# Production and economic growth

### From Baripedia

What can explain the fact that the average annual income in Norway is USD 76,000 in 2007 (GNP per capita) or USD 60,000 in Switzerland, while a resident of Burundi has an average income of only USD 110?

Why did the difference in GDP per capita between Europe and Asia double in the 18th century to a GDP 15 times greater in Europe than in Asia in 2006?

This chapter on growth and development allows us to sketch an answer to these questions (no development of formal models).

According to Robert Lucas (Nobel Prize in Economics in 1995): "The consequences that the answers to these questions can have for mankind are very great: once we start thinking about them, it is difficult to think about anything else".

See on this subject the podcast on econtalk with Robert Lucas.

## Formulas for calculating the GDP growth rate

GDP growth rate between GDP of year 1 and year 2 (in %): ${\displaystyle \Delta percentGDP_{2}={\frac {GDP_{2}-GDP_{1}}{GDP_{1}}}\times 100}$

To calculate GDP for the nth year based on a growth rate we uses the same formula as for compound interest:

${\displaystyle GDP_{n}=GDP_{1}(1+\gamma )^{n}}$

So if we have a period of n years and we know the GDP at the beginning and at the end of the period, to calculate the average annual growth rate:

${\displaystyle {\text{Average Annual Growth Rate (AAGR)}}=\gamma ={\sqrt[{n}]{GDP_{n}GDP_{1}}}-1}$

The rule of 70 (gives an approximation of the relationship between the annual growth rate of GDP per capita and the long-term change in GDP per capita):

${\displaystyle {\text{number of years for the variable to double}}\approx {\frac {70}{\text{annual growth rate of the variable}}}}$

# Economic growth in the world

## Global Economic Growth: A Relatively Recent Phenomenon

Before 1800, the population growth rate was less than 0.1% per year and until 1500, the output growth rate was almost zero.

It was only after 1800 that the population grew strongly and the growth rate of physical capital per capita increased from 0.15% per year between 1500 and 1800 to more than 2% per year in the last century.

Source : Angus Maddison : « The World Economy, a Millennium Perspective »

## Growth in the world

A very small change in the annual growth rate of an economy can turn into a huge difference in the level of GDP after a few generations: see the following table.

In 1900, Argentina had a per capita GDP that was 16% higher than Japan's (USD 1,915 versus USD 1,656 in 2000 dollars after adjusting for inflation between 1900 and 2000).

During the period 1900-2000 Argentina had an average annual growth rate of 1.8% and Japan of 2.8%.

This small difference is transformed into a GDP per capita differential, 100 years later, of around USD 26k in Japan and USD 12k in Argentina: GDP in 2000 in ARG. = ${\displaystyle 1915\times (1.0186)^{100}=12093}$and GDP in 2000 in JPN = ${\displaystyle 1656\times (1.0281)100=26461}$

Note: Of course, the key statistic for monitoring a country's long-term growth is real GDP per capita, although the press often reports data on the growth rate of real GDP (see The Economist, 13.03.2008).

Is the USD 12k in Argentina in 2000 comparable to the USD 26k in Japan in the same year? Probably not, as the prices of many goods are different in the two countries.

To get an idea of the "quality of life" of individuals in Argentina and Japan and to make international comparisons, GDP per capita must be adjusted by the cost of living in the two countries.

To construct an indicator of the cost of living in different countries, one proceeds in the same way as to construct an indicator of the cost of living in a country at different points in time (cf. CPI).

A standard basket of consumption is constructed (the same everywhere) and its cost is calculated in various countries of the world to construct a purchasing power parity (PPP) index.

## PPP correction

The World Bank and the IMF have a joint project for the construction of these indices in developing countries. The OECD does it for developed countries.

Even when corrected by PPP, the differences between countries' per capita GDPs remain striking.

Example of application :

• According to the World Bank, if the cost of living is 1 in the United States, it will be 1.37 in Norway and 0.27 in Burundi in 2007.
• Norway's GDP per capita in PPP is therefore ${\displaystyle {\frac {USD\,76000}{1.37}}=USD55474}$, and Burundi's GDP per capita at PPP is ${\displaystyle {\frac {USD\,110}{0.27}}=USD407}$ → differences are less significant than if GDP without adjustment is considered, but still extremely large .

