# Institute Mathematicians Define Economic Paradox

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In seeming defiance of common sense, the demand for certain goods may actually soar when they increase in price. While this paradox, referred to as the Giffen effect, has been know for about a century, Weizmann Institute scientists have now developed a mathematical model that defines the real-life conditions under which it may appear.

The Giffen effect may occur when the price of an item that is vital for poor people goes up. For example, if the price of bread increases, the poor will no longer be able to afford related foodstuffs that are even more expensive, such as bagels. As a result, their entire budget for flour products will be spent on bread, driving the demand for this foodstuff upwards. This scenario was first proposed at the end of the last century by the English economist Sir Robert Giffen to explain why the demand for potatoes sharply increased following a price hike during the Irish potato famine of the 1840s.

Although the Giffen effect is highly uncommon because most people are not sufficiently poor to cause its occurrence, Prof. Yakar Kannai of the Institute's Department of Theoretical Mathematics and graduate student Shmuel Baruch have discovered this paradox in the modern Japanese economy. By conducting a statistical analysis of data on household expenditures in that country, they showed that the demand for the cheap alcoholic beverage shochu, drunk largely by poorer Japanese, increased when its price rose. This occurred because the poorer people stopped buying more refined and expensive brands -- namely, first- and second-grade sake -- spending all their drinking money on shochu instead.

Kannai and Baruch have also developed a mathematical model that makes it possible to determine whether the Griffen effect is possible in a given economy. The model consists of graphs and equations describing various conditions prevailing in that economy, particularly the interplay between the intensity of demand and the distribution of income.

According to Kannai, this model is valid only when the people behave rationally and know the quality of the goods. It does not take into account the "snob appeal" of certain overpriced items or the tendency of some people to opt for more expensive goods on the assumption that these are better than equivalent cheap goods.

Prof. Kannai is the incumbent of the Erica and Ludwig Jesselson Chair of Theoretical Mathematics.