Imagine that you are about to purchase a stereo for $125 and a calculator for $15 from a store in Dallas. The salesman tells you that one of these two goods (to be specified next) is on sale for $5 less at the other branch of the store, located 20 minutes away in Plano. Suppose that you are indierent between $5 discount on the calculator and the same discount on the stereo. You would make the trip to the other store to get the discount on the calculator. You would not travel to the other store to get the discount on the stereo. (a) Do you think that your preferences can be represented by a utility function and why? (b) Assume that your preference relation can be represented by a utility function. Show that your preference relation must then be complete, transitive and reflexive.