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# Ice cream and utility maximization

PART 1

Bob values the utility of a single scoop of Baskin-Robbins ice cream at \$1.50. A double scoop gives total utility of \$2.25, while a triple scoop yields \$2.60. Baskin-Robbins charges \$1.35 for a single, \$1.95 for a double, and \$2.35 for a triple. How many scoops will Bob buy?

PART 2

Please answer the following questions. Provide numerical answers and state whether the changes are elastic or inelastic.

a. When people's incomes rise from \$28,000 to \$32,000 a year, their annual purchases of oranges rise from 78 to 82. What is the income elasticity of demand?

b. When the price of a box of herbal tea bags rises from \$0.99 to \$1.21, the quantity offered for sale rises from 400,000 to 600,000. What is the price elasticity of supply?

c. When the price of Lipton herbal teas rises 10 percent, the demand for Celestial Seasons herbal teas rises 12 percent. What is the cross-price elasticity of demand for CS teas?

d. When green fees at the golf course went up 20 percent, demand for golf balls at the pro shop fell by 12 percent. What is the cross-price elasticity of demand for golf balls?

e. When a beer company increased its advertising budget 18 percent, the demand for its beer increased 28 percent. What is the advertising elasticity for the company's product?

#### Solution Preview

Bob will buy ice cream until the cost equals his utility. At two scoops, the cost is still less than his utility, but at three it is more. So he will purchase two scoops.

Elasticity is the percentage change in quantity divided by the percentage change in price or income. When it is greater than one, it is elastic and when it is ...

\$2.19