# Economic Growth

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^{[1]}This article considers what factors affect economic growth For example, why is it that some countries have enjoyed consisted growth to the point of increased wealth, better medical services and higher standards of living while other countries are still struggling?

The article discusses these issues and explains a model for economic growth, in particular through a figure known as **GDP per capita** which can be split into average labour productivity and share of population employed. The article then introduces that production function to better understand economic growth.

## Contents |

## Textbook Readings

Bernanke, Olekalns and Frank, Principles of Macroeconomics, (3rd ed, Sydney, McGraw Hill, 2011), pp. 278-328 (Chapters 10 & 11).

## Initial Comments

^{[2]}When we look at the factors that contribute to economic growth, we are looking at the economy in the long run. However this does not mean we use the AS-DS model. This is because the AS-DS model explains how aggregate demand affects output ‘’around’’ potential, not how potential output changes. Hence a new model is used to explain economic growth.

^{[3]}One more comment is that economic growth is strongly related to small increases in economic performance **sustained over time**. That is, countries that have constantly had increased output over longer periods have enjoyed much larger economic growth that countries that haven’t. This growth is the same as that seen in compound interest.

## Average Labour Productivity

^{[4]}One major factor for economic growth can be measured by GDP per capita, that is, the amount of average output a country yields per person. GDP per capita is given by real GDP divided by the number of people in the population. Now GDP per capita can be split into two components: average labour productivity and share of population employed, mathematically given by:

- y/POP = y/N x N/POP

Where:

- y = real GDP
- POP = population
- N = number of employed workers

Mathematically, the two sides of the equation are the same since N can be cancelled out on the right hand side. Now, y/N is known as the average labour productivity, that is, how much output is a country yielding per number of people employed, while N/P is known as the share of population employed.

Importantly, GDP per capita can grow only if the labour productivity, or the share of population employed grows as well. However, the share of population employed, since it is a fraction, is generally assumed to be between 0 and 1 since you can’t have more workers than he population available. Hence, average labour productivity is seen as the major contributor to economic growth.

### Determinants of Average Labour Productivity

^{[5]}The question to answer is what determines growth in average labour productivity? The answer is that there are at least six major determinants:

- Human Capital – the talent, skills, education and training of workers
- Physical Capital – the tools and machinery available to workers
- Land and Natural Resources
- Technology
- Entrepreneurship and Management – the creative introduction of new and more efficient methods, products or services
- Political and Legal Environment – the encouragement by government/society to work hard, invest wisely and generally increase wealth

All of these factors affect labour productivity: better training for employees with more advanced technology increase their productivity, while land and natural resources means being able to utilize the employees for more production.

## Costs of Economic Growth

^{[6]}The discussion up to now suggests that countries should always strive for the highest growth rate possible. However this is not the case since intensive growth comes with costs as well. These costs include:

- Cost of Creating New Capital – by choosing to create new factories, resources such as designers, builders and project managers, along with physical resources such as building materials must be diverted from other sectors, such as leisure and hospitality. The result is that building new capital affects other areas of the economy and means that people save more and spend less, which may no necessarily be desirable.
- Increased Working Hours – intensive economic growth is often accompanied by workers working longer hours, having less leisure time and often means working in unsafe working environments.
- Costs of R&D and acquiring new skills that may be more expensive than the growth achieved later
- Destruction of the environment

## Limits of Economic Growth

^{[7]}Many theorists suggests that if economic growth continues along with population growth, natural resources such as air, water and fuel will run out very soon, and hence that there are limits to growth. While sustainability is a major issue, some factors to consider are:

- Economic growth does not necessarily mean growing by continuing what were doing now; for example better technology might replace the smoky factories and the use of non renewable energy sources
- Economic growth does not necessarily mean reduced quality of the environment. In fact, the most polluted areas are actually those in developing countries rather than the rich, fast growing ones.
- Economic forces can correct scarcity of depleting natural resources. The oil crisis of the 1970’s promoted higher prices, which in turn led consumers to buy more energy efficient appliances and machinery

## The Production Function

^{[8]}From the above discussion, we know that output is related to the amount of labour (L), capital stock (K) and the state of echnology (A). Mathematically, this can be written as:

- Y = A.f(L,K)

i.e. output is given by some function of labour and capital, multiplied by the state of technology.

Now if we take both sides of the function and divide by L, we get:

- Y/L = A. f(K/L,1)
- Y/L = A.f(k)
- y = A.f(k)

which is the per capita production function.

### Marginal Product of Capital and Labour

^{[9]}Now if marginal product of capital, denoted as MP_{K}, I given by:

- MP
_{K}= dy/dK = A.f(K,L)

- MP

And marginal product of labour is given by:

- MP
_{L}= dy/dL = A.f(K,L)

- MP

They both have the property of being positive (at least to comply with the cost-benefit principle) and they are also diminishing, so that as capital or labour increase, marginal product of labour or capital decrease. Pictorially, MP_{K} can be represented as a downward function of the real interest rate while labour is a downward sloping function of the real wage (W/P).

We can use these to estimate the value of alpha by simply rearranging the marginal product of labour and capital for alpha.

### The Cobb-Douglas Production Function

^{[10]}The Cobb-Douglas production function is probably the most widely used function. It is given by:

- Y = AK
^{a}L^{1-a}

- Y = AK

Where a is a parameter set between 0 and 1.

Now simple mathematical calculation shows that:

- MP
_{K}= aY/K - MP
_{L}= (1-a)Y/L

- MP

The Cobb-Douglas function gives some predictions about the income yielded by employees and by capital. They are given by:

- Real Labour Income = (1-a)Y/L * L = (1-a)Y
- Real Capital Income = aY/K * K = aY

And adding the two together yields:

- (1-a)Y + aY = Y

in other words, labour income + capital income = output which is consistent with out analysis throughout the course.

## Growth Accounting

^{[11]}Another application of the Cobb-Douglas function is that with a bit of mathematical manipulation, we can see that:

Where:

- ΔY
_{t}= change in output between the last period and the current period. This is the same for the other delta terms. - Y
_{t-1}= output in the previous period

- ΔY

which means that growth, i.e. the rate at which output changes is given by the addition of the growth rate in capital, labour and technology.

We can also use this function to estimate the growth rate of technology (which isn’t very easily measured from empirical data).

## References

"Textbook" refers to Bernanke, Olekalns and Frank, Principles of Macroeconomics, (3rd ed, Sydney, McGraw Hill, 2011).