Why these huge differences? See next section.

## Criticism of the PPP

PPP indices suffer from the same problems as those seen for the CPI (substitution bias, new goods, quality, and heterogeneity of consumption patterns).

And these problems are accentuated by the socio-economic and cultural differences between countries (in reality, consumption baskets are not the same everywhere!).

An alternative to PPP indices that tries to overcome at least some of the problems associated with standard PPP indices is the BigMac index proposed by The Economist: comparison of the price of a BigMac in different countries (takes into account the added value of the goods and services that make up the BigMac price and that are the same everywhere).

# Labour productivity

## Labour productivity

To understand the differences in per capita income between countries, it is necessary to understand why some countries produce more goods and services per capita than others.

To explain these differences, we will therefore look at the productivity of workers in the different economies.

Labour productivity = ${\displaystyle {\frac {\text{output}}{\text{operating hours}}}=PML}$

## Factors of production

Labour productivity is influenced by the availability of other factors of production (physical capital, human capital, natural resources and technological knowledge) in the economy.

Consider a production function (${\displaystyle F}$) of total output that depends on several factors of production:

• labour (${\displaystyle L}$) = the number of working hours employed in production *physical capital (${\displaystyle K}$) = equipment and infrastructure used in production
• human capital (${\displaystyle H}$) = knowledge and skills acquired by workers through education, training and experience
• natural resources (${\displaystyle N}$) = natural inputs, such as land, forests, raw materials, etc.
• technological knowledge (${\displaystyle A}$) = knowledge of the best possible production methods.

The production function ${\displaystyle F}$ describes the relationship between the quantity of inputs used in production and the quantity of output.

## Constant returns to scale

Generally it is assumed that the production function shows constant returns to scale (in mathematical terms this means that the function is homogeneous of degree 1) in L, K, H and N => if we double the available quantity of all these inputs, we double the quantity produced (α = 2 at the bottom):

${\displaystyle Y=A\times F(L,K,H,N)}$${\displaystyle \alpha Y=A\times F(\alpha L,\alpha K,\alpha H,\alpha N)}$

NB: The technology parameter A appears outside the parenthesis. This implies that doubling the level of technological knowledge can double the quantity produced. This parameter is often interpreted by economists as a measure of overall productivity or multifactor productivity. Multifactor productivity is not directly observable; it is a kind of "remainder" or "residual," which is valued as the difference between the % change in GDP and the sum of the % changes in the factors of production under consideration, and which gives us an estimate of the total efficiency of the factors of production.

## Determinants of Y/L

By taking α = 1/L and using the homogeneity property of degree 1 (constant returns to scale), we can rewrite the production function:

${\displaystyle Y=A\times F(L,K,H,N)}$${\displaystyle \alpha Y=A\times F(\alpha L,\alpha K,\alpha H,\alpha N)}$${\displaystyle y={\frac {Y}{L}}=A\times F(1,{\frac {K}{L}},{\frac {H}{L}},{\frac {N}{L}})}$

Thus, labour productivity will depend on the relative quantities of other factors of production and the state of technological progress.

The greater the stock of physical and human capital, and the stock of natural resources relative to the number of workers, the greater the capacity to produce Goods & Services in this economy per unit of worker (factor accumulation). The greater the technological knowledge, the higher the labour productivity (technical progress).

Any government policy that helps to increase the stocks of these factors of production or of ${\displaystyle A}$ will increase labour productivity and thus lead to faster growth (see below).

## The role of government

1. A higher stock of physical capital can be encouraged through a policy that favours savings rather than current consumption (tax deductions on savings, for example), but also through openness to foreign capital. Growth due to foreign capital investment will be captured only by GDP and not by GNP, but the foreign firm will need labour and B&S offered by nationals. These side effects will be captured by GDP and GNP.

Corrélation entre croissance du PIB et taux d’investissement

2. An increase in the stock of human capital increases the productivity of workers. A large part of the human capital stock of individuals is acquired through their training.

In OECD countries, an extra year of education increases people's wages (which, at equilibrium, is equal to their productivity) by about 10%. It also increases the productivity of other workers who also become more productive by combining their human capital → positive externalities.

