4. Learning-by-doing Model Flashcards
What is the learning by doing model?
It is an AK economy with technical progress
What does learning by doing stand for?
An innovation process where productivity gains are achieved through repetitions
What does the state of technology depend on?
The stack of capital per capita Bt=Kt/Lt
What is aggregate technology?
AK since all firms are identical
What is the social return to capital?
A
What is the private return to capital?
Alpha x A
Is the private return to capital bigger or smaller than the social return to capital?
Smaller
Alpha x A <A
Why is the equilibrium growth rate smaller than optimal?
Because private returns to investment are smaller than social ones
What would restore optimality?
A subsidy that increased the private return to A
At what rate does the state of technology grow?
g
What do Levitt, List, and Syverson 2013 find about technical progress?
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
What is the production technology when human capital is included?
Y= K^(alpha) H(1-alpha)
When human capital is included how can output be allocated?
Y=C+I+E where E is education
What is the optimal capital to human capital ratio?
K/H= alpha/(1-alpha)
How does the equilibrium with human capital compare to the AK model?
Y=AK
The economy is identical to the AK model
It has the same properties
Investment in human and physical capital are fully reversible
What does the economy learn from?
The production of capital goods
What is the equation that firms maximise?
Max AK^(alpha) x (BL)^(1-alpha)- (r+delta)Ki- wLi
From the Euler equation, what is the growth rate of output per capita at equilibrium?
g=ó(alpha x A- delta- rho)>0
What is the engine of growth?
Learning by doing. The state of technology grows at rate g
How do human and physical capital accumulate?
K(dot)=I- delta x K
H(dot)= E- delta x K
Delta’s may be different
What do firms maximise when they have human capital
Max K^(alpha) x H^(1-alpha)- (r+delta)K- (r+ delta)H
Arbitrage between the two forms of capital equalises both user costs
What does investment in human and physical capital being fully reversible imply?
Ko/Ho= alpha/(1-alpha)
What is the technology of firm i?
Yit= AKit^alpha x (BtLit)^(1-alpha)
What do we get when we differentiate Bt=Kt/Lt wrt time?
B(dot)t/Bt=K(dot)t/Kt- n
What is the real interest rate?
FOC from profit max problem gives
r+ delta= alpha x A(Ki/BLi)^(alpha-1)
r=alpha x A -delta
What are the FOCs from firm profit max with human capital?
r+delta= alpha x Y/K = (1-alpha) x Y/H
What is equilibrium technology in the model with human capital? Why is this significant?
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
Do the social planner and competitive equilibrium give the same answer?
No because private and social returns are different and the firms don’t consider the social returns
In ancient societies how might technology progress?
-technological progress isn’t self conscious
-mutations: imitation entails discrepancies (intentional or not)
-Selection implies progress: learning by doing
