Suppose a company dedicated to the illegal copying of CDROMs

Suppose a company dedicated to the illegal copying of CD-ROMs has a total short-term cost function that is given by CTS = q² + 25

A. If the illegal CD-ROMs are sold for $ 20, how many will the company copy? What will be its benefits?

Solution

The company would maximize benefits when P = MC

CTS = q² + 25 and P = $ 20

MC = d(CTS)/dq = 2q

2q = 20

q = 10 (Number of CD-ROMs copied)

Benefits = Pq - CTS = 20 x 10 - 100 - 25 = $ 75