Mathematical models of the Giffen effect

The Giffen effect is the contradictory phenomenon in economics that both the price and the consumption of a good are increased at the same time. The good in question is always an inferior one. Some economists try to deny the existence of Giffen goods, although it has been observed several times. E.g. the potato behaved in this way in 1995 in Hungary. The main result of the present paper is that the fact that the most popular utility functions exclude the Giffen effect is proven mathematically. A consequence of it is that the real life customer has a different utility function. Examples of utility function allowing Giffen effect are provided, too.