In 1796, Gottfried Christoph Härtel, a German music publisher, calculated the cost of printing music using an engraved plate technology and used these estimated cost functions to make production decisions. Härtel figured that the fixed cost of printing a musical page—the cost of engraving the plates—was 900 pfennings. The marginal cost of each additional copy of the page is 5 pfennings (Scherer 2001).
a. Graph the total cost, average total cost, average variable cost, and marginal cost functions.
b. Is there a cost advantage to having only one music publisher print a given composition? Why?
c. Härtel used his data to do the following type of analysis. Suppose he expects to sell exactly 300 copies of a composition at 15 pfennings per page of the composition. What is the greatest amount the publisher is willing to pay the composer per page of the composition?