Mr September 4 Notes

Arts Administration and the Cultural Sector Fall 2009 MR September 4 notes: Some very useful economics: Supply & demand & prices Marginal Benefits and Marginal Costs In this section of the course we learn how to think like an economist. We should clarify at the outset what this means. Thinking like an economist has two aspects. First, it is a guide for decision-making – as individuals, managers of organizations, or policy-advisors in government. Economics provides us with a systematic way to think about marginal decisions: • Should we add a matinee performance for a show for which all the evening performances have sold out? • Should we hire an extra person to work the ticket office? • Should our city increase its budget for public art? …and about big decisions: • Should we build a new performing arts center? • Should our orchestra add a series of pops concerts to its season? Second, economics helps us to understand the implications of everyone making economic decisions: • What determines the price(s) of a Broadway show? • What does your orchestra need to pay to hire a half-decent principal cellist? • Why do the live performing arts keep getting more expensive while quality recorded music keeps getting less expensive? To get us started, let’s think of a simple problem: Imagine some activity in which you are already engaged. Suppose, for example, you are a music student majoring in piano, and for the past few months you have been practicing 25 hours per week. Should you increase the time you spend practicing to 26 hours per week? How would you decide? Marginal benefits are the gains you realize from increasing the level of activity by a small amount. In our example, you might think of the gains you realize from increasing practice-time from 25 hours per week to 26. Remember that marginal is always used to represent small changes from your current level of activity. It must be distinguished from the total benefits of all of your practicing – we are just looking at the benefits that come from an increase. In this case, the marginal benefits of practice time will have a number of dimensions: there is the personal satisfaction that all artists feel as they develop their talents, plus the pure joy of playing; there are the benefits of increasing the respect you receive from your peers (this is quite important to some artists); there are the more

material concerns of achieving higher grades in performance, and the various benefits – in money and prestige - that might flow from this. A few things to notice from this example: • Marginal benefit is not solely concerned with the monetary benefits that might arise. Other benefits, in terms of personal satisfaction, reputation, and so on, all count as well. People who think that economics is only concerned with monetary values do not know economics. • Marginal benefits are going to be different for different individuals. The pleasure we get from perfecting our craft, our desire to impress teachers and peers, the degree to which we believe more practice will “pay off” in terms of scholarships and opportunities, are different for each person. • With so many subjective elements to marginal benefits, even in this simple example, the piano student who is the subject of this discussion knows what her marginal benefits of practice are better than anybody else could say what they are. Only she knows how much an extra hour will improve her performance, and how much that improvement matters to her. Nobody else has any way to measure her marginal benefits. Finally, we make a generalization: as the practice-time increases from 25 hours per week to 26, and then from 26 to 27, and then from 27 to 28, at each stage the marginal benefits become slightly lower. A music student only practicing 10 hours per week will get a significant benefit by increasing to 11, since he has much catching up to do. But a student already practicing 35 hours per week is not going to gain so much from a 36th hour – there might be very little improvement in performance, and possibly not much extra joy, if any, when playing that many hours. This phenomenon is known as declining marginal benefits: the higher your level of any activity, the lower is the marginal benefit from increasing it. Marginal costs are the losses you realize from increasing the level of activity by a small amount. Let us stay with the same example: An extra hour per week of practice means one less hour for doing other things – studying other courses, working at a part-time job, leisure time with friends, family, or in solitude. As with marginal benefits, notice that marginal costs are not solely about monetary costs. Economists think about costs in terms of what you forgo when you pursue this activity – what would you have to give up in order to increase your practice-time by one hour per week? The term we use for what you give up is opportunity cost. In our example, opportunity cost might change from week-to-week. During the week of final exams the opportunity cost of practicing piano might be quite high, since time for reviewing notes and getting into the right frame of mind for writing exams is highly valued. Early in the semester opportunity cost is probably lower. It is very important to distinguish between the marginal cost of piano practice and the total costs associated with studying piano. The price of owning your own piano is not a part of marginal cost, since the piano is there whether you practice 25 hours or 26 hours

