MICRO Week 13 & 14
The Optimality Condition for a Monopolist
*Why Interest in the Marginal Revenue Curve?* [8.2 slide 10] The vertical distance between the short-run total cost and total revenue curves is greatest when the two curves are parallel *MR(Q)=MC(Q)* Suppose this were not the case. For example, suppose that at the maximum-profit point the total cost curve were steeper than the total revenue curve. It would then be possible to earn higher profits by producing less output, because costs would go down by more than the corresponding reduction in total revenue. Conversely, if the total cost curve were less steep than the total revenue curve, the monopolist could earn higher profits by expanding output, because total revenue would go up by more than total cost.
Monopoly
A market structure in which a single seller of a product with no close substitutes serves the entire market. A simply definition; but exceedingly difficult to apply in practice Is a local movie theater a monopoly? Depends on what we mean by a close substitute: - To casual moviegoers, a theater showing Halloween Part 8 is likely to have a rich variety of close substitutes (the market of low-grade blood-and-gore movies) - To Spiderman fans, a theater that is in the midst of an exclusive 6-month, first-run engagement of the latest Spiderman film has no close substitute
decrease output until marginal revenue equals marginal cost.
A monopolist is producing at a point at which marginal cost exceeds marginal revenue. How should it adjust its output to increase profit? The monopolist should
Patents
A patent typically confers the right to exclusive benefit from all exchanges involving the invention to which it applies. - Cost: higher price to consumers - Benefit: encourages inventions that would not otherwise occur US: 17 years. A compromise figure that is too long for many inventions, too short for many others. For prescription drug, for example, the testing and approval process often consumes all but a few years of the current patent period.
Monopoly
Average revenue equals price. The profit-maximizing output is the one at which marginal revenue and marginal cost are equal. The monopolist's demand curve is the same as the market demand curve. The profit-maximizing output is the one at which the difference between total revenue and total cost is largest.
higher; smaller
Compared to the equilibrium price and quantity sold in a competitive market, a monopolist will charge a ____________ price and sell a ___________ quantity.
Does Monopoly Profits Persist?
Economic profit sometimes tend to vanish in the long run for a monopolist. - To the extent that the factors that gave rise to the firm's monopoly position come under attack in the long run, there will be downward pressure on its profits. But in other cases there may be a tendency for monopoly profits to persist. - Natural monopoly due to declining LAC. As we saw in Chapter 10, economic profits tend to vanish in the long run in perfectly competitive industries. This tendency will sometimes be present for monopoly. To the extent that the factors that gave rise to the firm's monopoly position come under attack in the long run, there will be downward pressure on its profits. For example, competing firms may develop substitutes for important inputs that were previously under the control of the monopolist. Or in the case of patented products, competitors may develop close substitutes that do not infringe on existing patents, which are in any event only temporary. But in other cases there may be a tendency for monopoly profits to persist. The firm shown in Figure 11.12, for example, has a declining long-run average cost curve, which means that it may enjoy a persistent cost advantage over potential rivals. In such natural monopolies, economic profits may be highly stable over time. And the same, of course, may be true for a firm whose monopoly comes from having a government license.
Exclusive Control over Important Inputs
Examples: - Perrier bottled mineral water: exclusive control over a spring - DeBeers Diamond Mines' exclusive control over most of the world's supply of raw diamonds Not a guarantee of permanent monopoly: New ways are constantly being devised of producing existing products. The Perrier Corporation of France spends millions of dollars each year advertising the unique properties of this water. The commercials says the water is of a once-in-eternity confluence of geological factors that created their mineral spring. A similar monopoly position has resulted from the deBeers Diamond Mines' exclusive control over most of the world's supply of raw diamonds. Exclusive control of key inputs is not a guarantee of permanent monopoly power. The preference for having a real diamond, for example, is based largely on the fact that mined diamonds have historically been genuinely superior to synthetic ones. But assuming that synthetic diamonds eventually do become completely in-distinguishable from real ones, there will no longer be any basis for this preference. And as a result, deBeers' control over the supply of mined diamonds will cease to confer monopoly power. New ways are constantly being devised of producing existing products, and the exclusive input that generates today's monopoly is likely to become obsolete tomorrow.
The Monopolist's Total Revenue Curve
Facing the entire market demand curve, the monopolist must cut its price - not only for the marginal unit but for all preceding units as well - to sell a larger amount of output. Total revenue for the monopolist does not rise linearly with output. [8.2 slide 6] As an example, consider market demand P=80-1/5 Q For the monopolist to increase sales, it is necessary to cut price (top panel). Total revenue (π=PQ=80Q-1/5 Q^2) rises with quantity, reaches a maximum value, and then declines (middle panel). Price elasticity: ϵ=-5 P/Q=-400/Q+1 The quantity level for which the price elasticity of demand is unity corresponds to the midpoint of the demand curve, and at that value total revenue is maximized.
