Problem
Demand and Engel curves, Quasi-linear utility. Suppose Kim likes chocolate and vanilla ice cream. Her utility function is given by U(C, V ) = ln C + 2V where C and V are the number of scoops of chocolate and vanilla she eats, respectively. She has I dollars to spend on chocolate and vanilla ice cream, and the per scoop prices are pC and pV , respectively.
(a) What is Kim's demand function for chocolate ice cream? What is Kim's demand function for vanilla ice cream? That is, solve for her optimal consumption of chocolate ice cream in terms of the variables I, pC, and pV . (Then do the same for vanilla ice cream.) Remember that I, pC, and pV stand in for numbers, so you should treat them as constants when you are taking derivatives with respect to other variables. You can assume that we are at an interior solution.
(b) Suppose the price of chocolate ice cream is $4 and the price of vanilla ice cream is $8. Provide a formula for Kim's Engel curve for chocolate ice cream, and graph the Engel curve. Be sure to show what happens for all positive incomes, and be careful to consider corner solutions.
(c) Determine whether or not chocolate ice cream is a normal good, an inferior good, or neither.
(d) If the price of vanilla ice cream increases by 1%, by what percent will the quantity of vanilla ice cream demanded change when income is $10, the price of vanilla ice cream is $5, and the price of chocolate ice cream is $2?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.