CHAPTER 5 APPENDIX 1 Other Types of Elasticities

Economists often compute elasticities any time one variable is related to another variable. Klick and Tabarrok, for example, find that a 50% increase in the number of police on the streets reduces automobile theft and theft from automobiles by 43%, so the elasticity of auto crime with respect to police is −43%/50% = −0.86. Gruber studies church attendance and he finds an interesting relationship: The more people give to their church, the less likely they are to attend! In other words, people regard money and time as substitutes and those who give more of one are likely to give less of the other. Gruber calculates that a 10% increase in giving leads to an 11% decline in attendance or an elasticity of attendance with respect to giving of −11%/10% = −1.1.15

Thus, any time there is a relationship between two variables A and B, you can always express the relationship in terms of an elasticity. Two other frequently used elasticities in economics are the cross-price elasticity of demand and the income elasticity of demand.

The Cross-Price Elasticity of Demand

The cross-price elasticity of demand measures how responsive the quantity demanded of good A is to the price of good B.

Given data on the quantity demanded of good A at two different prices of good B, the cross-price elasticity can be calculated using the following formula:

The cross-price elasticity of demand is closely related to the idea of substitutes and complements. If the cross-price elasticity is positive, an increase in the price of good B increases the quantity of good A demanded so the two goods are substitutes. If the cross-price elasticity is negative, an increase in the price of good B decreases the quantity of good A demanded so the two goods are complements.

If the cross-price elasticity > 0, then goods A and B are substitutes.

If the cross-price elasticity < 0, then goods A and B are complements.

The Income Elasticity of Demand

The income elasticity of demand measures how responsive the quantity demanded of a good is with respect to changes in income.

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As usual, given data on the quantity demanded at two different income levels, the income elasticity of demand can be calculated as

The income elasticity of demand can be used to distinguish normal from inferior goods. Recall from Chapter 3 that when an increase in income increases the demand for a good, we say the good is a normal good. And a good like Ramen noodles, for which an increase in income decreases the demand, is called an inferior good.

If the income elasticity of demand > 0, then the good is a normal good.

If the income elasticity of demand < 0, then the good is an inferior good.

Sometimes economists also distinguish normal from “luxury” goods, defined as one where, say, a 10% increase in income causes more than a 10% increase in the quantity of the good demanded. Thus,

If the income elasticity of demand > 1, then the good is a luxury good.

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