Suppose a monopolist is considering starting a $500,000 advertising campaign. The current demand for its product is given by

p = 150 - 3Q
where Q is the quantity of output in thousands. If the monopolist undertakes the advertising campaign, it expects demand to increase to
p = 200 - 4Q
The (non-advertising) cost for the monopolist is C(Q) = 30Q.
a. Determine whether the monopolist should undertake the advertising campaign assuming that it is correctly anticipating the potential increase in demand.
b. What is the most the monopolist will invest towards this advertising campaign?

a. The monopolist's profits without advertising are calculated by:
150 - 6Q = 30
Q = 20
Pi = 20 ∗ 90 - 30 ∗ 20 = 1200
By advertising, the gross profit will be:
200 - 8Q = 30
Q = 21.25
Pi = 1806.25
Because the profit rises by more than $500,000, the monopolist will advertise.
b. The difference in gross profits is $606,250, the maximum the monopolist will invest.