Problem 2 Demand curves Benjamin spends his time either watching movies x1 (he uses " on demand\" option, cable TV) or listening to songs - MP3 downloaded from the Internet (222). His pref- erences are described by U(IE1,.T2) = ln(:r1) +1(1'2). Answer the following questions: a) Derive Benjamin's demand for movies and MP3 les as a function of prices 101,112 and his income m. (do not use Magic Formula but instead derive demand using " two secrets of happiness\" ). b) Fix the price of MP3 at 302 = 1, and income on m = 10. Find the price offer curve (give an exact formula $2 = ea and plot it in the commodity space. Find the demand curve (121 = n) and plot it in the graph {with 311 on vertical axis and 2:1 on horizontal axis). 0) Is :31 an ordinary good or a Gien good? Explain. (1) Now x p1 = 1 and p2 = 1. In the commodity space, plot the income offer curve. Besides, in two separate graphs, plot Engel curves for both movies and MP3 les. Argue that the two commodities are normal (not inferior). Problem 6 2 e) For the demand functions from point 3), determine whether the two goods are gross complements, substitutes, or neither. Problem 4 Perfect Substitutes Kate's preferences are defined over consumption of two types of apples: Red Delicious (21) and Jonagold (12. They are represented by utility function U(X1, 12) = 2x1 + 12. Answer all the questions from Problem 2, starting from a) to e) using these prefer- ences