Dell is considering two versions of a new laptop. One version will meet high performance standards. The other will only meet medium performance standards. To make the second, Dell uses cheaper materials and then crimps the keyboard of the high-performance machine with the results that the marginal cost of the each product is an identical $500. There are two types of consumers for the new laptop. "Techies" have the (indirect) utility function Vt=2000(z-1). "Norms" have the (indirect) utility function Vn=1000z, where z is a measure of product quality. Dell can choose the quality level z for each machine from the interval (1,3), subject only to the restriction that the medium-performance machine have a lower z quality than the high-performance machine.
1) If Dell knows that there are Nt techies and Nn norms, and if Dell also can identify which type any consumer is, what is its optimum price and product quality strategy?
2) Suppose Dell cannot identify each customer but only knows the numbers of each type. Show that Dell's profit-maximizing strategy is determined by the relative numbers of each type.