Lecture notes 9
MONOPOLIES
This set of lecture notes examines price and output determination in industries dominated by a monopoly. Even though true monopolies are rare, due in part to increased international competition, and due to cost saving technology that allows for greater entry, exploring this topic is still useful for predicting behavior of firms that meet many of the conditions of a monopoly. Indeed, major divisions of the U.S. Department of Justice and the Federal Trade Commission consider possible monopoly pricing and output behavior when determining whether to approve the prospective mergers.
A. REASONS A MONOPOLY MAY EXIST
Monopolistic market structures can arise for several reasons, which are listed below.
1.) Government sanctioned monopoly: In the past the U.S. government awarded market franchises to firms typically for products that were essential to business operations, such as transportation and utilities. The argument for these awards was also supported by the notion that a single provider of these services was more efficient than several firms providing the same service. For example it is quite inefficient to have two railroad carriers using parallel track to service the same routes.
2.) Firms that own patent: AT&T’s patent on vital telephone equipment led to its market dominance by the beginning of the 20th century.
3.) One firm controls the supply of resources: Prior to World War II ALCOA controlled the supply of Bauxite. This attributed to its monopoly position in the Aluminum industry.
4.) Natural Monopoly: Some products are produced at a lower cost by one company rather than by a combination of several firms. The condition for this type of cost outcome is termed subadditivity. Subadditivity simply requires that the cost of a single firm producing an output is less than the cost of multiple firms producing the same quantity. This is depicted by the following equation:
C(Q) < C(q1)+ C(q2) + … C(qn ) and Q = q1 + q2 + …qn
Where the left hand side of this equation is the cost of a single firm producing at output Q and the right hand side of the equation is the sum of the cost of several firms producing at this same output level. This is graphically depicted by Figure 9.A. To guarantee that the condition for subadditivity is met a total cost curve that increases at a decreasing rate is used. This graph suggests that the sum of the separate outputs q1 and q2 give total the total cost of C(q1) + C(q2) which is above the total cost C(q1 + q2) that is associated with the single producer of this product.
C
Figure 9.A
C(q1) + C(q2)
C(q1+q2) C(q)
C(q2)
C(q1)
q1 q2 q1 + q2=Q
Note that from previous lectures, a total cost curve that increases at an increasing rate has a corresponding decreasing average cost curve. Thus, it would seem that firms facing declining average cost should satisfy the requirements for subadditivity. Indeed, the following proof supports this notion.
Decreasing average cost is depicted as follows:
(1) C(qi)/qi > C(Q)/Q; where 0<qi<Q and iqi = Q
(2) multiplying equation (1) by qi gives C(qi) > (C(Q)/Q) qi
(3) summing over ‘I’ gives iC(qi) > (C(Q)/Q) iqi
(4) Since iqi = Q then equation (2) can be rewritten as iC(qi) > C(Q),
which is the condition for subadditivity.
Recognizing that decreasing average cost satisfies the condition for a natural monopoly, we will use a downward sloping average cost curve when graphically examining the pricing behavior of a monopolist.
B. CONDITIONS FOR MONOPOLY STRUCTURE
Before analyzing price determination for a monopolistic market structure it is important to recognize the market conditions that are associated with such an industry structure.
1.) One seller: The industry is dominated by a single firm. For example, Intel in the microchip processing industry.
2.) The firm is a price setter: This suggests that the firm is able to deviate from setting price at the market equilibrium.
3.) High barriers to entry and exit: This suggests that potential entrants face substantial start-up cost. For example, I would be fairly difficult to acquire all the capital needed to compete with the regional Bell operating companies. Barriers to exit suggest that the incumbent monopoly incurs substantial sunk cost. For example Ameritech would find it fairly difficult to recoup all of its capital investment if it attempts to exit the communications industry.
4.) Few close substitutes: This suggests a relatively elastic demand curve.
5.) The market demand is the firm’s demand curve: This suggests a downward sloping demand curve with a corresponding marginal revenue curve that has twice the slope as the demand curve (This was proven in earlier lecture notes.)
C. LONG-RUN EQUILIBRIUM PRICE AND OUTPUT
Using the profit maximizing condition of marginal cost equaling marginal revenue allows for examining price and output determination in a monopolistic market. Assuming that the monopolist is a natural monopoly gives a downward sloping average cost curve with a marginal cost curve that always lies beneath it. The graphical representation of the monopolist is depicted when superimposing the monopoly demand and marginal revenue curve with these cost curves. Figure 9.B presents just such a graph.
Figure 9.B
$
Pm Z
ACm V
AC
MC
MR Demand
qm q
The profit maximizing output level is represented by qm and occurs where MC=MR. The corresponding price is taken from the demand curve and has the value of Pm for this graph. The corresponding unit cost at the monopoly output level is taken from the average cost, and is represented by the value ACm. The difference between the monopoly price and unit cost summed for each unit output up to the monopoly output level gives the monopoly profit. This is depicted by the rectangle Pm,Z,V,ACm. Note that unlike the situation with competitive markets the absence of potential competitors suggests that this is the long-run equilibrium because the monopolist does not face any profit erosion from the entry of such rivals.
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