Every January, many of us make New Year’s resolutions promising to change our behaviour, often to a healthier lifestyle. Yet whilst we’re all laying off the booze, cutting down on carbs, and toning up the tummy, high street retailers and their January sales who can be relied upon to dish up the same-old, same-old post Christmas.

Prices don’t simply tumble and fall, they either crash or get slashed. It’s as dramatic and as cut throat as that. Women who just two weeks earlier were happy to queue patiently in the Post Office, now think nothing of trampling over small children and elbowing the elderly in order to be first in line for that much sought-after designer hand bag at a never-to-be-repeated price. Just fifty quid plus a few cuts and bruises.

But whilst the technique of heavily discounting might be a good idea in January when retailers traditionally want to get shut of stock pronto, it’s now thought that discounting in general is not necessarily the best way to generate more sales and, crucially, more income. A study led by Akshay Rao of the University of Minnesota’s Carlson School of Management, suggests that many retailers are missing a trick because they fail to recognise the consumer’s attitudes to discounting. Or, more to the point, their misunderstanding of what is actually on offer. The result of this confusion is that most shoppers prefer to get something ‘extra’ for free, rather than to get the same thing cheaper.

Apparently, the main reason is that people are useless at fractions. Half of them can’t work them out, half of them can’t be bothered to work them out, and the other half haven’t got a clue about maths and take up public speaking. To prove the point, Rao’s research team offered two identical hand lotions for sale. One contained 50% more product for free, whilst the other had the price discounted by 33%. Almost three quarters of all consumers opted for the bigger pack believing that this offered the best value. Yet, of course, both offers are exactly the same. So I’m told, anyway.

This numerical blind spot remains even when the deal clearly favours the discounted product. Again, to prove the point, Mr Rao gave his undergraduates a choice of two deals when buying loose coffee beans. They could either have 33% extra for free or get 33% off the price. On this occasion, the discounted price is by far the better proposition, but the supposedly clever students viewed both deals as the same.

Further studies have shown other ways in which retailers can exploit the consumer’s innumeracy. One is to befuddle them with double discounting. For instance, people are more likely to see a bargain in a product that has been reduced by 20%, and then by an additional 25%, than one which has been subject to an equivalent, one-off, 40% reduction. As the American’s say, do the math, and you’ll find it’s the same.

So how does this help us in general marketing terms? Well according to Mr Rao, the principles can be applied beyond simple pricing. For instance, when advertising a new car’s fuel efficiency, it’s more impressive to quote the number of ‘extra’ miles it does to the gallon, rather than the equivalent percentage fall in fuel consumption. It’s just easier for consumers to understand and is therefore a more convincing argument. As the car salesman explained to me the last time I bought a car, “Mr Hesketh, on just one gallon of petrol you can not only get all the way to your mother-in-law’s house but you can also get all the way back again too.” Who wouldn’t buy a car from a man that generous?