# The pricing of complementary goods if one of them is purchased only once

Sorry for asking a homework question, however, I'll try to generalize it as much as possible for a future use.

There are two complementary goods (A and B). B is produced under perfect competition, while A is produced under monopoly (yes, and A and B are produced by separate companies). The customers have a combined demand curve for both (as they don't need A without B or B without A) that can be expressed by a particular demand function. Of course, each product has its production cost functions c(A) and c(B).

It looks like a classic textbook "nuts and bolts" case, where Q(a)=Q(b) and prices must be consistent (basically the equilibrium price there is the intersection of both demand curves), however, there's one big difference. The good A is purchased only one time while B can be purchased two, three or more times (the good A may be a CD player and good B a music CD). The example asks how should the monopolist who produces A behave if he wants to maximize his profits.

The standard approach of drawing the two demand curves for A and B does not work here as the only quantity of product A that can be purchased is 1. Alternatively, the straightforward way of monopoly pricing (solving MR=MC for Q and then determining the P(Q)) does neither, as we can't ignore the good B and the only Q(A) available is 1. The solution must be simple enough, but I really got stuck and will appreciate any help or guiding advice.

Paul