Consider a monopolist with a linear demand curve: q = a − bp, where a;b >...

Consider a monopolist with a linear demand curve: q = a − bp, where a;b > 0. It produces at constant marginal cost c and has no ﬁxed cost. Assume that 0 < c < a b.
(a) Find the monopoly price, quantity, and proﬁts. (b) Derive the inverse demand curve P(q). Draw P(q), the MRcurve, and the MC-curve in a diagram. Explain why we need the assumption c < a b. (c) Does it matter that the monopolist sets price instead of quantity? (d) Calculate the deadweight loss of monopoly. (e) A change in b results in two opposing eﬀects on the deadweight loss. Calculate the eﬀect of a change in b on the deadweight loss. (f) Derive the price elasticity of demand η for any price. How does η change with p? (g) Show mathematically as well as graphically that the price elasticity of demand η > 1 at the monopoly price.

Expert Solution

Rahul Sunny answered 2 hours ago

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