Income & Cross-Price Elasticity
- Compute income elasticity and classify a good from its sign
- Compute cross-price elasticity and classify a relationship from its sign
- Explain why the sign matters more than the magnitude for these two measures
For these two, the sign is the answer
Price elasticity of demand is always negative, so its sign carries no information and we report the absolute value. Income and cross-price elasticity are different: their signs are exactly what the question is asking. A positive income elasticity means a normal good, a negative one means inferior. A positive cross-price elasticity means substitutes, a negative one means complements. Dropping the sign on these throws away the answer.
Necessities and luxuries
Within normal goods, income elasticity distinguishes further. Between 0 and 1 the good is a necessity — demand rises with income but less than proportionally, so it takes a shrinking share of a growing budget. Above 1 it is a luxury — demand rises faster than income. Food in aggregate is a necessity; restaurant meals and foreign travel are luxuries. This is why recessions hit luxury sectors hardest.
Using cross-price elasticity to define a market
The magnitude of cross-price elasticity measures how close a substitute is, which makes it the practical tool for deciding what counts as the same market. Two brands of the same product have a large positive cross-price elasticity; a brand of shampoo and a brand of cement have one near zero. Competition authorities use exactly this to decide whether a merger reduces competition, which is a rare case of an AP formula having a direct professional use.
When income rises 10%, demand for good A falls 4% and demand for good B rises 15%. When the price of good C rises 20%, demand for good D falls 8%. Classify each relationship.
- 1.Good A: E_i = −4/10 = −0.4. Negative, so A is an inferior good.
- 2.Good B: E_i = 15/10 = +1.5. Positive and above 1, so B is a normal good and specifically a luxury.
- 3.C and D: E_xy = −8/20 = −0.4. Negative, so C and D are complements.
- 4.The magnitude 0.4 says the complementarity is fairly weak.
Do not take absolute values of income or cross-price elasticity. Reporting |E_i| = 0.4 loses the entire finding, because 0.4 and −0.4 describe opposite kinds of good.
The cross-price elasticity of demand between two goods is +1.8. The goods are:
A good has an income elasticity of demand of 0.3. The good is:
Income rises 8% and demand for a good falls 2%. The income elasticity is:
State the sign and the classification together — "−0.25, so the good is inferior". Rubrics typically award the coefficient and the interpretation as separate points, and the interpretation is the one students omit.
Answer the 3 checkpoints as you read.
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