Percentages

I've got something I have to confess. It's very embarassing, but I'm sure I'll feel better when I've told you. You see, the thing is...wait for it...I absolutely love percentages.

I know some people hate numbers of all sorts and run away from them faster than you can say "decimal point". I'm just the opposite. Yes, I like facts; but I love figures. And, in particular, I adore percentages.

This is fortunate because percentages play a key role in economics. So I've made them the subject of the 41st item in our regular Economics for Amateurs series, which you can find here each Monday.

Many key economic statistics are expressed in terms of percentages. For example, the unemployment rate is given as a percentage of the total labour force. If unemployment is 10 per cent (written "percent" in American English), this means that one in ten of all the people who would like to work are currently registered as unemployed.

But how are such percentages calculated? Simple. If we call the number of unemployed "U" and the total labour force "L", then the unemployment rate is calculated by:

• "U divided by L, multiplied by 100" or "U / L x 100".

Note that, if unemployment rises from 10 per cent to 11 per cent, this is not a 1 per cent rise, but rather a one "percentage point" rise (from 10 to 11). The percentage increase in this case is actually 10 per cent and is given by the same formula as for any percentage changes:

• (New figure minus old figure) divided by old figure, multiplied by 100. In this case that is (11-10) / 10 = 0.1 x 100 = 10 %

Other common changes in economics that are expressed as percentages include changes in GDP (called the growth rate) and changes in the price level (called "inflation" if the change is positive). These changes are usually expressed at an annualized rate, even though the period of comparison might be year-on-year, quarter-on-quarter or month-on-month.

For example, if you read that prices rose between November and December at an annualized rate of 5 per cent, this doesn't mean they rose by 5 per cent between the two months, but rather at a rate which, if it continued for a year, would lead to a 5 per cent increase in the price level.

Finally, as if you hadn't had enough fun already, here's an odd feature of percentage changes. If, for example, a stock market index falls from 5,000 to 4,000, this is a fall of 20 per cent:

• (4,000-5,000) / 5,000 = -0.2 x 100 = -20%.

But to get back up to 5,000 again, the index has to rise by 25 per cent:

• (5,000-4,000) / 4,000 = 0.25 x 100 = 25%.