{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

24 Monopoly - CHAPTER 2 4 MONOPOLY In the preceding...

Info icon This preview shows pages 1–21. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
Image of page 15

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 16
Image of page 17

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 18
Image of page 19

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 20
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 2 4 MONOPOLY In the preceding chapters we have analyzed the behavior of a competitive industry, a market structure that is most likely when there are a large number of small firms. In this chapter we turn to the opposite extreme and consider an industry structure when there is only one firm in the industry—a monopoly. When there is only one firm in a market, that firm is very unlikely to take the market price as given. Instead, a monopoly would recognize its influence over the market price and choose that level of price and output that maximized its overall profits. Of course, it can’t choose price and output independently; for any given price, the monopoly will be able to sell only what the market will bear. If it chooses a high price, it will be able to sell only a small quantity. The demand behaviortof the consumers will constrain the monopolist’s choice of price and quantity. We can View the monopolist as choosing the price and letting the con— sumers choose how much they wish to buy at that price, or we can think of the monopolist as choosing the quantity, and letting the consumers decide what price they will pay for that quantity. The first approach is probably more natural, but the second turns out to be analytically more convenient. Of course, both approaches are equivalent when done correctly. 424 MONOPOLY (Ch. 24) 24.1 Maximizing Profits We begin by studying the monopolist’s profit—maximization problem. Let us use fly) to denote the market inverse demand curve and C(31) to denote the cost function. Let My) 2 p(y)y denote the revenue function of the monopolist. The monopolist’s profit—maximization problem then takes the form mgx Hy) — cry). The optimality condition for this problem is straightforward: at the 0p- timal choice of output we must have marginal revenue equal to marginal cost. If marginal revenue were less than marginal cost it would pay the firm to decrease output, since the savings in cost would more than make up for the loss in revenue. If the marginal revenue were greater than the marginal cost, it would pay the firm to increase output. The only point where the firm has no incentive to change output is where marginal revenue equals marginal cost. In terms of algebra, we can write the optimization condition as MR=MC OI' £E_€E Ay—Ay The same MR : M C condition has to hold in the case of a competitive firm; in that case, marginal revenue is equal to the price and the condition reduces to price equals marginal cost. In the case of a monopolist, the marginal revenue term is slightly more complicated. If the monopolist decides to increase its output by Ay, there are two effects on revenues. First it sells more output and receives a revenue of pAy from that. But second, the monopolist pushes the price down by Ap and it gets this lower price on all the output it has been selling. Thus the total effect on revenues of changing output by Ay will be Ar=pAy+yAa so that the change in revenue divided by the change in output—the mar- ginal revenuewis A?" Ap ___ l: p _+_ ___ . Ay Ay (This is exactly the same derivation we went through in our discussion of marginal revenue in Chapter 15. You might want to review that material before proceeding.) LINEAR DEMAND CURVE AND MONOPOLY 425 Another way to think about this is to think of the monopolist as choosing its output and price simultaneouslyrrecognizing, of course, the constraint imposed by the demand curve. If the monopolist wants to sell more output it has to lower its price. But this lower price will mean a lower price for all of the units it is selling, not just the new units. Hence the term yAp. In the competitive case, a firm that could lower its price below the price charged by other firms would immediately capture the entire market from its competitors. But in the monopolistic case, the monopoly already has the entire market; when it lowers its price, it has to take into account the effect of the price reduction on all the units it sells. Following the discussion in Chapter 15, we can also express marginal revenue in terms of elasticity Via the formula MRW) = My) [1 + $] and write the “marginal revenue equals marginal costs” optimality condi— tion as 1 pg 1+——-]=MCy. 24.1 ( > [ 6w) ( ) < ) Since elasticity is naturally negative, we could also write this expression as 1 29(9) [1- l=MC(y)- l€(y)l From these equations it is easy to see the connection with the competitive case: in the competitive case, the firm faces a flat demand curveaan in— finitely elastic demand curve. This means that 1/ {cl 2 1/00 : 0, so the appropriate version of this equation for a competitive firm is simply price equals marginal cost. Note that a monopolist will never choose to operate where the demand curve is inelastic. For if |e| < 1, then 1/ '6' > 1, and the marginal revenue is negative, so it can’t possibly equal marginal cost. The meaning of this becomes clear when we think of what is implied by an inelastic demand curve: if [6' < 1, then reducing output will increase revenues, and reducing output must reduce total cost, so profits will necessarily increase. Thus any point where {cl < 1 cannot be a profit maximum for a monopolist, since it could increase its profits by producing less output. It follows that a point that yields maximum profits can only occur where [El 2 1. 