state This property is called balanced growth.
In the steady state, output per worker, Y/L, and capital stock per worker, K/L, both grow at rate g, which is the rate of technological progress. This is consistent with U.S. data in that g has been
about 2 percent consistently over the past 50 years.
Technological progress also affects factor prices. The real wage grows at the rate of technological progress, but the real rental price of capital remains constant over time. Again, over the last
The property of catch-up is called convergence. If there is not convergence, countries that start off poor are
likely to remain poor.
The Solow model makes predictions about when convergence should occur. According to the model, whether two economies will converge depends on why
they differ in the first place (i.e., savings rates,
Differences in income are a result of either:
1) Factors of production such as the quantities of physical and human capital
2) Efficiency with which economies use their factors of production
Put simply, workers in a poor country either don’t have the tools
In terms of the Solow model, the central question is whether the large gap between the rich and poor is explained by
differences in capital accumulation, or differences in the
The savings rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker. Let’s use the
Golden Rule to analyze the U.S. saving rate.
Marginal product of capital net of depreciation
(MPK – )
Growth rate of total output (n + g)
Amount of capital in the Golden Rule steady state
If the economy is operating with less capital than in the
Golden Rule steady state, then (MPK – > n + g)
If the economy is operating with more capital than in the
Marginal product of capital net of depreciation
(MPK – )
Marginal product of capital net of depreciation
(MPK – )
Growth rate of total output (n + g)
Growth rate of total output (n + g)
We solve for the rate of depreciation by dividing equation 2 by equation 1:
k/k = (0.1y)/(2.5y)
= 0.04
And we solve for the marginal product of capital (MPK) by dividing equation 3 by equation 1:
(MPK k)/k = (0.3y)/(2.5y) MPK = 0.12
1) The capital stock is about 2.5 times one year’s GDP, or k = 2.5y 2) Depreciation of capital is about 10 percent of GDP, or dk = 0.1y 3) Capital income is about 30 percent of GDP, or MPK k = 0.3y
We can now see that the returns to capital (MPK – = 8 percent per year) is well in excess of the economy’s growth rate (n + g = 3 percent per year).
This indicates that the capital stock in the U.S. economy is well
Public saving is the difference between what the government receives in tax revenue minus what it spends.
When spending > revenue, it is a budget deficit
When spending < revenue, it is a budget surplus
• In 2009, one of President Barack Obama’s
first economic proposals was to increase
spending on public infrastructure such as
new roads, bridges, and transit systems.
Nations may have different levels of productivity in part because they have different institutions that govern the allocation of their scare resources.
For example, a nation’s legal tradition is an institution. Other
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The Endogenous Growth Theory rejects
Start with a simple production function: Y = AK, where Y is output, K is the capital stock, and A is a constant measuring the amount of output produced for each unit of capital (noticing this production
function does not have diminishing returns to capital). One extra unit of capital produces A extra units of output regardless of how much capital there is. This absence of diminishing returns to capital is the key difference between this endogenous growth model and the Solow model.
Y/Y = K/K = sA -
This equation shows what determines the growth rate of output Y/Y. Notice that as long as sA > , the economy’s income grows forever, even without the assumption of exogenous technological progress.
In the Solow model, saving leads to growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady
state in which growth depends only on exogenous technological progress.
Creative
Destruction
Efficiency of labor
Labor-augmenting technological progress Endogenous growth theory
Creative Destruction
Efficiency of labor
Labor-augmenting technological progress Endogenous growth theory