(or 10 hours or 50 hours) per week. There is no additional piano cost from increasing the amount you practice. This would likewise apply to the costs of the sheet music. Additional wear-and-tear on the piano could be legitimately considered a part of marginal cost, but it is likely to be a trivial amount in this case [but wear-and-tear is not trivial in every case – ask anyone whose work requires a car and is constantly on the road…wearand-tear on the car from extra miles begins to add up]. Note some parallels with marginal benefits: for neither marginal benefits nor marginal costs are we concerned solely with monetary aspects, marginal benefits and costs are each going to be different for different people, and outsiders cannot know marginal benefits or costs as well as the individual we are talking about. A second generalization: increasing marginal costs. As you increase your level of practice to a high number of hours per week, you find that you are falling behind in other courses, you are broke because you are working very few hours at your job, and you have no time to relax or be with friends and family. With time so scarce, an additional hour of practice each week becomes quite costly – the opportunity cost of that extra hour has become quite high. And now we arrive at our two-part rule for making decisions at the margin: 1. If at the current level of activity marginal benefit is greater than marginal cost, then you should increase the level of that activity. 2. Increase the level of activity up to the point where marginal benefit equals marginal cost, but no further. Part 1 of the rule can be expressed in simple terms – if I increase this activity, will I gain more than it will cost me? If yes, then I ought to do it. The piano player weighs the additional benefits that would arise from an extra hour of practice with its cost in terms of having one less hour to do everything else. If the marginal benefit of the extra hour exceeds the marginal cost, then go ahead, you will be better off for it. Part 2 works as follows. Suppose that the piano player found that in fact the marginal benefit of increasing practice-time from a rate of 25 hours per week was greater than marginal cost. So, the pianist increases to 26 hours per week. Now the question is: should she increase practice hours from 26 hours per week to 27? It depends. As the hours per week increased to 26, two things happened: marginal benefits declined a bit, since she has increased her level of practice there is slightly less to be gained from even one more hour, and marginal costs have risen a bit, since increasing from 25 to 26 has meant that her time for other activities has become even more scarce than it was before. So marginal benefits and marginal costs are moving closer together. As we increase the practice hours per week further and further, eventually we reach a level where marginal benefits equal marginal costs. Suppose this happens at 30 hours per week, where the 30th hour was just barely worth it in terms of opportunity cost. Since we

have declining marginal benefits and increasing marginal costs, that would mean that for a 31st hour marginal costs would rise above marginal benefits. But that means the 31st hour per week is not worth it: the cost in terms of time used up is greater than the benefits that flow from the extra practice. The pianist should practice 30 hours per week, but no further. Examples Add an extra performance? You have produced a play, and planned on three evening performances as your run. But tickets have sold quite briskly, it looks like the three shows will sell-out, and someone suggests adding a matinee performance. Should you do it? The way to frame the problem is to think in terms of marginal benefits and marginal costs. The marginal benefits from the matinee would be the expected increase in revenues that you would receive. This might be a bit complicated to calculate, since with the addition of the matinee some people who originally planned on buying a ticket for an evening performance will buy for the matinee instead. So you cannot simply add up the expected box office for the matinee, since that probably overstates the true marginal benefit. Instead, estimate (you won’t be able to predict this perfectly – make an educated guess) (1) total box office if you just do three evening shows, and (2) total box office if you do three evening shows plus a matinee. (2) minus (1) is the marginal benefit from the matinee. There might be additional marginal benefits – suppose there is an increase in the “goodwill” attached to your theater company as you show how responsive you are to public demand. The marginal costs of the matinee come from the increase in costs that arise from an extra show. This might be complicated and depends on the circumstances: • Are you paying your performers? If so, then they will require compensation for this additional performance. If not, there is still the cost of their time to consider – amateurs have lives too. If your performers are amateurs who simply love every chance they can get to be on stage, then this particular aspect of marginal cost might be quite small. Don’t forget all the stage crew, box office, etc. • Have you already got the theater space booked, or would extra payments to the owners of the space be required? Remember, it is very important to think in terms of the margin – don’t ask what you had to pay the owners of the space to rent the hall for this run, ask what is the additional cost of the matinee. • Costumes and sets probably don’t enter the picture – they are already paid for and so not a part of marginal cost. • Rehearsal time is a big cost of putting on a show, but it is not a part of marginal cost, since the matinee would not require any extra rehearsal.

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There might be some additional costs in advertising and promotion to let people know about the extra performance.

To add it all up we could follow the rule we took with marginal benefits: calculate (1) the total costs of putting on this show if you just stick with the three evening performances, and (2) the total costs of putting on the show if you do three evenings plus a matinee, and your estimated marginal cost of the matinee is (2) minus (1). Add the matinee if marginal benefit exceeds marginal cost. Otherwise, don’t. Should we hire an extra person to work the ticket office? If you are not relying on volunteer labor then the marginal cost of an additional person at the box office is all the expenses of an additional employee. Obviously this includes wages plus benefits, but also includes the costs of advertising the position and the time spent going through application forms, interviewing applicants, checking references, etc. For simple jobs like box office these hiring costs are low, but they get expensive as you look to hire high-level staff or management, since skill-levels and work-history and references must be more carefully considered, especially since the cost of hiring the wrong person grow larger. The benefits from an extra employee come from the increase in revenues the person will bring. Potential customers are turned-off from buying tickets if line-ups are too long (or, with a long line, they might still attend this show but will not come back as a repeat customer). In the box-office staff case, marginal costs of employees are pretty constant. Marginal benefits will be declining. If you are running a big auditorium, then one person alone at the box office will lead to waits and disgruntled customers – there is a reasonably high marginal benefit from hiring an extra person. But the marginal benefit is smaller as you move from two box office employees to three, and smaller still as you move from three to four. Somewhere along the line you will find that the last person you hired was worth it (marginal benefits were still bigger than marginal costs) but that the next additional person would not be worth it (the marginal costs of the next person would be greater than marginal benefits). At that point you have just the right number of box office employees. Should our city increase its budget for public art? The costs of more public art are simply the dollars you would need to pay for it – artists, materials, installation. If the land needs to be purchased that is a marginal cost, easy to calculate. If the land is already owned by the city, it still has a marginal cost if it is to be applied to public art, but it is not quite so easy to calculate because you need to think of the opportunity cost of that land. Is the public art going to reduce sidewalk space, road space, open space? What are you giving up when you put a sculpture in some location…what else could you have used that location for? To elaborate: when calculating costs, it is easy to see if you have to purchase the goods, but harder to see if you already own the goods, because the costs are in the form of opportunity costs, and there won’t be an obvious price.

