The income distribution and probability

I haven’t posted for some time so thought I would write something short on a subject about which I feel quite strongly; income inequality. There is lots of data to suggest that the UK and the USA have become more unequal in the last few decades. This is indicated by the Gini coefficient, which has been increasing steadily. The concern I have is that many governments (the UK in particular) are becoming more conservative. The coalition government in the UK at the moment seem to be making many changes that ultimately benefit the rich and disadvantage the poor.

The conservative viewpoint, in a simple sense, seems to be that everyone should simply pull up their socks, work harder and therefore earn more. We shouldn’t penalise those who’ve done well. The problem that I have is that the income distribution (shown in the figure below) is essentially a probability distribution. The mean is about £25000, the mode is about £16000 and the median is about £21000. Assuming everyone has the same opportunities, you then have a 50% chance of earning below £21000, your most likely salary is £16000, you have a 1 in 10 chance of earning over £45000, and a 1 in 100 chance of earning over £150000. An individual could work extremely hard, be very creative and do very well, but the entire population cannot. Unless something is done to adjust the income distribution, 10% of the population will earn below £10000, 25% will earn below £12000, and 50% will earn below £21000.

UK Income Distribution

An approximate income distribution graph for the UK.

Of course, opportunities aren’t all the same. Some are disadvantaged the moment they are born and others have an immediate advantage. A person born into a poor household probably has a much smaller than 1 in 100 chance of ever earning the equivalent of £150000 or more. I guess the point I’m trying to make is that simply suggesting that everyone should simply work harder and earn more is, in itself, nonsense. If the coalition government wants to reduce public spending, they need to look at how to adjust the income distribution so that the lowest earners can still afford the basics. I don’t quite know how to do this. One way is to use taxation. Tax high salaries to discourage paying these high salaries and encourage increasing lower salaries. Alternatively, use taxation to redistribute income. The disadvantage here is that it then doesn’t encourage businesses to pay higher salaries (in a sense it is subsidising businesses and allowing them to pay salaries lower than they probably should). One could argue that it spreads the risk a little and might help to stabilise employment (i.e., we probably don’t want companies continually making people redundant when they can’t afford to pay salaries). Or, as seems to be happening, remove some of the support for lower earners and consequently encourage business to increase the lower salaries. The latter may be fine in principle, but I can’t, however, see it happening if there isn’t some support for doing so. At the moment it seems like the government wants to remove the support for the lower earners while keeping their salaries low so as to make us internationally competitive.

Essentially, what I’m suggesting is that if people could understand that the income distribution is really a probability distribution it may encourage the government to put more effort into influencing the income distribution. If they want the lowest earners to be self-sufficient, they need to act to narrow the income distribution. If they don’t care, they can let it continue to widen and then deal with the resulting poverty.


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