Chapter 23. Monopoly

Transcription

1 Chapter 23 Monopoly We will now turn toward an analysis of the polar opposite of the extreme assumption of perfect competition that we have employed thus far. 1 Under perfect competition, we have assumed that industries are composed of so many small firms that each firm has no impact on the economic environment in which decisions are made. As a result, we could assume that individual firms in an industry simply take the market price as given as they determine how much to produce in order to maximize profits. In the case of a monopoly, on the other hand, the firm must make a decision not only on how much to produce but also on what price to charge. There is, in the case of monopoly, no market to set the price. In this sense, the monopolist has some control over her economic environment (i.e. prices) that the competitive producer lacks. While we will often talk about a monopoly as if it was a fixed concept, it is important to keep in mind that monopoly power comes in more and less concentrated doses. Under perfect competition, the demand that a firm faces for its product is perfectly elastic because of the existence of many firms that produce the same product at the market price. Whenever a firm faces a demand curve for its product that is not perfectly elastic, it has some market power. For instance, I might produce a particular soft drink in a largely competitive market for soft drinks, but my soft drink is nevertheless a bit distinctive. In a sense, my soft drink is therefore a separate product with a separate market, but in another sense it is part of a larger market in which other firms produce close but imperfect substitutes. The demand curve for my soft drink may then not be perfectly elastic giving me some market power, but that power is limited by the fact that there are close substitutes in the larger soft drink market. If, on top of the existence of close substitutes, there is free entry into the soft-drink market, my market power is limited even more. We will treat this type of market in Chapter 26 as one characterized by monopolistic competition. In other settings, of course, there is less of an availability of substitutes for a particular firm s product. If there are market entry barriers that keep potential competitors from producing substitutes, my monopoly power would then be considerably more pronounced, and the demand for my product considerably less elastic. For now, we will simply treat monopolies as firms that face downward sloping demand curves in an environment where barriers to entry keep other firms from entering to produce substitute goods, and we will simply keep in mind that the elasticity of demand 1 This chapter presumes a basic understanding of demand and makes frequent references to the partial equilibrium models of Chapters 14 and 15. It furthermore presumes a basic understanding of cost curves as derived in Chapter 11 and summarized in Section 13A.1 of Chapter 13.

2 856 Chapter 23. Monopoly for the monopoly s product is closely connected to just how powerful a monopoly we are dealing with. When we get to Chapter 26, it will become clear that the stark model of monopoly in this chapter is an extreme model that rarely holds fully in the real world, but it gives us a good starting point to talk about market power just as perfect competition gives us a useful starting point to talk about competition. 23A Pricing Decisions by Monopolist We begin our analysis of monopoly power by analyzing how the profit maximizing condition of marginal revenue being equal to marginal cost translates into optimal firm decision making when a firm faces a downward sloping demand curve. At first, we ll assume that the firm is restricted in its pricing policy in the sense that it can only set a single price per unit of output a single price that is charged to every consumer. We then proceed to think about how a monopoly might want to differentiate the price it charges to different consumers and under what conditions that is possible. Finally, we will talk explicitly about what kinds of barriers to entry might in fact result in real-world monopolies, and how the nature of the barrier to entry might determine the extent to which we think monopoly power is a problem that requires government intervention. Before moving on, however, recall the two ways in which we thought about profit maximization for price taking firms in Chapter 11. We first set up the profit maximization problem under the assumption that the competitive firm takes price as fixed and solved for the profit maximizing production plan by finding the tangency between isoprofit curves with production frontiers. This method no longer holds for monopolists because the method presumed a fixed price that the price setting firm simply took as given. We then developed a two-step profit maximization method with the first step focusing solely on the cost side (where firms attempt to minimize cost) and the second step adding revenue considerations (given the price that competitive firms take as given). Since output price plays no role in the cost-minimizing problem where the firm simply asks what is the least cost way of producing different levels of output, this step is the same for monopolists. The difference enters in the second step where we compare revenue to cost with revenue for the monopolist depending on the price that the monopolist chooses (rather than the price that is set by the market). We can therefore use everything we learned about cost curves marginal costs, average costs, recurring fixed costs, etc. and will thus focus on step 2 of the two-step profit maximization method in analyzing monopoly decisions. 23A.1 Demand, Marginal Revenue and Profit For competitive producers, price is the same as marginal revenue. Put differently, the competitive producer knows that she can sell any amount of the good she could feasibly produce at the market price, and so the marginal revenue she receives for each good she produces is simply the price set by the interactions of producers and consumers in market equilibrium. She could, of course, choose to sell her goods at a lower price, but that would not be profit maximizing. If, on the other hand, she tries to sell her goods at a price above the market price, consumers will simply shop at a competitor. While the market demand curve in competitive markets is therefore downward sloping, the demand curve for each competitive producer is perfectly elastic at the market price. For a monopolist, however, the market demand is the same as the firm s demand since the monopolist is the only producer in the market. As a result, the monopolist gets to choose a point on the market demand curve which involves a simultaneous choice of how much to produce and

3 23A. Pricing Decisions by Monopolist 857 how much to charge. When a monopolist decides to increase output, she therefore confronts the following trade-off: On the one hand, she gets to sell more goods to consumers, but on the other hand she sells all her goods at a lower price than before. Thus, as a monopolist increases output, her marginal revenue is not equal to the price she charged initially because she will have to lower price in order to sell the additional output. 23A.1.1 Marginal Revenue along a Market Demand Curve Suppose we consider a demand curve first illustrated in Graph 18.3 in Chapter 18 and replicated here as Graph 23.1a. The first unit produced by a monopolist facing such a market demand for her goods can be sold for approximately $400. Thus, the marginal revenue for the first unit of output is approximately $400. Next, suppose the monopolist was currently producing 199 units of the output for $ each. Were this monopolist to produce two additional units of output, she would have to lower her price to $ in order to sell all 201 goods. She would therefore experience an increase in her total revenues of $599 for the 200th and 201st good, but she would simultaneously lose $1 on each of the first 199 goods she is producing. Her marginal revenue from producing two additional units is therefore $400, or approximately $200 for each of the two units. Graph 23.1: Linear Demand and Marginal Revenue Next, suppose that the monopolist was producing 399 units, selling each at $200.50, and suppose she considered producing two additional units. She would then have to lower the price to $ in order to sell the additional two units, earning an additional revenue of $399 on those units but losing $399 on the units she previously produced because she had to lower the price by $1 for each of the 399 units. Thus, her marginal revenue from producing two additional units is 0. The marginal revenue curve for this monopolist is then depicted in panel (b) of Graph It begins at the same point as the demand curve because the marginal revenue of the first good is approximately $400. When the monopolist is at approximately point B on the market demand curve, we demonstrated above that her marginal revenue from producing an additional unit is approximately $200, and when the monopolist is at approximately point A on her demand curve,