For example: when people buy a home by taking a mortgage, the interest costs of owning a home are pretty obvious. But suppose they buy a house out of their own savings, with no mortgage? There is still an interest cost – the money they used to buy the house could have been earning interest in a mutual fund. The marginal benefits of public art are very hard to calculate, because they are not the benefits to one person, like our pianist from our first example, or an organization, like the performing arts center that was hiring box office staff, but benefits to the entire community, where everyone in the community is going to place a different value on the art. Some care about it a lot, some don’t, and some might positively dislike it. Everyone’s individual marginal benefit needs to be added up. But we can expect that, even if it is hard to measure, everyone has a declining marginal benefit for public art…the more we have, the less we value an additional amount. So there is some optimum where marginal benefit just equals marginal cost. Big Decisions Now let’s consider a different sort of decision, a major investment in something new. An example would be whether to build a new wing on an art museum. We use the term capital budgeting to refer to decisions over major capital investments. This is a subject covered in some courses on financial management. Our goal here is to understand the logic behind these decisions, rather than simply to memorize some applicable rules. Also, we will not get involved in the taxation aspects of capital investment in for-profit firms – the opportunity cost of our time is too large. Costs Earlier we introduced the concept of marginal cost: the increase in costs that arise from increasing level of some activity by a small amount. Important in our discussion was the distinction between which costs actually would increase with an increase in activity, and which costs to the organization remain the same even when the rate of activity increases. Call those costs that vary with the level of activity variable costs, and those costs that don’t vary with the level of activity fixed costs. We emphasized that fixed costs do not play a role in making decisions at the margin. It sounds obvious, but I am certain you will encounter many individuals in your career who get this point wrong! But decisions about those things that become fixed costs have to be made sometime. So, how do we make the big decisions about investing in new buildings or major pieces of capital equipment?

Discounting An amount of money that you hold in your hand today is worth more to you than an ironclad promise of that same amount of money to be paid to you one year from now. Likewise, an obligation that you pay me an amount of money today is more painful to you than an obligation that you pay me exactly the same amount of money one year from now. Future receipts and payments are discounted, because we place less importance on them than today’s receipts and payments. Suppose I offered you a choice: I will give you $100 today, or some amount of money one year from now, and I ask you which deal you would prefer. Suppose your answers are as follows:

Money one year from now $110 $108 $106

Money today $100 $100 $100

Preference Money one year from now Indifferent Money today

We define the discount rate as follows. Suppose you are indifferent between receiving $X one year from now and $Y today. Then the discount rate is denoted by r and satisfies the following equation: Y = X / (1 + r). In our example, your discount rate is .08, or 8 percent, since $100 = $108 / (1 + .08). In ordinary language, a person with a high discount rate is someone who places great value on having money today and little value on expected future payments. A person with a low discount rate is more patient, and has more willingness to wait for the expected payoff. In organizations, the discount rate is the rate of return that could be earned on alternative investments. Consider the following example: an organization can do a project that would yield an immediate $100 in net revenue, or it could do a project that would yield $107, but where you would need to wait one year to receive the money. If the rate of return on alternative investments were 8%, the organization would choose the project that yields $100 right now. This is because it could do the project, take the immediate $100, invest it at 8% rate of return, and in one year would have $108, which is better than the project that would take one year to yield just $107. On the other hand, suppose the rate of return on investments was just 6%. Then the project that pays $107 one year from now looks better, since the project that yields $100 right now would only leave us with $106 in the bank one year from now.

If the rate of return on alternative investments were 7%, it is easy to see that the organization would be indifferent between the two projects: in organizations, the discount rate is the rate of return that can be earned in alternative investments. You could think of the discount rate as the opportunity cost of putting money into a project, since it represents what you could have earned with an alternative use of the funds. Everything we have done so far applies to a time horizon of one year. Now suppose the amount $Z is to be received n years into the future, and we are indifferent between that promise and receiving $Y right now. Then the discounting formula is: Y = Z / (1 + r)n. Notice that as either r or n gets large, the denominator rises and Y falls relative to Z. The further into the future a payment will be made, the less it matters to us now. And these numbers do get small. Suppose the discount rate is 6%. Then a promise that you will receive $100 fifty years from now (i.e. n = 50) is the equivalent of receiving $5.42 today. We use the term present value to refer to the value to us today of some amount to be paid or received in the future. In the example in the previous paragraph, the present value of a promise of $100 to be received fifty years from now is $5.42. Present value falls as the discount rate and/or the distance into the future rise. Now suppose we are looking at a project that will pay us $W per year for N years, with the first payment coming in one year from today. The present value of this stream of payments is that amount where we would be indifferent between a promise of the stream of payments and an amount right now. The present value of this project is $Y, where: Y = W / (1 + r) + W / (1 + r)2 + W / (1 + r)3 + … + W / (1 + r)N. If the project will pay us a different amount each year, say W1 one year from now, W2 two years from now and so on, then the present value of the stream of payments is: Y = W1 / (1 + r) + W2 / (1 + r)2 + …+ WN / (1 + r)N. For example, suppose a project would require us to pay out $C right now, and would yield revenues of $200 at the end of the first year, $300 during the second year, and $100 during the third year. Suppose the discount rate is 6%. Then: Y = 200 / (1.06) + 300 / (1.06)2 + 100 / (1.06)3 = 188.68 + 267.00 + 83.96 = $539.64. What should we do?

