Monopolies microeconomics
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.
D. COMPARISON OF MONOPOLY PRICING AND COMPETITIVE PRICING
Monopoly pricing has important implication for consumer welfare. Indeed, setting high prices may suggest a loss of total surplus. The monopoly price is compared to the competitive equilibrium to examine this possibility.
Using the condition for competitive price requires setting price equal to the firms demand curve (MC=P). The equilibrium price and quantity from this pricing behavior is represented by Pc and Qc, respectively on Figure 9.C. The monopoly prices and quantity are respectively, Pm and Qm. This suggests that monopoly pricing is associated with such a firm selling fewer products than the competitive equilibrium dictates and at higher prices. Furthermore the total surplus loss is represented by the shaded area V. In sum, monopoly pricing does not promote an efficient market for consumers. It should be noted however, that forcing the natural monopolist to satisfy the competitive pricing condition leads to the firm facing negative profits because marginal cost is always less than average cost for a natural monopoly. Hence, setting price equal to marginal cost results in a price that is less than average costs. This suggest that any pricing regulation of such a firm should consider incorporating the constraint that sets a firm’s price equal to average cost.
Figure 9.C
$
Pm
V
AC
Pc MC
MR Demand
qm qc q
E. PRICE DISCRIMINATION
Rather than engage in monopoly pricing such a firm may choose to generate greater profits by practicing price discrimination. This pricing behavior is defined as charging different consumers different prices for the same commodity without cost justification. The classic example of this is Standard Oil’s pricing its product at below competitive prices in regions where rivals existed during the turn of the century.
A graphical depiction of price discrimination is shown in Figure 9.D. This graph presents the demand curves for two consumer groups (D1 and D2) along with the corresponding marginal revenues (MR1 and MR2). Since only one firm supplies this product there is only one marginal cost curve, which is depicted by MC. To determine the price for each consumer group the monopolist initially determines the profit maximizing output level by setting the joint marginal revenue curve equal to marginal cost. The joint marginal revenue curve is the horizontal sum of the two groups marginal revenue curves. The marginal cost corresponding to the profit maximizing output level is depicted by MCm. This is the marginal cost faced by the price discriminating monopolist when selling the profit maximizing amount of goods. Thus far, then, the procedure for setting discriminatory prices does not differ from setting the standard monopoly price. However, at this juncture, instead of setting price off of the joint demand curve, (Remember the monopoly demand curve is the horizontal sum of consumers’ demand curves), prices are determined by separately equating the profit maximizing level of marginal cost with each consumer group’s marginal revenue curve. On Figure 9.D this gives the respective price and output levels of P1 and Q1 for consumer group one, and P2 and Q2 for consumer group two. The outcome from such pricing suggest that all else equal (for the same output level) a price discriminating monopolist will set a higher price for consumers who face a less elastic demand curve. This makes perfect sense, because this consumer group is less sensitive to price changes. For example restaurants typically charge lower prices to senior citizens for the same product served to other consumers primarily because seniors are thought to be highly price sensitive given that they receive a fixed income. Mathematical support of this notion is provided by the following:
Since price discrimination occurs when MR1=MCm=MR2 and as proved earlier the value of marginal revenue is as follows
MRk=Pk(1-(1/| k|)),
where k indexes consumer groups and represents the own price demand elasticity, then the following holds:
P1(1-(1/|1|)) = P2(1-(1/|2|)) or P1/P2= (1-(1/|2|))/(1-(1/|1|))
This equation suggests that the price ratio is less than one if the demand elasticity for consumer group 1 is less than that of consumer group two. In other words P1 is less than P2 if the demand curve for consumer group two is more elastic than that for consumer group one.
The type of price discrimination that we have just examined is termed 3rd degree price discrimination because prices are only set for two consumer groups. A second category of price discrimination is depicted if prices were set for some number of consumer groups greater than two but not such that each consumer faced a different price. This example is presented in Figure 9.E. Note that the monopolist is able to further increase producer surplus at the expense of consumers. Indeed the remaining consumer surplus depicted in Figure 9.E is the sum of the triangles A, B and C. A practical example of second degree price discrimination is the setting of different utility prices throughout the day.
Figure 9.D
$
P2 MC
P1
MCm
D1 D2 D1 + D2
MR1 MR2 MR1+ MR2
q
Figure 9.E
$
A
P2 MC
B
P1
Pe C
Demand
q2 q1 qe
q
Lastly, another category of price discrimination is first degree price discrimination. This type of discrimination occurs when a seller charges each consumer their reservation price. Hence, the seller receives all of the producer surplus. This is depicted by Figure 9.F. A practical example of this is the approach used to sell autos or appliances, in which sales people allow for haggling over prices. It should be noted, however, that engaging in this practice generates extra cost for the firm since products that are not sold using such methods do not require the employment of large sales forces.
Figure 9.F
$
Additional MC
Producer
Surplus
Pe
Demand
qe q