Problem 2 Benjamin spends his time either watching movies ($1) (he uses "on demand" option, cable TV) or listening to songs MP3 downloaded from the Internet (3:2) . His preferences are described by U(ac1, 3:2) = ln(a:1) + ln(a:2) Answer the following questions: a) Derive Benjamin's demand for movies and MP3 les as a function of prices p1, p2 and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at 1);; = 1, and income on m = 10. Find the price offer curve (give an exact formula $2 = f (3:1)) and plot it in the commodity space. Find the demand curve 331 = f(p1) and plot it in the graph (with p1 on vertical axis and 171 on horizontal axis). c) Is 921 an ordinary good or a Gi'en good? Explain. d) Now x p1 = 1 and p2 = 1. In the commodity Space, plot the income offer curve. In addition, in two separate graphs, plot Engel curves for both movies and MP3 les. Argue that the two commodities are normal (not inferior). e) For the demand functions from point a), determine whether the two goods are gross complements, substitutes or neither. Problem 3 (Perfect Complements) Consider Trevor from our previous problem set who begins his day with strawberry milkshake. To prepare it, he mixes milk, 11:1, strawberries 2:2 and does so always in his favorite: proportion 1 glass of milk to 2 strawberries. What is his utility function? Answer all the questions from Problem 2, from a) to e) using these preferenes