Cost-Benefit Analysis of Projects We should accept a project proposal if the present value of the stream of net revenue that will arise from the project is greater than the initial required outlay. In our example, the present value of the stream of revenue that will come from the project is $539.64. If that is greater than the initial required outlay, $C, then the project is worth doing. If $539.64 is less than $C, the project is not worth doing, and you would be better off simply investing the $C in some alternative project that yields a rate of return of r. All we are really doing here is weighing the costs and benefits of the project proposal. What has made it complicated is that the benefits are spread out over the future. But that doesn’t affect the basic logic: ask whether the benefits exceed the costs. What if we have to choose between different projects? If we have choices, then look for the project with the biggest difference between initial outlay and the present value of the stream of revenues that will be generated. For example, suppose two projects: A and B. Project A has an initial outlay of $500, and a stream of returns with a present value of $600. Project B has an initial outlay of $2,000, and a stream of returns with a net present value of $2,150. If you can only do one project, choose B, since $150 is better than $100. Actually, both are worth doing, so if you are able, choose both. But choose B if you are restricted. The fact that the ratio of benefits to costs is greater for A than for B (600 / 500 relative to 2,150 / 2,000) does not matter. What if the project involves annual costs? Suppose your theater is thinking of installing a new lighting system. It is a great improvement over your old one, but it will mean an increase in labor costs, since you need extra bodies to make it work. Further, the system will have maintenance costs that are higher than you have had in the past. But the shows will look better, and that means more audience demand for tickets. Here is how you could organize your decision: Year 0: Purchase and installation of new system, $C. Year 1 and future years: Increased revenue from ticket sales minus increased labor costs minus increased maintenance costs, all discounted at the appropriate rate. Notice that I am only counting the changes in revenues and costs that arise from the new lights. Also, if the new system means less maintenance, that is a benefit to be added.

Taxes? Suppose taxes apply to any net profit that arises from an investment: you can deduct all expenses but must pay tax on all revenues. If we had a tax system that simple, then our results about whether to make an investment are not affected at all. Suppose a project will cost you $C, and you can deduct that from your taxable income, and it will yield a present value of $Y in net revenue, which is taxable income. In the absence of taxes, we do the project if Y > C. But now suppose there is a tax rate of 25%, which applies to Y and C (as a write-off). Then your revenues only let you take home Y(1 - .25). And the investment only cost you C(1 - .25). So your question now is whether Y(1 - .25) is greater than C(1 - .25). But that is exactly the same question as whether Y is greater than C. An investment worth doing in a world without taxes is still worth doing in a world where all revenues are taxed and all costs are tax-deductible (and the converse is also true). Unfortunately, as any tax accountant will tell you, that is not the tax system we have, and notwithstanding all that we know about tax breaks for special interests, in general the US Corporate Income Tax discourages investment – it makes some projects that would be worthwhile in the absence of taxes not worthwhile. But you can learn all about that in your course on finance. Nonprofits? First, so long as the investment the nonprofit is considering is related to its mission as an arts organization – a new wing for exhibits or classrooms in a museum, capital equipment for a performing arts venue – then the Corporate Income Tax does not apply, since the activity will be tax exempt. So taxes do not enter the picture at all. Second, we need to ask whether the benefits from the investment can be entirely captured by the increased revenues that will come from it. Some nonprofits are described by economists as for-profits in disguise: they make investments, hiring decisions, and set ticket prices, trying to earn as much net revenue as possible, which can then be spent on things the decision-makers in the organization value – higher quality of production, special projects, or, if they are somewhat selfish, perks (but they cannot distribute the net revenues as dividends, if they still want the IRS to consider them a nonprofit). But often an arts nonprofit will have goals that go beyond revenues in their investments – improvements in capital equipment or buildings that will go to serve a subsidized, lowincome audience, for example. In this case the benefits must be estimated in terms of the return the investment would bring in serving the mission of the organization. While no one expects nonprofit leaders to place a firm dollar figure on the benefits of an investment meant to serve non-paying (or heavily subsidized) clients, the basic rule of cost-benefit analysis still applies. Investment decisions have real costs, and the leader of the organization needs to decide whether it is worth doing, which means that implicitly

