Derive an expression for the monopolist’s optimal quantity

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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.

Reference no: EM131253936

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