Download Handout #9

Handout #10
Monopoly
Characteristics:
1. Key resource owned by a single firm
2. government gives a single firm the exclusive right to produce some goods or
services
3. The costs of production make a single firm more efficient than a large number of
producers
Individual Demand and Marginal revenue Curve
In the monopoly market, firms demand curve is the market demand curve (of
course, since there is only one firm in this market).
As for Marginal revenue curve, if the demand function is linear, the marginal
revenue function has “same” y-intercept as demand function but its slope = 2 x slope of
demand function. Suppose that the demand function is given by P = b-mQ. Then the
marginal revenue function is MR = b-2mQ.
P,revenue
MR
Demand=AR
q
Firm’s demand and MR curves
Profit Maximization Condition
As usual, firm maximizes its profit at MC = MR. and also always P > MR except
when quantity is zero. Monopolist’s profit is then
Profit = TR – TC
= (TR/Q – TC/Q)Q
= (P – ATC )Q
Inefficiency of Monopoly
Since monopoly charges a price above MC, not all consumers who value the good
more than its cost will buy it. The quantity produced and sold by monopolist is then
lower than socially optimal level. The socially optimal level of quantity is where demand
intersects MC, or Price=MC.
price
MC
Qm=monopoly
output
DWL
Q* = efficient
output
Monopoly
price
MR
demand
Qm Q*
e
Example: A profit maximizing monopolist has cost function TC=10+2Q. Demand in
this market is given by the equation Q=14-P. Calculate the firm’s profit.
From the TC function, you can find MC. As MC = slope of TC function, MC =$2.
Next, you can find the MR function from the demand function. From demand function,
P=14-Q (note that you need to rewrite demand function so that “P” is on the right-hand
side of the demand function). The marginal revenue function is MR = 14-2Q.
The profit maximizing level of output is such that: MC = MR; therefore,
14-2Q = 2  Qm = 6.
Monopolist chooses to produce 6 units. Substitute quantity into the demand
function to find the profit maximizing price (as there is only one firm in the industry, the
monopolist quantity is also the market quantity. You can substitute profit maximizing
quantity into the demand function to find the price).
P = 14-Q = 14-6 = 8.
Therefore, TR = PxQ = 8x6 = $48. TC = 10+2Q = 10+2x6 = $22.
Profit= TR-TC = $48-$22 = $26.
Natural Monopoly
Characteristics:
A Natural Monopoly has declining average total cost. Therefore, marginal cost is always
less than average total cost. The following picture shows the natural monopoly in case
that the marginal cost is constant.
ATC
MC
Demand
quantity
Therefore, for a natural monopoly, if the government requires it to charge a price equal to
marginal cost (The price that brings about allocatively efficient quantity), price will be
below average total cost, and the monopoly will get loss. The shaded area is the loss for
monopolist if the government enforces marginal cost pricing.
ATC
MC
Demand
quantity
Price Discrimination
This is the situation in which the monopolist can sell different price to different
buyers. The key idea is to convert consumer surplus into economic profit.
1. First-degree (perfect) price discrimination
The monopolist can extract the entire consumer surplus. This is the case that the
monopolist can set price differently for every unit of goods sold. Recall that, for a single
monopoly, marginal revenue (MR) is less than price since when the price is cut in order
to sell a larger quantity, the price is lower on all units sold. However, for the first-degree
price discrimination, MR= P. In other words, the demand curve is also the marginal
revenue curve. The monopolist can obtain greater profit by increasing output up to the
point that P=MC.
Consider the following picture. If the monopolist set single price (set price that
MR=MC to maximize its profit), the monopolist has revenue equal to the rectangular
PB0Q* and consumers get consumer surplus equal to the triangle AP*B.
When there is prefect price discrimination, the monopolist has total revenue equal
to the rectangular AB0Q*, so he can extract all consumer surplus. In this case, consumers
get
nothing.
Price
MC
A
B
P*
Demand= MR
0
Quantity
Q*
Note that, with the first-degree price discrimination, the quantity that the
monopolist chooses to produce is the same level as the perfectly competitive quantity, the
allocative efficient.
Recall that the allocative efficient quantity is the quantity that MC=P. In the case
of first-degree price discrimination, the monopolist maximizes his profit at the quantity
Q*, where MC=P.
2. Second-degree price discrimination
The second-degree price discrimination occurs when the monopolist can
discriminate among units of good (buy not for every unit like the first degree one). A
discount for bulk buying is an example of this type of discrimination. The larger the order,
the larger is the discount and the lower is price.
Example 1:
Suppose that the monopolist can discriminate price in the way that if a consumer
buys less than Q1 units, he has to pay P1 per unit. If he buys more than Q1 units, he has
to pay P2 per unit. Then the monopolist can sell totally Q2 units. His revenue is
[P1xQ1+P2x(Q2-Q10)]. In case that he can set only a single price, he will produce Q1
units to maximize his profit and get the revenue equal to P1xQ1. Therefore, from the
picture, you can see that the monopolist gets higher profit when he uses price
discrimination.
3. Third-degree price discrimination
The third-degree price discrimination occurs when the monopolist can
discriminate among groups of buyers. In other words, the monopolist can charge different
prices from different groups of consumers.
Example 2: Men and women have different demand functions for pretzels. Specifically,
the demand function for men is given by Q=10-P; for women, demand is given by Q=5-P.
Assume a monopolist supplies the pretzel market and has no fixed or marginal costs
associated with producing pretzels (this just simplifies the math a little bit).
i) Derive the aggregate demand curve in the market for pretzels and graph it (Hint: this
is the horizontal summation of the two demand curves for P<=5, and it is just the demand
curve for men for P>5. Can you explain why?)