the benefits must be weighed against the costs. Further, if there is a choice of projects but a limit as to how many projects can be done, the nonprofit decision-maker needs to decide which projects have the greatest difference between benefit and cost, and choose those projects to do first. Maximizing profit when the market is competitive Now we will discuss competitive markets. A competitive market is one where: • There are many buyers and many sellers; • No single seller or buyer, or coalition of buyers or sellers, is so large relative to the rest of the market that by his actions he can influence the market price; • Any one seller can sell all she wants at the going market price, and any one buyer can buy all he wants, without affecting the price we see; • It is reasonably easy for new sellers and buyers to enter the market, or to leave the market to go and produce or buy something else. In a competitive market we expect to observe the law of one price: that is, given the quality level of the good, every seller will be offering the same price. Why? No seller can charge higher than the market price, since nobody would buy from him – they can just go to one of the other sellers. No seller would charge less than the market price, because there is no reason to do so, since you can sell all you want at the market price. So every seller picks the same price. These markets are not very common in the arts, since typically it is the case that a seller in the arts has something unique. We deal with the more common cases in the arts in the next few lectures. But competitive markets in the arts are not unknown. Consider the market for paperback editions of Shakespeare’s plays. Since they are in the public domain, many publishers can sell in this market. For similar quality paperbacks by different publishers we would expect to see the law of one price apply – a publisher could only charge a higher price if there were something about her edition that marked it as higher quality (a better scholarly introduction, better footnotes, more attractive cover, more durable-looking binding, etc.). The same would be true of recordings of classical symphonies by “ordinary” (rather than superstar) orchestras and conductors. Sellers Suppose you are selling a good in a competitive market. You don’t choose the price, since it is determined in the bigger marketplace. From your perspective, it is a given. But you do choose what quantity to bring to market. We know that the solution to the problem of how much quantity to sell will involve marginal benefits and marginal costs. In the case of competitive markets, the marginal benefit of increasing the amount of the good you bring to the market is simply the price of the good. After all, that is what you

will receive for bringing one more unit out for sale. Note that this result holds only in competitive markets (we see why below). Although we normally hold that marginal benefits are declining, in this particular case they are not: the price remains the same no matter how much you sell, and will not decline. What is the marginal cost of bringing extra units of the good to market? It would consist of all those variable costs that rise as you produce more – the additional labor, raw materials, transportation costs, but not your fixed costs, which do not change with output. We expect that as you produce more output, eventually marginal costs begin to increase. Why? Don’t forget we are focusing on the margin. As you produce more and more output, your inputs are probably falling in quality. After all, you hired the workers best suited to what it is you do first, and now that you are expanding you have to take on employees not quite as good a fit with your firm as the first people you hired. Suppose you are a farmer, so that part of your marginal cost is the opportunity cost of land. For your first units of output, say, lettuce, you used the available land that was the best suited for growing lettuce. But as you expand you must be moving into land that is less good, which means you need more of an increase in land to get the same increase in output. The simplest analogy is that your business is picking and selling apples, and your only marginal cost is labor. Which apples do you pick first? The low-hanging fruit, of course. But the more apples you try to pick, the higher up the trees you must go, at greater marginal cost. Overall, because the quality of your inputs is falling, the marginal cost of producing extra output is rising. How much output to produce? Choose the output where the price of output (marginal benefit) equals marginal cost. Don’t produce any more than that, even though you could, because you would be going into a range where the marginal cost of the extra units exceeds the price you would get for them. Now suppose that every seller is following the same rule. Even though they will probably face slightly different marginal costs (each seller has their own strengths and weaknesses), they all see the same market price, and they all produce to where their own marginal cost just equals price (which will likely be different amounts for each producer). If the market price were to rise, each producer would find it worthwhile to expand output a bit, up to the point where marginal costs equal the new market price. But that is not a very surprising result: as the market price rises, sellers have the incentive to increase their supply of the good. Buyers Suppose you are buying a good in a competitive market. How much should you buy?

The cost to you of buying one extra unit is the price of the good. That stays constant – in a competitive market the price will be the same no matter how much you buy. The marginal benefit is a subjective thing, although we know that it will decline the more of the good you already have in your basket. The optimal amount of the good to buy is the amount where marginal benefit equals price. Don’t purchase any more than that, since you will be entering a range where the marginal benefit of the last units has become less than the price. All buyers do the same thing. They all place different subjective valuations on goods, and will buy different amounts, but they all follow the same rule of buying to the point where marginal benefits equal the market price. If the market price were to rise, each buyer would find it worthwhile to reduce purchases, back to the point where marginal benefit equals the new market price. And that is not a very surprising result: as the market price rises, buyers have the incentive to decrease their purchases of the good. What determines price in a competitive market? Everybody knows that prices are determined by supply and demand. But now we can better see how this works. According to the analysis so far, at high prices suppliers have incentives to bring a lot of the good to market, following their set-quantity-wheremarginal-cost-equals-price strategy. And at high prices buyers will not buy much of the good, following their buy-quantity-where-marginal-benefit-equals-price strategy. At prices that are too high, we have excess supply: the quantity sellers would like to sell is more than buyers want to buy. At prices that are too low, we have excess demand: the quantity buyers want to buy is more than sellers want to supply. We predict, and observe in the real world, that market prices will move to equilibrium, where there is no excess demand or excess supply, and the amount sellers want to sell is just what buyers want to buy. How do we get to equilibrium? Suppose we begin with a price that is too low, and there is excess demand. At the going price, sellers run out of the good, and buyers are sent home disappointed. Smart sellers will realize: why not charge a slightly higher price? I could still sell all my output (since there is so much demand), and I will take home more profit. But we know that all sellers will probably have the same idea, and prices start to rise.

