Monopoly, setting quantity X

Inverse demand function p demand function inverse demand function X

Revenue, costs and profit

Marginal revenue with respect to quantity When a firm increases the quantity by one unit, revenue goes up by p, but goes down by dp/dX (the quantity increase diminishes the price) multiplied by X Amoroso-Robinson relation:

Exercise (marginal revenue) State three cases where the marginal revenue equals the price.

First order condition Notation:

Linear demand curve in a monopoly Revenue: Marginal revenue:

Exercise (Depicting the linear demand curve) Slope of demand curve: .... Slope of marginal revenue curve: .... The .... has the same vertical intercept as the demand curve. Economically, the vertical intercept is ..., the horizontal intercept is ... .

Depicting demand and marginal revenue 1 b 2b 1 a/(2b) a/b

Depicting the Cournot monopoly Cournot point

Profit in a monopoly Marginal point of view: Average point of view:

Exercise (monopoly) Consider a monopoly facing the inverse demand function p(X)=40-X2. Assume that the cost function is given by C(X)=13X+19. Find the profit-maximizing price and calculate the profit.

Price discrimination First degree price discrimination: Second degree price discrimination: Third degree price discrimination: Every consumer pays a different price which is equal to his or her willingness to pay. Prices differ according to the quantity demanded and sold (quantity rebate). Consumer groups (students, children, ...) are treated differently.

Inverse elasticities rule for third degree price discrimination Supplying a good X to two markets results in the inverse demand functions p1(x1) and p2(x2). Profit function: First order conditions: Equating the marginal revenues (using the Amoroso-Robinson relation) leads to:

Exercise I (price discriminating monopoly) A monopoly sells in two markets: p1(x1)=100-x1 and p2(x2)=80-x2. The cost function is given by C(X)=X2. a) Calculate the maximizing quantities and the profit at these quantities. b) Suppose now that the monopoly plant is decomposed into two plants, where each plant sells in one market independently (profit center). Calculate the sum of profits.

Exercise II (price discriminating monopoly) c) Assume now that the cost function is given by C(X)=10X. Repeat the comparison. d) What happens if price discrimination between both markets will not be possible anymore? Find the profit-maximizing quantity and price. Consider the cost function C(X)=10X. (Hint: Differentiate between quantities below and above 20.) Oz Shy; Industrial Organization

The deadweight loss of a monopoly Without price discrimination a monopoly realizes a deadweight loss.

Exercise (deadweight loss) Consider a monopoly where the demand is given by p(X)=-2X+12. Suppose that the marginal costs are given by MC=2X. Calculate the deadweight loss.

Exercises (price cap in a monopoly) How does a price cap influence the demand and the marginal revenue curves?

Right or wrong? Why?

Additional deadweight loss due to quantity tax consumer’ surplus: ABCA producer’s surplus: TEF EB additional deadweight loss A C B E F T

Taxes on profits

Exercise (quantitiy taxes) A monopoly is facing a demand curve given by p(X)=a-X. The monopoly’s unit production cost is given by c>0. Now, suppose that the government imposes a specific tax of t dollars per unit sold. a) Show that this tax would raise the price paid by consumers by less than t. b) Would your answer change if the market inverse demand curve is given by p(X)=-ln(X)+5. c) If the demand curve is given by p(X)=X-1/2, what is the influence on price? Oz Shy; Industrial Organization

Illustrating the solutions b)

Lerner index of monopoly power First order condition: Lerner index:

Monopoly profits and monopoly power Cournot point

Comparison: monopoly and monopsony Monopolist Monopsonist = the only supplier = the only demander First order condition (Output): First order condition (input) of factor labor (L):

The monopsonist’s profit function Production function: X=X(L,K) Profit function:

Demand for labor Cost: Supply elasticity: Marginal costs: Amoroso-Robinson relation:

First order condition (concerning labor) MRL MCL

First order condition for the factor input Marginal revenue product of factor 1 Marginal costs of factor 1 Product market Factor market Special case: price taker i.e. p = const. : Special case: price taker i.e. : Value of the marginal product

Depicting the labor market

Exercise (Equal wages for the same work?) Monopsonist: employs men and women, equal productivity M men wage rate: AM, A>0 F women wage rate: BFc, B, c>0 Find A, B and c such that the monopsonist pays lower wages to women than to men.

Exercise (Minumum wages in a monopsony) How does a minimum wage change the supply of labor and the marginal costs of labor?

Executive summary A profit-maximizing monopolist always sets the quantity in the elastic region of the demand curve. The lower the marginal cost and the higher the demand at each price, the higher the profit and the monopoly quantity. Distinction between monopolistic power and monopoly profits: Monopolistic power: price will be set above the marginal cost by a profit maximizer. If the demand curve is tangent to the average cost curve, the profit-maximizing price is set above marginal cost and equal to the average cost  monopolistic power, zero profits.