One of the most newsworthy features of yesterday’s budget was the announcement that the UK will introduce a tax on sugary drinks.

There is reason to think this may have primarily been done as a dead cat move, to draw attention away from the fact the the Chancellor is missing all his deficit reduction targets and cutting disability benefits (though apparently he can still afford tax cuts for higher rate tax payers).

But what effect might a tax on sugary drinks have?

Obviously it will reduce consumption of sugary drinks:  it’s economics 101 that when the price of something goes up, consumption falls. But that by itself is not interesting or useful. The question is what effect will that have on health and well-being?

The only honest answer to that is we don’t know, as few countries have tried such a tax, and we do not have good data on what the effects have been in countries that have.

For millionaires such as George Osborne and Jamie Oliver, the tax is unlikely to make much difference. Sugary drinks are such a tiny part of their expenditure, they will probably not notice.

But what about those at the other end of the income scale? While George Osborne may not realise this, there are some people for whom the weekly grocery shop is a significant proportion of their total expenditure. For such people, taxing sugary drinks may well have a noticeable effect.

For a family who currently spends money on sugary drinks, 3 outcomes are possible.

The first possibility is that they continue to buy the same quantity of sugary drinks as before (or sufficiently close to the same quantity that their total expenditure still rises). They will then be worse off, as they will have less money to spend on other things. This is bad in itself, but also one of the strongest determinants of ill health is poverty, so taking money away from people is unlikely to make them healthier.

The second possibility is that they reduce their consumption of sugary drinks by an amount roughly equivalent to the increased price. They will then be no better or worse off in terms of the money left in their pocket after the weekly grocery shopping, but they will be worse off in welfare terms, as they will have less of something that they value (sugary drinks). We know that they value sugary drinks, because if they didn’t, they wouldn’t buy them in the first place.

Proponents of the sugar tax will argue that they will be better off in health terms, as sugary drinks are bad for you, and they are now consuming less of them. Well, maybe. But that really needs a great big [citation needed]. This would be a relatively modest decrease in sugary drink consumption, and personally I would be surprised if it made much difference to health. There is certainly no good evidence that it would have benefits on health, and given that you are harming people by depriving them of something they value, I think it is up to proponents of the sugar tax to come up with evidence that the benefits outweigh those harms. It seems rather simplistic to suppose that obesity, diabetes, and the other things the the sugar tax is supposed to benefit are primarily a function of sugary drink consumption, when there are so many other aspects of diet, and of course exercise, which the sugar tax will not affect.

The third possibility is that they reduce their consumption by more than the amount of the price increase. They will now have more money in their pocket at the end of the weekly grocery shop. Perhaps they will spend that money on vegan tofu health drinks and gym membership, and be healthier as a result, as the supporters of the sugar tax seem to believe. Or maybe they’ll spend it on cigarettes and boiled sweets. We simply don’t know, as there are no data to show what happens here. The supposed health benefits of the sugar tax are at this stage entirely hypothetical.

But whatever they spend it on, they would have preferred to spend it on sugary drinks, so we are again making them worse off in terms of the things that they value.

All these considerations are trivial for people on high incomes. They may not be for people on low incomes. What seems certain is that the costs of the sugar tax will fall disproportionately on the poor.

You may think that’s a good idea. George Osborne obviously does. But personally, I’m not a fan of regressive taxation.

Although this is primarily a blog about medical stuff, I did warn you that there might be the occasional social science themed post. This is one such post.

In his recent speech to the Conservative Party conference, David Cameron came up with many fine words about equality of opportunity. He led us to believe that he was for it. Here is an extract from the relevant part of his speech:

If we tackle the causes of poverty, we can make our country greater.

But there’s another big social problem we need to fix.

In politicians’ speak: a “lack of social mobility”.

In normal language: people unable to rise from the bottom to the top, or even from the middle to the top, because of their background.

Listen to this: Britain has the lowest social mobility in the developed world.

Here, the salary you earn is more linked to what your father got paid than in any other major country.

I’m sorry, for us Conservatives, the party of aspiration, we cannot accept that.

We know that education is the springboard to opportunity.

Fine words indeed. Cameron is quite right to identify lack of social mobility as a major problem. It cannot be right that your life chances should depend so much on who your parents are.

Cameron is also quite right to highlight the important role of education. Inequality of opportunity starts at school. If you have pushy middle class parents who get you into a good school, then you are likely to do better than if you have disadvantaged parents and end up in a poor school.

But it is very hard to reconcile Cameron’s fine words with today’s announcement of a new grammar school. In theory, grammar schools are supposed to aid social mobility by allowing bright kids from disadvantaged backgrounds to have a great education.

But in practice, they do no such thing.

In practice, grammar schools perpetuate social inequalities. Grammar schools are largely the preserve of the middle classes. According to research from the Institute for Fiscal studies, children from disadvantaged backgrounds are less likely than their better off peers to get into grammar schools, even if they have the same level of academic achievement.