4 858 Chapter 23. Monopoly her marginal revenue from producing an additional unit is approximately 0. Connecting these gives us the blue line that shares the intercept of the demand curve but has twice the slope. Exercise 23A.1 What is the marginal revenue of producing an additional good if the producer is at point C on the demand curve in Graph 23.1? 23A.1.2 Price Elasticity of Demand and Revenue Maximization You can already see in Graph 23.1 that marginal revenue is positive when price elasticity is below -1, becomes zero as the price elasticity of demand approaches -1 (and becomes negative when price elasticity lies between -1 and 0). This implies that total revenue for the monopolist increases as she moves down the demand curve until she reaches the midpoint where price elasticity is equal to -1, and total revenue falls if she moves beyond that midpoint into the range of the demand curve where price elasticity is between -1 and 0. As a result, the maximum revenue the monopolist can raise occurs at the midpoint of a linear demand curve where price elasticity is equal to -1. Exercise 23A.2 Where does MR lie when price elasticity falls between -1 and 0? This is closely related to our discussion of consumer spending and price elasticity in Chapter 18. In Graph 18.4, we illustrated that consumer spending rises with an increase in price along the inelastic portion of demand while it falls with an increase in price along the elastic portion of demand. For the monopolist, consumer spending is the same as revenue. Thus, if a monopolist finds herself on the inelastic portion of demand, she knows she can increase revenue by raising the price. If, on the other hand, she finds herself on the elastic portion of demand, she can increase revenue by lowering price. Consumer spending and thus revenue is therefore maximized when price elasticity of demand is exactly -1. Exercise 23A.3 Where does a monopolist maximize revenue if she faces a unitary elastic demand curve such as the one in Graph 18.5? 23A.1.3 Profit Maximization for a Monopolist Like all producers, however, monopolists do not maximize revenue they try to maximize profit which is economic revenue minus economic costs. Thus, in order for us to see what combination of price and quantity a monopolist will choose (assuming she produces at all), we need to know not only marginal revenue but also marginal cost. First, suppose that the marginal cost of producing is zero. In that case, the monopolist s MC curve is a flat line that lies on the horizontal axis on Graph 23.1b, intersecting the MR curve at 400 units of output. If the monopolist has no variable costs, maximizing revenue and maximizing profit is exactly the same thing and so the monopolist would simply choose point A on the demand curve where price elasticity is exactly equal to -1. By selling 400 units at $200 each, revenue and profit (not counting recurring fixed costs) is then equal to $80,000. So long as recurring fixed costs are not larger than $80,000, the monopolist would then choose to produce 400 units of output in both the short and the long run. Exercise 23A.4 True or False: If recurring fixed costs are $40,000, then the monopolist will earn $80,000 in short run economic profit and $40,000 in long run economic profit.

5 23A. Pricing Decisions by Monopolist 859 Next, suppose that the monopolist has the more common U-shaped MC curve depicted in Graph 23.2a. If this monopolist produces a positive quantity, she will choose the quantity x M where MC intersects MR and charge the price p M that allows her to sell everything she is producing. So long as the short run average (variable) cost at x M is less than p M, this implies the monopolist will in fact produce in the short run, and so long as average long run cost (including recurring fixed costs) at the quantity x M lies below p M, she will produce in the long run. Graph 23.2: Profit Maximization for a Monopolist Exercise 23A.5 Suppose MC is equal to $200 for all quantities for a monopolist who faces a market demand curve of the type in Graph At what point on the demand curve will she choose to produce? The first thing we can then observe is that, whenever MC is positive, a monopolist will choose to produce on the elastic part of demand. This is because, for any positive MC, the intersection of MC and MR must lie to the left of the intercept of MR with the horizontal axis which in turn occurs where price elasticity is exactly equal to -1. This should make intuitive sense: We know that, if a monopolist ever finds herself on the inelastic portion of demand, she can raise revenue by increasing price and producing less. If producing costs something, this implies that, whenever a monopolist is on the inelastic portion of demand, she can raise revenue and reduce costs by producing less and charging a higher price. As a result, it makes no sense for a monopolist to produce on the inelastic portion of demand. Exercise 23A.6 Suppose a deep freeze causes the Florida orange crop to be reduced by 50% causing the price for oranges to increase. As a result, we observe that the total revenues of Florida orange growers increases. Could the Florida orange industry be a monopoly? (Hint: The answer is no.) Second, the concept of a supply curve that we developed for competitive firms does not make any sense when we talk about monopolists. A supply curve illustrates the relationship between the price set by the market and the quantity of output produced by a profit maximizing firm. But a monopolist does not have a market that sets price the monopolist herself sets the price. Thus,

