6. Schumpeterian Model Flashcards by owen Knowles

How is the state of technology represented in the model?

By the distribution of quality Qjt across the intermediate inputs

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What is the engine of growth

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

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

Their current quality

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

Uniform with density 1

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

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

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What is the cost of hiring a researcher?

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What is the value of the patent denoted by?

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

The better the quality of the patent the more it cost

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What does r denote?

The stationary interest rate

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What does the returns of patents result from?

Profits to value ratio
Capital gains
Business stealing
Obsolescence

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What needs to be satisfied at the equilibrium?

Feasibility condition
Euler equation
Return to innovation
Transversality condition

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What does growth rate depend on?

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

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What are preferences of the representative household represented by?

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

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What is the euler equation?

c(dot)t/ct= rt- rho

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

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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What is hjt?

The mass of researchers in j

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

A poisson process with arrival rate
mu jt =Ahjt

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What is a schumpeterian assumption?

That creative destruction leads to business stealing

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

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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What does the frontier technology evolve according to?

Q(dot)t/Qt= Aht

Where ht = integral of hjt dj
Aggregate research effort

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

Their current quality

What is Ah?

The rate of technical progress which endogenously depends on research

What is qj?

qj= Qj/Q

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

What is the equilibrium density distribution denoted by?

Ø(q)

At the monopolistically competitive equilibrium what is the price?

pt= 1/alpha x wt

At the monopolistically competitive equilibrium, what are the quantities?

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

How is demand affected by quality?

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

What is the aggregate consumption technology?

ct= Aq(bar)QtLt= A£tLt This is total factor production

What is the production labour?

Lt= integral of łj dj

What is q(bar) equal to?

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

What is the state of tech defined as?

q(bar)Qt= £

How does the state of knowledge evolve?

Following Q(dot)t/Qt= £(dot)t/£t= Aht

How does the actual state of tech evolve?

£(dot)t= A£t(1-Lt) Where (1-Lt)= ht

Whet is the feasibility condition?

£(dot)t=A£t-ct

What is the relative price of intermediate products?

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

What is the zero profit condition for R&D?

wt=Avt vt=alpha£t

What is the production cost of a patent increasing with?

The average quality of patents £t

What is the value of a patent?

The expected discounted flow of profits generated by the profits

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

e^(-Ah(s-t))

What is the profits to value ratio given by?

Profits tt/ vt =AL/alpha

What are capital gains equal to?

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

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

Profits ts= (1-alpha)ps x xts So profits depend on the time t the innovation was patented

Obsolescence of patents

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

Return to innovation equation

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

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

£t=£0e^gt ct=(A-g)£t With g=(1-alpha)(A-alpha x p) > (1-alpha)A- alpha x p

What does growth rate depend on in equilibrium?

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

How does business stealing and obsolescence compare to rent rent spillovers

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

What is the optimal growth rate?

g = A-rho The economy is AK