ECON 500

ECON 500 –Microeconomic Theory

Monopoly

Econ 500 - Microeconomic Analysis and Policy

ECON 500

Monopoly

A monopoly is a single firm that serves an entire market and faces the

market demand curve for its output.

Unlike the perfectly competitive firm’s output decision (which has no

effect on market price), the monopoly’s output decision will, in fact,

determine the good’s price.

Furthermore, due to barriers to entry, other firms find it impossible or unprofitable to enter the market a monopoly operates in.

Therefore, monopoly markets and markets characterized by perfect

competition are polar opposite cases.

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Barriers to Entry

The reason a monopoly exists is that other firms find it unprofitable or

impossible to enter the market. Barriers to entry are therefore the source of all monopoly power. If other firms could enter a market then the firm

would, by definition, no longer be a monopoly.

There are two general types of barriers to entry:

Technical Barriers to Entry Legal Barriers to Entry

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Barriers to Entry

There are two general types of barriers to entry:

Technical Barriers to Entry:

Economies of Scale

Proprietary Technology Ownership of unique resources

Legal Barriers to Entry:

Intellectual Property Rights Government Designation

Firms may also expand productive resources to create barriers to entry.

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Monopoly Output Choice

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Monopoly Output Choice

Monopoly Markup

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Monopoly Output Choice

Two General Conclusions:

A monopoly will choose to operate only in regions where the market demand curve is elastic, eQ,P < -1

The firm’s “markup” over marginal cost depends inversely on the

elasticity of market demand

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Monopoly and Supply

There is no unique relationship between price and quantity supplied in the

case of a monopoly. Monopoly has no supply curve.

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Monopoly and Profit

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Monopoly and Welfare

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Measuring Monopoly Power

Lerner Index of Monopoly Power:

Measure of monopoly power calculated as excess of price over marginal

cost as a fraction of price.

𝐿 = (𝑃 − MC) 𝑃⁄ = −1 𝐸𝑑⁄

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Measuring Monopoly Power

Capturing Consumer Surplus

CAPTURING CONSUMER SURPLUS

● price discrimination Practice of charging different prices to different

consumers for similar goods.

If a firm can charge only one price for all its customers, that price will be P* and the quantity produced will be Q*.

Ideally, the firm would like to charge a higher price to consumers willing to pay more than P*, thereby capturing some of the consumer surplus under region A of the demand curve.

The firm would also like to sell to consumers willing to pay prices lower than P*, but only if doing so does not entail lowering the price to other consumers.

In that way, the firm could also capture some of the surplus under region B of the demand curve.

● first degree price discrimination Practice of charging each customer her

reservation price.

First-Degree Price Discrimination

● reservation price Maximum price that a customer is willing to pay

for a good.

Price Discrimination

ADDITIONAL PROFIT FROM PERFECT FIRST-DEGREE PRICE DISCRIMINATION

Because the firm charges each consumer her reservation price, it is profitable to expand output to Q**.

When only a single price, P*, is charged, the firm’s variable

profit is the area between the marginal revenue and marginal cost curves.

With perfect price discrimination, this profit expands to the area between the demand curve and the marginal cost curve.

SECOND-DEGREE PRICE DISCRIMINATION

Second-Degree Price Discrimination

● second-degree price discrimination Practice of charging different

prices per unit for different quantities of the same good or service.

● block pricing Practice of charging different prices for different

quantities or “blocks” of a good.

Different prices are charged for different quantities, or “blocks,” of the

same good. Here, there are three blocks, with corresponding prices P1, P2, and P3.

There are also economies of scale, and average and marginal costs are declining. Second-degree price discrimination can then make consumers better off by expanding output and lowering cost.

Third-Degree Price Discrimination

● third-degree price discrimination Practice of dividing

consumers into two or more groups with separate demand curves and charging different prices to each group.

CREATING CONSUMER GROUPS

If third-degree price discrimination is feasible, how should the firm decide what price to charge each group of consumers?

1. We know that however much is produced, total output should be divided between the groups of customers so that marginal revenues for each group are equal.

2. We know that total output must be such that the marginal revenue for eachgroup of consumers is equal to the marginal cost of production.

