Romer Growth Model Flashcards
What are objects?
Inputs which are finite and rivalrous e.g. capital and labour in the Solow model
What are ideas?
Inputs which are virtually infinite and nonrivalrous. Used to make and improve objects
(not necessarily public goods as still may be excludable e.g. through a patent)
How are ideas accounted for in the Cobb-Douglass production function?
π΄ accounts for ideas just as it does productivity
Labour Resource Constraint Equation
- πΏπ¦π‘ workers produce output
- πΏππ‘ workers produce ideas
πΏπ¦π‘ + πΏππ‘ = πΏ
Workers on output + workers on ideas = total workers
πΏπ¦π‘ + πΏππ‘ = πΏ
Labour Resource Constraint Equation
Allocation of Labour Equations
πΏπ¦π‘ = (1 β π)πΏ
πΏππ‘= ππΏ
Where (1 β π) is the proportion of workers producing output and π is the proportion producing ideas
πΏπ¦π‘ = (1 β π)πΏ
πΏππ‘= ππΏ
Allocation of Labour Equations
Output Production Function
ππ‘ = π΄π‘πΏπ¦π‘
Output = Stock of Existing Knowledge x Workers producing Output
ππ‘ = π΄π‘πΏπ¦π‘
Output Production Function
Ideas Production Function
βπ΄π‘+1 = π§π΄π‘πΏππ‘
Change in Stock = Productivity of Workers producing Ideas x Existing Stock x Workers producing Ideas
βπ΄π‘+1 = π§π΄π‘πΏππ‘
Ideas Production Function
Output-per-Person Equation (Dependent on π΄π‘)
π¦π‘ β‘ ππ‘/πΏ = (π΄π‘πΏπ¦π‘)/πΏ = π΄π‘(1 β π)
Output per person dependent on the total stock of ideas (π΄π‘)
π¦π‘ = π΄π‘(1 β π)
Output-per-Person Equation (Dependent on π΄π‘)
Growth Rate of Knowledge Equation
(βπ΄π‘+1)/π΄π‘ = π§πΏππ‘ = π§ππΏ
Growth rate of knowledge is constant as z, l, and L and all exogenous (should have bars)
(βπ΄π‘+1)/π΄π‘ = π§ππΏ
Growth Rate of Knowledge Equation
Total Stock of Knowledge Equation
π΄π‘ = π΄0(1 + π)^π‘ where π β‘ π§ππΏ
The stock of knowledge depends on its initial value and its growth rate
π΄π‘ = π΄0(1 + π)^π‘
Total Stock of Knowledge Equation
Output-per-Person Equation (entirely as a function of parameters)
π¦π‘ = π΄0(1β π)(1 + π)^π‘
Combined Output-per-Person Equation (Dependent on π΄π‘) and Total Stock of Knowledge Equation
π¦π‘ = π΄0(1β π)(1 + π)^π‘
Output-per-Person Equation (entirely as a function of parameters)
Describe output-per-person growth under the Romer model
Output per person grows at a
constant rate and is a straight
line on a ratio scale
What happens in the Romer model if πΏ increases?
When population increases, the growth rate of knowledge also increases because π β‘ π§ππΏ.
Because π is a component of the output-per-person growth rate, the growth rate will immediately and permanently increase
The growth curve increase in gradient from the point in time when πΏ increases
What happens in the Romer model if
π increases?
When the fraction of labour producing ideas increases:
a) the growth rate of knowledge will increase because π β‘ π§ππΏ. As π is a component of the output-per-person growth rate, the growth rate will increase for all future years
b) more people work to produce ideas rather than output so the level of output-per-person initially falls
The growth curve breaks downwards at the point in time when π increases but then increases at a greater rate than before
What are growth effects and level effects?
- Growth effects are permanent changes to the growth rate of per capita output
- Level effects are changes to the long-run level of per capita output
If the exponent on ideas in the production function is < 1, what happens?
Increases in π and πΏ no longer result in a permanently increased output-per-person growth rate due to diminishing returns to ideas
Overall however, the Romer model continues to show sustained growth because ideas and labour taken together still see increasing returns to scale
