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ECON 4016 Macro Theory > 6. Schumpeterian Model > Flashcards

6. Schumpeterian Model Flashcards

1
Q

How is the state of technology represented in the model?

A

By the distribution of quality Qjt across the intermediate inputs

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2
Q

What is the engine of growth

A

Quality improvement which is made possible by R&D raising the quality of intermediate inputs

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3
Q

What is the probability of improving the quality of any variety dependent on?

A

Their current quality

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4
Q

What can be said about the distribution of relative qualities in equilibrium?

A

Uniform with density 1

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5
Q

How do prices and demand interact in the monopolistic competition of final products?

A

All firms set the and price but demand is larger for firms with better quality goods

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6
Q

What is the cost of hiring a researcher?

A

wt

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7
Q

What is the value of the patent denoted by?

A

vt

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8
Q

How are the average production cost of a patent and the average quality of a patent related?

A

The better the quality of the patent the more it cost

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9
Q

What does r denote?

A

The stationary interest rate

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10
Q

What does the returns of patents result from?

A

Profits to value ratio
Capital gains
Business stealing
Obsolescence

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11
Q

What needs to be satisfied at the equilibrium?

A

Feasibility condition
Euler equation
Return to innovation
Transversality condition

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12
Q

What does growth rate depend on?

A

Positively on productivity A and the mark up 1/alpha, negatively on rho

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13
Q

What are preferences of the representative household represented by?

A

U= integral of log(cte^(-rhot)) dt

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14
Q

What is the euler equation?

A

c(dot)t/ct= rt- rho

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15
Q

What is the equation showing how the firm produces final consumption by operating technology?

A

ct= A( integral of (Qjt x xjt)^alpha dj)^1/alpha

xjt is the quantity of intermediate input j
Qjt is the quality of intermediate input j

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16
Q

What is hjt?

A

The mass of researchers in j

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17
Q

What is the probably for each xjt that a new version arrives?

A

A poisson process with arrival rate
mu jt =Ahjt

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18
Q

What is a schumpeterian assumption?

A

That creative destruction leads to business stealing

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19
Q

What happens when a discovery takes place in sector j at time t?

A

The quality of the new version moves to the technological frontier, Qt. Qt is the leading edge quality in period t

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20
Q

What does the frontier technology evolve according to?

A

Q(dot)t/Qt= Aht

Where ht = integral of hjt dj
Aggregate research effort

21
Q

What is the probability of improving the quality of any variety independent to?

A

Their current quality

22
Q

What is Ah?

A

The rate of technical progress which endogenously depends on research

23
Q

What is qj?

A

qj= Qj/Q

the relative quality of variety j (relative to the frontier technology)

24
Q

What is the equilibrium density distribution denoted by?

A

Ø(q)

25
Q

At the monopolistically competitive equilibrium what is the price?

A

pt= 1/alpha x wt

26
Q

At the monopolistically competitive equilibrium, what are the quantities?

A

xqt = Ätq^(alpha/1-alpha) x pt^(1/alpha-1)
Where Ät= (AQt)^(alpha/1-alpha) x ct

27
Q

How is demand affected by quality?

A

All firms set the same price but demand is larger for firms producing better quality

28
Q

What is the aggregate consumption technology?

A

ct= Aq(bar)QtLt= A£tLt

This is total factor production

29
Q

What is the production labour?

A

Lt= integral of łj dj

30
Q

What is q(bar) equal to?

A

q(bar)= integral of (q^(alpha/1-alpha) dq)^(1-alpha/alpha) = (1-alpha)^(1-alpha/alpha)

31
Q

What is the state of tech defined as?

A

q(bar)Qt= £

32
Q

How does the state of knowledge evolve?

A

Following

Q(dot)t/Qt= £(dot)t/£t= Aht

33
Q

How does the actual state of tech evolve?

A

£(dot)t= A£t(1-Lt)

Where (1-Lt)= ht

34
Q

Whet is the feasibility condition?

A

£(dot)t=A£t-ct

35
Q

What is the relative price of intermediate products?

A

pt=A£t

Since one unit of labour produced one unit of intermediate inputs but it can also produce A£t units of aggregate consumption

36
Q

What is the zero profit condition for R&D?

A

wt=Avt

vt=alpha£t

37
Q

What is the production cost of a patent increasing with?

A

The average quality of patents £t

38
Q

What is the value of a patent?

A

The expected discounted flow of profits generated by the profits

39
Q

What is the survival probability of a new patent from t to s?

A

e^(-Ah(s-t))

40
Q

What is the profits to value ratio given by?

A

Profits tt/ vt =AL/alpha

41
Q

What are capital gains equal to?

A

The innovation rate Ah since at equilibrium the value of patents follow the average quality

42
Q

What are the profits of an innovation patented at time t, s>t

A

Profits ts= (1-alpha)ps x xts

So profits depend on the time t the innovation was patented

43
Q

Obsolescence of patents

A

As time passes, demand and profits of current patents fall due to innovation

44
Q

Return to innovation equation

A

rt=ALt/alpha - alpha/(1-alpha) x A(1-Lt)

45
Q

Under the assumption alpha< A/(rho+A) what is the equilibrium?

A

£t=£0e^gt
ct=(A-g)£t

With
g=(1-alpha)(A-alpha x p) > (1-alpha)A- alpha x p

46
Q

What does growth rate depend on in equilibrium?

A

Depends positively on productivity A and the markup 1/alpha, negatively on rho

47
Q

How does business stealing and obsolescence compare to rent rent spillovers

A

The direct and negative cost of business stealing and obsolescence may more than compensate rent spillovers

48
Q

What is the optimal growth rate?

A

g = A-rho

The economy is AK

ECON 4016 Macro Theory (8 decks)

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