magine that there are two types of consumers indexed by θi with i = H, L. Let the inverse demand curve for each be: P = θi(1 − qi) with θH > θL. Let the shares of the total population of N for each type be λ and 1 − λ, for groups θH and θL respectively. (a) Show that the aggregate demand is Q(P) =( N 1 − P ˜θ ) where ˜θ = λ/θH + 1−λ/θL , assuming that both groups are induced to buy. (b) Find the profit-maximizing menu-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c.
magine that there are two types of consumers indexed by θi with i = H, L. Let the inverse demand curve for each be: P = θi(1 − qi) with θH > θL. Let the shares of the total population of N for each type be λ and 1 − λ, for groups θH and θL respectively. (a) Show that the aggregate demand is Q(P) =( N 1 − P ˜θ ) where ˜θ = λ/θH + 1−λ/θL , assuming that both groups are induced to buy. (b) Find the profit-maximizing menu-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Imagine that there are two types of consumers indexed by θi with i = H, L. Let the inverse demand curve for each be: P = θi(1 − qi) with θH > θL. Let the shares of the total population of N for each type be λ and 1 − λ, for groups θH and θL respectively.
(a) Show that the aggregate demand is Q(P) =( N 1 − P ˜θ ) where ˜θ = λ/θH + 1−λ/θL , assuming that both groups are induced to buy.
(b) Find the profit-maximizing menu-pricing strategy for a monopolist with constant marginal cost c. (c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c.
(c) Find the profit-maximizing uniform-pricing strategy for a monopolist with constant marginal cost c.
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