Lecture 11

Source: Mankiw, Principles of Economics, Ch. 25

ECONOMIC GROWTH AROUND THE WORLD

Real GDP per person
(in 2017 dollars)
Compound
Growth
At Annual
Beginning End At Beginning rates with
Country End Growth
Period Period Period natural log
Period Rate
(CAGR)
China 1900 2017 $ 794 $ 16,807 2.64% 2.61% COMPOUND ANNUAL GROWTH RATE (CAGR): The CAGR is a measure of growth over multiple time periods.
Japan 1890 2017 $ 1,667 $ 43,279 2.60% 2.56% It is the rate at which the initial value had to grow every year
Brazil 1900 2017 $ 863 $ 15,484 2.50% 2.47% (column G) in the defined time period to obtain the final value.
Mexico 1900 2017 $ 1,285 $ 18,258 2.29% 2.27% The CAGR ignores short-run fluctuations around the long-run trend and
Indonesia 1900 2017 $ 988 $ 12,284 2.18% 2.15% represents an average growth rate
Germany 1870 2017 $ 2,422 $ 50,639 2.09% 2.07%
Canada 1870 2017 $ 2,633 $ 46,705 1.98% 1.96% EV Ending Value
India 1900 2017 $ 748 $ 7,056 1.94% 1.92% 𝐸𝑉 BV Beginning Value
CAGR = −1
Argentina 1900 2017 $ 2,542 $ 20,787 1.81% 1.80% 𝐵𝑉 n number of periods
USA 1870 2017 $ 4,443 $ 59,532 1.78% 1.77%
Pakistan 1900 2017 $ 818 $ 5,527 1.65% 1.63%
Bangladesh 1900 2017 $ 691 $ 3,869 1.48% 1.47% The CAGR tells you that 𝐸𝑉 = 𝐵𝑉(1 + 𝐶𝐴𝐺𝑅)
UK 1870 2017 $ 5,332 $ 43,269 1.43% 1.42%
Check EV China $ 16,807
Economic Growth Around the World Japan $ 43,279
Brazil $ 15,484
(Real GDP per person in 2017 dollars)
Mexico $ 18,258
$70,000 3.00% Indonesia $ 12,284
$60,000 2.50% Germany $ 50,639
$50,000 2.00%
$40,000 Canada $ 46,705
1.50% India $ 7,056
$30,000
$20,000 1.00% Argentina $ 20,787
$10,000 0.50% USA $ 59,532
$- 0.00% Pakistan $ 5,527
Bangladesh $ 3,869
UK $ 43,269

Beginning Period (1870/1890/1990) End Period (2017) CAGR

ln 𝐸𝑉 − ln(𝐵𝑉)
In colum H, the formula is 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 =
𝑛

ln natural logarithm

Check & compare China 0.026089

0.026089

PRODUCTIVITY: Its role and determinant

Productivity the quantity of goods and services produced from each unit of labor input

Y Real GDP (quantity of output produced)

L quantity of labor

𝒀 productivity
𝑳 (output per worker)

Determinants of productivity

(Physical) capital K the stock of equipment and structures that are used to produce goods & services

capital is a factor of production used to produce all kinds of goods and services, including more capital

𝑲 capital per worker

𝑳
 𝑲 𝒀
Productivity is higher when the average worker has more capital (machines, equipment, etc.). an increase in causes an increase in
𝑳 𝑳

Human capital H the knowledge and skills that workers acquire through education, training, and experience

𝑯 human capital per worker (the average worker's human capital)

𝑳

𝑯 𝒀
Productivity is higher when the average worker has more human capital (education, skills, etc.). an increase in causes an increase in
𝑳 𝑳

Natural resources N the inputs into the production of goods and services that are provided by nature, such as land, rivers, and mineral deposit

𝑵 natural resources per worker

𝑳

Other things equal, more N allows a country to produce more Y.

Technological knowledge any advance in knowledge that boosts productivity (allows society to get more output from its resources).
(e.g. technology, improvement of production process)

Difference bwtween technological knowledge & human capital

Technological knowledge society's understanding of the best way to produce goods and services

Human capital resources expended transmitting this understanding to the labor force
effort people expend to acquire this knowledge

Both are important for productivity

PRODUCTION FUNCTION describes the relationship between the quantity of inputs used in production and the quantity of output from production

Y = AF(L, K, H, N) (eq. 1)

Y quantity of output

L quantity of labor

K quantity of physical capital

H quantity of human capital

N quantity of natural resources

F() function that shows how the inputs are combined to produced output

A level of technology
A multiplies the function F( ), so improvements in technology (increases in A) allow more output (Y) to be produced from any given combination of inputs.
Note that inputs go into the function.
What matters for productivity is not “technical knowledge per worker” but simply “technological knowledge.”
Unlike physical capital or other resources, technological knowledge can be freely shared among all workers.
If the number of workers increases, you must purchase new capital for the new workers (or spread the existing capital more thinly), but technological knowledge can be freely shared with the new workers.
That's why A is outside of the function and multiplies it

