The document discusses linear stages of economic growth and the Harrod-Domar growth model. It describes the five stages of economic growth: traditional society, preconditions for take-off, take-off, drive to maturity, and age of mass consumption. Countries move through these stages through capital accumulation. It then explains the Harrod-Domar growth model, which models economic growth as a function of the savings rate and the capital-output ratio. The model assumes savings equals investment and does not explicitly model technological change or labor. It indicates economic growth depends on accumulating capital through savings.

1. LINEAR STAGES OF GROWTH AND
THE HARROD-DOMAR GROWTH
MODEL

2. LINEAR STAGES OF GROWTH
What are the five different stages of growth?
i. Traditional society
ii. Pre-conditions for take-off
iii. Take-off
iv. The drive to maturity
v. The age of mass consumption
How does a country move through these stages?
Capital accumulation

3. LINEAR STAGES OF GROWTH
What is the historical justifications for this model?
The Marshall Plan
Path of developed nations
0
10
20
30
40
50
60
70
80
90
1800 1840 1880 1920 1960
PERCENT
Agriculture Labor Share

4. HARROD-DOMAR GROWTH MODEL
𝑁𝑒𝑡 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 ≡ 𝑆
𝑆 = 𝑠𝑌
𝑆 = 𝑠 𝐺 𝑌 − 𝛿𝐾
𝐺𝐷𝑃
𝑛𝑒𝑡 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑟𝑎𝑡𝑒
𝑔𝑟𝑜𝑠𝑠 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑟𝑎𝑡𝑒
𝑑𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒
𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑠𝑡𝑜𝑐𝑘
What is the definition of
net savings?
Total absolute amount
saved… Savings minus
depreciation

5. HARROD-DOMAR GROWTH MODEL
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 ≡ 𝐼
𝐼 = ∆𝐾
Total production in the country is equal to:
𝑌 =
1
𝑐
𝐾
What is another name
for the Harrod-Domar
growth model?
 AK model (where
1
𝑐
is
usually 𝐴)𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑟𝑎𝑡𝑖𝑜

6. HARROD-DOMAR GROWTH MODEL
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 ≡ 𝐼
𝐼 = ∆𝐾
Total production in the country is equal to:
𝑌 =
1
𝑐
𝐾
Why is labor not
explicitly modeled?
 It is assumed to not
be a constraining
factor.𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑟𝑎𝑡𝑖𝑜

7. HARROD-DOMAR GROWTH MODEL
Absolute change in GDP, ∆𝑌, can then be
expressed as:
∆𝑌 =
1
𝑐
∆𝐾
Why this outcome?
 We are assuming 𝑐 is
constant.

8. HARROD-DOMAR GROWTH MODEL
We assume that 𝑆 = 𝐼
𝐼 = ∆𝐾
𝑆 = 𝑠𝑌
𝑠𝑌 = 𝑐∆𝑌
∆𝑌
𝑌
=
𝑠
𝑐
= 𝑐∆𝑌
= 𝐼= ∆𝐾= 𝑐∆𝑌
What does this say?
 Growth is a function
of the savings rate
and the inverse of
the capital-output
ratio𝐺𝐷𝑃 𝑔𝑟𝑜𝑤𝑡ℎ

9. HARROD-DOMAR GROWTH MODEL
Result:
∆𝑌
𝑌
=
𝑠
𝑐
If you want to develop, what do you have to do?
Accumulate capital!
What factor which is always mentioned as key in an industrial
revolution is not determined in the model?
Technological change

10. HARROD-DOMAR GROWTH MODEL
Result:
∆𝑌
𝑌
=
𝑠
𝑐
What can be done if domestic savings is insufficient?
How does this relate back to the Marshall Plan?

11. HARROD-DOMAR GROWTH MODEL
Result:
∆𝑌
𝑌
=
𝑠
𝑐
If this was the only explainer for differences in GDP and
growth, what would you expect differences in savings to look
like?

12. HARROD-DOMAR GROWTH MODEL
Result:
∆𝑌
𝑌
=
𝑠
𝑐
“Unfortunately, the mechanisms of development embodied in
the theory of stages of growth did not always work.”
Why?