By providing an efficient and easily accessible education system, the government promotes long-term productivity growth.

Developing countries (DCs), recognizing the importance of human capital and the lack of opportunity for the most disadvantaged groups to access education and health, have begun to introduce systems of subsidies to parents conditional on children's attendance and success in school and medical check-ups (e.g. PROGRESA programme in Mexico).

A potential problem for developing countries linked to the increase in expenditure on education is that a significant proportion of workers then leave with their human capital stock abroad. This phenomenon is called the "brain-drain".

In some Caribbean countries, for example, between 30 and 60% of trained nurses and doctors move to other OECD countries, leading some to question whether their education is a good investment for the government.

A counter-argument is that brain-drain is a positive thing for developing countries because it increases incentives to educate (individuals respond to incentives).

A second counter-argument is that professionals who have emigrated will send remittances to their home countries and therefore part of their income abroad will be spent in the home economy.

Maybe, but this is not always enough:

« I have at least nine hospitals that have no doctor at all, and 20 hospitals with only one doctor looking after a whole district of 80,000 to 120,000 people »

— Dr. Agyeman Akosa, Ghana, Director General of Health.

3. 'Natural Resources. Good stewardship of renewable and non-renewable natural resources is essential for sustainable growth.

The "natural resource curse" is sometimes referred to as the corruption associated with the appropriation of rents generated by the exploitation of natural resources. It is clear that the problem is not the existence of natural resources but corruption itself. Norway (the richest country in the world in terms of GDP per capita and very rich in natural resources) is a good counter-example of how one can benefit from natural resource wealth without having problems with corruption.

4. 'Technological knowledge. They can be encouraged through research and development grant programs (especially in basic research, which has no direct commercial application) and through the development of a good patent system that is efficient and safe for everything patentable.

However, the patent system opens up a debate on very sensitive issues: patents encourage innovation, but also help to keep prices high and create an advantage over other producers (monopoly) → cf. The Economist, 07.07.2007 and 27.08.2009.

Other policies are also important for economic development:

• Respect for private property and, more generally, for the law and the legal system (rule of law), which encourage investment in physical capital and the formation of technological knowledge (cf. The Economist, 13.03.2008);
• political and macroeconomic stability, which creates an environment conducive to investment and business;
• the openness of the economy to the rest of the world, which in principle increases incentives to invest when faced with a larger market.

# Declining Marginal Productivity and Convergence

## Marginal product

Under the assumption of diminishing marginal factor returns, economic growth is not unlimited if it is due to the accumulation of a single factor of production (given the others).

Consider again the aggregate production function at constant returns to scale :

${\displaystyle Y=A\times F(L,K,H,N)}$ => ${\displaystyle y={\frac {Y}{L}}=A\times F(1,{\frac {K}{L}},{\frac {H}{L}},{\frac {N}{L}})}$.

The marginal product of capital (${\displaystyle PmK}$) is the additional quantity of production produced by the economy using one unit more than capital.

For discrete variations :

${\displaystyle PmK={\frac {\Delta Y}{\Delta K}}={\frac {A\times F(K+\Delta K,L,...)-A\times F(K,L,...)}{\Delta K}}}$

For small variations:

${\displaystyle PmK={\frac {dY}{dK}}}$ (= pente de la fonction de production)

Normally it is assumed that, if all other inputs are constant, the marginal productivity of capital is characterized by decreasing marginal returns (= given the level of other inputs, an additional unit of capital increases output by an increasingly smaller amount → function of increasing output but at decreasing rates).

Intuition: when ${\displaystyle K}$ is low, the amount of capital each worker has at his disposal is small. Consequently, an additional unit of capital produces a lot of additional output. The higher the K/L ratio, the greater the amount of capital available to each worker and an additional unit of capital increases the output by very little (= decreasing PmK).

Fonction de production.

## Accumulation vs. progress

NB: an improvement in technical progress, A, shifts the production function upwards, while an accumulation of physical capital translates into a shift to the right along the production function → two sources of growth.

## Marginal product and convergence

The declining productivity of physical (or human) capital implies that:

a) when one accumulates only physical capital, one will have very rapid growth at the beginning, but this will slow down as one continues to accumulate and even ultimately cancel itself out in the long term → Solow's growth model, Nobel Prize in Economics 1987;

b)trying to beat declining marginal returns requires simultaneous accumulation of physical and human capital or continuous technological progress.