As prices rise, two things happen. More of the good will be brought to market, since the higher price induces greater supply. And the quantity demanded will begin to fall, in light of the higher prices. Eventually, we get to a price where quantity demanded equals quantity supplied, and the price will not rise any further [an exercise for yourself: at the equilibrium price, why doesn’t a seller try to increase his price just a little bit further?]. Actually, the word “eventually” in the previous paragraph isn’t quite right. In the real world prices move very quickly to equilibrium. When there is excess demand, there is money to be made in increasing prices. And nobody waits to do that – it is immediate. That is why farmers listen to the early morning radio for farm commodity prices (or they did…they no doubt check their blackberries now) – they change daily, hourly, in response to market conditions, always moving towards equilibrium. Nobody waits. This is as good a place as any to make an observation about markets: when an opportunity for easy profit arises, it is rapidly taken, and the opportunity quickly disappears. To use the punch-line from an old joke about economists, nobody walks by $20 bills lying on the sidewalk. A consequence of this is that prices always move quickly to equilibrium. Persistent excess demand is the equivalent of suppliers walking past $20 bills without picking them up. This also means that in competitive markets there is no chance for sellers to earn profits above the ordinary rate of return on investments. If there is great profit to be made in a competitive industry, new firms will come along getting into the business. But that competition drives down equilibrium prices, and the extraordinary profits disappear. High profits in a sector of the economy are like $20 bills lying on the sidewalk…new suppliers come along trying to pick them up, and the bills disappear. This is an insight that will arise frequently in this course: as prices are always moving to equilibrium levels, we find that in competition there is no such thing as easy money. The only way firms or individuals are able to make profits in excess of what anybody else could make with the same effort is if they have some way of preventing new suppliers from coming along and providing the same good. For individuals, great profits come from having a talent that cannot be matched – writers, performers, composers who are able to create cultural goods in a way that others cannot match. The ordinary artists will not do better than ordinary wages. Setting price when the market is not perfectly competitive Above we considered decisions in a competitive market, where the seller takes a market price as given. But most arts organizations have some scope in setting prices. Here we consider the situation where the organization sells one good and sets one price. Later, in great detail, we complicate matters by allowing the organization to set a “menu” of prices, and to discriminate in terms of what prices are offered to different groups of people.

For a simple example, suppose we consider a ceramic artist who makes custom-designed plates. The marginal cost of making plates is $20, and we suppose for simplicity that this does not rise with the quantity of plates produced. The artist has done some market research, to determine what price to charge for her plates. The figures she has arrived at are: Price

Quantity Sold per Week

$40 $39.50 $38.50 $37

15 16 17 18

The lower the price, the more plates she can sell each week. What quantity should she aim to sell each week? We know the answer will involve finding where marginal costs equal marginal benefits. We already know that marginal costs are $20 per plate. But what are marginal benefits from selling more plates? The answer is complicated, because, unlike for a competitive market, marginal benefit is not simply equal to the price. The key difference is that in this case, the artist must lower her price to sell more units, and therefore the extra revenue is not as high as price. Define marginal revenue as the increase in revenue that comes from selling one more unit. To find it, we need to calculate the total revenue for each possible quantity, and see how that changes as we increase quantity. Using the same numbers as above, we find that: Price $40 $39.50 $38.50 $37

Quantity Sold 15 16 17 18

Total Revenue $600 $632 $654.50 $666

Marginal Revenue

$32 $22.50 $11.50

We can see pretty clearly that marginal revenue, which is the true marginal benefit from selling more units, is significantly less than price. Suppose we start with a price of $40, selling 15 plates per week. Should she reduce her price to $39.50 and sell 16 plates per week? Yes: the additional revenue will be $32, and it only costs $20 to make the extra plate. Should she reduce her price further to $38.50 and sell 17 plates per week? Yes: the additional revenue will be $22.50, and it only costs $20 to make the extra plate.