24.2 Linear Demand Curve and Monopoly Suppose that the monopolist faces a linear demand curve 10(9) = a — by- Figure 24.1 426 MONOPOLY (Ch. 24) Then the revenue function is 719) : p(y)y = ay — b312, and the marginal revenue function is fl/IRW) = a f 2by. (This follows from the formula given at the end of Chapter 15. It is easy to derive using simple calculus. If you don't know calculus, just memorize the formula, since we will use it quite a bit.) Note that the marginal revenue function has the same vertical intercept, a, as the demand curve, but it is twice as steep. This gives us an easy way to draw the marginal revenue curve. We know that the vertical intercept is a. To get the horizontal intercept, just take half of the horizontal intercept of the demand curve. Then connect the two intercepts with a straight line. We have illustrated the demand curve and the marginal revenue curve in Figure 24.1. PRICE AC Profits = In Demand (slope = —-b) (slope = «213) y* OUTPUT Monopoly with a linear demand curve. The monopolist’s profit-maximizing output occurs where marginal revenue equals marginal cost. MARKUP PRICING 427 The optimal output, 3/“, is where the marginal revenue curve intersects the marginal cost curve. The monopolist will then charge the maximum price it can get at this output, p(y*). This gives the monopolist a revenue of p(y*)y* from which we subtract the total cost c(y*) 2 AC(y*)y*, leaving a profit area as illustrated. 24.3 Markup Pricing We can use the elasticity formula for the monopolist to express its optimal pricing policy in another way. Rearranging equation (24.1) we have [email protected] [email protected])=fjjmfima mam This formulation indicates that the market price is a markup over marginal cost, where the amount of the markup depends on the elasticity of demand. The markup is given by 1 1 — 1/ |€(y)l‘ Since the monopolist always operates where the demand curve is elastic, we are assured that [6| > 1, and thus the markup is greater than 1. In the case of a constant-elasticity demand curve, this formula is espe- cially simple since 6(y) is a constant. A monopolist who faces a constant- elasticity demand curve will charge a price that is a constant markup on marginal cost. This is illustrated in Figure 24.2. The curve labeled M C/ (1 -— 1/ |e[) is a constant fraction higher than the marginal cost curve; the optimal level of output occurs where p : MC/(l — 1/|€l) EXAMPLE: The Impact of Taxes on a Monopolist Let us consider a firm with constant marginal costs and ask what happens to the price charged when a quantity tax is imposed. Clearly the marginal costs go up by the amOunt of the tax, but what happens to the market price? Let’s first consider the case of a linear demand curve, as depicted in Figure 24.3. When the marginal cost curve, M C , shifts up by the amount of the tax to M C +15, the intersection of marginal revenue and marginal cost moves to the left. Since the demand curve is half as steep as the marginal revenue curve, the price goes up by half the amount of the tax. This is easy to see algebraically. The marginal revenue equals marginal cost plus the tax condition is a—2by=c+t. 428 MONOPOLY (Ch. 24) PRICE yak OUTPUT Monopoly with constant elasticity demand. To locate the profit-maximizing output level we find the output level where the curve M C/ (1 — 1/ Id) crosses the demand curve. Solving for y yields fi (1 —- 0 ~ t y ‘ 2b ' Thus the change in output is given by Ag __ __ i At T 2b' The demand curve is p(y) = a — by, so price will change by —b times the change in output: Ap 1 1 —— = —b —~—— 2 —. At X 25 2 In this calculation the factor 1/2 occurs because of the assumptions of the linear demand curve and constant marginal costs. Together these as— sumptions imply that the price rises by less than the tax increase. Is this likely to be true in general? The answer is no—in general a tax may increase the price by more or less than the amount of the tax. For an easy example, consider the case of a monopolist facing a constant-elasticity demand curve. Then we have _ c—f—t 19‘ 1—1/|e|’ INEFFICIENCY OF MONOPOLY 429 PRICE After tax Before tax MC+t MC Demand y’ y" OUTPUT Linear demand and taxation. Imposition of a tax on a monopolist facing a linear demand. Note that the price will rise by half the amount of the tax. so that Ap _ 1 EUq/W which is certainly bigger than 1. In this case, the monopolist passes on more than the amount of the tax. Another kind of tax that we might consider is the case of a profits tax. In this case the monopolist is required to pay some fraction T of its profits to the government. The maximization problem that it faces is then m5): (1 — mph/)9 - C(11)]- But the value of 3; that maximizes profits will also maximize (1 — 7') times profits. Thus a pure profits tax will have no effect on a monopolist’s choice of output. 