The average quantity of ice cream demanded is (750 + 600) 12 = 675 scoops, so the percentage change in the quantity of ice cream demanded is (750 - 600) / 675 = +22.2%. The average price for frozen yogurt is (\$1.25 + \$1.75) / 2 = \$1.50 per scoop, so the percentage change in the price of frozen yogurt is (\$1.75 - \$1.25) / \$1.50 = +33.3%. The cross elasticity of demand for ice cream relative to the price of yogurt is 22.2 / 33.3 = +0.67.

Professor's Note: For many people, ice cream and frozen yogurt are substitutes, so the cross elasticity of ice cream relative to the price of frozen yogurt is positive.

Example: Cross elasticity of demand (complements)

Suppose that the price of donuts is \$0.50 and the local donut shop serves 800 donuts per day. At the same donut shop, the price of coffee is increased from \$0.75 to \$1.25 per cup. No other changes have occurred and the number of donuts sold decreases to 600 per day. Calculate the cross elasticity of demand for donuts relative to the price of coffee.

The average quantity of donuts demanded is (800 + 600) 1 2 = 700, so the percentage change in the quantity of donuts demanded is (600 - 800) / 700 = -28.6%. The average price for a cup of coffee is (\$0.75 + \$1.25) / 2 = \$1.00 per cup, so the percentage change in the price of coffee is (\$1.25 - \$0.75) / \$1.00 = 50%. The cross elasticity of demand for donuts relative to the price of coffee is -28.6 / 50 = -0.57.

I^Bggajjj-, Professor's Note: Coffee and donuts are complements, so the cross elasticity of vi^tSl^ donut demand relative to the price of coffee is negative.

lncom? Elasticity

The income elasticity of demand measures the sensitivity of the quantity of a good or service demanded to a change in a consumer's income. The formula for income elasticity of demand is:

. . . . percent change in quantity demanded income elasticity or demand =-;-

percent change in income

Income elasticity of demand is related to the type of good being evaluated. An inferior good has negative income elasticity. As income increases (decreases), quantity demanded decreases (increases). Inferior goods include things like bus travel and generic margarine. In contrast, a normal good has positive income elasticity, which means that as income increases (decreases), demand for the good increases (decreases). Bread and tobacco are generally considered normal goods. Normal goods that have relatively low income elasticities (between 0 and +1) are considered necessities, while normal goods with high income elasticities (values greater than 1) are generally considered luxury goods.

Example: Income elasticity

Suppose that your income has risen by \$10,000 from an initial rate of \$50,000. Further, your consumption of bread has increased from 100 loaves per year to 110 loaves per year. Given this information, determine whether bread is a necessity or a luxury good.

Your average income is (\$50,000 + \$60,000) / 2 = \$55,000, so the percentage change in income is (\$60,000 - \$50,000) / \$55,000 = 18.2%. Similarly, the average quantity of bread demanded is (100 + 110) / 2 = 105 loaves, so the percentage change in the quantity of bread demanded is (110 - 100) / 105 = 9.5%. Thus, the income elasticity of bread is 9.5/18.2 = 0.52. Since its income elasticity of demand is less than 1.0, bread must be a necessity.

### Elasticity of Supply

The price elasticity of supply is similar to the price elasticity of demand. It is a measure of the responsiveness of the quantitv supplied to changes in price. That is:

price elasiicits of supplv =

percent change in quantity supplied %AQ

percent change in price

As shown in panel (a) of Figure 2 below, a perfectly inelastic (vertical) suppK curve has an elasticity of supply of zero. Panel (b) illustrates a perfectly clastic (horizontal) supplv curve with an elasticity of supply equal to infinity. For most goods and services, however, the elasticity of supply falls somewhere between these two extremes.

Figure 2: Inelastic and Elastic Supply

(a) Perfectly inelastic supply (elasticity = 0)

(b) Perfectly elastic supply (elasticity = oo )

Example: Elasticity of supply

Suppose that the demand curve for coffee increases and that the equilibrium price for a pound of coffee increases from \$8 to \$10 per pound. At the new price, the quantity supplied increases from 100,000 kilograms per month to 120,000 kilograms per month, although the supply curve has not shifted. Calculate the elasticity of supply for coffee.