6 860 Chapter 23. Monopoly for any given demand curve and any technology that results in cost curves, the monopolist simply picks a supply point. 23A.1.4 Monopoly and Dead Weight Loss Finally, we can see in Graph 23.2 that the profit maximizing monopolist will produce an inefficiently low quantity. In panel (b) of the graph, consumer surplus (assuming no income effects) can be identified as area (a + b) and monopolist surplus (in the short run, or in the absence of recurring fixed costs) as area (c + d). But there are additional units of output that could be produced at a marginal cost below the value consumers place on that output. Such additional output could be produced all the way up to the intersection of MC and demand at output x, and additional surplus of (e) could be produced if a benevolent social planner rather than a monopolist were in charge of production. Thus, area (e) is a deadweight loss which arises because the monopolist strategically restricts output in order to raise price to its profit maximizing level. Notice that the deadweight loss does not arise because the monopolist makes a profit. Even if a social planner forced the monopolist to produce the quantity x and sell it at the appropriate price along the demand curve, the monopolist might make a profit it just would not be as large as it is when the monopolist raises price to p M and restricts output. Rather, the deadweight loss emerges from the fact that the monopolist is using her power to strategically restrict output in order to raise price. The monopolist s market power then causes self-interest to come into conflict with the social good at least when the social good is measured in efficiency terms unless something else interferes and causes the monopolist to produce more. Exercise 23A.7 Suppose that demand is as depicted in Graph 23.1 and MC=0. What is the monopolist s profit maximizing output level and what is the efficient output level? What if MC=300? Exercise 23A.8 True or False: Depending on the shape of the MC curve, the efficient output level might lie on the elastic or the inelastic portion of the demand curve. Exercise 23A.9 True or False: In the presence of negative production externalities, a monopolist may produce the efficient quantity of output. Exercise 23A.10 True or False: If demand were not equal to marginal willingness to pay (due to the presence of income effects on the consumer side), the deadweight loss area may be larger or smaller but would would nevertheless arise. 23A.1.5 Monopoly Rent Seeking Behavior and Dead Weight Loss We have demonstrated that monopolists are able to achieve economic profits if they have indeed secured monopoly power in some way. We have furthermore demonstrated that this economic profit comes at a social cost as the monopolist produces below the socially optimal level in order to raise price above marginal cost and we have denoted that social cost as deadweight loss. The actual deadweight loss may, however, be larger than what we have derived thus far because firms may engage in socially wasteful activity in order to secure and maintain the monopoly power that gives them the opportunity to generate economic profits. There are a variety of ways in which barriers to entry that lead to monopoly power can arise, and we will say more about this later on in this chapter. One possibility, for instance, is that monopoly power is granted through government intervention with governments granting to a single firm

7 23A. Pricing Decisions by Monopolist 861 the exclusive right to produce a certain product. In such circumstances, firms may compete for such government favor in the process expending resources on lobbying politicians. The maximum amount that a firm would be willing to invest in order to secure a government granted monopoly is then equal to the present discounted value of the future profits the firm can expect to make from exercising its monopoly power. It is therefore conceivable that firms will expend resources equal to their monopoly profits in order to get the monopoly power, and it is similarly conceivable that much of these resources are spent in socially wasteful ways. This is referred to as political rent seeking i.e. the seeking of rents or profits in the political arena. To the extent to which the resources spent on political rent seeking are socially wasteful, this would add to deadweight loss beyond what we have derived in our graphs thus far. 23A.2 Market Segmentation and Price Discrimination So far, we have assumed that the monopolist is constrained in the sense that she can only charge a single price to all of her customers. This is the case when a monopolist cannot effectively differentiate between consumers and their marginal willingness to pay for her product, or when charging different prices to different consumers is illegal. In this section, we will suppose that charging different prices to different consumers a practice known as price discrimination, is permitted and that the monopolist can segment the set of consumers into those that are willing to pay relatively more and those that are willing to pay relatively less. Even when a monopolist can segment the market into different types of consumers, however, she must have some way of preventing resale to keep those consumers that purchase the product at a low price from selling to those that are being offered the same product at a higher price. Below, we will illustrate three different ways in which monopolists may price discriminate under different circumstances. We will begin with the case where monopolists can perfectly identify each consumer s demand and can offer each consumer a particular quantity at a particular overall price for that quantity. This is known as perfect (or first degree ) price discrimination. Then we will consider a case where the monopolist, while still being able to identify each consumer s demand perfectly, can offer different per-unit prices to different customers who potentially want to buy multiple units of the good. We will call this imperfect (or third degree ) price discrimination. Finally, we will consider the case where a monopolist knows that there are different types of consumers with different demands but she does not know what type each particular consumer is. We will see that the monopolist can then construct price/quantity packages that cause customers to reveal their type, a practice known as second degree price discrimination. 23A.2.1 Perfect (or First Degree ) Price Discrimination We can begin with another extreme assumption: Suppose that the monopolist knows all of her customers extremely well and can thus perfectly ascertain each consumer s willingness to pay for her product. For example, suppose that I am an artist that has his own studio and gallery. I am the only one who produces my unique type of art, and I know my customers personally and invite them individually to sip snooty wine while pretentiously gazing at my art. To make the analysis as simple as possible, let s further suppose that each of my clients will buy a single piece of art from me. (After all, my art is so special that owning a single piece produces complete intoxication as my clients spend all their time simply gazing at their wall to view it.) The demand curve for my art is then composed of many different individuals who each place a certain value on one of my pieces of art. As I produce my art, I can therefore invite first the

8 862 Chapter 23. Monopoly individual who places the most value on my art and who therefore sits at the very top of the demand curve that I face. Suppose this individual of impeccable taste places a value of $10,000 on my art. In that case, I will charge that individual exactly $10,000. Next, I invite my second biggest fan who might place a value of only $9,900 on my art. I can then sell a piece of art to this individual for exactly $9,900. My marginal revenue for the first piece was $10,000, and my marginal revenue for the second piece was $9,900. Since I can charge different prices to each of my clients, I can therefore produce a second piece of art without foregoing any profit on the first piece. As a result, the demand curve becomes my marginal revenue curve when I can price discriminate perfectly between all my clients. Graph 23.3 illustrates the behavior by a profit maximizing producer who can perfectly price discriminate in this way. Since demand is equal to M R, this producer simply chooses to produce x M where MC intersects demand. No single price is charged as each consumer is charged exactly what she is willing to pay along the market demand curve. Consumers therefore attain no surplus and all the surplus, equal to the shaded area, accrues to the monopolist. In the process, the efficient quantity is supplied with any additional quantity costing more than the level at which it is valued in society. Graph 23.3: Perfect Price Discrimination This form of perfect price discrimination is also referred to as first degree price discrimination. While it leads to an efficient quantity of output, it clearly leaves consumers worse off than the non-price discriminating outcome in the previous section. This is because consumers now attain no consumer surplus while they do attain some consumer surplus (albeit at a lower output level) when there is no price discrimination. Efficiency is, as we know, a statement about the maximum overall surplus and says nothing about whether the distribution of the surplus is desirable. Exercise 23A.11 * We simplified the analysis by assuming that each person will buy only 1 piece of art. How would you extend the idea of perfect price discrimination (resulting in demand being equal to marginal revenue) to the case where consumers bought multiple pieces? (The answer is provided in the next section.) 23A.2.2 Imperfect or Third Degree Price Discrimination Perfect price discrimination assumes that a monopolist can not only identify perfectly each type of consumer s demand but can also charge an amount that is exactly equal to each consumer s total