24.4 Inefficiency of Monopoly A competitive industry operates at a point where price equals marginal cost. A monopolized industry operates where price is greater than mar- ginal cost. Thus in general the price will be higher and the output lower Figure 24.4 430 MONOPOLY (Ch. 24) if a firm behaves monopolistically rather than competitively. For this rea— son, consumers will typically be worse off in an industry organized as a monopoly than in one organized competitively. But, by the same token, the firm will be better off! Counting both the firm and the consumer, it is not clear whether competition or monopoly will be a “better” arrangement. It appears that one must make a value judgment about the relative welfare of consumers and the owners of firms. However, we will see that one can argue against monopoly on grounds of efficiency alone. Consider a monopoly situation, as depicted in Figure 24.4. Suppose that we could somehow costlessly force this firm to behave as a competitor and take the market price as being set exogenously. Then we would have (pc, ya) for the competitive price and output. Alternatively, if the firm recognized its influence on the market price and chose its level of output so as to maximize profits, we would see the monopoly price and output (pm, ym). PRICE ym y}: OUTPUT Inefficienoy of monopoly. A monopolist produces less than the competitive amount of output and is therefore Pareto inef- ficient. Recall that an economic arrangement is Pareto efficient if there is no way to make anyone better off without making somebody else worse off. Is the monopoly level of output Pareto efficient? DEADWEIGHT LOSS OF MONOPOLY 431 Remember the definition of the inverse demand curve. At each level of output, p(y) measures how much people are willing to pay for an additional unit of the good. Since p(y) is greater than M C (y) for all the output levels between ym and ya, there is a whole range of output where people are willing to pay more for a unit of output than it costs to produce it. Clearly there is a potential for Pareto improvement here! For example, consider the situation at the monopoly level of output ym. Since p(ym) > M C (ym) we know that there is someone who is willing to pay more for an extra unit of output than it costs to produce that extra unit. Suppose that the firm produces this extra output and sells it to this person at any price p where p(ym) > p > M C (ym). Then this consumer is made better off because he or she was just willing to pay p(ym) for that unit of consumption, and it was sold for p <: p(ym). Similarly, it cost the monopolist M C (ym) to produce that extra unit of output and it sold it for p > M C(ym). All the other units of output are being sold for the same price as before, so nothing has changed there. But in the sale of the extra unit of output, each side of the market gets some extra surplus—each side of the market is made better off and no one else is made worse off We have found a Pareto improvement. It is worthwhile considering the reason for this inefficiency. The efficient level of output is when the willingness to pay for an extra unit of output just equals the cost of producing this extra unit. A competitive firm makes this comparison. But a monopolist also looks at the effect of increasing output on the revenue received from the inframarginal units, and these inframarginal units have nothing to do with efficiency. A monopolist would always be ready to sell an additional unit at a lower price than it is currently charging if it did not have to lower the price of all the other inframarginal units that it is currently selling. 24.5 Deadweight Loss of Monopoly Now that we know that a monopoly is inefficient, we might want to know just how inefficient it is. Is there a way to measure the total loss in efficiency due to a monopoly? We know how to measure the loss to the consumers from having to pay pm rather than pciwe just look at the change in consumers’ surplus. Similarly, for the firm we know how to measure the gain in profits from charging pm rather than pc~we just use the change in producer’s surplus. The most natural way to combine these two numbers is to treat the firmior, more properly, the owners of the firmfiand the censumers of the firm’s output symmetrically and add together the profits of the firm and the consumers’ surplus. The change in the profits of the firmethe change in producer’s surplus—measures how much the owners would be willing to pay to get the higher price under monopoly, and the change in 432 MONOPOLY (Ch. 24) consumers” surplus measures how much the consumers would have to be paid to compensate them for the higher price. Thus the difference between these two numbers should give a sensible measure of the net benefit or cost of