Today the Mail and the Guardian/Observer both have an article the MAGIC FORMULA for cheap air travel. Are you ready for this?

Here it is…

∏^{A} = *gU _{G}* + min(

*k*–

*g*, (1 –

*g*)(1 –

*r*))

What does it mean? Apparently ∏^{A} means “profit” (as opposed to every time we use upper-case pi in mathematics, where it means a cumulative product). As to the other symbols, neither newspaper will deign to tell us.

Apparently the formula tells you how far in advance you should book a plane ticket for a discount, though you have to take the papers’ word for it or dig up the original article, a horribly long winded economics paper comparing selling in advance to selling at clearance (PDF). That’s already one important difference; this isn’t about people buying things as cheaply as possible, it’s selling them at a discount for maximum profit. It also assumes the seller has a monopoly over their market, which for air travel is only partly true; there’s competition on most major routes these days. Anyway, here’s the complete list of variables:

∏^{A} – profit from selling in advance

*g* – the fraction of buyers defined as “good type” buyers; “good type” buyers being buyers who are likely to get a lot of value out of the product.

*k* – capacity. They don’t define explicitly what capacity means in this case, but I assume it’s the number of buyers they can cater for.

*r* – the likelihood a “bad type” buyer will get little value from the product.

*U _{G}* – expected value a “good type” buyer will get from the product. Defined as 1 –

*ar*+

*aru*(which I’d write as 1 –

*ar*(1 – u) but idk, I’m not an economist).

*a* – a coefficient to be applied to *r* such that *ar* is the likelihood a “good type” buyer will get little value from the product.

*u* – the value the buyer gets from the product on a scale of 0-1.

Great! All I have to do now is calculate the number of “good type” buyers and “bad type” buyers intending to travel EasyJet in 8 weeks time, assign them all a randomly distributed normalised consumption value defined by probabilities *r* and *ar*, then work out whether the number of seats not taken up by “good type” buyers will exceed the number of “bad type” buyers who get a lot of value out of an EasyJet flight, and I too can… err

Actually, there’s nothing anyone who is not Chief Economist of a major airline could do with that information. It certainly won’t get anyone cheap air travel!

The *Daily Mail* and *The Guardian* both claim to have “tested the formula”, but in fact all they’ve done is go onto the EasyJet website and look up plane fares for the next few weeks. Good job guys.

#1 by

Ferguson Monday, 23rd August 2010 - 12:28 GMT+0100Just to point out that pi is always used to represent profit in economics, something which has occasionally caused me problems in my subsequent career as an accountant – most accountants not having previously been economists!