Download Econ 500 - bcf.usc.edu

ECON 500
ECON 500 –Microeconomic Theory
Econ 500 - Microeconomic Analysis and Policy
Monopoly
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.
ECON 500
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
ECON 500
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.
ECON 500
Monopoly Output Choice
ECON 500
Monopoly Output Choice
Monopoly Markup
ECON 500
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
ECON 500
Monopoly and Supply
There is no unique relationship between price and quantity supplied in the
case of a monopoly. Monopoly has no supply curve.
ECON 500
Monopoly and Profit
ECON 500
Monopoly and Welfare
ECON 500
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
ECON 500
Measuring Monopoly Power
Capturing Consumer Surplus
CAPTURING CONSUMER SURPLUS
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.
● price discrimination
Practice of charging different prices to different
consumers for similar goods.
Price Discrimination
First-Degree Price Discrimination
● reservation price
for a good.
Maximum price that a customer is willing to pay
● first degree price discrimination
reservation price.
Practice of charging each customer her
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 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.
SECOND-DEGREE PRICE
DISCRIMINATION
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 each
group of consumers is equal to the marginal cost of production.
Let P1 be the price charged to the first group of consumers, P2 the
price charged to the second group, and C(QT) the total cost of
producing output QT = Q1 + Q2. Total profit is then
𝜋 = 𝑃1 𝑄1 + 𝑃2 𝑄2 − 𝐶 𝑄𝑇
∆𝜋
∆ 𝑃1 𝑄1
∆𝐶
=
−
=0
∆𝑄1
∆𝑄1
∆𝑄1
MR1 = MC
MR 2 = MC
MR1 = MR 2 = MC
•
(11.1)
DETERMINING RELATIVE PRICES
𝑀𝑅 = 𝑃 1 + 1 𝐸𝑑
𝑃1
1 + 1 𝐸2
=
𝑃2
1 + 1 𝐸1
(11.2)
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 Discrimination
and Peak-Load Pricing
● intertemporal price discrimination :Spending
socially
Chargingmoney
differentinprices
at different times
unproductive efforts to acquire, maintain, or exercise monopoly.
● peak-load pricing Spending
money
in socially
effortsloads
to
: Charging
different
prices unproductive
at different demand
acquire, maintain, or exercise monopoly.
Intertemporal Price Discrimination
INTERTEMPORAL PRICE
DISCRIMINATION
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
Form of pricing in which consumers are charged
both an entry and a usage fee.
SINGLE CONSUMER
TWO-PART TARIFF WITH A
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 CONSUMERS
TWO-PART TARIFF WITH 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.
ECON 500
Regulation of Monopoly
Price Regulation
ECON 500
Regulation of Monopoly
Price Regulation
ECON 500
Regulation of Monopoly
Price Regulation – Natural Monopoly Dilemma
ECON 500
ECON 500
ECON 500 –Microeconomic Theory
Econ 500 - Microeconomic Analysis and Policy
Imperfect Competition
ECON 500
ECON 500
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
ECON 500
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.
The Cournot Model
● Cournot model
Oligopoly model in which firms produce a
homogeneous good, each firm treats the output of its competitors as
fixed, and all firms decide simultaneously how much to produce.
FIRM 1’S OUTPUT DECISION
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
● reaction curve
Relationship between a firm’s profit-maximizing output and
the amount it thinks its competitor will produce.
REACTION CURVES AND COURNOT
EQUILIBRIUM
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.
COURNOT EQUILIBRIUM
● 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 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 curve 𝑃 = 30 − 𝑄
Also, MC1 = MC2 = 0
Total revenue for firm 1:
then
𝑅1 = 𝑃𝑄1 = 𝑎 − 𝑄 𝑄1 = 𝑎𝑄1 − 𝑄12 − 𝑄2 𝑄1
MR1 = ∆𝑅1 ∆𝑄1 = 30 − 2𝑄1 − 𝑄2
Setting MR1 = 0 (the firm’s marginal cost) and solving for Q1, we find
1
𝑄
=
15
−
𝑄
Firm 1’s reaction curve:
1
2 2
By the same calculation, Firm 2’s reaction curve:
Cournot equilibrium:
(12.1)
1
𝑄2 = 15 − 𝑄2
2
(12.2)
𝑄1 = 𝑄2 = 10
Total quantity produced:
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
DUOPOLY EXAMPLE
The demand curve is
P = 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.
ECON 500
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.
ECON 500
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
ECON 500
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
ECON 500
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
ECON 500
Natural Spring Duopoly
ECON 500
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

∂πi /∂qi = a – 2qi – Q-i – c = 0
Q-i = Q - qi
qi =
imposing symmetry Q-i* = Q* - qi* = n qi* - qi* = (n-1) qi*
qi* = (a-c) / (n+1)
Q* =
P* =
(a-c)
a+
* = n (
c
)
ECON 500
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.
ECON 500
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.
ECON 500
Price Competition with Product Differentiation
ECON 500
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.
ECON 500
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
b  a pB  p A
x

2
2t (b  a)
ECON 500
Hotelling’s Beach
The two firms’ demands are:
Nash Equilibrium prices then become:
ECON 500
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
ECON 500
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
PC = 30
PM = 30-ε
Πi = 0
ΠC = 20000
ΠM = 40000
Collusion can be sustained if
δ >1/2 ↔ r <1
ECON 500
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
PC = 30
PM = 30-ε
Πi = 0
ΠC = 20000
ΠM = 40000
With n firms collusion can be sustained if
δ >1-(1/n) ↔ n <12