Combined Romer-Solow Growth Model

Question 1

Combined Production Function (Total Output Equation)

Answer 1

𝑌𝑡 = 𝐴𝑡𝐾𝑡^1/3𝐿𝑦𝑡^2/3

The production function has constant returns to scale in objects but increasing returns in ideas and objects together

Question 2

𝑌𝑡 = 𝐴𝑡𝐾𝑡^1/3𝐿𝑦𝑡^2/3

Answer 2

Combined Production Function (Total Output Equation)

Question 3

What two issues does combining the Romer and Solow models solve?

Answer 3

1. The consistent increase in world incomes not explained by Solow’s TFP theory is explained by Romer’s insight that the a consistent growth in world knowledge will result in upward trending world income
2. The lack of deviation from a trend in the Romer model, e.g. why countries spend time growing faster and slower in the short-run can be explained by Solow’s transition dynamics

Question 4

Total Output Growth Rate (simple application of growth accounting rules)

Answer 4

𝑔𝑌𝑡 = 𝑔𝐴𝑡 + 1/3𝑔𝐾𝑡 + 2/3𝑔𝐿𝑦𝑡

Question 5

𝑔𝑌𝑡 = 𝑔𝐴𝑡 + 1/3𝑔𝐾𝑡 + 2/3𝑔𝐿𝑦𝑡

Answer 5

Total Output Growth Rate (simple application of growth accounting rules)

Question 6

Growth Rate of Knowledge Equation

Answer 6

𝑔𝐴𝑡 ≡ 𝑧𝑙𝐿 = 𝑔 (bar)

Growth rate is constant = sustained long-run growth

Question 7

𝑔𝐴𝑡 ≡ 𝑧𝑙𝐿

Answer 7

Growth Rate of Knowledge Equation

Question 8

Growth Rate of Capital Equation

Answer 8

𝑔𝐾𝑡 ≡ (∆𝐾𝑡+1)/𝐾𝑡 = 𝑠𝑌𝑡/𝐾𝑡 − 𝑑

𝑌𝑡/𝐾𝑡 must be constant because growth is constant

Question 9

If 𝑌𝑡/𝐾𝑡 is constant, what must be true?

Answer 9

The growth rates of capital and output must be the same (𝑔𝐾* = 𝑔𝑌*)

Question 10

Long-Run Total Output Growth Rate

Answer 10

𝑔𝑌* = 3/2𝑔= 3/2𝑧𝑙𝐿

Sub the three component growth rates into the simple output growth rate

Question 11

Is 𝑔𝑌* higher in the combined model or the Romer model and why?

Answer 11

𝑔𝑌* is larger in the combined model because:
- ideas have a direct and indirect effect
- Increasing productivity raises output both because 1. productivity itself increases and 2. higher productivity results in a larger capital stock, leading to even higher output growth

Question 12

Equation for the capital-output ratio along a balanced growth path

Answer 12

𝐾𝑡/𝑌𝑡 = 𝑠/(𝑔𝑌*+𝑑)

Question 13

𝐾𝑡/𝑌𝑡 = 𝑠/(𝑔𝑌*+𝑑)

Answer 13

Equation for the capital-output ratio along a balanced growth path

Question 14

Output-per-Capita Equation

Answer 14

𝑦𝑡* = (𝑠/(𝑔𝑌+𝑑))^1/2 𝐴𝑡^3/2 (1−𝑙)

Question 15

𝑦𝑡* = (𝑠/(𝑔𝑌+𝑑))^1/2 𝐴𝑡^3/2 (1−𝑙)

Answer 15

Output-per-Capita Equation