Economics (Monopoly Pricing)
posted by Nihl .
A monopolist produces a product whose demand price and production costs
vary with quality s and quantity q according to
P (s; q) = s (1 - q)
C (s; q) = s^2 q [s-squared multiplied by q]
Calculate the price and quality levels that a monopolist would choose, and the
corresponding quantity sold.
A monopolist will produce where marginal cost = marginal revenue.
Total revenue is P*Q = s(1-Q)*Q = sQ - sQ^2
Total cost is s^2Q
Take the first derivitive (with respect to Q):
MR = s - 2sQ
MC = s^2
Take it from here, Solve for Q.