the monopoly. The changes in the producer’s and consumers” surplus from a movement from monopolistic to competitive output are illustrated in Figure 24.5. The monopolist’s surplus goes down by A due to the lower price on the units he was already selling. It goes up by C dUe to the profits on the extra units it is now selling. PRICE MC P“ = monopoly price \ Competitive price —/ * y OUTPUT Deadweight loss of monopoly. The deadweight loss due to the monopoly is given by the area B + C. The consumers’ surplus goes up by A, since the consumers are now get- ting all the units they were buying before at a cheaper price; and it goes up by B, since they get some surplus on the extra units that are being sold. The area A is just a transfer from the monopolist to the consumer; one side of the market is made better off and one side is made worse off, but the total surplus doesn’t change. The area B + C represents a true increase in surplus—this area measures the value that the consumers and the producers place on the extra output that has been produced. The area B + C is known as the deadweight loss due to the monopoly. It provides a measure of how much worse off people are paying the mon— DEADWEIGHT LOSS OF MONOPOLY 433 opoly price than paying the competitive price. The deadweight loss due to monopoly, like the deadweight loss due to a tax, measures the value of the lost output by valuing each unit of lost output at the price that people are willing to pay for that unit. To see that the deadweight loss measures the value of the lost output, think about starting at the monopoly point and providing one additinal unit of output. The value of that marginal unit of output is the market price. The cost of producing the additional unit of output is the marginal cost. Thus the “social value” of producing an extra unit will be simply the price minus the marginal cost. Now consider the value of the next unit of output; again its social value will be the gap between price and marginal cost at that level of output. And so it goes. As we m0ve from the monopoly level of output to the competitive level of output, we “sum up” the distances between the demand curve and the marginal cost curve to generate the value of the lost output due to the monopoly behavior. The total area between the two curves from the monopoly output to the competitive output is the deadweight loss. EXAMPLE: The Optimal Life of a Patent A patent offers inventors the exclusive right to benefit from their inven— tions for a limited period of time. Thus a patent offers a kind of limited monopoly. The reason for offering such patent protection is to encourage innovation. In the absence of a patent system, it is likely that individuals and firms would be unwilling to invest much in research and development, since any new discoveries that they would make could be copied by com- petitors. In the United States the life of a patent is 17 years. During that period, the holders of the patent have a monopoly on the invention; after the patent expires, anyone is free to utilize the technology described in the patent. The longer the life of a patent, the more gains can be accrued by the inventors, and thus the more incentive they have to invest in research and development. However, the longer the monopoly is allowed to exist, the more deadweight loss will be generated. The benefit from a long patent life is that it encourages innovation; the cost is that it encourages monopoly. The “optimal” patent life is the period that balances these two conflicting effects. The problem of determining the optimal patent life has been examined by William Nordhaus of Yale University.1 As Nordhaus indicates, the prob— lem is very complex and there are many unknown relationships involved. Nevertheless, some simple calculations can give some insight as to whether 1 William Nordhaus, Invention, Growth, and Welfare (Cambridge, Mass: M.I.T. Press, 1969). 434 MONOPOLY (Ch. 24) the current patent life is wildly out of line with the estimated benefits and costs described above. Nordhaus found that for “run—of-the-mill” inventions, a patent life of 17 years was roughly 90 percent efficientAmeaning that it achieved 90 percent of the maximum possible consumers’ surplus. On the basis of these figures, it does not seem like there is a compelling reason to make drastic changes in the patent system. EXAMPLE: Patent Thickets The intellectual property protection offered by patents provides incentives to innovate, but this right can be abused. Some observers have argued that the extensions of intellectual property rights to business processes, software, and other domains has resulted in lower patent quality. One might think of patents as having three dimensions: length, width, and height. The “length” is the time that the patent protection applies. The “width” is how broadly the claims in the patent are interpreted. The “height” is the standard of novelty applied in determining whether the patent really represents a new idea. Unfortunately, only the length is easily quantified. The other aspects of...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern