MACROECONOMICS III

TUTORIAL 2

Paul Romer (1990) developed a relationship between idea and economic growth.

Idea Non-rivalry Increasing ImperfectReturns Competition

a) Explain the above relationship.

• Ideas: Non-rivalry, not for competition, increasing returns, imperfect competition (when it goes into R&D)

• Goods such as TV, radio, taxi, lawyers are rivalrous. (eg:Panasonic,Sony,Toshiba)

• Non-rivalry implies the presence of return to scale. Economic goods are rivalrous but ideas are not.

• Once an idea is created, people with the knowledge can take advantages of it. One company can produce computer chips, but other factories can use it provided they have the plan in hand.

• The company has an idea. This will lead to competition as firms will start hiring skilled engineers. Not everyone can interpret the ideas.

• The owner of an idea can charge fees/payments/royalty if others would like to copy the idea.

• Goods that are excludable allow their producers to capture the benefits. Also involve substantial “spillover” that are not captured by producers. Such spillover are called “externalities”.

• Goods for competition must be reproduced each time they’re sold. Non-rivalry products (ideas) involve a fixed cost of production cost and zero costs can only produce one.

• The hard part is coming up with the first copy and the rest will just be copies of the first.

b) Give Romer’s production function that takes into account idea.

α= parameter (0-1)

A=technology (stock of ideas)

• describe how capital stock, K and labor, LY combine using a stock of knowledge, A in production.

• for a given level of technology, A, the production function shows constant returns to scale in K and LY.

• if A ↑, there will be IRS.

c) Give the equation that show the number of new idea created.

=the number of new ideas produced at any given point of time

= the number of people attempting to discover new Ideas

= the average productivity in research sector

• The rate at which researchers discover new idea might be constant, increasing or diminishing function of the stock of ideas, A.

• It depends on the stock of ideas that have already been invented.

d) Explain each symbol.

A

• A = Changes in the stock of idea

• = The rate of new idea• A = Labor involved in the production of

new idea (R&D)• = The rate of new idea created by labor• = The rate of new idea created by labor

in (R&D)• = Productivity of idea• = Total new creation of idea from R&D.

e) Explain the equation on (d)• A = • Individual researchers, being small to the

economy as a whole, take as given and see constant return to research.

• As in formula, an individual engage in research creates new ideas.

• < 1 may reflect an externality associated with the duplication example: some ideas created by an individual researcher may not be new to the economy as whole.

• The externality known as ‘stepping on toes’ effect.

• is treated as external to the individual agent.

• > 0 is the externality known as ‘standing on shoulder’ effect, indicate that the productivity of research increase with the stock of ideas that have already been discovered.

• < 0 is the externality known as ‘fishing out’ case, in which knowledge become harder to obtain over time.

• = 0 in of indicates that the tendency for most obvious ideas to be discovered first exactly offsets the fact that old ideas may facilitate the discovery of new ideas, for example, the productivity of research is independent if the stock of knowledge.

• Consider the case where > 0 reflecting the positive knowledge spillover to future researchers in R&D.

f) Rewrite and explain the equation given = 1 and = 1

• This is the special case where

AA Rewriting the equation slightly, we can see

that this version of the Romer model will generate sustained growth in the presence of a constant research effort:

A A

• In this case, Romer assumes that the productivity of research is proportional to the existing stock of ideas:

= LA

• So there is no steady-state growth path with this assumption. The growth rate increases over time even if the number of researchers is constant.

g) Given

a. What is SR ?SR : share of the population engaged in R&D- i.e., LA = SR L

b. Explain the equation.

Figure 1: Technological Progress: An Increase in the R&D Share

• Figure shows what happens to technological progress when SR increases permanently to S’R,

assuming that the economy begins in STEADY STATE.

• In STEADY STATE, the economy grows along a balanced growth path (BGP) at the rate of technological progress, gA, which happens to equal the rate of population growth under our simplifying assumptions.

• The ratio LA/A is therefore= gA/δ.

• Suppose the increase in SR occurs at time t=0.

• With a population of L0, the number of researchers increases as SR increases so that the ratio LA/A jumps to a higher level.

• The additional researchers produce an increased number of new ideas, so the growth rate of technological is also higher at the point.

• This situation corresponds to the point labeled “X” in the above figure.

• At point X, technological progress Å/A> population growth n, so the ratio LA/A declines over time, as indicated by the arrows.

• As this ratio drops, the rate of technological change gradually falls also, until the economy returns to the BGP where gA=n.

• So, 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.

(h) 3 Distortions in achieving R&D optimal

First:The market value the research according to the

stream of profits that earned from new design but when market missing, new invention may affect the future research.

If Φ>1 = productivity of research↑ with stock of ideas.

The problem : Missing market, researchers not compensated of contribution toward improving the productivity of future research .

So , Φ > 0 , there is tendency (other things equal) for the market provide too little research.

‘Knowledge spills over ’

Second

‘Steeping on toes’ effectThere may be too many researchers either

duplicating the same research work, which may provide negative externality.

When λ < 1 , lower research productivity, show some ideas created by an individual researcher may not be new to the economy .

Third: ‘Consumer surplus’ effect Standard monopoly Inventors of new design

capture profit shown but potential gain to society is whole triangle above MC of production.

Incentive to innovate (profit)< gain to society , this will tends to generate little innovations, other things being equal.

P

MC

Price

Consumer surplus ( whole triangle

above MC)

Demand

Q

Profit

0