Should she reduce her price further to $37 and sell 18 plates per week? No: the additional revenue would be $11.50, but the plate would cost $20 to make. So the best choice is to set a price of $38.50 and plan on selling 17 plates per week. Notice that she is holding output to 17 even though at that level the price she is charging per plate is well above marginal cost. It is not worth expanding because in lowering price the extra revenue turns out to be fairly small. When an organization is able to set its price, and charges a single price, it finds the price and quantity combination that equates marginal revenue with marginal cost. The Unexpected Customer Suppose our artist has followed our advice, and posted a sign in her window advertising fine plates for $38.50. Each week she expects 17 customers. One week in particular, it is getting close to the end of the week, and she has made 17 sales, as predicted. But then a traveler enters the shop, and expresses an interest in buying a custom-designed plate at the advertised price of $38.50. Should she make a plate for this customer, or tell him that unfortunately the shop won’t be able to do that? The answer, of course, lies in comparing marginal benefits and costs. We know the marginal cost of making a plate for this man is $20. What is the marginal benefit of selling to him? It is $38.50: he knows that is the price and he is willing to pay it. So, it is worth making a plate for him. But why didn’t we plan on making 18 plates per week in the first place? Because we thought (mistakenly) that to sell 18 plates per week we would have to lower the price to $37, which would generate marginal revenue less than marginal cost. But if we don’t have to lower the price to sell the 18th plate, then it is worth doing. A price-setter is always happy to sell to an unexpected customer willing to pay the posted price. For arts organizations this will almost always be the case – price is at a level above marginal cost (which is close to zero for most live performances, until you hit seating capacity). So you would never turn away an unexpectedly high number of customers willing to pay the posted price. This principle helps explain the patterns we see in advertising. Anyone watching television in the evening will be struck by how many of the commercials are for different sorts of drugs. Why? Because drugs are a case where the price being charged is very much higher than marginal cost – after all, the marginal cost of a pill is typically measured in cents rather than dollars (remember, we are talking about marginal cost here, which excludes all the costs of research, development, and testing of the drug). Drug

companies are price setters. Once they have set their price, they will welcome as many customers as they can get at the posted price, since there is a lot of extra profit from each additional customer. They could get more customers by lowering price, but that isn’t worth it if the marginal revenue is low. As an aside, what then is the optimal advertising budget? Marginal benefit of advertising is the extra customers willing to pay the posted price, and the difference between the price they pay and the marginal cost of making the pills. Marginal cost is whatever it takes to buy advertising space. Marginal benefits will be declining – the first advertisements might have a great impact, but by the time someone has seen the ad 50 times they are probably not going to be swayed by seeing it a 51st time. So there is an optimal amount of advertising where marginal benefit equals marginal cost. [As another aside, we don’t notice people who sell in competitive markets, as defined earlier, doing any advertising. That is because they can already sell as much as they want at the going price – they don’t need to troll for more buyers]. Fixed Costs Again Notice that fixed costs do not play a part in setting the optimal price, which depends on marginal costs and marginal revenues. If you set ticket prices for one event, finding that the optimal price is $20 per ticket, the fact that the next event has higher fixed costs tells us nothing about whether the best ticket price will be higher or lower than $20, it all depends on marginal costs (again, near zero for live performing arts) and what people are willing to pay, as expressed by marginal revenue. I don’t know how many times I have read the sports pages to find a writer complaining that rising players’ salaries are driving up ticket prices. This is wrong. Players’ salaries are a fixed cost of producing a ball game and so have no influence on prices. Ticket prices are set by marginal cost and marginal revenue, in other words the public’s willingness to pay for tickets. What if you are setting prices for a live performance? The rules are the same: set a price where marginal cost equals marginal revenue. For performances, marginal cost is around zero. So, set a ticket price where marginal revenue equals zero. Does that sell-out the house? Not necessarily. Consider the following example of estimated demand for tickets for a single performance: Price $40 $39.50 $38.50

Quantity Sold 150 160 170

Total Revenue $6,000 $6,320 $6,545

Marginal Revenue

$320 $225

$37 $35.10 $33

180 190 200

$6,660 $6,669 $6,600

$115 $9 - $69

In this example, it is worth lowering your ticket price all the way to $35.10 to sell 190 tickets, since there is a small amount of marginal revenue to be gained, and no marginal cost. But it is not worth lowering ticket price even further in order to sell 200 tickets, since the marginal revenue from doing so would be negative – you would lose money on the move. So with these numbers a price of $35.10 and a quantity of tickets sold of 190 is optimal. Now suppose I tell you the house capacity is 250 seats. How does knowing that affect the optimal ticket price? Not at all. It wasn’t worth trying to lower price to increase ticket sales from 190 to 200, and it makes no difference that there will be 60 empty seats. Setting ticket prices to aim for a full house is not necessarily good policy. Now, with the same chart of ticket prices and quantity demanded, suppose I tell you the house capacity is 170 seats. What do you do? In this case, aiming to fill the house is good policy. To see that, imagine an initial idea of a price of $39.50 and customer demand for 160 seats. Is it worth lowering price to $38.50 to sell an extra 10 seats? Yes: the marginal revenue from doing so is $225, which beats the marginal cost of 0. Now, is it worth lowering ticket price below $38.50, the price that sells out the house? No: you won’t sell any more tickets, since you are sold-out, so all you have done is lost some revenue. So let’s formulate a practical rule for the performing arts: If, at house capacity, marginal revenue is still above marginal cost, set a ticket price that aims to sell out. But if, at house capacity, marginal revenue would be below marginal cost, set a ticket price such that marginal revenue equals marginal cost, knowing that this will leave some empty seats. When you attend an event and notice empty seats around you, do not make the mistake of thinking that management made a mistake by setting the price too high. It could well be the case that the price they set was optimal from their point of view. If marginal costs fall, will consumers see prices fall? Yes. We know that price-setters choose a price and quantity combination where marginal revenue equals marginal cost. If marginal cost falls, say due to a new technology, or cheaper costs of materials, then the producer finds herself in a position where marginal