DETERMINING RELATIVE PRICES

𝜋 = 𝑃1𝑄1 + 𝑃2𝑄2 − 𝐶 𝑄𝑇

∆𝜋

∆𝑄1=∆ 𝑃1𝑄1∆𝑄1

−∆𝐶

∆𝑄1= 0

MR1 = MC

MR2 = MC

•

(11.1)MR1 = MR2 = MC

𝑀𝑅 = 𝑃 1 + 1 𝐸𝑑

(11.2)𝑃1𝑃2

=1 + 1 𝐸21 + 1 𝐸1

Let P1 be the price charged to the first group of consumers, P2 theprice charged to the second group, and C(QT) the total cost ofproducing output QT = Q1 + Q2. Total profit is then

THIRD-DEGREE PRICE DISCRIMINATION

Consumers are divided into two groups, with separate demand curves for each group. The optimal prices and quantities are such that the marginal revenue from each group is the same and equal to marginal cost.

Here group 1, with demand curve D1, is charged P1,

and group 2, with the more elastic demand curve D2, is charged the lower price P2.

Marginal cost depends on the total quantity produced QT.

Note that Q1 and Q2 are chosen so that MR1 = MR2 = MC.

NO SALES TO SMALLER MARKETS

Even if third-degree price discrimination is feasible, it may not pay to sell to both groups of consumers if marginal cost is rising.

Here the first group of consumers, with demand D1, are not willing to pay much for the product.

It is unprofitable to sell to them because the price would have to be too low to compensate for the resulting increase in marginal cost.

Intertemporal Price Discriminationand Peak-Load Pricing

INTERTEMPORAL PRICE DISCRIMINATION

Intertemporal Price Discrimination

● intertemporal price discrimination Spending money in socially

unproductive efforts to acquire, maintain, or exercise monopoly.

● peak-load pricing Spending money in socially unproductive efforts to

acquire, maintain, or exercise monopoly.

Consumers are divided into groups by changing the price over time.

Initially, the price is high. The firm captures surplus from consumers who have a high demand for the good and who are unwilling to wait to buy it.

Later the price is reduced to appeal to the mass market.

PEAK-LOAD PRICING

Peak-Load Pricing

Demands for some goods and services increase sharply during particular times of the day or year.

Charging a higher price P1 during the peak periods is more profitable for the firm than charging a single price at all times.

It is also more efficient because marginal cost is higher during peak periods.

The Two-Part Tariff

TWO-PART TARIFF WITH A SINGLE CONSUMER

● two-part tariff Form of pricing in which consumers are charged

both an entry and a usage fee.

SINGLE CONSUMER

The consumer has demand curve D.

The firm maximizes profit by setting usage fee P equal to marginal cost

and entry fee T* equal to the entire surplus of the consumer.

TWO-PART TARIFF WITH TWO CONSUMERS

TWO CONSUMERS

The profit-maximizing usage fee P* will exceed marginal cost.

The entry fee T* is equal to the surplus of the consumer with the smaller demand.

The resulting profit is 2T* + (P* −

MC)(Q1 + Q2). Note that this profit is larger than twice the area of triangle ABC.

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Regulation of Monopoly

Price Regulation

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Regulation of Monopoly

Price Regulation

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Regulation of Monopoly

Price Regulation – Natural Monopoly Dilemma

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ECON 500

ECON 500 –Microeconomic Theory

Imperfect Competition

Econ 500 - Microeconomic Analysis and Policy

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Bertrand Competition

Two identical firms, producing identical products at a constant marginal cost (and constant average cost) c.

The firms choose prices p1 and p2 simultaneously in a single period of

competition.

Since firms’ products are perfect substitutes, all sales go to the firm with the lowest price.

Sales are split evenly if p1= p2.

The only pure-strategy (Nash) equilibrium of the Bertrand game is

p1 = p2 = c

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Cournot Competition

Two identical firms, producing identical products at a constant marginal cost (and constant average cost) c.

The firms choose prices q1 and q2 simultaneously in a single period of

competition.

The pure strategy (Nash) equilibrium of the Cournot game is a set of quantities where each firm correctly assumes how much its competitor

will produce and sets its own production level accordingly.

After this simple change in strategic variable, equilibrium price will be above marginal cost and firms will earn positive profit in the Nash

equilibrium of the Cournot game.

FIRM 1’S OUTPUT DECISION

The Cournot Model● Cournot model Oligopoly model in which firms produce a

homogeneous good, each firm treats the output of its competitors asfixed, and all firms decide simultaneously how much to produce.

Firm 1’s profit-maximizing output depends on how much it thinks that Firm 2 will produce.

If it thinks Firm 2 will produce nothing, its demand curve, labeled D1(0), is the market demand curve. The corresponding marginal revenue curve, labeled MR1(0), intersects Firm 1’s marginal cost curve MC1 at an output of 50 units.