The Profit-Maximization Condition for a Monopolist
For any firm, when the firm produces, the profit-maximization condition is MR(Q)=MC(Q) For a monopolist, MR(Q)=ΔTR(Q)/ΔQ=P(Q)+(ΔP(Q))/ΔQ Q In particular, for a linear market demand P=t-kQ *MR(Q)=t-2kQ*
Marginal Revenue for a Monopolist: Any P(Q)
Generally, for any inverse demand function P(Q), when a monopolist raises output from Q_0 to (Q_0+ΔQ), the price drops from P_0 to (P_0+ΔP). (Note that ΔP is negative.) Two effects on his revenue 1. gain in revenue from new sales =(P_0+ΔP)ΔQ 2. loss in revenue from selling the previous output level at the new, lower price =ΔP ∙Q_0 The change in revenue at Q_0 due to this change ΔQ is ΔTR(Q_0)=(P_0+ΔP)ΔQ+ΔP ∙Q_0 The marginal revenue is MR(Q_0 ) = (ΔTR(Q_0))/ΔQ = ((P_0+ΔP)ΔQ+ΔP ∙Q_0)/ΔQ = (P_0+ΔP)+ΔP/ΔQ Q_0≈P_0+ΔP/ΔQ Q_0 The argument above holds for any Q_0 and P_0 on the demand curve, so we can drop the subscript 0 and write MR(Q) = P(Q)+(ΔP(Q))/ΔQ Q where P(Q) emphasizes that it is a function of Q. (ΔP(Q)) / ΔQ<0. Hence, the monopolist's marginal revenue at any output level is always less than the corresponding price
Five Sources of Monopoly
How does a firm come to be the only one that serves its market? Economists discuss five factors, any one or combination of which can enable a firm to become a monopoly. 1. Exclusive Control over Important Inputs 2. Economies of Scale 3. Patents 4. Network Economies 5. Government Licenses or Franchises
The Monopolist's Total Revenue Curve
Mathematically, for any form of P(Q) TR(Q)=P(Q)∙Q where ∙ denotes multiplication. For the example P(Q)=80-1/5 Q, TR(Q)=(80-1/5 Q)Q =80Q-1/5 Q^2 For the parabola y=ax^2+bx+c, the axis of symmetry is -b/2a. Apply the result here, the axis of symmetry is -b/2a=-80/2(-1/5) =200.
Government Licenses or Franchises
In many markets, the law prevents any-one but a government-licensed firm from doing business. - At rest areas on the Massachusetts Turnpike, the Turnpike Authority negotiates with several fast-food companies, chooses one, and then grants it an exclusive license to serve a particular area. (A scale economy acting in another form.) - Some airport authorities auction their terminal counter space to the highest bidders. The Turnpike's purpose in restricting access in the first place is that there is simply not room for more than one establishment in these locations. Price and government licenses Government licenses are sometimes accompanied by strict regulations that spell out what the licensee can and cannot do. Where the government gives a chain restaurant an exclusive license, for example, the restaurant will often be required to charge prices no more than, say, 10 percent higher than it charges in its unregulated outlets. •In other cases, the government simply charges an extremely high fee for the license, virtually forcing the licensee to charge premium prices. This is the practice of some airport authorities, who essentially auction their terminal counter space to the highest bidders. Your annoyance at having to pay $5 for a hot dog in LaGuardia Airport is thus more properly focused on the Port Authority of New York than on the vendor.
Adjustments in the Long Run
In the long run, the monopolist is of course free to adjust all inputs, just as the competitive firm is. What is the optimal quantity in the long run for a monopolist with a given technology? The best the monopolist can do is to produce the quantity for which long-run marginal cost is equal to marginal revenue.
Network Economies
On the demand side of many markets, a product becomes more valuable as greater numbers of consumers use it. - Ecosystem; - Microsoft's Windows operating system on personal computers: the inventory of available software and games is vastly larger than for any competing operating system. The more people who own the product, the higher its effective quality level. - Put different, any given quality level can be produced at lower cost as sales volume increases. - Thus can be viewed as another form of economies of scale
No Supply Curve For The Monopolist
Reason: the monopolist is not a price taker - There is no unique correspondence between price and marginal revenue when the market demand curve shifts - As a result, it is possible to observe the monopolist producing Q1* and selling at P*, and then selling Q2* at P* in another period - No unique correspondence between P and Q and thus no supply curve exists for the monopolist.
