Transcript Engine of Growth

Engine of Growth
ECON 401: Growth Theory
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Engine of Growth
Objective: develop an explicit theory of technological progress
and answer the questions:
Where does the technological progress come from?
Can we expect the growth to continue?
Is there a limit to economic growth?
The theories that tries to answer these questions are known as
endogenous growth theory or new growth theory.
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Basic Elements: Model is designed to explain why and how
the advanced countries sustained growth
 We will introduce search for new ideas to endogenize
technological progress

Technological progress is driven by R&D
Production function is given by
Y=Ka(ALY)1-a
(5.1)
Where K is capital stock, LY is labor, and A is the stock of
ideas.
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For a given level of technology, this production function
exhibits constant returns to scale in K and L.
 It must exhibit increasing returns with respect to all
three inputs.
Capital accumulation is given by
  s Y  dK
K
K
Labor and population grows at a constant rate of n.
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A(t) is the stock of knowledge or the number of ideas that have
been invented until time t. Change in A, then , will be
determined by the number of people working to discover new
ideas, LA, and the rate at which they discover new ideas.
   L , where  shows the rate of discovering new ideas
A
A
Rate of discovering new ideas might
- be a constant, or
- might depend on the stock of ideas
- it might be an increasing function of A if the level of A
positively impacts productivity of researcher
- it might be a decreasing function of A if the obvious ideas
are discovered first, leaving the most difficult ones
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Hence, we can model
  A , where  and are constants
What does it tell us if >0?
 indicates that productivity of research increases with
the stock of ideas.
<0? =0?
It is also possible that average productivity of research
depends on the number of people searching for new ideas at
any point in time (duplication).
 LAg , where 0<g<1, should enter the production function
and not LA.
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General production function for ideas
   L  A
A
A
We will assume <1. Individual researchers take the discovery rate of
new ideas as given and see constant returns to research. However,
for the economy as a whole, production function for ideas may not be
characterized by constant returns to scale.
Allocation of resources:
 Constant fraction of output is invested in capital
 Allocation of labor between output production and idea production is
determined by utility maximization and markets.
LA+LY=L
However, we will assume a constant fraction: sR=LA/L
We assume economy starts out with K0 and L0, and A0.
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Growth In Romer Model:
 Per capita growth is due to technological progress
 Balanced growth path has:
gy= gk= gA
What is the rate of technological progress along a balanced growth
path?

Rewrite the production function for ideas as

A
LA
  1
A
A
Growth rate of A is gA along a balanced growth path.
 happens if both numerator and denominator grows at the
same rate
 Along a balanced growth path, growth rate of number of
researchers must be equal to the growth rate of population.
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If the growth rate of researchers is higher, the number of researchers
would eventually exceed the population which is impossible.
Solving for gA : gA=(n/1-) – long run growth rate of this economy is
determined by the parameters of the production function for ideas and the
rate of growth of researchers (or population)
What if =1 and =0?

Productivity of researcher is constant

No duplication problem
Production function looks like:
A  LA
Economy generates a constant number of new ideas each period. Over
time, this constant number becomes a smaller fraction of A. Hence,
growth rate of new ideas falls over time, approaching to zero. However,
technological progress never ceases.
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To generate exponential growth number of ideas must be
expanding over time  number of researchers is increasing. So
growth of ideas is clearly related to growth in population
How is this different from Neoclassical model?
 In neo-classical model, higher n reduces level of income
along a balanced growth path
 Here, an additional effect – input to creative process 
ideas are non-rivalrous and hence everybody benefits
Do we expect long-run growth to cease if the population stops
growing?
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Special case: If =1 and =1 we can have sustained growth in the
presence of a constant research effort. In this case, productivity
of researcher is proportional to the existing stock of ideas.
Drawback: World research effort has increased enormously over
the last 40 years, but the growth rate of advanced economies did
not rise as predicted by the Romer model.
- So we can reject =1 (knowledge spillover parameter) is
rejected by this evidence. It can be positive and large but less
than 1.
As in neoclassical model, changes in government policy and
changes in investment rate do not have long-run effect on growth
rate.
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The idea-based models in which changes in policy can
permanently increase the growth rate all rely on the assumption
that =1. But thıs generates a counterfactual prediction. Setting
<1, however, eliminates the long run growth effect of policy as
well.
What happens if the share of population searching for ideas
increase permanently?
(1) Consider the effect on technological progress and on
stock of ideas
(2) Analyze the model
To simplify, assume =1 and =0. Figure 5.1 shows what happens
to technological progress when sR increases.
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A permanent increase in the share of the population devoted to
research raises the rate of technological progress temporarily, but
not in the long run.
Figure 5.2.
What happend to the level of technology? Figure 5.3.
- The level of technology is permamnently higher as a
result of the permanent increase in R&D.
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Along a balanced growth path,

sK
y * (t )  
 n  gA  d
 /(1 )



