Suppose a monopolist faces the market demand function P = a - bQ. Its marginal cost is given by MC = c + eQ. Assume that a > c and 2b + e > 0.
a) Derive an expression for the monopolist's optimal quantity and price in terms of a, b, c, and e.
b) Show that an increase in c (which corresponds to an upward parallel shift in marginal cost) or a decrease in a (which corresponds to a leftward parallel shift in demand) must decrease the equilibrium quantity of output.
c) Show that when e ≥ 0, an increase in a must increase the equilibrium price.