Problem
Consider a monopoly that faces a downward sloping demand curve X = D(P) and constant unit costs c. We are interested in how this monopoly will adjust the price it charges as c 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(c) as the monopoly price, given as a function of cost c, then dp(c)/dc
(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(c)/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(c)/de = 1 ?) You should give demand functions for which this works at every level of c. (Hint: If you begin by drawing the obvious picture in part [a], it may help you see what to do in part [c].)
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.