Engine of Growth

1
Engine of Growth

• ECON 401 Growth Theory

2
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.

3
Engine of Growth

• 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 RD
• Production function is given by
• YKa(ALY)1-a (5.1)
• Where K is capital stock, LY is labor, and A is
  the stock of ideas.

4
Engine of Growth

• 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

Labor and population grows at a constant rate of
n.
5
Engine of Growth

• 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.

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
6
Engine of Growth

• Hence, we can model

• What does it tell us if fgt0?
• indicates that productivity of research increases
  with the stock of ideas.
• flt0? f0?
• 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 0ltglt1, should enter the production
  function and not LA.

7
Engine of Growth

• General production function for ideas

• We will assume flt1. 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.
• LALYL
• However, we will assume a constant fraction
  sRLA/L
• We assume economy starts out with K0 and L0, and
  A0.

8
Engine of Growth

• 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

• 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.

9
Engine of Growth

• If the growth rate of researchers is higher, the
  number of researchers would eventually exceed the
  population which is impossible.
• Solving for gA gA(ln/1-f) 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 l1 and f0?
• Productivity of researcher is constant
• No duplication problem
• Production function looks like
• 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.

10
Engine of Growth

• 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?

11
Engine of Growth

• Special case If l1 and f1 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 f1 (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.

12
Engine of Growth

• The idea-based models in which changes in policy
  can permanently increase the growth rate all rely
  on the assumption that f1. But this generates a
  counterfactual prediction. Setting flt1, 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 l1 and f0. Figure 5.1 shows
  what happens to technological progress when sR
  increases.

13
Fig. 5.1
14
Engine of Growth

• 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 RD.

15
Fig. 5.2
16
Fig. 5.3
17
Engine of Growth

• Along a balanced growth path,

• - 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

18
Engine of Growth

• 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.

19
Engine of Growth

• 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 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.
20
Engine of Growth

• 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.

21
Engine of Growth

• 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.

22
Engine of Growth

• Solving the Model
• Remember
• Aggregate production function exhibits increasing
  returns to scale
• Increasing returns require imperfect competition.
  
• Capital goods sell at a price that is greater
  than marginal cost
• 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.

23
Engine of Growth

• 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 productvalue 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)

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.
24
Engine of Growth

• 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, rKwLY 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.

25
Engine of Growth

• Optimal RD
• 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.

26
Engine of Growth

• (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 PgtMC) 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.

27
Fig. 5.4