4. Learning-by-doing Model

Question 1

What is the learning by doing model?

Answer 1

It is an AK economy with technical progress

Question 2

What does learning by doing stand for?

Answer 2

An innovation process where productivity gains are achieved through repetitions

Question 3

What does the state of technology depend on?

Answer 3

The stack of capital per capita Bt=Kt/Lt

Question 4

What is aggregate technology?

Answer 4

AK since all firms are identical

Question 5

What is the social return to capital?

Answer 5

A

Question 6

What is the private return to capital?

Answer 6

Alpha x A

Question 7

Is the private return to capital bigger or smaller than the social return to capital?

Answer 7

Smaller

Alpha x A <A

Question 8

Why is the equilibrium growth rate smaller than optimal?

Answer 8

Because private returns to investment are smaller than social ones

Question 9

What would restore optimality?

Answer 9

A subsidy that increased the private return to A

Question 10

At what rate does the state of technology grow?

Answer 10

g

Question 11

What do Levitt, List, and Syverson 2013 find about technical progress?

Answer 11

Cumulative production improves productivity but at a decreasing rate. This casts doubt on the assumption that in modern times growth is the result of pure learning by doing

Question 12

What is the production technology when human capital is included?

Answer 12

Y= K^(alpha) H(1-alpha)

Question 13

When human capital is included how can output be allocated?

Answer 13

Y=C+I+E where E is education

Question 14

What is the optimal capital to human capital ratio?

Answer 14

K/H= alpha/(1-alpha)

Question 15

How does the equilibrium with human capital compare to the AK model?

Answer 15

Y=AK
The economy is identical to the AK model
It has the same properties
Investment in human and physical capital are fully reversible

Question 16

What does the economy learn from?

Answer 16

The production of capital goods

Question 17

What is the equation that firms maximise?

Answer 17

Max AK^(alpha) x (BL)^(1-alpha)- (r+delta)Ki- wLi

Question 18

From the Euler equation, what is the growth rate of output per capita at equilibrium?

Answer 18

g=ó(alpha x A- delta- rho)>0

Question 19

What is the engine of growth?

Answer 19

Learning by doing. The state of technology grows at rate g

Question 20

How do human and physical capital accumulate?

Answer 20

K(dot)=I- delta x K

H(dot)= E- delta x K

Delta’s may be different

Question 21

What do firms maximise when they have human capital

Answer 21

Max K^(alpha) x H^(1-alpha)- (r+delta)K- (r+ delta)H

Arbitrage between the two forms of capital equalises both user costs

Question 22

What does investment in human and physical capital being fully reversible imply?

Answer 22

Ko/Ho= alpha/(1-alpha)

Question 23

What is the technology of firm i?

Answer 23

Yit= AKit^alpha x (BtLit)^(1-alpha)

Question 24

What do we get when we differentiate Bt=Kt/Lt wrt time?

Answer 24

B(dot)t/Bt=K(dot)t/Kt- n

Question 25

What is the real interest rate?

Answer 25

FOC from profit max problem gives

r+ delta= alpha x A(Ki/BLi)^(alpha-1)

r=alpha x A -delta

Question 26

What are the FOCs from firm profit max with human capital?

Answer 26

r+delta= alpha x Y/K = (1-alpha) x Y/H

Question 27

What is equilibrium technology in the model with human capital? Why is this significant?

Answer 27

Y=AK

A=(1-alpha)/alpha)^(1-alpha)

The economy is formally identical to the AK model. It has the same properties. Investment in human and physical capital are fully reversible

Question 28

Do the social planner and competitive equilibrium give the same answer?

Answer 28

No because private and social returns are different and the firms don’t consider the social returns

Question 29

In ancient societies how might technology progress?

Answer 29

-technological progress isn’t self conscious
-mutations: imitation entails discrepancies (intentional or not)
-Selection implies progress: learning by doing