13. PROBLEMS: HARROD-DOMAR
GROWTH MODEL
Show that
∆𝑌
𝑌
=
𝑠 𝐺
𝑐
− 𝛿
𝑆 = 𝑠 𝐺
𝑌 − 𝛿𝐾
𝑆 = 𝐼 = 𝑐∆𝑌
𝑠 𝐺
𝑌 − 𝛿𝐾 = 𝑐∆𝑌
∆𝑌
𝑌
=
𝑠 𝐺
𝑐
−
𝛿𝐾
𝑐𝑌
𝐾 = 𝑐𝑌
∆𝑌
𝑌
=
𝑠 𝐺
𝑐
− 𝛿

14. PROBLEMS: HARROD-DOMAR
GROWTH MODEL
If 𝑐 = 3, what savings rate is needed to obtain 10% GDP growth?
∆𝑌
𝑌
=
𝑠
𝑐
Where
∆𝑌
𝑌
= 10%
𝑐 = 3
𝑠 = 3 ∗ 10% = 30%

15. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
If the poor save more than the rich, how would policies that
benefit the rich affect growth in the model looked at above?
Think about how we can formulate this into the model….
𝑆 = 𝑠𝑌
𝑆 = 𝑠 𝑅 𝛼 𝑅 𝑌 + 𝑠 𝑃 1 − 𝛼 𝑅 𝑌
𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑖𝑐ℎ
𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑜𝑟
Lets assume
depreciation is
zero…
𝑊ℎ𝑒𝑟𝑒 𝑠 𝑅 > 𝑠 𝑃

16. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
If the poor save more than the rich, how would policies that
benefit the rich affect growth in the model looked at above?
Think about how we can formulate this into the model….
𝑆 = 𝑠𝑌
𝑆 = 𝑠 𝑅 𝛼 𝑅 𝑌 + 𝑠 𝑃 1 − 𝛼 𝑅 𝑌Lets assume
depreciation is
zero…
𝑊ℎ𝑒𝑟𝑒 𝑠 𝑅 > 𝑠 𝑃
𝑖𝑛𝑐𝑜𝑚𝑒 𝑠ℎ𝑎𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑖𝑐ℎ
𝑖𝑛𝑐𝑜𝑚𝑒 𝑠ℎ𝑎𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑜𝑟

17. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
If the poor save more than the rich, how would policies that
benefit the rich affect growth in the model looked at above?
Think about how we can formulate this into the model….
𝑆 = 𝑠𝑌
𝑆 = 𝑠 𝑅 𝛼 𝑅 𝑌 + 𝑠 𝑃 1 − 𝛼 𝑅 𝑌Lets assume
depreciation is
zero…
𝑊ℎ𝑒𝑟𝑒 𝑠 𝑅 > 𝑠 𝑃
𝑛𝑒𝑡 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑜𝑓 𝑟𝑖𝑐ℎ
𝑛𝑒𝑡 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑜𝑓 𝑝𝑜𝑜𝑟

18. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
If we solve, we get:
∆𝑌
𝑌
=
𝑠 𝑅 𝛼 𝑅 + 𝑠 𝑃 1 − 𝛼 𝑅
𝑐
∆𝑌
𝑌
=
𝑠 𝑅 𝛼 𝑅 𝑌 + 𝑠 𝑃 − 𝑠 𝑃 𝛼 𝑅
𝑐
How can we analyze the affect of changing income
inequality?

19. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
Which is:
𝜕
∆𝑌
𝑌
𝜕𝛼 𝑅
=
𝜕
𝑠 𝑅 𝛼 𝑅 + 𝑠 𝑃 − 𝑠 𝑃 𝛼 𝑅
𝑐
𝜕𝛼 𝑅
𝜕
∆𝑌
𝑌
𝜕𝛼 𝑅
=
𝑠 𝑅
𝑐
−
𝑠 𝑃
𝑐
If we increase 𝛼 𝑅, i.e. inequality, we increase
∆𝑌
𝑌
, i.e. growth…
𝑊ℎ𝑒𝑟𝑒 𝑠 𝑅 > 𝑠 𝑃> 0
𝛼 𝑅 𝑎𝑛𝑑
∆𝑌
𝑌
ℎ𝑎𝑣𝑒 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝

20. TOTHINK ABOUT: HARROD-DOMAR
GROWTH MODEL
If we increase 𝛼 𝑅, i.e. inequality, we increase
∆𝑌
𝑌
, i.e.
growth…
𝜕
∆𝑌
𝑌
𝜕𝛼 𝑅
=
𝑠 𝑅
𝑐
−
𝑠 𝑃
𝑐
> 0
Why is this the case?
What is missing from this analysis that makes such a result
possible?

21. HOMEWORK
Read section 3.3