9 23A. Pricing Decisions by Monopolist 863 willingness to pay. In our somewhat artificial example of my art studio, we had assumed that each consumer only demands one piece of art (implicitly assuming that the marginal value of the second piece is zero for each consumer). As a result, perfect price discrimination meant that I simply arrived at an individualized price equal to exactly each consumer s willingness to pay for one piece of art. More generally, consumers have downward sloping demand curves and thus place value on more than one unit of output. Consider, for instance, two types of consumers whose demands are given as D 1 and D 2 in panels (a) and (b) of Graph Suppose further that the producer faces a constant marginal cost of $10 per unit of output. Under perfect price discrimination, the producer would sell 200 units of the output to type 1 consumers and 100 units of the output to type 2 consumers, and she would charge type 1 consumers the entire shaded blue area in panel (a) and type 2 consumers the entire shaded magenta area in panel (b). Thus, when consumers place value on more than one good, perfect price discrimination implies that the monopolist will not charge a per unit price but rather a single price for all the units sold to a consumer together. Graph 23.4: Imperfect ( Third Degree ) Price Discrimination Exercise 23A.12 We might also think of the perfectly price discriminating firm as charging what is called a two-part tariff which consists of a fixed payment that is independent of the quantity a consumer buys and a per-unit price for each unit purchased. Can you identify in the graph above which portion would be the fixed payment and what would be the per unit price for each of the two consumers? In many situations, this seems rather unrealistic. Instead, it might be that a monopolist who can identify different types of consumers is restricted to charging a per-unit price for the goods a price that can differ for different types of consumers but remains constant for any amount a particular consumer chooses to purchase. If this is the case, the monopolist can no longer perfectly price discriminate but will rather price discriminate imperfectly. Such price discrimination is also known as third degree price discrimination.

10 864 Chapter 23. Monopoly For our example in Graph 23.4, this would imply that the monopolist determines the marginal revenue curve for each of the two types of consumers and then sets output where the constant MC intersects MR. This leads the monopolist to charge the price p 1 to type 1 consumers, with those consumers choosing to consume x 1 (in panel (a)). Similarly, a potentially different price p 2 would be charged to type 2 consumers who would then consume x 2 (in panel (b)). Thus, when monopolists can charge a per unit price that differs across identifiable consumer types, they will restrict output below what it would be under efficient first degree price discrimination. As a result, a deadweight loss will arise under imperfect (or third degree) price discrimination. Exercise 23A.13 In our example of me running my art studio and selling to consumers who place value only on the first piece of art they purchase, is there a difference between first and third degree price discrimination? Explain. (Hint: The answer is no.) While we therefore know that deadweight loss will emerge under third degree price discrimination, it is not clear whether eliminating the ability by the monopolist to price discriminate in this way will lead to greater or less deadweight loss. If such price discrimination were deemed illegal, the monopolist would revert to charging a single price to all consumers which would entail a lower price for the high demanders and a higher price for the low demanders. Conceivably, this uniform price could be such that low demanders will no longer consume any of the good, thus leading to the effective closing of the market in the low demand consumer sector. The welfare losses sustained by low demanders combined with the reduction in profit for monopolists would then have to be weighed against the welfare gains by high demanders. Depending on the types of demand the different consumers have, the elimination of third degree price discrimination could then lead to either a welfare improvement (if the high demanders gain more than the low demanders and the monopolist lose) or an additional welfare loss (if the low demanders and the monopolist lose more than the high demanders gain). Without knowing the specifics in any particular case of third degree price discrimination, it is therefore not possible to make a uniform efficiency-based policy recommendation on how to treat monopolists who engage in third degree price discrimination. Exercise 23A.14 Why do we not run into similar problems of ambiguity in thinking about the welfare effects of first degree price discrimination? 23A.2.3 Non-Linear Pricing and Second Degree Price Discrimination Sometimes there are external signals that a firm can use to infer the type of consumer she is facing. Movie theaters know that students will generally have different demands than adults in the labor force, and they may therefore offer student prices that are different from regular prices (and not available to non-students). This is an example of third degree price discrimination. But in many real world circumstances, firms do not have such external signals and therefore are unsure of what types of consumers they face at any given moment. Put differently, it is often difficult to tell by just looking at someone whether that person is a high demander or a low demander even if a firm knows how many high demanders there are relative to low demanders. Even in such cases, however, the monopolist can try to find ways of increasing profit through strategic pricing. But since the monopolist cannot tell what type of consumer she is facing, she has to structure her pricing in such a way as to give the incentive to consumers to self-identify who they are. This involves the setting of a single non-linear price schedule or offering different quantities of the good at different prices. Such a pricing strategy does not explicitly discriminate between different consumers because all consumers are offered the same price schedule for different

