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In this section, we attempt to understand how to economy acts in the short run. It is well known that all economies tend to move through periods of economic growth (expansions) and periods of economic downfalls (contractions) in the short run, though in the long run GDP usually increases. Generally, GDP levels reach a high, known as a peak and then tend to fall to a low, known as a trough after which GDP levels increase. A contraction is then observed as a period between a peak and a trough in GDP graphs, whereas an expansion is observed as a period between a trough and a peak. This continuous cycle of expansions and contractions is known as the business cycle. A recession is usually referred to as a period of two consecutive contractions.

This article introduces a model for the business cycle that tries to explain why the level of GDP tends to fluctuate. The first observation is that recessions are linked to higher unemployment rates, and this is evident by comparing data for GDP and unemployment levels. The rest of the analysis revolves around this link.

## Contents

Bernanke, Olekalns and Frank, Principles of Macroeconomics, (3rd ed, Sydney, McGraw Hill, 2011), pp. 108 - 125 (Chapter 4).

## Output Gaps and Cyclical Unemployment

In order to get a measure of GDP fluctuation, a reference point is chosen. The reference point is known as the potential output or potential GDP and is the level of GDP that would be attained if the economy was using its resources at normal rates (different to maximum output). Once this reference point is chosen (though it changes every period), it is easy to compare actual GDP levels in order to determine the fluctuations.

It can already be concluded that a recession can be caused by one of two possibilities:

1. Potential output has dropped due to various reasons such as weather
2. Actual output is different from potential

If we define:

y = Actual Output (GDP)
y* = Potential Output (GDP)

Then the difference between them is the output gap. In other words:

Output Gap = y - y*

As a result, if y - y* > 0, then the economy is said to be in an expansion period (expansionary gap), while y - y* < 0 implies the economy is in a recession (contractionary gap). In general, both expansionary and contractionary gaps are seen as negative. While a contractionary gap implies the economy is losing potential output, an expansionary gap implies that inflation rates will increase.

## The Natural Rate of Unemployment

The connection between unemployment and recessions can be explained by output gaps. In a contractionary gap, unemployment tends to be high meaning that labour is not utilised to its potential whereas in an expansionary gap unemployment tends to be low for the reverse reasons.

To understand this connection further, we define the natural rate of unemployment as:

u* = Natural Rate of Unemployment
u = Total Unemployment Rare

Then from the analysis of unemployment, cyclical unemployment is the difference between the two. In other words:

Cyclical Unemployment = u - u*

If u - u* > 0, then the economy is said to be undergoing a contraction (since actual unemployment is greater than the natural, so cyclical unemployment is greater than 0), whereas if u - u* < 0, the economy is said to be undergoing an expansion.

### Okun's Law

To put the relationship between output gap and cyclical unemployment in mathematical terms, Okun's Law states that: Where β is usually given (in Australia it's roughly equal to 1.5).

Essentially Okun's law tries to predict by how much an increase in one percent of output gap would increase cyclical unemployment.

Note: a conclusion to be drawn from this analysis is that if we want to reduce cyclical unemployment then we need to reduce the output gap.