Compare to a Competitive Firm's Total Revenue Curve
Recall that a competitive firm is facing a horizontal demand curve for its products. P(Q)=P^∗ Hence, TR(Q)=P(Q)∙Q =P^∗ Q
Does Monopoly Result in Efficiency?
Recall the claim that perfect competition led to an efficient allocation of resources. - In a perfectly competitive equilibrium, there are no possibilities for additional gains from exchange. - The value to buyers of the last unit of output is exactly the same as the market value of the resources required to produce it. - The total surplus (consumer surplus + producer surplus) is maximized. How does the equilibrium under monopoly measure up by the same criteria?
Marginal Revenue and Elasticity
Recall the price elasticity of demand ϵ = ΔQ / ΔP P/Q Implies: ΔP/ΔQ = 1/ϵ P/Q Hence MR(Q) = (1+1/ϵ)P(Q)
Review: Supply Curves of Competitive Firms
The competitive firm has a well-defined supply curve. It takes market price as given and responds by choosing the output level for which marginal cost and price are equal. At the industry level, a shifting demand curve will trace out a well-defined industry supply curve, which is the horizontal summation of the individual firm supply curves Can we derive a supply curve for a monopolist? (8.3 video)
Example: A Competitive Firm's Marginal Revenue
The demand curve facing a competitive firm is horizontal: • P(Q)=P^∗ • (ΔP(Q))/ΔQ=0 Hence, MR(Q) = P(Q)+ΔP(Q)/ΔQ Q = P^∗+0×Q = P^∗
The Key Feature that Differentiates the Monopoly from the Competitive Firm
The feature is the price elasticity of demand facing the firm For the perfectly competitive firm, price elasticity is infinite: each firm faces a horizontal demand curve for its products. A monopoly faces the market demand curve and thus has significant control over the price it charges.
Concept Check
The market demand for a local movie theater tickets is Q=100-1/2 P. Suppose the market is a monopoly. What is the theater's marginal revenue function? P=200-2Q MR(Q)=200-4Q * Q = 100 - 1/2P 1/2P = 100-Q P = 200 - 2Q
The Most Important Factor
The most important of the five factors: economies of scale Exclusive control over important inputs and patents are transitory sources of monopoly Network economies and government licenses can both be persistent. But network economies can be viewed as another form of economies of scale; the same is true for many of the government licenses. Production processes change over time, which makes exclusive control over important inputs only a transitory source of monopoly Patents too are inherently transitory. One way to view network economies is that the product of any given quality level can be produced at lower costs as sales volume increases. many of these licenses are themselves merely an implicit recognition of scale economies that would lead to monopoly in any event.
Marginal Revenue
The slope of the total revenue curve is the definition of marginal revenue. It is the change in total revenue when the sale of output changes by 1 unit. MR(Q)=(ΔTR(Q))/ΔQ Recall that for perfectly competitive firms, MR(Q)=P^∗, where P^∗ is the constant market equilibrium price taken as given by the firms. - Implied by TR(Q)=P^∗ Q. For a monopolist, will show that MR(Q)=P(Q)+(ΔP(Q))/ΔQ Q, where P(Q) is the market inverse demand function - Implied by TR(Q)=P(Q)∙Q
does not exist
The supply curve for a monopolist
Preview [8.1]
Virtually every movie theater charges different admission prices to moviegoers who belong to different groups: - students, adults, senior citizens; - "ten-packs" at a discount, Tuesday discount, dinner hour discount. None of these practices would be expected under our model of perfect competition, which holds that all buyers pay a single price for a completely standardized product. The same movie theater charges everyone the same prices for items like popcorns, soft drinks and candy. But theses prices are usually much higher than those of the same items sold in grocery stores, certainly far greater than any reasonable measure of the marginal cost of providing them. Both behaviors—charging differential admission prices on the one hand and uniformly high concession prices on the other—are, as we will see, perfectly consistent with what the economic model predicts about the single seller of a good or service. This chapter examines the market structure that least resembles perfect competition—namely, monopoly, a market served by a single seller of a product with no close substitutes. Five factors that lead to this market structure. Monopolist's rule for maximizing profits in the short run is the same as the one used by perfectly competitive firms.
Keep price and output the same.
What would a profit-maximizing monopoly do in the short run if its fixed costs increased?
less than price
When the demand curve is downward sloping, marginal revenue is
The monopolist is not maximizing profit and should decrease output.
Which of the following is true at the output level where P = MC?
