Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Her preferences over these lollies are Cobb-Douglas, and can be presented by the utility function u(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frog costs 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectly divisible goods. (a) Find Ginny’s optimal bundle. (b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the time she is there, she is left only with 75 Knuts. What is her optimal bundle now? (c) Now, consider the general case, where Ginny’s income is m, the price of Every Flavour Beans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat Chocolate Frogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .
Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Her
preferences over these lollies are Cobb-Douglas, and can be presented by the utility function
u(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frog
costs 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectly
divisible goods.
(a) Find Ginny’s optimal bundle.
(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the time
she is there, she is left only with 75 Knuts. What is her optimal bundle now?
(c) Now, consider the general case, where Ginny’s income is m, the
Beans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat Chocolate
Frogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .
(d) Find the good on which Ginny will always spend more than half of her income.
(e) Find the own-price, cross-price, and income elasticities of good 2.
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