ECMC41:
Monopoly

Some Price Discrimination Examples
Suppose your firm is the only supplier of a product with no close substitute (i.e. you are a
monopolist). For simplicity we will assume for now that your firm can produce any level
of output with a constant marginal cost of $2 per unit and faces no fixed costs (i.e., these
two assumptions combine nicely to tell us MC = AC = AVC= $2/unit).
Further, imagine there are two consumers of your product person A and person B. Person
A has a demand curve given by
P
A
= 100 – 2Q
A
where P
A
is the price this person is
charged and Q
A
refers to person A’s quantity demanded (or level of demand) for this
product at this price. Similarly, person B has a demand curve given by
P
B
= 200 – 10Q
B
where P
B
is the price this person is charged and Q
B
refers to person B’s quantity
demanded (or level of demand) for this product at this price.
Clearly the type A person is a low demand person as the intercept of their demand curve
is smaller and their curve is not as steep as the demand curve for the type B person. So
type A is the low demand type OR has a more price sensitive (more elastic) demand
curve (than the type B person). The type B person is the high demand/less price sensitive/
less elastic/more inelastic demand type.
Lets’ now look into this environment in several situations (or cases):
Case #1: Uniform Pricing
OR
Single Price Monopoly
1
Assume
•
Suppose our firm has no way to identify these consumers’ by type (A versus B).
•
One alternative for us is to decide to charge a single price to all consumers for all
units of output sold. This part investigates what happens if we do this.
The market demand curve is found via horizontal summation of the individual demand
curves (i.e. fixing our point of reference on the vertical axis and summing along the
horizontal axis). For prices above $100 the type A person demands no units so for this
range of prices the market demand curve is given by person B’s demand curve. For prices
below $100 both demand curves (levels) are added together.
Market Demand Curve
1)
When P ≥ $100
then
P = 200 – 10Q
2)
When
P ≤ $100
then
P = 116.67 – 1.67Q
Horizontal summation of demand curves (derivation of market demand curve):
P
A
= 100 – 2Q
A
➪
Q
A
= 50 – ½P
A
P
B
= 200 – 10Q
B
➪
Q
B
= 20 – (1/10)P
B
1
Of course charging all purchasers the same price for output they buy means the firm is NOT price
discriminating (presently). By looking at the level of output, price and in particular firm profit that results
when the firm does not price discrimination we can define a baseline. This baseline can be used to
demonstrate just how the effectively firm is able to raise its level of profit via price discrimination.
1 
P a g e
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When summing this way hold P fixed (i.e. P = P
A
= P
B
) and sum along the horizontal
axis, so we have:
Q
A
= 50 – ½P
Q
B
= 20 – (1/10)P
.
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 Summer '10
 JackParkinson
 Supply And Demand, CSB

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