Below we consider some logical relationships between preferences and types of goods.
A. Suppose you consider all the goods that you might potentially want to consume.
(a) Is it possible for all these goods to be luxury goods at every consumption bundle? Is it possible for all of them to be necessities?
(b) Is it possible for all goods to be inferior goods at every consumption bundle? Is it possible for all of them to be normal goods?
(c) True or False: When tastes are homothetic, all goods are normal goods.
(d) True or False: When tastes are homothetic, some goods could be luxuries while others could be necessities.
(e) True or False: When tastes are quasilinear, one of the goods is a necessity.
(f) True or False: In a two good model, if the two goods are perfect complements, they must both be normal goods.
(g) True or False: In a 3-goodmodel, if two of the goods are perfect complements; they must both be normal goods.
B. In each of the following cases, suppose that a person whose tastes can be characterized by the given utility function has income I and faces prices that are all equal to 1. Illustrate mathematically how his consumption of each good changes with income and use your answer to determine whether the goods are normal or inferior, luxuries or necessities.
(a) u(x1,x2) = x1x2
(b) u(x1,x2) = x1 +lnx2
(c) u(x1,x2) = lnx1 +lnx2
(d) u(x1,x2,x3) = 2lnx1 +lnx2 +4lnx3
(e) u(x1,x2) = 2x10.5 +lnx2