Output decisions depend not only on marginal cost but also on the demand curve. Shifts in demand lead to changes in price, output, or both. Thus, there is no one-to-one correspondence between price and the seller's quantity.
Why is there no market supply curve under conditions of monopoly?
will not always result in a higher price because the monopolist's output decision depends on marginal cost and the shape of the demand curve.
Will an increase in the demand for a monopolist's product always result in a higher price? Explain. An increase in the demand for a monopolist's product
net loss in consumer and producer surplus due to a monopolist's pricing strategy/policy.
With respect to monopolies, deadweight loss refers to the
Economies of Scale
[8.1 slide 12] When the long-run average cost curve is downward sloping, the least costly way to serve the market is to concentrate production in the hands of a single firm. A market that is most cheaply served by a single firm is called a *natural monopoly.* Often the case for industries with large fixed cost. - local telephone landlines
Marginal Revenue for a Monopolist (Calculus)*
[8.2 Slide 12] The chain rule in calculus: if f(x)=g(x)h(x), then f^′ (x)=g(x) h^′ (x)+g^′ (x)h(x) The chain rule in calculus implies MR(Q)=ΔTR(Q)/ΔQ=P(Q)+(ΔP(Q))/ΔQ Q
Marginal Revenue for a Monopolist: A Linear Demand Curve Example
[8.2 slide 13-14] Consider the example P=80-1/5 Q. Start with Q_0=100 and P_0=60. If the monopolist wishes to increase the output from Q_0=100 to 150 so that ΔQ=50, correspondingly he must cut the price from P_0=60 to 50 so that ΔP=-10. (Note the negative sign.) The change in his revenue results from two effects 1. The gain in revenue from the 50 units of new sales (B in next figure). (P+ΔP)ΔQ=50×50=250 2. The loss in revenue from selling the previous output level 100 units at the new, lower price (A in next figure). ΔP ∙Q_0=(-10)×100=-1000 The change in the revenue is ΔTR(Q_0)=2500-1000=1500 The marginal revenue at Q_0=100 associates with this particular change ΔQ=50 is MR(Q_0 )=(ΔTR(Q_0))/ΔQ=1500/(50 )=30
Example: The Monopolist's Marginal Revenue with Linear Demand Functions
[8.2 slide 18-19] Consider again P=80-1/5 Q. Then (ΔP(Q))/ΔQ=-1/5. Hence, MR(Q)=P(Q)+ΔP(Q)/ΔQ Q = (80-1/5 Q)+(-1/5)Q = 80-2/5 Q Generalize: for any P=t-kQ, the monopolist's marginal revenue is MR(Q)=t-2kQ The monopolist's marginal revenue curve is a straight line
Marginal Revenue and Elasticity for Linear Demand Curves
[8.2 slide 23-24] Elasticity changes along a linear demand curve ϵ<-1 for prices higher than the middle point of the linear demand curve ϵ=-1 at the middle point ϵ>-1 for prices higher than the middle point Hence, the marginal revenue is positive only on the upper half of the linear demand curve.
The Profit-Maximizing Price and Quantity for a Monopolist
[8.3 slide 6] Maximum profit occurs at the output level Q*, where MR=MC At Q*, the firm charges P* and earns an economic profit of Π.
Numerical Example
[8.3 slide 7] A monopolist faces a demand curve of P=100 -2Q and a short-run total cost curve of TC=640+20Q. The associated marginal cost curve is MC=20. What is the profit-maximizing price? How much will the monopolist sell, and how much economic profit will it earn at that price? MR = 100-4Q Q* = 20 P* = 60 ATC(Q*) = 52 Profit per unit = 8 Π = (P* - ATC(Q*)) * Q* = 160 *Demand: P*=100-2Q = 100-2*20=60 *Change in TC(Q*) = 640/Q + 20 =52
The Monopolist's Shutdown Condition
[8.3 slide 9-10] The shutdown condition for a monopolist: there exists no quantity for which the demand curve lies above the average variable cost curve. Mathematically: Π=TR-TC =TR-VC-FC =(P-AVC) Q^∗-FC Hence, produce at Q^∗ as long as (P-AVC)>0 at Q^∗. No positive level of output for which price exceeds AVC, and so the monopolist does best by ceasing production in the short run.
Long-Run Equilibrium for a Profit-Maximizing Monopolist
[8.4 slide 6] LMC = MR determines Q^∗. The optimal capital stock in the long run gives rise to the short-run marginal cost curve SMC^∗, which passes through the intersection of LMC and MR. For the conditions pictured, the long-run economic profit level, Π, is positive.
