Giffen Good vs Inferior Good

A weekly food budget of $24 shows why the income effect has to win

Fix a weekly food budget of $24. Rice costs $1 a unit and delivers 5 units of calories. Meat costs $6 a unit and delivers 10. The household must reach 80 units of calories to get through the week, and subject to that line it buys as much meat as it can. At the starting prices that means 2 meat and 12 rice, spending $12 and $12 and landing on exactly 80. Three meat would leave only $6 for rice and yield 60, which does not clear the week. Rice now rises to $1.50. Holding 2 meat leaves $12 for rice, which buys 8 units and yields 60. Dropping to 1 meat and 12 rice costs the full $24 and yields 70, still short. The only bundle that still reaches 80 is 16 rice and no meat, which uses the whole budget. Rice consumption rose from 12 units to 16 after the price of rice rose. The substitution effect pushed the household away from rice, which is now relatively dearer, but the price rise also made a poor household poorer, and the cheapest source of calories is the thing it had to buy more of. Giffen behavior needs exactly this setup: a staple that eats most of the budget, and no substitute within reach.

The same household demonstrates inferiority when only income moves

Hold the price of rice at $1 and raise the weekly budget from $24 to $36. Buying as much meat as the calorie line allows now means 5 meat and 6 rice, spending $30 and $6 and again landing on exactly 80, since six meat would use the whole $36 and yield only 60. Rice purchases fell from 12 units to 6 while income rose by half, which is the definition of an inferior good and gives an income elasticity of demand of negative one, dividing the 50 percent fall in quantity by the 50 percent rise in income. Nothing about rice changed. No price moved. Only the budget did. That negative income response is the raw material for the Giffen case, which is why every Giffen good is inferior. The reverse fails. Rice is inferior in both stories, but it behaves as a Giffen good only in the first one, where the price rise was large relative to the budget and no substitute was affordable. Give the same household a $60 budget and the same fifty cent rise in the price of rice, and it buys less rice and more meat, exactly as the law of demand predicts.

Two different elasticities, and a question can only be asking about one

A Giffen good is identified by price elasticity of demand and an inferior good by income elasticity of demand, so the two claims are not even measured on the same axis. Suppose the price of a staple rises 10 percent and quantity demanded rises 4 percent. Price elasticity is positive 0.4, the Giffen signature, because the demand curve slopes upward across that range. Suppose instead household income rises 10 percent and purchases of the same staple fall 6 percent. Income elasticity is negative 0.6, which marks the good inferior. On a diagram the split is just as sharp. An inferior good keeps an ordinary downward-sloping demand curve and a rise in income shifts that curve left. A Giffen good has a demand curve that slopes upward over the relevant range, so a change in its own price moves you along the curve in the direction that looks wrong. A stem describing a shift is testing inferiority. A stem describing movement along the curve is testing the law of demand and, rarely, its exception.

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