Romer Growth Model

Question 1

What are objects?

Answer 1

Inputs which are finite and rivalrous e.g. capital and labour in the Solow model

Question 2

What are ideas?

Answer 2

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)

Question 3

How are ideas accounted for in the Cobb-Douglass production function?

Answer 3

𝐴 accounts for ideas just as it does productivity

Question 4

Labour Resource Constraint Equation

Answer 4

• 𝐿𝑦𝑡 workers produce output
• 𝐿𝑎𝑡 workers produce ideas
  𝐿𝑦𝑡 + 𝐿𝑎𝑡 = 𝐿
  Workers on output + workers on ideas = total workers

Question 5

𝐿𝑦𝑡 + 𝐿𝑎𝑡 = 𝐿

Answer 5

Labour Resource Constraint Equation

Question 6

Allocation of Labour Equations

Answer 6

𝐿𝑦𝑡 = (1 − 𝑙)𝐿
𝐿𝑎𝑡= 𝑙𝐿
Where (1 − 𝑙) is the proportion of workers producing output and 𝑙 is the proportion producing ideas

Question 7

𝐿𝑦𝑡 = (1 − 𝑙)𝐿
𝐿𝑎𝑡= 𝑙𝐿

Answer 7

Allocation of Labour Equations

Question 8

Output Production Function

Answer 8

𝑌𝑡 = 𝐴𝑡𝐿𝑦𝑡
Output = Stock of Existing Knowledge x Workers producing Output

Question 9

𝑌𝑡 = 𝐴𝑡𝐿𝑦𝑡

Answer 9

Output Production Function

Question 10

Ideas Production Function

Answer 10

∆𝐴𝑡+1 = 𝑧𝐴𝑡𝐿𝑎𝑡
Change in Stock = Productivity of Workers producing Ideas x Existing Stock x Workers producing Ideas

Question 11

∆𝐴𝑡+1 = 𝑧𝐴𝑡𝐿𝑎𝑡

Answer 11

Ideas Production Function

Question 12

Output-per-Person Equation (Dependent on 𝐴𝑡)

Answer 12

𝑦𝑡 ≡ 𝑌𝑡/𝐿 = (𝐴𝑡𝐿𝑦𝑡)/𝐿 = 𝐴𝑡(1 − 𝑙)
Output per person dependent on the total stock of ideas (𝐴𝑡)

Question 13

𝑦𝑡 = 𝐴𝑡(1 − 𝑙)

Answer 13

Output-per-Person Equation (Dependent on 𝐴𝑡)

Question 14

Growth Rate of Knowledge Equation

Answer 14

(∆𝐴𝑡+1)/𝐴𝑡 = 𝑧𝐿𝑎𝑡 = 𝑧𝑙𝐿
Growth rate of knowledge is constant as z, l, and L and all exogenous (should have bars)

Question 15

(∆𝐴𝑡+1)/𝐴𝑡 = 𝑧𝑙𝐿

Answer 15

Growth Rate of Knowledge Equation

Question 16

Total Stock of Knowledge Equation

Answer 16

𝐴𝑡 = 𝐴0(1 + 𝑔)^𝑡 where 𝑔 ≡ 𝑧𝑙𝐿
The stock of knowledge depends on its initial value and its growth rate

Question 17

𝐴𝑡 = 𝐴0(1 + 𝑔)^𝑡

Answer 17

Total Stock of Knowledge Equation

Question 18

Output-per-Person Equation (entirely as a function of parameters)

Answer 18

𝑦𝑡 = 𝐴0(1− 𝑙)(1 + 𝑔)^𝑡

Combined Output-per-Person Equation (Dependent on 𝐴𝑡) and Total Stock of Knowledge Equation

Question 19

𝑦𝑡 = 𝐴0(1− 𝑙)(1 + 𝑔)^𝑡

Answer 19

Output-per-Person Equation (entirely as a function of parameters)

Question 20

Describe output-per-person growth under the Romer model

Answer 20

Output per person grows at a
constant rate and is a straight
line on a ratio scale

Question 21

What happens in the Romer model if 𝐿 increases?

Answer 21

When population increases, the growth rate of knowledge also increases because 𝑔 ≡ 𝑧𝑙𝐿.
Because 𝑔 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 𝐿 increases

Question 22

What happens in the Romer model if
𝑙 increases?

Answer 22

When the fraction of labour producing ideas increases:
a) the growth rate of knowledge will increase because 𝑔 ≡ 𝑧𝑙𝐿. As 𝑔 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 𝑙 increases but then increases at a greater rate than before

Question 23

What are growth effects and level effects?

Answer 23

• 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

Question 24

If the exponent on ideas in the production function is < 1, what happens?

Answer 24

Increases in 𝑙 and 𝐿 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