It’s almost as if Cameron says one thing but means something else entirely, isn’t it?

If Cameron is serious about equality of opportunity, I have one little trick from the statistician’s toolkit which I think could help, namely randomisation.

My suggestion is this. All children should be randomly allocated to a school. Parents would have no say in which school their child goes to: it would be determined purely by randomisation. The available pool of schools would of course need to be within reasonable travelling distance of where the child lives, but that distance could be defined quite generously, so that you wouldn’t still have cosy middle class schools in cosy middle class neighbourhoods and poor schools in disadvantaged neighbourhoods.

At the moment, it is perfectly accepted by the political classes that some schools are good schools and others are poor. Once the middle classes realise that their own children might have to go to the poor schools, my guess is that the acceptance of the existence of poor schools would rapidly diminish. Political pressure would soon make sure that all schools are good schools.

That way, all children would have an equal start in life, no matter how rich their parents were.

This suggestion is, of course, pure fantasy. There is absolutely no way that our political classes would ever allow it. Under a system like that, their own children might have to go to school with the plebs, and that would never do, would it?

But please don’t expect me to take any politician seriously if they talk about equality of opportunity on the one hand but still support a system in which the school that kids go to is determined mainly by the socioeconomic status of their parents.

Today we have learned that the big six energy providers have been overcharging customers to the tune of over £1 billion per year.

Obviously your first thought on this story is “And what will we learn next week? Which religion the Pope follows? Or perhaps what do bears do in the woods?” But I think it’s worth taking a moment to think about why the energy companies have got away with this, and what might be done about it.

Energy companies were privatised by the Thatcher government back in the late 1980s and early 1990s, based on the ideological belief that competition would make the market more efficient. I’m not sure I’d call overcharging consumers by over £1 billion efficient.

It’s as if Thatcher had read the first few pages of an economics textbook that talks about the advantages of competition and the free market, and then gave up on the book without reading the rest of it to find out what can go wrong with free markets in practice.

Many things can go wrong with free markets, but the big one here is information asymmetry. It’s an important assumption of free market competition that buyers and sellers have perfect information. If buyers do not know how much something is costing them, how can they choose the cheapest supplier?

It is extraordinarily difficult to compare prices among energy suppliers. When I last switched my energy supplier, I spent well over an hour constructing a spreadsheet to figure out which supplier would be cheapest for me. And I’m a professional statistician, so I’m probably better equipped to do that task than most.

Even finding out the prices is a struggle. Here is what I was presented with after I looked on NPower’s website to try to find the prices of their energy:

It seems that they want to know everything about me before they’ll reveal their prices. And I’d already had to give them my postcode before I even got that far. Not exactly transparent, is it?

It was similarly impossible to find out Eon’s prices without giving them my entire life history. EDF and SSE were a bit more transparent, though both of them needed to know my postcode before they’d reveal their prices.

Here are EDF’s rates:

And here are SSE’s rates:

Which of those is cheaper? Without going through that spreadsheet exercise, I have no idea. And that’s just the electricity prices. Obviously I have to do the same calculations for gas, and given that they all give dual fuel discounts, I then have to calculate a total as well as figuring out whether I would be better off going with separate suppliers for gas and electricity to take the cheapest deal on each and whether that would compensate for the dual fuel discount.

And then of course I also have to take into account how long prices are fixed for, what the exit charges are, etc etc.

Seriously, if I as a professional statistician find this impossibly difficult, how is anyone else supposed to figure it out? There are price comparison websites that are supposed to help people compare prices, but of course they have to make a living, and have their own problems.

It’s no wonder that competition is not working for the benefit of consumers.

So what is to be done about it?

I think there is a simple solution here. All suppliers should be required to charge in a simple and transparent way. The standing charge should go. Suppliers should be required simply to quote a price per unit, and should also be required to publish those prices prominently on their website without consumers having to give their inside leg measurements first. If different rates are given for day and night use, a common ratio of day rate to night rate should be required (the ratio used could be reviewed annually in response to market conditions).

Suppliers will no doubt argue that a flat price per unit is inefficient, as there are costs involved in simply having a customer even before any energy is used, and a customer who uses twice as much energy as another does not cost them twice as much.

Tough. The energy companies have had over 20 years to sort out their act, and have failed. While I’m not a fan of governments intervening in markets as a general principle, there are times when it is useful, and this is one of them. I don’t see how anyone can argue that an industry that overcharges consumers by over £1 billion per year is efficient. No one energy company would be at  a disadvantage, as all their competitors would be in the same position.

There would be a further benefit to this idea, in that it would add an element of progressiveness to energy pricing. At the moment, poor people who don’t use much energy pay more per unit than rich people. That doesn’t really seem fair, does it?

This is such a simple and workable idea it is hard to understand why it hasn’t already been implemented. Unless, of course, recent governments were somehow on the side of big business and cared far less about ordinary consumers.

But that can’t be true, can it?