Answer Happy

5. (11 points) A consumer consumes two goods: 1 and 2. His utility function is U21, 12) = v(21)+22 where v(x1) is a positively sloped function and 21, 22 > 0. Assume V'(21) > 0) and v" (21) < 0 for all x1 > 0. a) (2 point) What is the gradient of U for some bundle of good (21, x2)? b) (2 point) If the consumer must consume a given quantity of good 2, 22, but can consume as much good 1 as desired, how much would he choose to consume of good 1? Justify your answer. c) (2 point) If the consumer has a budget constraint P121 + P2:22 m where pı and p2 are the prices of goods 1 and 2 and m is his budget, show that he will consume such that V'(x1) = 21 21= . e) (3 point) Still using the fact that the consumer will consume such that v'(x1) = p., show that good 1 is an ordinary good and a substitute of good 2. (Hint, use total differentials.) P2 f) (2 point) Is good 1 a luxury good? Is it an inferior good?