Income Elasticity of Demand

Income elasticity of demand measures the percentage change in a buyer’s purchase of a product as a result of a percentage change in her/his income. So income elasticity of demand is

ei = the percentage change in demand / percentage change in income
or
ei = (change in demand / average demand) / (change in income / average income)

Example 1
If a person decides to buy 20% more bananas because of a 10% income increase, the person’s income elasticity of demand for bananas is 20% / 10%, or 2.

Example 2
If a person decides to buy 50% fewer hamburgers because of a 20% income increase, the income elasticity of demand for hamburgers is (-50%) / (+20%), or -2.5. Note that when income elasticity is negative, the product is an “inferior” product (see Unit 2 for the difference between inferior and normal products). A person may decide to buy fewer hamburgers after an income increase, because the person can now afford to buy steak.

Unlike price elasticity of demand, we cannot leave off the minus sign for income elasticity of demand, because income elasticity of demand can be either positive (for a normal good), or negative (for an inferior product).

Cross Price Elasticity of Demand

In the case of a product that has a substitute (like oranges and apples), the price change of one product affects the demand for the other. Cross price elasticity of demand measures this effect. The formula for the cross price elasticity of demand for product A relative to a price change in product B is

e cp = the percentage change in the demand for product A / the percentage change in the price of substitute product B
or
e cp = (change in the quantities of product A / the average of the quantities of product A) / (change in price of product B / average of product B prices)

Example 1
Problem: What is the cross price elasticity of demand for Pepsi if the demand for Pepsi decreases by 10% after the price of Coke decreases by 5%?

Solution: Coke and Pepsi are substitute products. If Pepsi’s demand decreases by 10% because Coke’s price decreases by 5%, and assuming no change in the price of Pepsi and no change in other variables in the economy (ceteris paribus), then the cross price elasticity of demand for Pepsi relative to a price change in Coke is

e cp = (-10%) / (-5%) = +2.

Example 2
Cross price elasticity of demand can also be computed for complementary products. Complementary products are products that are consumed together. Computer software and personal computers are complementary products.

Problem: What will be the cross price elasticity of demand for computer software if the demand for computer software increases by 45% because of a decrease of 15% in the price of personal computers?

Solution: The cross price elasticity of demand for computer software relative to a price change in personal computers is

e cp = (+45) / (-15) = -3.

For cross price elasticity of demand, if the number is negative, the two products are complements. If the number is positive, the two products are substitutes.

Price Elasticity of Supply

Price elasticity of supply measures the percentage change in the quantity supplied by producers divided by the percentage change in the price of the product. We know from the law of supply that as the equilibrium price of the product increases, producers will supply more of the product. How much more will they supply as the price of a product increases by, for example, 10%?

Example 1
Problem: What is the price elasticity of supply if producers increase their quantity supplied by 30% as a result of a 10% price increase in the market price?

Solution: The price elasticity of supply is

e s= (+30) / (+10) = 3

Price elasticity of supply is always positive, because the law of supply states that (ceteris paribus) as the market price increases, the quantity supplied increases.

In the above example, the price elasticity of supply is greater than 1. This means that it is elastic. An important determinant of price elasticity of supply is time. If a supplier is not able to increase its supply within a certain period of time because it doesn’t have the resources to expand, or the resources are very inflexible (large pieces of machinery, fixed amount of land, etc.), then the price elasticity of supply is low. On the other hand, if a supplier’s production process is very flexible, then its ability to expand its supply is greater. This increases the price elasticity of supply.

Video Explanation
For a video explanation of income elasticity of demand, cross price elasticity of demand, and price elasticity of supply, please watch: