AAEC 3315
Agricultural Price Theory
Chapter 13
Price and Output Under Monopoly
Objectives

To learn:

How the prices & quantities of goods & services
produced & consumed are determined under a
monopoly market structure.
Characteristics of
a Monopoly

Characteristics of monopolies are:
 Single seller but a large number of buyers
 Unique Product, i.e., there are no close substitutes
 Ability to Set Prices (monopolist is a price maker;
discriminating monopolists charge different prices
to different classes of consumers)
 Barriers to Entry (a monopoly generally has an
economic, legal or technical barrier to entry to other
firms)
Characteristics of
a Monopoly


These characteristics of monopolies, clearly, make a
monopolist a price-maker. However, a monopolist’s
control over price is not absolute.
What causes Monopoly?

Barriers to entry is the single most important factor that
contributes the existence of monopolies. A strong barrier for
entry may exist because:



Control of the supply of key raw materials
Patents on the product or on the production process
A market franchise awarded by the government
The Monopolist’s TR, AR, and MR
Curves

Since the monopolist is the
only firm producing a
product, the monopolist’s
demand curve is precisely the
same as the market demand
curve.



So, AR is the monopolist’s
demand curve
And it is negatively sloped
TR
Since AR is negatively
sloped, AR & MR are not the
same.


P
MR is also negatively
sloped, and is twice as steep
as the AR.
The Total Revenue curve is
concave downward because
the monopolist’s demand
curve is downward sloping.
MR
AR
Q
The Monopolist’s Cost Curves
TOTAL COSTS

In that case, the concept of
cost curves do not change.

The TC, TVC, TFC, ATC,
AVC, AFC, and MC curves,
therefore, are as discussed
before for perfect
competition.
TC
TVC
Costs
If the monopolist in the
product market faces a
perfectly competitive input
market, then it can not affect
input prices.
TFC
Output
MC
ATC
AVC
Costs/unit

AFC
Output
Profit Maximizing Output Decision
under Monopoly in the Short-run
The Total Curves Approach
Profit maximization output
decision rule for a monopolist
depends on two considerations.
$
TR
TC

One, whether there is any
output level at which TR
exceeds the TVC. If not, the
profit maximizing strategy is
to shut down.

If there are output levels at
which TR > TVC, the
monopolist will produce
where the vertical distance
between TR and TC is at its
maximum.
TVC
Q
Profit Maximizing Output Decision
under Monopoly in the Short-run
The Total Curves Approach

In this case, the vertical
distance between TR and TC
is at maximum at the Q* level
of output.

Note that at Q* units of
output, TR and TC curves
have the same slope, i.e.,
MR = MC. (This is called
the Necessary Condition of
profit maximization)

Further, the slope of MC
exceeds that of the MR (MC
has a positive slope and MR
has a negative slope). (This
is called the Sufficient
Condition of profit
maximization)
$
TR
TC
TVC
Q*
Q
Profit Maximizing Output Decision
under Monopoly in the Short-run
The Average & Marginal
Curves Approach
$/unit
MC
AC
Again, the same decision rules
should be considered.



Does the AR lie above the
AVC in some output range?
If not, the best strategy in the
short-run is to shut down.
If yes, the profit maximizing
output is where MR=MC and
the slope of the MC is greater
than the slope of the MR.
This is the Q* level of output.
AVC
AR
MR
Q*
Q
Price Determination under Monopoly
After deciding that Q* is the profit
maximizing level of output, the
monopolist must decide the price
at which the output is to be sold.



The monopolist will sell the
output at the maximum price at
which he can sell the output.
That maximum price is the price
that the consumers are willing to
pay (derived from the demand/AR
Curve) – that is P*
At that price of P*, note that profit
per unit is BA dollars and the total
economic profit received by the
monopolist is P*ABC.
$/unit
MC
AC
P*
C
A
AVC
B
AR
MR
Q*
Q
A Mathematical Example


Suppose that the Monopolist’s TR and TC curves are given by:
TR = 50 Q – 4 Q2
TC = 10 Q
What is the Profit Maximizing level of output?


Note that at the profit max level of output, MR must equal to MC (the Necessary
Condition of profit maximization)
MR = ∂TR/∂Q = 50 – 8Q
MC = ∂TC/∂Q = 10
At MR = MC, 50 – 8Q = 10
8Q = 40 or Q = 5
Also note that at the profit max level of output, the slope of MC must exceed the slope
of the MR (the Sufficient Condition of profit maximization)
Slope of MR = ∂MR/∂Q = – 8
Slope of MC = ∂MC/∂Q = 0
Thus the Slope of MC > the slope of MR
A Mathematical Example


The Monopolist’s TR and TC curves are given by:
TR = 50 Q – 4 Q2
TC = 10 Q
What is Equilibrium Price?


Note that TR = P*Q = 50Q - 4Q2
So, P = 50 – 4Q
Since Q = 5, then P = 50 – 20 = $30
What is the Profit?

Note that Profit = TR – TC
TR = 50 (5) – 4 (5)2 = $150
TC = 10 (5) = $50
So, Profit = $150 - $50 = $100
Multiplant Monopolist



This section extends the analysis to cover the case
where the monopolist operates more than one plant.
How does a monopolist determine the profit
maximizing allocation of production between multiple
plants when it has multiple plants to produce the output
that he sells in a single market?
The profit maximizing multiplant monopolist allocates
the production of output between two plants by
equalizing the MC in each plant.
Multiplant Monopolist

Let’s assume that the monopolist operates two plants.


MCA and MCB show the MCs of two plants A & B, and MCt represents the firm’s MC.
Note that MCt is the horizontal summation of MCA and MCB and shows the firm’s MC
when it uses either plant A or B, whichever has a lower MC.
AR and MR represent the monopolist’s Average Revenue and Marginal Revenue curves.
$/unit
$/unit
MCA
$/unit
MCB
Firm
MCt
Plant A
Plant B
AR
MR
Q
Q
Q
Multiplant Monopolist



By equating its MR and MCt, the monopolist determines the profit maximizing output of q t and
price of Pt.
To produce qt at the least cost, the monopolist allocates production between the two plants
such that the MC of production in each plant is the same.
That is, plant A produces qA and plant B produces qB, where qA + qB = qt.
$/unit
$/unit
$/unit
MCA
MCB
Firm
MCt
Pt
Plant A
Plant B
AR
MR
qA
Q
qB
Q
qt
Q
A Mathematical Example of
Multiplant Monopolist




Suppose that the Monopolist’s TR and TC curves for two plants are
given by:
TR = 136 Q – 4 Q2, TC1 = 20 Q1 + Q12, and TC2 = 10Q2 + 2.5 Q22
Now then
MR = 136 – 8 Q = 136 – 8 (Q1 + Q2)
AR = 136 – 4 (Q1 + Q2)
MC1 = 20 + 2Q1
MC2 = 10 + 5Q2
To maximize profit, the multiplant monopolist will equate MC1 with MR
and MC2 with MR.
That is 20 + 2Q1 = 136 – 8 (Q1 + Q2) ------ (1)
and
10 + 5Q2 = 136 – 8 (Q1 + Q2) ------ (2)
A Mathematical Example of
Multiplant Monopolist

Taking equation (1), we have

20 + 2Q1 = 136 – 8Q1 - 8Q2
Or, 2Q1 + 8Q1 = 136 – 20 - 8Q2
Or, 10Q1 = 116 - 8Q2
Or, Q1 = 11.6 – 0.8Q2 -------- (3)

Note that equation (2) is 10 + 5Q2 = 136 – 8 (Q1 + Q2)
Or, 10 + 5Q2 = 136 – 8Q1 - 8Q2

Now substituting (3) in equation (2), we have
10 + 5Q2 = 136 – 8(11.6 – 0.8Q2) - 8Q2
Or, 10 + 5Q2 = 136 – 92.8 + 6.4Q2 - 8Q2
Or, 5Q2 - 6.4Q2 + 8Q2 = 136 – 10 - 92.8
Or, 6.6 Q2 = 33.2
Or, Q2 = 5.03 units

Now substituting Q2 = 5.03 into equation (3), we calculate Q1 = 7.576
A Mathematical Example of
Multiplant Monopolist



The profit maximizing production levels in plant 1 and plant 2 are then
7.576 and 5.03 units, respectively.
Now we can calculate the Price that the multiplant monopolist will charge
in the market.
Note that:
AR = P = 136 – 4 (Q1 + Q2)
Or, AR = P =136 – 4(7.576+5.03)
Or, P = 136 – 50.424 = $85.576

Thus, we have this multiplant monopolist who produces 7.576 units of
the output in Plant 1 and 5.03 units of the output in Plant 2 at the least
cost of production and sells the product in the marketplace for $85.576
per unit.

Can you calculate the amount of profit for this multiplant
monopolist?
Price Discrimination

Price Discrimination is said to exist when an identical
good is sold at different prices or when two similar
goods are sold at prices that are in different ratios to
marginal costs.

Prerequisites of Discriminatory Pricing



The seller must have a monopoly or market power
The market can be separated (i.e., product can’t be transferred from
one market to another)
The elasticities of demand in different markets must be different
First Degree or
Perfect Price Discrimination




The discriminatory pricing that
attempts to take away the entire
Consumers Surplus is called first
degree price discrimination.
It assumes that the monopolist
knows the demand of each
customer and attempts to extract
the maximum amount possible
from each customer.
The monopolist charges different
prices to each of the customers
and takes away the entire
consumer surplus.
This is a limiting case unless
customers are few in numbers
and can be well separated.
$/unit
MC
AR
MR
Q*
Q
Second Degree or
Perfect Price Discrimination




The discriminatory pricing that
attempts to siphon off a part of
the CS is called the second
degree price discrimination.
It charges different prices for
different size purchases, as in the
case of electric or gas utilities.
The monopolist charges P1 for
up to Q1 units, P2 for between Q1
and Q2, and P3 for purchases
exceeding Q2.
Note that the shaded triangles
represent CS retained by the
consumers.
$/unit
MC
P1
P2
P3
AR
MR
Q1
Q2
Q3
Q
Third Degree or
Perfect Price Discrimination


Third degree price discrimination refers to a discriminatory pricing by
which a monopolist sells his good at different prices in different markets,
but keeps the price uniform within each separate market.
In the figure below, the two markets are identified separately. The MRt
is the MR for the firm and is obtained by summing the MR1 and MR2
horizontally.
$/unit
$/unit
Market 1
$/unit
Market 2
D1
MR2
MR1
Q
Firm
D2
MRt
Q
Q
Third Degree or
Perfect Price Discrimination


The MRt (MR for the firm) shows the additional revenue the firm can
secure by selling an additional unit of the output either in Market 1 or
Market 2, whichever has a higher MR.
To maximize profit, the monopolist must produce Qt – the level of output
at which MRt = MC.
$/unit
$/unit
$/unit
MC
Market 1
Firm
Market 2
D1
MR2
MR1
Q
D2
MRt
Q
Qt
Q
Third Degree or
Perfect Price Discrimination



The monopolist must now allocate this output between Markets 1 and 2 in
such a way as to equalize the MR in the two markets.
This is the case at Q1 level of output in Market 1 and Q2 level of output in
Market 2.
Note that Q1+Q2 = Qt (This is necessarily true because MRt curve is
obtained as the summation of MR1 and MR2)
$/unit
$/unit
$/unit
MC
Market 1
Market 2
D1
MR2
MR1
Q1
Q
Q2
Firm
D2
MRt
Q
Qt
Q
Third Degree or
Perfect Price Discrimination



The prices charged in the two markets are P1 in Market 1 and P2 Market 2
as determined from their respective AR curves.
Note that the monopolist is charging a higher price in Market 1 than in
Market 2.
That is because demand in Market 1 is relatively inelastic and demand in
Market 2 is relatively elastic.
$/unit
$/unit
$/unit
MC
P1
Market 1
Market 2
Relatively Inelastic
Relatively Elastic
Firm
P2
D1
MR2
MR1
Q1
Q
Q2
D2
MRt
Q
Qt
Q