11 23A. Pricing Decisions by Monopolist 865 quantities of the good. Rather, consumers end up paying different average prices based on their choices once they see the non-linear price schedule posted by the monopolist. Suppose, for instance, that the monopolist knows that she has two types of customers just as in Graph 23.4 in the previous section. But now she cannot tell in any particular instance which type of consumer has entered her store; all she knows is that there is an equal number of both types of consumers in the economy. In Graph 23.5a, we then illustrate the blue type 1 demand curve D 1 and the magenta type 2 demand curve D 2 within the same picture and again assume a constant marginal cost of $10 per unit of output. If the monopolist could price discriminate perfectly, she would want to offer 200 units of output to type 1 consumers and charge the entire area under D 1 ($ a + b + c). Similarly, she would want to offer 100 units of the output to type 2 consumers and charge the entire area under D 2 ($1000+a). This would result in no consumer surplus and a surplus for the monopolist of (2a + b + c) assuming there is one consumer of each type. Graph 23.5: Second Degree Price Discrimination Exercise 23A.15 Explain how this represents separate two-part tariffs for the two consumer types (as defined in exercise 23A.12). When the monopolist cannot tell which consumers are type 1 and which are type 2, she cannot

12 866 Chapter 23. Monopoly implement this perfect price discrimination (nor can she implement the third degree price discrimination from Graph 23.4). This is because type 1 consumers now have an incentive to simply pretend to be type 2 consumers, purchase 100 units at the price ($1000+a) and get consumer surplus of (b). Were the monopolist to offer the 100 and 200 unit packages at the prices suggested above, she could look ahead and know that no one will pick the 200 unit package, leaving her with surplus of only (2a). 2 Exercise 23A.16 Why would the monopolist not be able to offer two per-unit prices as in Graph 23.4? In order to induce type 1 consumers to behave differently than type 2 consumers, the monopolist must therefore come up with a different set of price/quantity packages. For instance, the monopolist might continue to offer 100 units at the price ($1000+a) while reducing the price of 200 units to ($2000+a + c). This would equalize the surplus a type 1 consumer will get under the two packages and would therefore make it optimal for type 1 consumers to pick 200 units. (In fact, the monopolist has to charge a price just under ($2000+a+c) for 200 units in order to insure that type 1 consumers will in fact strictly prefer the 200 unit package over the 100 unit package.) As a result, the monopolist would be able to expect a surplus of (2a + c) which is larger than the surplus of (2a) she could expect under the previous price/quantity combinations. Exercise 23A.17 In exercise 23A.12, we introduced the notion of a two-part tariff. Can you express the pricing suggested above in terms of two-part tariffs? In panel (b) of Graph 23.5, however, we can see that the monopolist can do even better by making the package targeted at type 2 consumers less attractive and thus charging more for the package containing 200 units. Consider, for instance, the scenario under which the monopolist offers a package with 90 units and another with 200 units. Type 2 consumers will be willing to buy the 90 units at a price of ($900+d). But now the monopolist can charge ($2000+d + f + g + h) for the 200 unit package giving an overall surplus of (2d + f + g + h). The surplus of (2a + c) in panel (a) is the same as a surplus of (2d + 2g + h) in panel (b) which implies that the monopolist s surplus has changed by (f g) as she switched from offering the 100 unit package to offering only a 90 unit package. Area (f) is larger than area (g) so profit has increased. But once the monopolist recognizes that she can earn higher profit by reducing the attractiveness of the package targeted at type 2 consumers, she can do even better. In panel (b) of the graph, the vertical magenta distance represents the approximate loss in profit from type 2 consumers if the monopolist decreases the type 2 package by another unit (from 90 to 89) while the vertical blue distance represents the approximate increase in profit from type 1 consumers that can now be charged a higher price for the 200 unit package. The monopolist can increase profit by reducing the type 2 package so long as the vertical magenta distance is shorter than the vertical blue distance. Thus, a forward looking monopolist would reduce the type 2 package to a quantity x (where the two distances are equal to one another). This is represented in panel (c) of the graph. Exercise 23A.18 What price will the profit maximizing monopolist charge for x and for 200 units in panel (c) of Graph 23.5? Exercise 23A.19 * We have assumed in our example that there is an equal number of type 1 and type 2 consumers in the economy. How would our analysis change if the monopolist knew that there were twice as many type 1 consumers as type 2 consumers? 2 In Chapter 24, we will introduce the idea of a sequential game in which some players move first. We could then say that the monopolist plays such a sequential game with consumers setting her pricing schedule in stage 1 knowing that consumers will optimize in stage 2.

13 23A. Pricing Decisions by Monopolist 867 Exercise 23A.20 In Chapter 22, we analyzed situations in which there is asymmetric information between consumers and producers (as in the insurance market). Can you see how the problems faced by an insurance company that does not know the risk-types of its consumers are similar to the problem faced by the monopolist who is trying to second-degree price discriminate? The above example is just one of many that might arise for a monopolist who seeks to offer different per-unit prices to different customers whose type she cannot identify. We will see further examples later on. In the real world, the packages offered to different types of consumers may also vary in ways that are related to not just quantity but also quality. For instance, in the airline industry, fares for the same flights are often priced quite differently for business travelers and leisure travelers, with business travelers facing fewer restrictions on when and how they can change their tickets. If these topics are of interest, you should consider taking a course in industrial organization. 23A.3 Barriers to Entry and Remedies for Inefficient Monopoly Behavior So far, we have simply assumed that a particular firm has a monopoly in the market for good x. But how does a firm get such monopoly status in the first place? And how does it hold onto it? We began to discuss this a bit in our brief section on political rent seeking and its implications for deadweight loss. In this section, we will try to dig a bit deeper and point out more explicitly that there must exist some barrier to entry of new firms in order for a monopoly to be able to earn long run positive profits. Such a barrier might emerge simply from the technological nature of production, from different types of legal barriers to entry that we introduced when thinking about political rent seeking or through other channels. 23A.3.1 Technological Barriers to Entry and Natural Monopolies In our discussion of perfectly competitive firms, we never considered the case of a firm that has increasing returns to scale for all output quantities. Rather, we focused on firms that may have increasing returns to scale in their production process for low levels of output but eventually face decreasing returns to scale as output increases. It is because of this assumption that MC and AC curves eventually sloped up. But, while we argued in Chapter 11 that the logic of scarcity requires that marginal product of each input eventually diminishes, there is no particular reason that the production process itself cannot have increasing returns to scale. Exercise 23A.21 Review the logic of how a production process can have diminishing marginal product of all inputs while still exhibiting increasing returns to scale. Now suppose the production process for good x always has increasing returns to scale. This implies, as we illustrated in Graph 12.9, that the MC curve is always downward sloping and always lies below AC, which further implies that any price taking firm will either produce nothing at a particular price or will produce an infinite quantity of the good. But, in a world of scarcity, consumers will not demand an infinite quantity of the good at a positive price which implies that the assumption of price taking behavior on the part of the firm is not reasonable under increasing returns to scale. It is for this reason that no competitive industry can have firms whose production process always has increasing returns to scale. Similar logic applies when a production process has a large initial or a significant recurring fixed cost together with a constant marginal cost, a case which is illustrated in Graph 23.6a. This can arise in many different contexts. For instance, a large investment in research and development may

