Are all Giffen goods inferior, and all inferior goods Giffen?

Key ideas.

• Normal and inferior goods. For a normal good, demand moves in the same direction as the consumer's income. For an inferior good it moves the other way: demand falls when income rises and rises when income falls. Low-quality foods such as coarse cereals are the usual case, and a good can be normal at low incomes and inferior beyond some level of income.
• Two effects of a price change. When a good becomes cheaper, the consumer substitutes it for other goods (the substitution effect), and her purchasing power rises, which changes her demand as a rise in income would (the income effect). A price rise works the other way round: the substitution effect lowers demand for the good, and her real purchasing power falls.
• Giffen good. For a normal good both effects push demand in the same direction, so demand rises when price falls. For an inferior good the two effects pull in opposite directions. If the income effect is the stronger of the two, demand moves in the same direction as price, and the good is called a Giffen good. Its demand curve slopes upward, against the law of demand.

(i) All Giffen goods are inferior goods: TRUE. Take a rise in the price of a good. The substitution effect cuts its demand. Demand can rise on balance only if the income effect pushes the opposite way, and harder. The income effect of a price rise is that of a fall in real income, so it raises demand only for a good whose demand rises when income falls, which is an inferior good. For a normal good the income effect reinforces the substitution effect, so its demand must fall when its price rises; a normal good can never be Giffen. Hence every Giffen good has to be inferior.

(ii) All inferior goods are Giffen goods: FALSE. Being inferior is not enough. For an inferior good the income effect runs against the substitution effect, but if it is the weaker of the two, the substitution effect decides the outcome: demand still falls when price rises, the demand curve still slopes downward, and the good obeys the law of demand.

• Example (our own): suppose that for a hostel student, packets of plain unbranded biscuits are inferior: when her pocket money goes up she switches to branded cookies. If the price of the unbranded biscuits then rises, she buys fewer packets, not more, turning to fruit or peanuts instead. The packets cost her little, so the rise in price hardly dents her purchasing power; the income effect is small, the substitution effect wins, and the good is inferior but not Giffen.

Conclusion. Inferiority is necessary but not sufficient for a Giffen good. Statement (i) is true, because only an inferior good can have an income effect that works against the substitution effect; statement (ii) is false, because an inferior good is Giffen only when that income effect is strong enough to outweigh the substitution effect.