A monopolist faces the demand curve q = 150 - p/3
The cost function is
C = 3/2q^2.
a) Find the output that maximizes this monopolist's profits. What are prices and profits at that output?
b) Suppose that the firm must pay a per-unit tax, t, on output q. Find the profit maximizing level of output, in terms of arbitrary levels of t.
c) What level of tax t, should the government choose if it wishes to extract the maximum tax revenue from the monopolist?