We defined a Giffen good as a good that consumers (with exogenous incomes) buy more of when the price increases. When students first hear about such goods, they often think of luxury goods such as expensive Gucci purses and accessories. If the marketing departments for firms like Gucci are very successful, they may find a way of associating price with “prestige” in the minds of consumers — and this may allow them to raise the price and sell more products. But would that make Gucci products Giffen goods? The answer, as you will see in this exercise, is no.
A. Suppose we model a consumer who cares about the “practical value and style of Gucci products”, dollars of other consumption and the “prestige value” of being seen with Gucci products. Denote these as x1, x2 and x3 respectively.
(a) The consumer only has to buy x1 and x2 —the prestige value x3 comes with the Gucci products. Let p1 denote the price of Gucci products and p2 = 1 be the price of dollars of other consumption. Illustrate the consumer’s budget constraint (assuming an exogenous income I).
(b) The prestige value of Gucci purchases — x3 — is something an individual consumer has no control over. If x3 is fixed at a particular level 3, the consumer therefore operates on a 2- dimensional slice of her 3-dimensional indifference map over x1, x2 and x3. Draw such a slice for the indifference curve that contains the consumer’s optimal bundle A on the budget from part (a).
(c) Now suppose that Gucci manages to raise the prestige value of its products—and thus x3 that comes with the purchase of Gucci products. For now, suppose they do this without changing p1. This implies you will shift to a different 2-dimensional slice of your 3-dimensional indifference map. Illustrate the new 2-dimensional indifference curve that contains A. Is the new MRS at A greater or smaller in absolute value than it was before?
(d)Would the consumer consume more or fewer Gucci products after the increase in prestige value?
(e) Now suppose that Gucci manages to convince consumers that Gucci products become more desirable the more expensive they are. Put differently, the prestige value x3 is linked to p1, the price of the Gucci products. On a new graph, illustrate the change in the consumer’s budget as a result of an increase in p1.
(f) Suppose that our consumer increases her purchases of Gucci products as a result of the increase in the price p1. Illustrate two indifference curves— one that gives rise to the original optimum A and another that gives rise to the new optimum C. Can these indifference curves cross?
(g) Explain why, even though the behavior is consistent with what we would expect if Gucci products were a Giffen good, Gucci products are not a Giffen good in this case.
(h) In a footnote in the chapter we defined the following: A good is a Veblen good if preferences for the good change as price increase—with this change in preferences possibly leading to an increase in consumption as price increases. Are Gucci products a Veblen good in this exercise?
B. Consider the same definition of x1, x2 and x3 as in part A. Suppose that the tastes for our consumer can be captured by the utility function u(x1,x2,x3) = αx32 lnx1 +x2.
(a) Set up the consumer’s utility maximization problem—keeping in mind that x3 is not a choice variable.
(b) Solve for the optimal consumption of x1 (which will be a function of the prestige value x3).
(c) Is x1 normal or inferior? Is it Giffen?