Christopher likes cupcakes (C) and muffins (M). His preferences can be represented by the utility function U(C, M) = C0.5M0.5. He received a gift basket with 16 cupcakes and 4 muffins, but when he was about to eat them, he found out his younger brother Dan had eaten 14 cupcakes and 2 muffins. Christopher made Dan buy what he'd eaten back. However, the bakery was out of muffins and Dan only bought cupcakes. How many cupcakes did Dan buy if, in addition to what he had not eaten from the basket, the new cupcakes provide Christopher with the same level of utility as the original gift basket?

16 cupcakes

Explanation:

U(C, M) = C⁰°⁵ x M⁰°⁵ = √C x √M

total utility obtained by eating 16 cupcakes and 4 muffins = √16 x √4 = 4 + 2 = 6

since the bakery is out of muffins, then utility function = √C x √2 = √C x 1.4142

√C x 1.4142 = 6

√C = 6 / 1.4142 = 4.2426

C = 4.2426² = 18

since there were 2 cupcakes left, Christopher must purchase 18 - 2 = 16 cupcakes

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