Lecture 13 - Endogenous Growth

Question 1

Creative destruction growth model

Answer 1

Economy is in a permanent state of flux, with old firms, market and industries dying out, and new ones arising to create growth.

Question 2

Why was this a positive

Answer 2

New products developed and more being produced.

Question 3

What negative effects

Answer 3

Old industries disappear, old skills no longer required.

Question 4

So what is there constant need for? And what must firms be able to do?

2. What may policymakers have to do, and evaluate it.

Answer 4

Innovation - firms must be able to exploit monopoly power when they innovate successfully to receive reward (monopoly profit) and continue to innovate

2. policy may have to intervene to incentivise innovation e.g through patents to allow monopoly profits.

Eval: we don’t wanna restrict it too much, as innovation has a public good component; much innovation is built on previous innovations. (patents could limit potentials)

Question 5

Ideas are what? And evaluation

Answer 5

Non rival - can be used by anyone.

However their application can be excludable e.g by patents

Question 6

What does ideas as a driver of growth move us away from?

Answer 6

The assumption of diminishing returns.

As ideas are non-rival, they can interact with other inputs to prevent diminishing returns.

e.g using knowledge and physical capital as a single input can generate constant returns

Question 7

We can use this idea of ideas/knowledge combining as a single input to eliminate DMR and create constant returns by the
Basic AK Romer Model

Answer 7

1. Use production function, and assume K with knowlegde delivers CRS. (Since when we find MPK we just get A)
   Y=AK
   (leave out labour for now)
2. Use basic Solow model with savings rate s and depreciation rate δ, to work out change in capital formula
   Savings S=sY (savings is investment, just rewritten i=sY)
   ΔK = sY -δK (just rewritten ΔK=i-δk)
3. Sub in Y=AK into the change in capital formula.
   ΔK=sAK - δK and we can divide by K to get growth rate of capital. (Essentially difference/original)
   ΔK/K = sA - δ

Assuming A constant we can see that that
ΔY/Y = ΔK/K = sA - δ
Because Y=AK, if K is growing at rate g= sA-δ, then Y is also growing at that rate.

Question 8

What does this show?

2. Graph of time of the AK Romer Model (over period 1, 2 and 3

Answer 8

As output and capital grow at the same rate (sA - δ), it shows a balanced growth path.

2. Graph shows output, savings and capital all grow by 1+g each period (constant returns)
   Remember g=sA - δ

Question 9

Romer model with production of ideas: 5 steps.
(i.e how much ideas influence growth)

(Hint: we need 2 production functions, a G&S and ideas one)

Answer 9

1. Use a (g&s) prod function that has ideas (A) and labour as inputs.
   Yt = AtNyt

Nyt is labour used for output at time t

2. Then create another prod function for ideas.
   ΔAt+1= At+1 - At = zAtNat
   (Change in ideas between t+1 and t) = zAtNat

z measures productivity for producing ideas
Nat is labour used in producing ideas

3. Add labour market equilibrium
   N*= Nyt + Nat
   (labour at time t (for g&s) + labour used at time t (for ideas)
4. Assume a fixed proportion of labour μ works in production of ideas

Nat= μN* (since μ is a proportion e.g 60% or 0.6 of total N)
Nyt= (1-μ)N (0.4 of total N* in this case work in G&S)

5. Put this Nyt into original G&S production function (AtNyt)
   Yt=At(1-μ)N*

Then divide by ideas production function by At, also replace Nat for the new one to find growth rate of knowledge
ΔAt+1/At = zNat = zμN*

Growth of knowledge g=zμN*
Which shows if ideas grow at this rate, so does output Y (since Yt = AtNyt is Yt=At(1-μ)N* includes At which grows at zμN*

Question 10

Diagram visualising the output path of
Romer model vs Solow model

Answer 10

Pg 8.

Romer is linear upward sloping meaning constant growth rate, since we assume CRS(no diminishing returns due to ideas). Balanced growth path substitutes for steady state

Solow is concave as DMR exist.

Question 11

An increase in total labour force

Use Romer model

Answer 11

Using g = zμN*

N* increases, so g increases.
More people increase idea production.

Diagramatically, assume N* increase occurs at time t=₀, we see a steepening since g increases from the orginal path.

Question 12

Scenario 2:
An increase in the proportion of workers in the ideas industry (μ)

Answer 12

Increased μ means g increases.

However, we also see a fall in Y since fewer workers are employed in G&S market. Recall Nyt = (1-μ)N*

So output falls initially, but then grows quicker as g higher.

Question 13

What if an economy adopted a skilled migration policy

Answer 13

Add Nm to ideas production function

Change in ideas from t+1 to t = ZAt(ZμN* + Nm)

Then divide this function by At to get growth rate of ideas (
ΔAt/At (difference/original = growth rate)
g= Z(μN* + Nm)

Question 14

How is this shown graphically

Answer 14

We have the initial slope of g=zμN* , and then g=z(μN*+Nm) creates another slope steeper at t₀ (the time when the skilled migration policy is implemented)

Question 15

So what if z>1, or <1

Answer 15

If z>1 , labour in the ideas industry is more productive than the labour in the G&S industry.

Vice versa.

Extra: Bloom et al in real life, Z seems to be going down; more people enter ideas industry but production of ideas has fallen.

Question 16

So basic romer model shows how ideas contained in capital stock K influences output (K and Y same growth rate sA-δ

Romer model with ideas shows how production of ideas influence output (Ideas At and Y same growth rate zμN*)