(1  s R )
s R
gA
L(t )
(5.11)
- Per capita output is proportional to the population of the world
economy along a balanced growth path. That is, model has a scale
effect: larger world economy will be a richer worl economy 
nonrivalrous nature of ideas  larger market for an idea and larger
potential creators of ideas
- Economies that invest more will be richer
- Share of labor devoted to research has two effects:
-
More researchers mean fewer workers producing output
More researchers mean more ideas
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Economis of the Model:
Romer economy has
- a final goods sector
- produce output
- an intermediate goods sector
- Reason: presence of increasing returns to scale
- a research sector
- produce ideas
Research sector creates new ideas, which take the form of new
varieties of capital goods. Research sector sells the exclusive
right to produce a specific capital good to an intermediate goods
firm. The intermediate goods firm, as a monopolist,
manufactures the capital good and sells it to the final goods
sector.
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Final Goods Sector:
-Large number of perfectly competitive firms
- Uses capital and labor to produce final output Y
- Final output is produced using labor and a number of different
capital goods (intermediate goods)
A
Y  L1Y  xj
j 1
A measures the number of capital goods that are available to be
used in the final goods sector. For a given A, production function
exhibits constant returns to scale.
Firms decide on how much labor and how much of each capital
good to use in producing final good by solving the profit
maximization problem.
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-Firms hire labor until marginal product of labor equals wage.
-Firms rent capital goods until the marginal product of each kind of capital
equals the rental price.
Intermediate-goods Sector:
Consists of monopolists. They gain their monopoly power by purchasing the
design for a specific capital good. Because of patent protection, only one firm
manufactures each capital good.
Simple production function: one unit of raw capital can be automatically
translated into one unit of capital good.
Firm charges a price that is simply a markup over marginal cost. All capital
goods sell for the same price and hence each capital good is employed by the
final goods sector by the same amount. Each capital goods firm earn the same
profit.
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Research Sector:
Ideas are new designs for capital goods (e.g., a faster computer chip)
Inventor receives a patent for a new design (patent lasts forever).
Inventor sells the patent to an intermediate goods firm and uses the
proceeds to consume and save.
How much will a potential bidder pay for the patent?
Present discounted value of the profits to be earned by an
intermediate goods firm.
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Solving the Model:
Remember:
(1)Aggregate production function exhibits increasing returns to scale
(2)Increasing returns require imperfect competition.
a)
Capital goods sell at a price that is greater than marginal
cost
b) Profits earned by these firms are extracted by the inventors
This framework is called monopolistic competition
(no economic profits in the model).
Because of arbitrage, individuals are indifferent between working in
the final goods sector or in the research sector.
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Labor earns a wage that is equal to marginal product in that sector.
Researchers earn a wage based on the value of the designs they
discover = marginal product*value of the new ideas created.
 Because of arbitrage, these wages has to be equal.
The share of the population that works in the research sector is
(after some algebra):
sR
1

r n
1
g A
Note that faster the economy
grows, the higher the fraction of
the population that works in
research. The higher the discount
rates that applies to current profits
to get the present discounted value
(r-n), the lower theis fraction.
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Interest rate in this economy is less than the marginal product of
capital.
How is this different from Solow model?
In the Romer model, production in the economy is characterized by
increasing returns and all factors cannot be paid their marginal
products.
In Solow, rK+wL=Y – all factors are paid their marginal product – no
output remains to compensate individuals for their effort in creating
new A. In this model, capital is paid less than its marginal product,
and the remainder is used to compensate researchers for creation of
new ideas.
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Optimal R&D:
Is the share of the population that works in research optimal?
Three distortions:
(1) Market values research according to the stream of profits that are
earned from the new design
- ignores the impact of new invention on the productivity of
future research. Hence, researchers are not compensated for this
effect. This distortion is often called “knowledge spillover”.
(2) “Stepping on toes” effect. Researchers do not take into account
the lower research productivity through duplication.
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(3) “Consumer surplus effect”. Figure 5.4. Potential gain to society is
larger than the monopoly profit and hence too little innovation is
generated.
In general, these distortions can be very large. Consider the cure for
malaria or cholera – consumer surplus and thge knowledge
spillovers has to be large - governments fund research in general.
Empirically, positive externality of research outweigh the negative
externalities, social rate of return far exceeds the private rate of
return – market tend to produce too little innovation.
Classical economic theory argues that monopolies (or P>MC) are
bad for welfare and efficiency (deadweight losses). However,
economics of ideas suggest that it is critical for firms to set their
prices above MC for innovation.
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