Dr. Barry Haworth
University of Louisville
Department of Economics
Economics 201

### Demand-related Elasticities

We can calculate elasticity measures for every pair of related variables out there, but our focus here will be to concentrate on several demand-related elasticities. The point here will be to determine how consumer purchases of a particular good respond to changes in one of three different variables: the price of that good, consumer income, and the price of a related good.

Each of these demand-related elasticities will be calculated by comparing the percentage change in consumer purchases to a percentage change in one of various changes mentioned above. We can most easily do this comparison by dividing the percentage change in one variable (consumer purchases) by the percentage change in the other variable. Let’s look at these measures one at a time.

Own-price elasticity: calculated by dividing the percentage change in the quantity purchased of a good by a percentage change in the price of that same good. For example, suppose a 5% decrease in the number of apples sold corresponds with a 10% increase in the price of apples. Dividing -5% by +10%, we have an own-price elasticity that's equal to -0.5 (note that the negative and positive signs correspond with percentage decrease and increase respectively).

Interpretation: because the percentage change in price (cause) is greater in absolute value than the percentage change in quantity purchased (effect), we say that the demand for apples is inelastic. If the percentage change in price was smaller than the percentage change in quantity purchased, then the demand for the good would be elastic.

Income elasticity: calculated by dividing the percentage change in the quantity purchased of a good by a percentage change in consumer income. For example, suppose a 20% increase in the number of apples purchased comes as the result of a 50% increase in consumer income. Dividing +20% by +50%, we have an income elasticity is equal to 0.4.

Interpretation: because the percentage change in quantity is less than the percentage change in income, we say that the demand for apples is income inelastic. That is, that apples are a necessity. If the percentage change in quantity was greater than the percentage change in income, we would characterize the demand for apples as being income elastic, or as being a luxury good.

Note further that the increase in consumer income led to an increase in apple purchases - implying that apples are a normal good. If the relationship between apples and consumer income was negative (instead of positive), then apples would be considered an inferior good.

Cross-price elasticity: calculated by dividing the percentage change in the quantity purchased of a good by a percentage change in the price of a related good. For example, suppose 25% more apples are purchased when the price of some related good increases by 25%. Dividing +25% by +25%, we have an cross-price elasticity is equal to 1.0.

Interpretation: because the percentage change in quantity is moving in the same direction as the percentage change in the price of some related good, the related good must be a substitute. For example, if we substitute a known substitute like oranges for the words “related good”, then the finding makes sense since apple purchases are obviously replacing the (now more expensive) orange purchases. If these changes were moving in the oppositive direction, then the goods would be complements.