If Firm 1 thinks that Firm 2 will produce 50 units, its demand curve, D1(50), is shifted to the left by this amount. Profit maximization now implies an output of 25 units.

Finally, if Firm 1 thinks that Firm 2 will produce 75 units, Firm 1 will produce only 12.5 units.

5 75

REACTION CURVES AND COURNOT EQUILIBRIUM

● reaction curve Relationship between a firm’s profit-maximizing output and

the amount it thinks its competitor will produce.

Firm 1’s reaction curve shows how much it will

produce as a function of how much it thinks Firm 2 will produce. (The xs at Q2 = 0, 50, and 75 correspond to the examples shown in Figure 12.3.)

Firm 2’s reaction curve shows its output as a

function of how much it thinks Firm 1 will produce.

In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore, neither firm will move from this equilibrium.

REACTION CURVES

● Cournot equilibrium Equilibrium in the Cournot model in which each firm

correctly assumes how much its competitor will produce and sets its own production level accordingly.

COURNOT EQUILIBRIUM

Cournot equilibrium is an example of a Nash equilibrium (and thus it is sometimes called a Cournot-Nash equilibrium).

In a Nash equilibrium, each firm is doing the best it can given what its competitors are doing.

As a result, no firm would individually want to change its behavior. In the Cournot equilibrium, each firm is producing an amount that maximizes its profit given what its competitor is producing, so neither would want to change its output.

The Linear Demand Curve—An Example

Two identical firms face the following market demand curveAlso,

Total revenue for firm 1:

then

Setting MR1 = 0 (the firm’s marginal cost) and solving for Q1, we find

Firm 1’s reaction curve:

By the same calculation, Firm 2’s reaction curve:

Cournot equilibrium:

Total quantity produced:

𝑃 = 30 − 𝑄MC1 = MC2 = 0

𝑅1 = 𝑃𝑄1 = 𝑎 − 𝑄 𝑄1 = 𝑎𝑄1 − 𝑄12 − 𝑄2𝑄1

MR1 = ∆𝑅1 ∆𝑄1 = 30 − 2𝑄1 − 𝑄2

𝑄1 = 15 −1

2𝑄2

𝑄2 = 15 −1

2𝑄2

𝑄1 = 𝑄2 = 10

𝑄 = 𝑄1 + 𝑄2 = 20

If the two firms collude, then the total profit-maximizing quantity is:

Total revenue for the two firms: R = PQ = (30 –Q)Q = 30Q – Q2, then MR1 = ∆R/∆Q = 30 – 2Q

Setting MR = 0 (the firm’s marginal cost) we find that total profit is maximized at Q = 15.

Then, Q1 + Q2 = 15 is the collusion curve.

If the firms agree to share profits equally, each will produce half of the total output:𝑄1 = 𝑄2 = 7.5

(12.1)

(12.2)

DUOPOLY EXAMPLE

The demand curve isP = 30 − Q, and both firms have zero marginal cost. In Cournot equilibrium, each firm produces 10.

The collusion curve shows combinations of Q1 and Q2 that maximize total profits.

If the firms collude and share profits equally, each will produce 7.5.

Also shown is the competitive equilibrium, in which price equals marginal cost and profit is zero.

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Cournot Competition – General Model

n firms, indexed by i = 1,…,n each of which is producing qi with the cost function Ci(qi)

where the total industry output is Q = q1 + q2 + … + qn

and where the inverse demand revealing the market price is P(Q) with P’(Q) < 0

A representative firm i maximizes it’s profit

πi = P(Q) qi - Ci(qi)

where the first order condition with respect to it’s own quantity is

P(Q) qi + P’(Q) qi – Ci

’(qi) = 0

This first order condition must hold for all firms i = 1,…,n and this system of equations can be

solved for the Cournot-Nash equilibrium quantity qi* by imposing symmetry.

