WEEK 7 - Endogenous Growth Theory Flashcards
What does Endogenous Growth Theory explain?
Explain the behaviour of the rates of technological progress and/or productivity growth, rather than merely taking these rates as given.
- a set of models in which the growth rate of productivity and living standards is endogenous
What is the production function behind the growth theory?
Y = AK
Where:
A is amount of output for each unit of capital (A is exogenous and constant)
- MPK constant here and diminishes in Solow
What is Investment and Depreciation denoted by?
sY - Investment
δK - Depreciation
What is the law of motion for total capital?
ΔK = sY - δK
How do we get the overall equation behind the law of motion?
ΔK = sY - δK
1. Divide through by K and use Y = AK to get,
ΔY/Y = ΔK/K = sA - δ
- If sA >δ , then income grow forever and investment is engine of growth
- Here perm growth rate depends on s, In solow model it doesn’t
Why are Y and K equal?
Y = AK, so the growth rate of Y equals the sum of the growth rates of A and K. A is constant, so its growth rate is zero.
Hence, output and capital grow at the same rate.
What are 3 facts about R&D in the real world?
- Much research is done by firms seeking profits.
- Firms profit from research because new inventions can be patented, creating a stream of monopoly profits until the patent expires there is an advantage to being the first firm on the market with a new product
- Innovation produces externalities that reduce the cost of subsequent innovation.
The Growth theory attempts to incorporate that into better understanding tech progress
What is the assumptions of the arrow approach?
R&D as accidental by-product of production process
Model of economy given by:
Y = BKαL1-α
Also assume accumulation of capital results in externality capturing ‘learning by doing’ where A is a constant:
B = AK1-α
Combining both equations yield:
Y = AK1-αKαL1-α = AKL1-α
What does Endogenous growth theory argue regarding capital?
Knowledge is a type of capital
So, constant returns to capital plausible
How do we find out about the other economic implications of the basic AK Model?
Finding growth rate of Y, via taking logs then derivatives of Y = AK with respect to time.
Will imply that Y/Y = K/K
- Growth rate of capital = Growth rate of output
What can be implied via K/K?
Assume motion for capital given by;
K = sY - δK
- If all savings = Investment and no pop growth
-dividing motion of capital through by K will yield K/K = sY/K - δ
- AK production function can be manipulated to give A = Y /K, this implies that:
K /K = sA
So,an increase in the saving rate leads to a permanently higher growth
What is the Solow Diagram for the AK model?
SEE IN NOTES
How does the ‘learning by doing’ model of Arrow fit into the AK model?
- If B (from production function) is accumulated endogenously, implies overall, production characterised by increasing returns to scale
- B captures knowledge about the economy, generated
as a result of capital accumulation by firms - B=AKa shows B increases as K does
- capital accumulation leads to new knowledge, which is an unintended consequence of the production process, because firms only accumulate capital because useful production input
What is the shortcomings of the Arrow Model?
Shows knowledge accumulated accidentally.
When firms actually search for knowledge purposefully shown in Romer’s model
What does Romer’s model argue?
models of endogenous growth in which technological progress was driven by the (purposeful) production of ideas and innovation
What is Charles Jones view on R&D being an accidental spillover?
- That’s BS
- Knowledge accumulation desired outcome of entrepreneurial effort
What is Romer and Jones argument on excludability and rivalrous goods?
Romer emphasizes
that ideas differ significantly from other goods, in drawing on the concepts of their rivalrous / non-rivalrous nature, and their excludability
- Jones: Ideas are non-rivalrous, but can be excludable (copyrights and patents in order to keep incentive to innovate higher)
SEE GRAPH IN NOTES
Why ideas tied to the presence of increasing returns to scale?
- Attributable to a high fixed cost of developing the product and constant MC of producing units of the product once fully developed
- doubling the input hours
more than doubles output.
SEE GRAPH IN NOTES
How do prices and costs differ as a result of production
- At higher lvls of production, inital fixed cost spead over more and more units, AC declines as scale of production rises
- If P set at MC, AC outweigh MC of production
Under increasing returns, firm would not set price equal to MC as it leads to negative profit. Firms thus charge more than MC to recover Fixed costs associated with product development
What is a way to quantify the rate of innovation?
Jones notes that patent counts can show number of ideas produced
Numbers on patents?
US 1880: 13,000
US 1999: 150,000
What is the downside to using the number of patents as a tracker to new ideas?