14 868 Chapter 23. Monopoly be required prior to the production of a vaccine, but, once the research is complete, the vaccine can be produced easily at constant MC. Or a utility company might have to invest a large amount in laying electricity lines within a city in order to then be able to provide electricity to everyone at a constant MC. Or a software company might work for years to produce a piece of software that can then be offered at virtually no marginal cost by having customers download it from the internet. Graph 23.6: A Natural Monopoly A natural monopoly is then defined as a firm that faces an AC curve that declines at all output quantities. This declining AC curve can be due to increasing returns to scale everywhere or due to the presence of a recurring fixed cost with constant marginal cost. In either case, we cannot identify a supply curve that is equal to the MC curve above AC because MC never lies above AC. It is therefore natural for a single firm to emerge as a monopoly. Exercise 23A.22 Can you see in Graph 23.6a that a price taking firm facing a downward sloping AC curve would produce either no output or an infinite amount of the output depending on what the price is? Exercise 23A.23 Suppose the technology is such that AC is U-shaped but the upward sloping part of the U- shape happens at an output level that is high relative to market demand. Can the same natural monopoly situation arise? Panels (b) and (c) of Graph 23.6 then add demand and MR curves to the cost curves from panel (a). In panel (b), demand is relatively high, and the usual profit maximizing single price p M read off the demand curve at quantity x M where MC and MR intersect results in a positive profit for the monopoly firm. In panel (c), on the other hand, demand is relatively low causing the monopoly to make a loss if it simply produced where MR intersects MC. In order for a firm facing the situation in panel (c) to make a positive profit, it would therefore have to price output differently thus employing one of the price discrimination strategies discussed in the previous section. In the absence of being able to identify different consumer types, this implies that, in order to produce, the firm would have to engage in a form of pricing that involves more than just a single per-unit price. The most common such strategy for natural monopolists (in the absence of price regulation) is to charge a fixed fee plus a per unit price, which we referred to as a

15 23A. Pricing Decisions by Monopolist 869 two part tariff in exercise 23A.12. In the case of utility companies, for instance, there might be a fixed service fee per month plus a price per unit of electricity consumed. Because the technological constraints are such that multiple firms in such industries would entail higher per unit costs, governments have often favored regulation of natural monopolies over alternative policies to address the deadweight loss from monopoly pricing. Such regulation typically focuses on pricing policies that guarantee a fair market return for the natural monopolist while moving production closer to the socially optimal level. Given that the fixed cost is a sunk cost once the monopolist is operating, efficiency would require output where MC crosses the demand curve. But because AC lies above MC, forcing the natural monopolist to price the output at MC would imply negative profits for the monopolist (when profit is defined as long run profit that includes recurring fixed costs). Exercise 23A.24 In a graph similar to Graph 23.6b, illustrate the negative profit that arises when the monopolist is forced to price at MC. Exercise 23A.25 Suppose the fixed cost is a one-time fixed entry cost that is sufficiently large to result in a picture like panel (c). True or False: If the government pays the fixed cost for the firm, it will not have to regulate the firm in order to make sure the firm makes a profit but he monopoly outcome will be inefficient. For instance, suppose the monopolist faces high recurring fixed costs. Then regulators who attempt to achieve efficient output levels in natural monopolies might aim to set price at MC and allow monopolists to charge an additional fixed fee that each customer has to pay independent of the level of consumption. For instance, an electricity provider might charge a fixed hook up fee for connecting a household to the service and then a per unit price for each unit of electricity consumed, or a phone company might charge a fixed monthly fee plus a per minute charge for phone calls made. The fixed fees can then be set in such a way as to make the natural monopoly profitable even though the per-unit prices do not cover any of the fixed costs. Exercise 23A.26 Is this an example of a two-part tariff? Does it result in efficiency? While it is easy to see how this type of regulation works in principle, in practice the regulator unfortunately does not have all the required information to implement the optimal two-part pricing. In particular, the regulator does not typically know the cost functions of the natural monopoly, and the natural monopolist has every incentive to inflate her costs to the regulator in order to obtain higher fixed fees and higher per-unit prices. There are examples in the real world of natural monopolists devising clever schemes involving fake billing from secondary firms in order to show higher costs than they actually incur, and it is not always easy for regulators to identify such falsifications of cost records. The monopolist furthermore has no particular incentive to find innovative ways of lowering costs through technological innovations even if she is perfectly honest in how she reports the costs she actually incurs. For some of these reasons, more recent policy approaches have made an effort to introduce competition into some industries that face these cost curves by having the government pay the fixed costs that cause AC curves to be downward sloping. In the utility industry, for instance, the government could lay (and maintain) the electricity lines to all the houses in a city and then allow any utility company to use these lines in order to ship electricity to individual houses. It is much like the government laying a system of roads that different trucking companies can use to deliver goods. With the fixed costs paid by the government, individual electricity suppliers then have only variable costs and thus flat or upward sloping MC curves. It then becomes once