Many production functions have a property called constant returns to scale (CRS)
If a production function has CRS, then doubling the inputs causes the amount to double as well

xY = A F(xL, xK, xH, xN) (eq. 2)

when x is 2 represents a double of all inputs

𝟏
 𝟏
What about x = ?
𝑳
1 𝐿 𝐾 𝐻 𝑁
𝑌 = 𝐴𝐹 , , ,
𝐿 𝐿 𝐿 𝐿 𝐿

𝑌 𝐾 𝐻 𝑁
= 𝐴𝐹 1, , , (eq. 3)
𝐿 𝐿 𝐿 𝐿

But what 𝒀 is ? It is productivity

𝑳

Eq. 3 shows that productivity (output per worker) depends on:

- the level of technology (A)

- physical capital per worker

- human capital per worker

- natural resources per worker

Note 1 in the function means number of workers per workers. That's always 1

ECONOMIC GROWTH & PUBLIC POLICY

What can government policy do to raise productivity and living standards?

- Saving & Investment

We can raise productivity by increasing K, which requires investment

Since resources scarce, producing more capital requires producing fewer consumption goods. (trade-off)

The extra saving due to consumption reduction funds the produciton of investment goods

That is, less current consumption of goods and services for more consumption of goods and services in future (trade-off)

- Diminishing returns and the catch-up effect The figure shows how the amount of capital per worker
𝒀 influences the amount of output per worker,
The government can implement policies that raise saving and investment. 𝑳 holding constant all other determinants of output
Then K will rise, causing productivity and living standards to rise. (such as natural resources, technological knowledge).
The curve becomes flatter as the amount of capital
However, this faster growth is temporary, due to diminishing returns to capital increases because of diminishing returns to capital

Diminishing returns the property whereby the benefit from an extra unit of an input declines as the quantity of the input increases

As K rises, the extra output from an additional unit of K falls

In the long run, the higher saving rate leads to a higher level of productivity and income but not to higher growth in these variables
𝑲
𝑳
catch-up effect the property wherby countries that start off poor tend to grow more rapidly than countries that start off rich When economy has a low level of capital, an extra unit of capital leads to a large increase in output
(convergence) When economy has a high level of capital, an extra unit of capital leads to a small increase in output

In order for the catch-up effect to work, it must be true that both countries have the same technology and hence production function.
If the poor country has inferior technology, its production function will be lower;
then, it won’t necessarily grow faster than the rich one, and the gap won’t necessarily shrink over time.

- Investment from abroad

government policy to attract more investment from abroad

 Foreign Direct Investment (FDI) a capital investment that is owned and operated by a foreign entity
(e.g. a US multinational company set up a manufacturing plant in a third country)

Foreign portfolio investment an investment financed with foreign money operated by domestic residents
(e.g. you buy a stock of a foreign company)

In both cases the foreign capital can be used to increase the stock of capital in the domestic economy

Some of the returns from these investments flow back to the foreign countries that supplied the funds.

Investment from abroad is one way for poor countries to learn the state-of-the-art technologies developed and used in richer countries

- Education

government can increase productivity by promoting education–investment in human capital (H).

- Health & Nutrition

Health care expenditure is a type of investment in human capital

Other things being equal, healthier workers are more productive

- Property rights & Political stability

- Free trade
Inward-oriented policies
(e.g., tariffs, limits on investment from abroad)
aim to raise living standards by avoiding interaction with other countries.

Outward-oriented policies
(e.g., the elimination of restrictions on trade or foreign investment)
promote integration with the world economy.

Trade can make everyone better off.

Trade has similar effects as discovering new technologies—it improves productivity and living standards.

- Research & Development

- Population growth
…may affect living standards in 3 different ways:

1 Stretching natural resources

Since Malthus argued that population growth would strain society’s ability to provide for itself (200 years ago),
the world population has increased sixfold. If Malthus was right, living standards would have fallen. Instead, they’ve risen.

Malthus failed to account for technological progress and productivity growth

2 Diluting the capital stock

Bigger population = higher L = lower K/L = lower productivity & living standards.

This applies to H as well as K

fast population growth = more children = greater strain on educational system

Countries with fast population growth tend to have lower educational attainment

To combat this, many developing countries use policy to control population growth
 For example,
China’s one child per family laws

Contraception education & availability

Promote female literacy to raise opportunity cost of having babies

3 Promoting technological progress

More people
= more scientists, inventors, engineers
= more frequent discoveries
= faster tech. progress & economic growth