Not all ideas are patented
e.g Coca Cola, if patented when created in 1886, people could copy, instead just hide recipe
What is one of the most convincing mechanisms for the creation of ideas?
Considering scientific and research activity as an input
- governments associate the benefits and spillovers from domestic R&D activity with increased economic competitiveness and economic strength (i.e STEM encouragement)
What are the elements of Romer’s model?
- Technological progress is explicitly modelled: we are therefore introducing a theory of technological progress
- The production of ideas is viewed as process driven by the desire to make profits
- innovation is driven by the possibility that higher profits will be generated.
model can be viewed as building directly on Solow’s contribution
How do we denote the capital stock in Romer’s model?
ΔK = skY - δK
Change in capital stock at a given point in time defined as the difference between investment and depreciation
How do we assume total population to grow in Romer’s model?
ΔL/L = n
How do we model technology in Romer’s model?
A(t) - Stock of ideas at time t (Sum of all ideas ever produced)
A dot = δ bar LA
Where:
- A dot: Number of ideas produced at given point in time
- La: Number of individuals in economy responsible for production of ideas
- δbar: Rate at which new ideas discovered (also function of stock of ideas)
Assuming δ bar is the function of the stock of ideas how can we rewrite the model of technology?
δ bar = δ Aφ
Where φ and δ are constants
Can rewrite tech as:
A dot = δAφ La
Why is the φ parameter important?
φ > 0 implies research productivity increases with stock of ideas
φ <0 is fishing out case where fish become harder to catch over time
φ = 0, implies both of above cases cancel out. As A0 = 1, implies productivity of research independent of knowledge stock
What is Romer’s expression of labour?
L = La + Ly
Where:
La is no of individual responsible for production of ideas
Ly is no of individuals responsible for production of output
What can we assume about the overall labour market therefore?
La/L = sr Ly/L = (1-sr)
Where:
sr denotes total proportion of people in the economy devoted to research
How can finally rewrite the Number of ideas produced at given point in time? (Final number of ideas formula)
A dot = δAφLλA
Where;
Parameter 0
What does Jones refer to with λ and φ?
φ as standing on the shoulders of giants effect
λ as standing on the toes of other effect
What is meant by the standing on the shoulders of giants effect?
Spillover effects of previous researchers/innovators allows for others to further innovate
What is meant by the stepping on the toes of others effect?
Essentially stopping someone else from innovating so you can innovate
What is the steady state in Romer’s model?
gy = gk = ga
Where:
e growth rate of both output per worker
(gY ) and capital per worker (gK ) must be the same as that for the growth rate of technology, (gA).
In absence of tech progress (ga =0), no growth in y
How do we find the steady state?
To find steady state of ga, get expression for tech (final one) and divide through by a
Adot/A = δAφLλA/A = δAφLλA/ A1- φ = ga
How do we find precise ga considering a balanced growth rate?
Taking logs and derivatives of steady state finding (ga)
Equation is:
- 0 = λ1/L L* - (1 - φ) 1/A A dot
How do we find the growth rate of researchers?
the growth rate
of the number of researchers must equal the growth rate of the whole
population. Put another way,
LdotA/LA= n
Implies precise Ga can be rewritten as:
0 = λ n - (1 - φ) ga
How do we find the growth rate of technology along the balanced growth path?
Ga = λ n/(1 - φ)
Ga is function of λ, n, φ
What is the effect of a rise in the proportion of population devoted to R&D?
Assuming λ = 1 (no standing on toes), φ = 0, so growth rate of A equals growth rate of population
SEE NOTES AND GRAPH IN NOTES
What does the growth rate of technology over time look like?
SEE GRAPH IN NOTES
What does the lvl of technology look like over time?
SEE GRAPH IN NOTES
Impact of number of researchers, permanently increases lvl of A: level effect arises
What does steady state growth per capita look like?
y*(t) = (sk/n+ga+d)to power of a/1-a x (1-sr) x δsr/ga
1-sr: Increasing number of researcher reduces number of workers producing goods in factories. Leads to fall in y*
-Offset by positive sr term: more researchers implies more ideas, which increases economic productivity.
-The presence of L(t) implies that a greater population leads to higher
levels of output per worker.
What are the 2 effects Jones identifies from the presence of L(t)?
- Supply Effect:
the greater the population, the more potential creators
of ideas (so higher populations are more desirable - Demand Effect:
the greater the population, the larger the market for
an idea, raising the return to research.
What is Romer’s production function?
Y = Ka(ALy)1-a
assume that A is going to be a function of some other variables and parameter (technology parameter)
