Problem 5 (Quasilinear preferences) George is a stamp (3:1) collector, but he also likes fancy clothes (932). His utility function is given by U(LE1,$2) = $1 + 10352 (1/2)(L'22. Each stamp costs 191 = 1 and a, piece of his favorite clothing costs p2 = 2 a) Assuming that his total income is given by m:$10, nd his optimal choice of 9:1 and $2. (Is it interior?) b) Suppose next year George's salary doubles, resulting in his higher income m=$20. Find his new demanded quantities of stamps and clothes. (Is it interior?). c) Harder: In point a) and b) what is the marginal utility from one dollar invested in stamps, and in clothing (at the Optimal demand). Are they equal? Hint: Unlike in a CobbDouglas utility function, with quasilinear preferences we might have corners