16 870 Chapter 23. Monopoly again possible for many different electricity providers to compete for households, with households choosing a provider based on quality of service and price. Exercise 23A.27 Suppose that instead a private company is charged with laying all the infrastructure and then charges competing electricity firms to use the electrical grid. How might this raise a different set of efficiency issues related to monopoly pricing? Would these issues still arise if the government auctioned off the right to build an electricity grid to a single private company? 23A.3.2 Legal Barriers to Entry While monopoly power can certainly arise from technological barriers that prevent several firms from operating simultaneously, it may alternatively arise from legal barriers. Such legal barriers might arise because of general patent and copyright laws that grant the exclusive right to produce particular products (for a certain number of years) to those firms that were awarded the patent or copyright. The motivation behind such laws is not to encourage the formation of monopolies but rather to provide incentives for innovations by ensuring that innovators can profit from their activities for some period. We will discuss the role of patents and copyrights in more detail in Chapter 26. Patent and copyright laws are not, however, the only legal barriers to entry. As we have seen, free entry (in the absence of technological barriers) tends to drive economic profits to zero. Thus, if a firm can successfully lobby the government to protect it from competitors, it will invest resources to accomplish this if the required resources are smaller than the present discounted value of the monopoly profits the firm can expect to earn if legal barriers to entry were erected. As we have already mentioned, to the extent to which such lobbying involves socially wasteful activities, the deadweight loss from government created monopolies may therefore exceed the loss due to the decline in production that results under monopoly profit maximization. Monopoly power has been granted by governments to a variety of firms throughout history. In the 15th and 16th centuries, for instance, the British Crown awarded exclusive rights to shipping companies to establish trade routes in the West Indies and other parts of the world. More recently, airlines routes were regulated in a similar manner, with airlines being assigned exclusive rights to certain routes within the US (prior to airline deregulation). The same was true until the 1970s in the trucking industry and the phone industry. Today, the US Post Office continues to hold the exclusive right to deliver first class mail, although the government now permits carriers like UPS and FedEx to deliver express packages and large ground packages. In each of these cases, you should be able to see how the firm that attained the exclusive rights to serve a particular market benefits from the governments entry barriers and how it might have a vested interest in engaging in socially wasteful lobbying activities in order to retain its monopoly power. 23A.3.3 Restraining Monopoly Power While governments have, as we have mentioned, been prime culprits for better or worse of granting monopoly power to certain firms, the increasing awareness of potential social losses from the exercise of monopoly power has also led to government policies aimed at restraining monopolies. The question of when and under what circumstances government intervention is desirable is a complicated one. The tendency of monopolies to limit output in order to raise price has the clear deadweight loss implications that we have discussed. At the same time, patent-protection of innovation may have led to the emergence of products that might otherwise never have seen the light

17 23A. Pricing Decisions by Monopolist 871 of day implying the creation of social surplus despite the fact that, at any given moment, more surplus could be gained by forcing monopolies to produce more. (We will have more to say about this in Chapter 26.) And the existence of increasing returns to scale in certain industries implies that natural monopolies may lower per unit costs even as they attempt to use their monopoly status to raise price above marginal cost. We will show in end-of-chapter exercise 23.9 that some of the potential remedies that one might think of applying to monopolies are either ineffective or counterproductive. These include per unit taxes and profit taxes. We have already discussed (in our treatment of regulation of natural monopolies) that attempts to directly regulate the pricing of monopoly goods run into informational constraints because regulators typically do not know the real costs of firms and because such regulation would give little incentive for cost innovations by monopolies. This does not imply that regulation in some circumstances is not the appropriate policy, but it does imply that regulation is no panacea in all cases. In some instances, governments have forced the break-up of monopolies (as in the case of large oil companies many years ago or large phone companies more recently), and in other cases they have found ways of addressing the root causes of natural monopolies by disconnecting the fixed cost infrastructure from the marginal cost provision of services. And in other cases, governments have actively blocked mergers of large companies that might have resulted in excessive monopoly power. Finally, there has been an increasing trend toward deregulation of industries where regulation itself (such as in the airline industry) created monopolies to begin with. If these topics seem interesting to you, you might consider taking a course on antitrust economics or law and economics. In many circumstances, however, the most effective tool for restraining monopoly power has little to do with direct government actions and more to do with the fact that, when a monopoly does exercise its power to create profit, there is a powerful incentive for entrepreneurs to find new ways to challenge that monopoly power. A firm may, for instance, have captured a large portion of the market, perhaps for no other reason than being first and making early, strategically smart decisions (as in the case of Microsoft and its Windows operating system). There is no doubt that such firms will use their monopoly power to their advantage, but they may also be more cognizant of the threat of competitors (that may find ways of producing substitutes) than our simple static models of monopoly behavior predict. The more a firm exercises its monopoly power, the greater is the incentive for others to find ways of producing such substitutes, and a forward looking monopolist should take that into account when setting current prices, as we will see in upcoming chapters. Sometimes barriers to entry that may seem rock-solid at one time can fall quickly with new technological innovations, as, for instance, with the sudden emergence of cell phone technology, internet calling and cable provision of telephone service that are challenging traditional phone companies. In such environments, governments can play in important role in insuring that existing firms (such as traditional phone companies) do not successfully erect barriers of entry through legislation or regulation (by prohibiting, for instance, cable companies or internet providers from providing telephone service). Just as there exists a powerful incentive for innovators to find ways of breaking barriers to entry by existing firms, there is a similarly powerful incentive on the part of existing firms to find other ways of shoring up these barriers to entry in order to preserve market power. Exercise 23A.28 In the 1970s when OPEC countries raised world prices for oil substantially by exercising their market power, the Saudi oil minister is said to have warned them: Remember, the Stone Age did not end because we ran out of stones. Explain what he meant and how his words relate to constraints that monopolies face.

