Consider a monopoly that faces a downward sloping demand curve X = D(P) and constant unit costs e. We are interested in how this monopoly will adjust the price it charges as e changes.
(a) If demand is linear X = A - P, show that less than the full .change in costs is passed on to the customers. (That is, if we think of p(e) as the monopoly price, given as a function of cost e, then dp(e)/ de 1.)
(b) Suppose that demand takes the form X = p-a for a > 1. Show that the monopoly passes on more than the full cost increase to consumers. (That is, dp(e)/ de > 1.)
(c) For which demand functions (if any) will the monopoly precisely pass on to consumers any cost increase? (That is, for which demand functions will dp(e)/de = 1?) You should give demand functions for which this works at every level of e. (Hint: If you begin by drawing the obvious picture in part [a], it may help you see what to do in part [c].)
Since we introduced linear demand in the last two chapters, it might be a good idea to say something about where it comes from.