Steak, Ramen, and Recessions:
Other Elasticities
ECON 201: Principles of Microeconomics
Lecture 8
Last Class: Price Elasticity of Demand
\[\varepsilon = -\frac{\%\text{ change in demand}}{\%\text{ change in price}}\]
- Last class we measured how much demand responds to a change in price.
- But price is not the only thing that moves demand. Income changes, and so do the prices of other goods.
Today’s terms: the income elasticity of demand, normal and inferior goods, necessities and luxuries, the cross-price elasticity of demand, substitutes and complements.
Income Elasticity of Demand
The income elasticity of demand is the percentage change in demand that would occur in response to a 1% increase in income:
\[\varepsilon_{\text{income}} = \frac{\%\text{ change in demand}}{\%\text{ change in income}}\]
- There is no minus sign this time, because the sign is part of the answer.
- A positive elasticity means demand rises with income. A negative one means demand falls with income.
Worksheet, Activity 1
Maya works part time, and her monthly income rises from $1,000 to $1,200. Find the income elasticity for each good below.
\[\varepsilon_{\text{income}} = \frac{\%\text{ change in demand}}{\%\text{ change in income}}\]
| Packs of ramen |
40 |
32 |
|
|
| Gallons of gas |
20 |
22 |
|
|
| Steak dinners |
2 |
3 |
|
|
Normal and Inferior Goods
- A normal good is one people buy more of as their income rises, so its income elasticity is positive.
- An inferior good is one people buy less of as their income rises, so its income elasticity is negative.
- Maya’s income rose 20% and her ramen fell 20%, so \(\varepsilon_{\text{income}} = -1\). Ramen is inferior for her.
- Her gas rose 10% and her steak dinners 50%, so both are normal, at 0.5 and 2.5.
- In US spending data, breads and cereals are inferior, with an income elasticity of \(-0.09\).
Necessities and Luxuries
- Normal goods split in two, depending on whether the income elasticity is below or above 1.
- A necessity has an income elasticity between 0 and 1. People buy more of it as they get richer, but demand grows more slowly than income.
- A luxury has an income elasticity greater than 1. Demand for it grows faster than income.
- Gas is a necessity for Maya, at 0.5. Steak dinners are a luxury, at 2.5.
Income Elasticities in the United States
Estimates for the United States (Muhammad et al., 2011):
| Food, beverages, and tobacco |
0.35 |
| Education |
0.91 |
| Housing |
1.06 |
| Transport and communications |
1.13 |
| Recreation |
1.25 |
Below 1 is a necessity and above 1 a luxury. Housing counts as a luxury here, so the word is technical rather than everyday.
What Happens in a Recession
- In a recession, incomes fall. The goods with the highest income elasticities lose the most demand.
- Take a 10% fall in income. Spending on recreation falls by about 12.5%, and spending on food by about 3.5%.
- Demand for an inferior good moves the other way. It rises when incomes fall.
- As the 2008 recession set in, Nielsen recorded Spam sales up 10.6% over the twelve weeks to May 3, against the same weeks a year earlier.
Cross-Price Elasticity of Demand
The cross-price elasticity of demand for good A is the percentage change in demand for A that would occur in response to a 1% increase in the price of good B:
\[\varepsilon_{\text{cross}} = \frac{\%\text{ change in demand for A}}{\%\text{ change in the price of B}}\]
- Again there is no minus sign, because the sign is what tells us how the two goods are related.
- A rise in the price of one good sends some buyers toward another good, and away from a third.
Worksheet, Activity 2
The campus cafe raises the price of a coffee from $2.50 to $3.00. Find the cross-price elasticity for each good below.
\[\varepsilon_{\text{cross}} = \frac{\%\text{ change in demand for A}}{\%\text{ change in the price of B}}\]
| Coffee across the street |
6 |
9 |
|
|
| Donuts at the campus cafe |
8 |
6 |
|
|
| Packs of ramen |
32 |
32 |
|
|
Substitutes and Complements
- Two goods are substitutes if a rise in the price of one raises demand for the other, so \(\varepsilon_{\text{cross}}\) is positive.
- Two goods are complements if a rise in the price of one lowers demand for the other, so \(\varepsilon_{\text{cross}}\) is negative.
- The campus price rose 20% and coffee across the street rose 50%, so \(\varepsilon_{\text{cross}} = 2.5\). The cafes are substitutes.
- Donuts fell 25%, so \(\varepsilon_{\text{cross}} = -1.25\): coffee and donuts are complements. Ramen did not move, so at 0 it is neither.
Soda Just Outside Philadelphia
Philadelphia’s tax raised the price of a sweetened drink inside the city by 34%. What happened at the stores just outside it?
- Sales at the average store inside the city fell by about 56,000 ounces a week.
- Sales at the average store within two miles outside the city rose by about 64,000 ounces a week.
- Soda inside the city and soda just outside it are close substitutes, so the cross-price elasticity between them is large and positive (Seiler, Tuchman, and Yao, 2021).
Sources
- Muhammad, Seale, Meade, and Regmi (2011), “International Evidence on Food Consumption Patterns: An Update Using 2005 International Comparison Program Data,” USDA Economic Research Service Technical Bulletin 1929, appendix tables 1 and 5.
- Associated Press (2008), “Sales of Spam rise as consumers trim spending,” NBC News, May 28, reporting Nielsen Company data.
- Seiler, Tuchman, and Yao (2021), “The Impact of Soda Taxes: Pass-Through, Tax Avoidance, and Nutritional Effects,” Journal of Marketing Research 58(1), table 5.