18 872 Chapter 23. Monopoly 23B The Mathematics of Monopoly From a mathematical point of view, monopolies engage in the same optimization problem that competitive firms undertake except that monopolies have additional choice variables. Both types of firm face some cost function that emerges from the cost minimization problem and tells them the total cost c(x) of producing any quantity x. We should note at the outset that for much of our development below we will assume that dc(x)/dx = c i.e. the firm faces a constant marginal cost. This simplifies some of the analysis in convenient ways, and we will explore different marginal cost schedules in some of the end-of-chapter exercises. Exercise 23B.1 Explain why the cost minimization problem in the firm s duality picture is identical for firms regardless of whether they are monopolies or perfect competitors. A monopoly that is restricted to charging a single per-unit price then solves the problem maxπ = px c(x) subject to p p(x), (23.1) x,p where the price the monopolist charges when trying to sell the quantity x cannot be greater than the price for that quantity given by the inverse demand function p(x). The perfect competitor s problem could be written in exactly the same way, except that for the perfect competitor the inverse demand function is simply p(x) = p, where p is the market price. Thus, price ceases to be a choice variable when price is set by the competitive market, but it is a choice variable for a monopolist who faces a downward sloping demand curve. Since the monopolist will set price as high as she can while still selling all the goods she produces, the inequality in equation (23.1) will bind i.e. p = p(x). The monopolist s problem can therefore be re-written as max π = p(x)x c(x). (23.2) x Note that by choosing the optimal quantity x M, the monopolist implicitly chooses the optimal price p M = p(x M ) once we have substituted the constraint into the objective function of the optimization problem. And because of the resulting one-to-one mapping from quantity to price, the monopolist s problem could alternatively be written as maxπ = px(p) c(x(p)) (23.3) p where x(p) is the market demand function (as opposed to the inverse market demand function p(x) in the previous problem.) Whether we view the monopolist as choosing quantity as in equation (23.1) or price as in equation (23.3), the same monopoly quantity and price will emerge. When a monopolist is not restricted to charging a single per-unit price, she has additional decisions to make as we have seen in our discussion of price discrimination in Section A. The exact nature of that choice problem then depends on what the firm knows and what pricing strategies are available to the firm. If the firm can identify consumer types prior to consumption choices by consumers, first and third degree price discrimination become possible (assuming re-sale can be prevented), and if the firm only knows the distribution of consumer types in the population, second degree price discrimination becomes possible. Different forms of such discrimination are furthermore restricted by the types of pricing schedules that firms are permitted to post, as we will see a little later in the chapter. Fundamentally, however, the firm is still just maximizing profit by making production choices and potentially by engaging in strategic price differentiation.

19 23B. The Mathematics of Monopoly B.1 Demand, Marginal Revenue and Profit Suppose that the market demand facing a monopolist is of the form which gives rise to an inverse market demand x(p) = A αp, (23.4) p(x) = A α 1 x. (23.5) α For consistency, we will use this market demand specification repeatedly, both in this chapter as well as in the following chapters that deal with other market structures within which firms might operate. 23B.1.1 Marginal Revenue and Price Elasticity For the monopolist, total revenue is then equal to price times output, where price is determined by the inverse market demand curve; i.e. ( A TR = p(x)x = α 1 ) α x x = A α x 1 α x2. (23.6) In Section A, we argued verbally that the marginal revenue curve for a monopolist has the same intercept as the inverse demand curve but twice the slope. This is easily verified mathematically, with marginal revenue simply the derivative of TR with respect to output MR = dtr dx = A α 2 x. (23.7) α More generally, we can write the inverse demand function as p(x) and total revenue as TR = p(x)x. Using this expression, we can differentiate TR with respect to x to get MR = p(x) + dp x. (23.8) dx Now suppose we multiply the second term in equation (23.8) by (p(x)/p(x)). Then we can write the expression for MR as ( MR = p(x) 1 + dp dx x p(x) ). (23.9) Recall that the price elasticity of demand for an inverse demand function p(x) is given by ǫ D = (dx/dp)(p(x)/x), which is just the inverse of the second term in parenthesis in the above equation. Thus, we can write the expression for MR as ( MR = p(x) ). (23.10) ǫ D Suppose, for instance, that we are currently at the mid-point of a linear demand curve (such as the one in Graph 23.1a) where the price elasticity of demand is equal to -1. Equation (23.10) then tells us that marginal revenue at that point is equal to 0, precisely as we derived in panel (b) of Graph 23.1.

20 874 Chapter 23. Monopoly Exercise 23B.2 Use equation (23.10) to verify the vertical intercept of the marginal revenue curve in Graph 23.1b. 23B.1.2 Revenue Maximization In order to maximize total revenue T R, the monopolist would simply set M R equal to zero. Using equation (23.10) for MR, it follows immediately that revenue is maximized when ǫ D = 1. With the linear demand specified in equation (23.4), this implies an output level of A/2. Exercise 23B.3 Set up a revenue maximization problem for the firm. Then verify that this is indeed the revenue maximizing output level and that, at that output, ǫ D = 1. 23B.1.3 Profit Maximization The monopolist s profit maximization problem differs from revenue maximization in that costs are taken into account. This problem, already introduced at the beginning of this section, can be written as max π = p(x)x c(x), (23.11) x where c(x) is the total cost function (that is derived from the production function as described in our producer theory chapters earlier in the text). 3 Taking first order conditions, we get MR = p(x) + dp dx x = dc(x) = MC. (23.12) dx Exercise 23B.4 Can you use equation (23.10) to now prove that, so long as MC > 0, the monopolist will produce where ǫ D < 1? For instance, suppose that market demand is linear as specified in equation (23.4) and c(x) = cx. Then our MR = MC condition implies which further implies a monopoly output x M and price p M of x M = A αc 2 A α 2 α = c (23.13) and p M = A + αc 2α. (23.14) Exercise 23B.5 Illustrate that profit maximization approaches revenue maximization as MC = c approaches zero. Exercise 23B.6 Verify for the example of our linear demand curve and constant marginal cost c that it does not matter whether the firm maximizes profit by choosing x or p (as in the problems defined in equations (23.1) and (23.3) above). 3 Recall that the cost function is really a function of output x as well as input prices. We are suppressing the input price notation since input markets are not a focus for us here.