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Course outline I. Introduction Game theory Price setting monopoly oligopoly Quantity setting monopoly oligopoly Process innovation. Homogeneous goods. Monopoly (quantity setting). Inverse demand function Revenues, costs, profits Profit maximizing quantity Basic model

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Course outline i l.jpg
Course outline I

  • Introduction

  • Game theory

  • Price setting

    • monopoly

    • oligopoly

  • Quantity setting

    • monopoly

    • oligopoly

  • Process innovation

Homogeneous goods


Monopoly quantity setting l.jpg
Monopoly (quantity setting)

  • Inverse demand function

  • Revenues, costs, profits

  • Profit maximizing quantity

    • Basic model

    • Price discrimination

    • Several factories

  • Double marginalization

  • Welfare analysis

  • Executive summary



Inverse demand function l.jpg
Inverse demand function

p

demand function

inverse demand function

X


Revenue costs and profit l.jpg
Revenue, costs and profit

  • Revenue:

  • Costs:

  • Profit:


Marginal revenue with respect to quantity l.jpg
Marginal revenue with respect to quantity

  • goes up by p (the price of the last unit),

  • but goes down by dp/dX X (the quantity increase diminishes the price and this price decrease is applied to all units)

When a firm increases the quantity by one unit, revenue

Amoroso-Robinson

relation:


Marginal revenue price l.jpg
Marginal revenue = price?

1.  i.e. horizontal demand curve, perfect competition

2. X=0  sale of first unit

 first degree price discrimination


Slide8 l.jpg

Linear demand curve in a monopoly

  • Demand:

  • Revenue:

  • Marginal revenue:


Exercise depicting the linear demand curve l.jpg
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 l.jpg
Depicting demand and marginal revenue )

a

1

b

2b

1

a/(2b)

a/b





Exercise quantity l.jpg
Exercise (Quantity) )

Consider a monopolist facing the inverse demand function p(X)=24-X. Assume that the average and marginal costs are given by AC=2.

Find the profit-maximizing quantity!


Profit in a monopoly l.jpg
Profit in a monopoly )

Marginal point of view:

Average point of view:


Exercise monopoly l.jpg
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.


Slide17 l.jpg

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 l.jpg
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 two markets or one l.jpg
Exercise (two markets or one) discrimination

A monopoly sells in two markets:

p1(x1)=100-x1 and p2(x2)=80-x2.

a) Calculate the profit-maximizing quantities and the profit at these quantities, if the cost function is given by C(X)=X2.

b) Calculate the profit-maximizing quantities and the profit at these quantities, if the cost function is given by C(X)=10X.

c) What happens if price discrimination between the two markets is not possible anymore? Consider C(X)=10X.

Hint: Differentiate between quantities below and above 20.


Solution iii one market l.jpg
Solution III (one market) discrimination

100

90

80

50

10

20

50

80

100


One market two factories l.jpg
One market, two factories discrimination

  • Profit function:

  • First order conditions:

=


One market two factories ii l.jpg
One market, two factories II discrimination

factory 2

factory 1

total output


Double marginalization idea l.jpg
Double marginalization - idea discrimination

  • Retailer, not producer sells to consumers.

  • Assumptions:

    • Zero costs for retailing.

    • Producer decides on a quantity and charges a price ppro to the retailer.

    • ppro is the retailer‘s marginal cost.

    • The retailer‘s MR=MC condition defines the producer‘s demand function.


Double marginalization linear case l.jpg
Double marginalization - linear case discrimination

  • p(x)=a-bX

  • MCpro=ACpro=c

  • Second stage: First order condition for the retailer:

  • First stage: First order condition for the producer:


Double marginalization depicting the solution l.jpg
Double marginalization - depicting the solution discrimination

  • Producer decides on quantity and announces ppro* to retailer.

  • Retailer decides on quantity (fore-seen by producer).

retailer

producer


Double marginalization exercise l.jpg
Double marginalization - exercise discrimination

p(X)=110-X

c=10

a) Calculate the price the consumers have to pay!

b) What price would they pay if the producer sold directly to the consumers?


Welfare analysis l.jpg
Welfare Analysis discrimination

  • Evaluation of economic policy measures

  • Welfare = consumer surplus (CS) + producer surplus (PS) + taxes - subsidies

  • CS = willingness to pay - price

  • PS = revenue - variable costs

    = profit + fixed costs


Cs ps graphically l.jpg
CS, PS - graphically discrimination

supply (=MC)

 Welfare is maximized at the equilibrium.

demand


The deadweight loss of a monopoly l.jpg
The deadweight loss of a monopoly discrimination

Without price discrimination a monopoly realizes a deadweight loss.

Perfect

competition


Exercise deadweight loss l.jpg
Exercise (deadweight loss) discrimination

  • 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

    • without price discrimination,

    • with perfect price discrimination.


Exercise price cap in a monopoly l.jpg
Exercise (price cap in a monopoly) discrimination

How does a price cap influence the demand and the marginal revenue curves?


Right or wrong why l.jpg
Right or wrong? Why? discrimination


Price cap and welfare l.jpg
Price cap and welfare discrimination

additional welfare


Taxes on profits l.jpg
Taxes on profits discrimination


Taxes on profits and welfare l.jpg
Taxes on profits and welfare discrimination

  • Quantity / price unchanged

  • CS is constant

  • PS decrease; in the same extent net public revenues increase

  • deadweight loss is zero


Additional deadweight loss due to quantity tax l.jpg
Additional deadweight loss due to quantity tax discrimination

consumer’s surplus: A+B+CA

producer’s surplus: T+E+F E+B

net public revenue: 0 T

additional

deadweight loss

A

C

B

E

F

T


Exercise quantity taxes l.jpg
Exercise (quantity taxes) discrimination

A monopolist 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?

Industrial Organization ; Oz Shy


Illustrating the solutions l.jpg
Illustrating the solutions discrimination

b)

a)


Lerner index of monopoly power l.jpg
Lerner index of monopoly power discrimination

  • First order condition:

  • Lerner index:


Monopoly profits and monopoly power l.jpg
Monopoly profits discriminationand monopoly power

Cournot point


Executive summary l.jpg
Executive summary discrimination

  • A profit-maximizing monopolist always sets the quantity in the elastic region of the demand curve.

  • 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 average cost.  monopolistic power and zero profits

  • Monopolistic quantities without price discrimination (!) lead to a welfare loss.

  • A quantity tax leads to a welfare loss, a tax on profits does not.


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