6. Schumpeterian Model Flashcards
How is the state of technology represented in the model?
By the distribution of quality Qjt across the intermediate inputs
What is the engine of growth
Quality improvement which is made possible by R&D raising the quality of intermediate inputs
What is the probability of improving the quality of any variety dependent on?
Their current quality
What can be said about the distribution of relative qualities in equilibrium?
Uniform with density 1
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
What is the cost of hiring a researcher?
wt
What is the value of the patent denoted by?
vt
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
What does r denote?
The stationary interest rate
What does the returns of patents result from?
Profits to value ratio
Capital gains
Business stealing
Obsolescence
What needs to be satisfied at the equilibrium?
Feasibility condition
Euler equation
Return to innovation
Transversality condition
What does growth rate depend on?
Positively on productivity A and the mark up 1/alpha, negatively on rho
What are preferences of the representative household represented by?
U= integral of log(cte^(-rhot)) dt
What is the euler equation?
c(dot)t/ct= rt- rho
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
What is hjt?
The mass of researchers in j
What is the probably for each xjt that a new version arrives?
A poisson process with arrival rate
mu jt =Ahjt
What is a schumpeterian assumption?
That creative destruction leads to business stealing
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
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