An important implication of a) is that the richest countries (which have already accumulated quite a lot of physical capital), will grow more slowly than the poorest countries which have very little physical capital. This is called economic convergence: the poorer countries are catching up with the richer ones through this phenomenon.

Are these forces of economic convergence associated with diminishing marginal returns observed? Yes, but only if we check for other institutional, political, and socio-economic differences between countries.

## Convergence: Evidence

Neither convergence nor divergence among the countries of the world: no relationship between GDP per capita in 1960 and growth 1960-1985. If there had been convergence, a negative relationship would have been found between these two variables.

Rather divergence when you take a longer period.

But convergence is found when we take "economies" that share the same political institutions and socio-economic conditions (conditional convergence).

The 48 states of the United States: the states that had the highest growth in the period 1979-1984 were those that had the lowest GDP per capita initially.

Convergence cannot explain everything, but if we take similar economies we will find conditional convergence.

## Declining PmL and Malthus forecasts

An important implication of b) is that growth generated by the accumulation of a single pdf will not be unlimited.

Source: Angus Maddison, "The Global Economy, A Millennial Perspective".

Idea: Like all other production functions, labour is also characterized by decreasing marginal returns (if all other inputs and technology remain constant, an increase in labour does not increase output in the long run). The enormous demographic growth at the beginning of the 19th century led Thomas R. Malthus (1766-1834) to predict a progressive impoverishment of the population, since the growth rate of the world population was much higher than the increase in resources.

According to Malthus, with technical progress the population grew faster and faster to the point where the amount of land and natural resources per capita decreased, thus reducing labour productivity and thus the standard of living.

Malthus' pessimistic predictions have been punctually delayed by the Industrial Revolution and the Green Revolution (great increase in resources and agricultural yields). Labour productivity has not decreased, mainly thanks to new technologies and better organisation of production, which have slowed the impact of natural resource scarcity (until when? → sustainable growth?). See The Economist, 17.05.2008.

Key: The speed of technological progress has increased sharply since 1800 (reminder: labour productivity depends on the relative quantities of other factors of production and technological progress, which have not remained constant over time).

## Neo-Malthusian Concerns and the Environmental Issue

Return of concerns about the limited supply of non-renewable resources. Most economists remain optimistic: scarcity of resources leads to higher prices => strong incentive to find alternatives. But what's new?

The environmental problem: economic growth amplifies the impact of human activities on the environment.

Management of local impacts relatively easy (many historical examples, e.g. use of coal for heating); management of global impacts more delicate and problematic (international cooperation + state intervention).
Problem: in contrast to resource scarcity, environmental problems do not automatically generate incentives for change (strong negative externalities) → public intervention indispensable.
Open questions and uncertainties: What kind of growth decline are we prepared to accept? What is the extent of climate change? ...

# Summary

There is a big difference in per capita income levels around the world and their growth.

Income in the richest economy in the world (Norway) is more than 100 times higher than in the poorest economy (Ethiopia) when measured in terms of GDP per capita. And a little less when corrected for PPP.

A small difference in the annual growth rate can result in large differences in income levels over the long term.

The standard of living in an economy will depend on its ability to produce goods and services.

And its ability to produce goods and services will depend on its labour productivity.

Labour productivity in turn depends on the amount of physical capital, human capital, natural resources and technological knowledge available to workers.

Government can affect the growth rate of an economy in a number of ways. The objective will always be to increase the productivity of workers by increasing the stock of physical capital, human capital, natural resources or technological knowledge available to workers.

The accumulation of physical (and human) capital will be subject to diminishing marginal returns.

This implies that by accumulating physical capital through investment, the growth rate will increase rapidly at the outset, but the rate of growth will slow down as one continues to accumulate physical capital.

There should therefore be a phenomenon of economic convergence whereby the poorest countries (which have accumulated little capital to date) will grow faster than the richer countries with a lot of capital.

- But this phenomenon of economic convergence is only observed in countries where political institutions and other socio-economic characteristics are similar. This is known as conditional convergence.