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Natural Spring Duopoly

Inverse demand: P(Q) = a – Q where Q = ∑

Cost functions Ci(qi) = cqi

Bertrand Equilibrium:

P* = c; total output = Q* = a – c *i = 0; total profit for all firms = * = 0

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Natural Spring Duopoly

Inverse demand: P(Q) = a – Q where Q = ∑

Cost functions Ci(qi) = cqi

Cournot Equilibrium:

1 = P(Q)q1 – cq1 = (a – q1 – q2 – c)q1 2 = P(Q)q2 – cq2 = (a – q1 – q2 – c)q2

a – 2q1 – q2 – c = 0 ↔ q1 =

a – q1 – 2q2 – c = 0 ↔ q2 =

q1* = q2* = (a – c)/3

total output = Q* = (2/3)(a – c) P* = (a + 2c)/3;

1* = 2* = (1/9)(a – c)2 * = (2/9)(a – c)2

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Natural Spring Duopoly

Inverse demand: P(Q) = a – Q where Q = ∑

Cost functions Ci(qi) = cqi

Cartel Equilibrium:

1 + 2 = (a – q1 – q2 – c)q1 + (a – q1 – q2 – c)q2

a – 2q1 – 2q2 – c = 0

q1* = q2* = (a – c)/4

total output = Q* = (a – c)/2 P* = (a + c)/2;

1* = 2* = (a – c)2/8 * = (a – c)2/4

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Natural Spring Duopoly

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Number of Firms and Range of Outcomes:

n = perfect competition n = 1 perfect cartel / monopoly

πi = P(Q)qi – cqi = (a – qi – Q-i - c)qi where Q-i = Q - qi

∂πi /∂qi = a – 2qi – Q-i – c = 0 qi =

imposing symmetry Q-i* = Q* - qi* = n qi* - qi* = (n-1) qi*

qi* = (a-c) / (n+1)

Q* =

(a-c)

P* =

a +

c

* = n (

)

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Prices or Quantities

Cournot model admits more realistic market structure outcomes as n varies. However, firms tend to set prices rather than quantities

Allowing for capacity constraints in price competition establishes an isomorphism between price

and quantity competition.

First stage: choose capacities q1, q2

Second stage: price competition p1, p2

p1 = p2 < p or p1 = p2 > p can not be a Nash Eq.

p1 = p2 = p is the only Nash Eq. in the pricing stage.

Having observed the outcome of the second stage, capacity choices are made in a Cournot fashion in the fisrt stage.

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Price Competition with Product Differentiation

Suppose n firms simultaneously choose prices p1, p2,…, pn of their differentiated goods.

Firm i’s demand is

where, ai is the product specific attributes that enable differentiation.

Firm i’s profit function is

with the first order condition

These FOCs can be solved simultaneously to yield the Nash Equilibrium prices.

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Price Competition with Product Differentiation

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Other Sources of Price Dispersion

Even if the physical characteristics of the goods they sell are identical, competitors may have some ability to charge prices above marginal cost

and earn positive profits if their location choices (quality, variety, transportation, etc. dimension) lead to spatial differentiation.

Any positive search cost s incurred by the consumer that demand a single

unit with identical gross surplus v to learn the prices of a number n of firms avoids the Bertrand Paradox and allows firms to arrive at a Nash Eq.

where all firms charge the monopoly price v.

Firms choices of where to locate in an attribute space in which consumers are distributed according to some density function with an increasing cost of buying at a location different than theirs also avoids Bertrand Paradox

and allows for price (>MC) dispersion.

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Hotelling’s Beach

Two firms locate at points a and b on the line of length L.

Consumers are uniformly distributed along the same line and have quadratic costs of traveling to their firm of choice t(x-a)2

A consumer at x will be indifferent between the two firms if

pA + t(x – a)2 = pB + t(b – x)2

2 2 ( )B Ap pb a

xt b a

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Hotelling’s Beach

The two firms’ demands are:

Nash Equilibrium prices then become:

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Tacit Collusion

Do firms have to endure the Bertrand paradox (marginal cost pricing and zero profits) in each period of a repeated game or can they instead achieve

more profitable outcomes through tacit collusion?

In order for collusion to be sustainable collusive profit should exceed one time deviation profit

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Tacit Collusion

Do firms have to endure the Bertrand paradox (marginal cost pricing and

zero profits) in each period of a repeated game or can they instead achieve more profitable outcomes through tacit collusion?

Suppose Q = 5000 – 100P

MC=AC=10

PB = 10 Πi = 0

PC = 30 ΠC = 20000 PM = 30-ε ΠM = 40000

Collusion can be sustained if

δ >1/2 ↔ r <1

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Tacit Collusion

Do firms have to endure the Bertrand paradox (marginal cost pricing and

zero profits) in each period of a repeated game or can they instead achieve more profitable outcomes through tacit collusion?

Suppose Q = 5000 – 100P

MC=AC=10

PB = 10 Πi = 0

PC = 30 ΠC = 20000 PM = 30-ε ΠM = 40000

With n firms collusion can be sustained if

δ >1-(1/n) ↔ n <12