Goods which do not obey the ‘law of demand‘, viz. that less is bought as price rises. Rather, the quantity demanded of a Giffen good increases as its price rises, and it therefore has a positively sloped demand curve. The expression is named after Sir Robert Giffen, to whom A. Marshall attributed the observation that, among the labouring classes, when the price of bread (the main item of their diet) rose, their consumption rose, and when its price fell, their consumption also fell. This he saw as a refutation of the ‘law of demand’. However, Giffen goods are nowadays seen as special cases of standard demand analysis rather than refutations of it. lf the total expenditure on a particular good by a consumer constitutes a large proportion of his income, then changes in price of that good have a significant effect on his real income. If a good is an inferior good (a rise in consumer’s income causes a fall in demand, a fall in income causes a rise in demand), it is then possible that a rise in price could cause an increase in demand, and a fall in price a fall in demand, via this income effect. For quantity demanded actually to change in the same direction as price it is not enough that the income effect work in the way just described; it must also be strong enough to outweigh the substitution effect. Given a change in the price of a good, if the consumer’s real income is held constant (by a compensating change in money income), the quantity of the good demanded will always change in the opposite direction to the price change: if the price rises, substitute goods whose prices have stayed the same are now relatively cheaper than the good in question and will be substituted for the latter; if price falls, substitute goods will now be relatively more expensive and the good in question will be substituted for them. The overall change in quantity of the good demanded following a change in its price is the resultant of these two effects – the income effect and the substitution effect. If the income effect works so as to change demand in the same direction as the price change (i.e. the good is an inferior good), while the substitution effect works so as to change demand in the opposite direction to the price change (always the case), and if the former effect outweighs the latter, the net effect is that the quantity demanded changes in the same direction as price. It was this special case which was observed by Giffen.
Reference: The Penguin Business Dictionary, 3rd edt.