Tastes for Cars and Product Characteristics: People buy all sorts of different cars depending on their income levels as well as their tastes. Industrial organization economists who study product characteristic choices (and advise firms like car manufacturers) often model consumer tastes as tastes over product characteristics (rather than as tastes over different types of products). We explore this concept below.

A: Suppose people cared about two different aspects of cars: the size of the interior passenger cabin and the quality of handling of the car on the road.

(a) Putting x₁ = “cubic feet of interior space" on the horizontal axis and x₂ =“speed at which the car can handle a curved mountain road” on the vertical, where would you generally locate the following types of cars assuming that they will fall on one line in your graph: a Chevrolet Minivan, a Porsche 944, and a Toyota Camry.

(b) Suppose we considered three different individuals whose tastes satisfy our 5 basic assumptions, and suppose each person owns one of the three types of cars. Suppose further that each indifference curve from one person’s indifference map crosses any indifference curve from another person’s indifference map at most once. (When two indifference maps satisfy this condition, we often say that they satisfy the single crossing property.) Now suppose you know person A’s MRS at the Toyota Camry is larger (in absolute value) than person B’s, and person

B’s MRS at the Toyota Camry is larger (in absolute value) than person C’s. Who owns which car?

(c) Suppose we had not assumed the “single crossing property” in part (a). Would you have been able to answer the question “Who owns which car” assuming everything else remained the same?

(d) Suppose you are currently person B and you just found out that your uncle has passed away and bequeathed to you his 3 children, aged 4, 6 and 8 (and nothing else). This results in a change in how you value space and maneuverability. Is your new MRS at the Toyota Camry now larger or smaller (in absolute value)?

(e) What are some other features of cars that might matter to consumers but that you could not fit easily into a 2-dimensional graphical model?

B: Let x₁ denote cubic feet of interior space and let x₂ denote maneuverability as defined in part A.

Suppose that the tastes of persons A, B and C can be represented by the utility functions uA(x₁,x₂) =respectively.

(a) Calculate the MRS for each person.

(b) Assuming α, β and γ take on different values, is the “single crossing property” defined in part A(b) satisfied?

(c) Given the description of the three persons in part A(b), what is the relationship between α, βand γ?

(d) How could you turn your graphical model into a mathematical model that includes factors you raised in part A(e)?

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