New Growth Theory Flashcards
(27 cards)
Issue with Solow model
Cannot account for cross-country income differences as capital’s share is small - everything is explained by A (tech) which is not sufficient
Hence introduced new growth theory
Focus on 1st approach: R&D
Why are ideas different from other economic goods (2)
PUBLIC GOODS
Ideas are non-rivalrous (using an idea does not prevent others from using it too)
Ideas also only partially excludable (depending on tech and legal system
What would we expect the cost of an idea to be
Fixed cost - since non-rival.
Either bought from independent R&D firm, or developed internally. Either way once acquired, use of ideas are costless
Suppose cost function C(q) = F + cq
q is quantity of product
F is fixed (research) cost (likely large)
c is constant MC
What would AC be
B) is AC><=MC
AC = F/Q + c
B) AC>MC
If producer of idea is a small perfect competitor.
How does it compete
B) draw diag
Price taker so P=MC
B) draw AC downward sloping, but recall AC>MC.
Also no production at this point, as making a loss
So no production of ideas with perfect competition.
What about monopolies
B) Draw diagr
C) what is a caveat to this
Yes
C) underproduce ideas compared to a social optimum.
Problems with public production of ideas (2)
Financed by distortionary taxes - public dishappy
Public may also prefer private R&D and accept monopoly power, as long as they get innovation!
Issue of non-excludability
Non-excludability means private production will not occur (since cannot stop others from using ideas, thus no one produces! Free rider problem)
Hence why we need ideas to have some excludability e.g patent
Now model it:
2 sectors - goods sector and R&D sector
Fraction aL of labour in R&D, 1-aL in goods sector.
Both use knowledge/tech A
What is key difference from Solow model
Tech growth was exogenous in Solow, now is endogenised.
How is it tech growth now endogenised?
Production function for new ideas i.e more researches = more ideas
So what is output equation Y (in goods sector)
B) what about the production function for new knowledge (A.)( (R&D sector)
Pg13
Y = A(1-aL)L
B)
A. = B[aLL] to the γ A to the ø
A is current ideas
A. - new ideas
aLL : number of people attempting to discover new ideas
Ø > 0 productivity of research increases with stock of ideas already discovered (since built upon ideas! Ideas are rarely completely new!!)
What about R&D sector’s returns to scale to labour
Can be IRS CRS or DRS i.e γ>=<1
I.e increasing labour, can have knowledge transfer and IRS, or increasing labour could cause distractions working together! So decreasing returns.
How is K. (Change in capital stock) different to normal Solow
B) K. = sY (saving is a constant proportion of output)
(No δk in this as looking at human capital not physical)
Call growth rate of A gA.
What does output Y grow at
B) what does output per worker Y/L grow at
n + gA
B)
gA (since /L removes L from both sides which grows at rate n, so now just gA!
Growth in A gA expression (pg 17)
A. = B[aLL] to the γ A to the Ø
Divide by A
gA = A./A = B[aLL) to the γ A to the ø-1
Simple: we just divided by A. Basically the same except last term because
A to the ø / A = A to the ø-1 !!!!
Take logs of gA expression pg17
B) then differentiate with respect to time, why? Show 2 final expressions (g.A/gA and g.A)
LogGa = logBaL to the γ + ylogL + (ø-1)logA
Ba constant so do not separate
B) differentiate to get growth rates. Final eq:
g.A/gA = yn + (ø-1)gA
g.a = [γn + (ø-1)gA]gA
Scenario 1: ø<1
When is there a stable equilibrium value of gA (expression)
Pg 19
B) draw diagram
C) on diagram, where is highest growth rate (turning point)
Rearrange to get stable value
g*A = yn/1-ø
B) Y axis g.A, X axis gA
When gA<gA, positive growth rate of knowledge
gA>gA, negative/falling growth rate of knowledge.
Stable equilibrium value as left of g*a increases, while right of it moves back left.
C) ga = yn/2(1-ø) since its halfway of g*a!
When Ø<1 , what can we say about aL
B) add it onto the diagram
aL is not in the ga equation!!!
aL does not effect the growth rate gA - it has a level effect on A
(Just like how savings rate s only has level effect in Solow model, affects growth rate only temporarily)
B) draw arrow increasing ga but then arrows go backwards as only temporarily, then return to steady state.
So when ø<1, an increase in aL does not affect the growth rate of tech.
What does it affect
B) diagram to show effect pg21
An increase in aL increases PERMANENT level of technology (A), but not the growth rate of it! (LEVEL EFFECT NOT GROWTH EFFECT)
B) lnA y axis,
Time x axis.
Draw dotted line as counterfactual, but then an increase in slope to show higher temporary growth rate. (This will fall back down overtime)
Scenario 2: if ø>1
Is g.a still positive?
Using g.a = [yn - (ø-1)ga]ga
Since gA>0, g.A>0
Since growth rate is positive, growth rate is also increasing! (Unlike when ø<1 since growth rate could be negative beyond steady state g*A= yn/1-ø)
So if positive growth rate (gA>0) and also increasing rate of growth g.A>0
What does this look like on diagram
Convex, curving upwards since ever increasing g.A>0!
So ever increasing growth rather than convergence!
Unlike when ø<1 where growth rate is positive and increasing, and then goes negative!
We saw with ø<1 an increase in aL does not effect gA.
What about now when >1?
aL ↑⇒ gA ↑⇒ g ̇A ↑
So now it does have a permanent effect on growth rate!
Scenario 3: ø=1
What do we get for gA and g.A
gA = B[aLL] to the γ
(A disappears since A¹-¹=0)
g.A = [yn - (1-1)ga]ga
=yngA
So when ø=1, if n>0, and how does this look in diagram
B) what if n=0
gA grows overtime at rate yn (straight upward sloping)
B)
Growth rates of K,Y and Y/L all constant and positive equaling B[aLL] to the γ,
thus aL impacts long run growth rate (permanently rises it to a higher constant level)