revenue is now above the new, lower marginal cost. And that means she should expand output, and that means lower prices. In our example of the plate-maker, if marginal costs fell below $11.50 it would become worthwhile to sell 18 plates per week (remember the marginal revenue of the 18th plate was $11.50). And if that occurred, the plate-maker would be lowering her price to $37, since that is the price that generates expected sales of 18 per week. So, falling marginal costs translate into lower prices and more units being sold. Direct price discrimination Price discrimination is the practice of employing multiple prices as a strategy of increasing profit. Let us start with a simple problem. Suppose there are two groups of consumers between whom you can easily distinguish – say students (S) and non-students (N). Each group has a different demand curve, and you know the relevant numbers. You have the ability to charge S and N different prices, but you are offering them the same quality product (for example, general admission seating). How do you do it? Suppose there is a constant marginal cost, MC (which for many arts organizations is very close to zero). If there is no likelihood of reaching your capacity constraint, set prices such that for each segment of the market that segment’s marginal revenue equals marginal cost. Example: Suppose marginal costs are zero, and demand by S and N are as follows: Non-students Price Quantity Sold $40 $39.50 $38.50 $37 $35.10 $33 Students Price $37 $34.50 $31.25 $27.80 $24

150 160 170 180 190 200

Quantity Sold 60 70 80 90 100

Total Revenue $6,000 $5,320 $6,545 $6,660 $6,669 $6,600

Total Revenue $2,220 $2,415 $2,500 $2,502 $2,400

Marginal Revenue

$320 $225 $115 $9 -$69

Marginal Revenue $195 $85 $2 -$102

Then the optimal prices are $35.10 for N (who will buy 190 tickets) and $27.80 for S (who will buy 90 tickets). You will sell 280 tickets in total. But wait: if you are going to sell 280 tickets, since N pays more per ticket would it not make sense to try to sell more N tickets and fewer S tickets? Why not charge $33 for N and $31.25 for S? After all, total demand would still be 280? To see why not, note that in lowering the N price to $33 you lose $69 from that group. And in raising your price for S to $31.25, you lose another $2. You would be making yourself $71 worse off. If you are going to be selling to capacity, set prices such that marginal revenue is equalized between market segments. Let’s use the same tables as above, but now suppose your capacity is 240 seats. As a rough approximation, charge N $38.50 (who will buy 170 seats) and S $34.50 (who will buy 70 seats). To see why, pick any other combination and show yourself how you could do better. For example, suppose instead of following our rule you set N’s price at $39.50 and S’s price at $31.25, which would sell out the house. I can do better by lowering N’s price to $38.50, selling 10 more N tickets, which nets me $225 in extra revenue, and raising S’s price to $34.50, selling 10 fewer S tickets, which only loses me $85 in revenue – this shift would benefit me by $120 ($225 - $85). Other example, suppose instead of following our rule you set all tickets at $37, which would sell 180 to N’s and 60 to S’s. In fact, this might seem initially appealing – a single price that just sells out the house. But by raising the N price to $38.50 I lose $115 from sales to them, and by lowering the S price to $34.50 I gain $195 from sales to them, for a net gain of $80 ($195 - $115). Here is a big, general rule that applies to lots of situations: If you have a resource whose amount is fixed, and it can be divided between activities, make the allocation such that the marginal benefits are equalized between the alternative activities. In the example above, our fixed resource is house capacity, and we will divide it between Students and Non-students such that the marginal benefits (i.e. marginal revenue) from selling to each group are equalized. If you have a fixed amount of personal time that must be divided between two (or more) activities, divide your time such that in the end the marginal benefit of time devoted to one activity is the same as the marginal benefit of time devoted to the others.

There is a common sense to this: if you do not follow the equate-at-the-margin rule, then you are missing the chance of improving your position by doing slightly less of the activity with lower marginal benefits and slightly more of the activity with higher marginal benefits. Reallocate until the marginal benefits of the two activities are equalized. Back to our ticket pricing example – what are some possible complications? First is that we need to find out, by survey and by trial-and-error, what the demand curves for the two groups actually look like. Notice that you don’t need to know all the numbers Rather, you just need to get a picture of what marginal revenue looks like in the relevant range of prices. In particular be able to ask and answer the following: “At our current prices for S and N, by how much would I have to lower prices to N to sell x more tickets, and by how much would I raise prices to S to sell x fewer tickets? Now, if I actually did this, how much additional revenue would I get from N’s and how much would I lose from S’s? Would the gain exceed the loss? If so, then marginal revenue for N must be higher than marginal revenue for S, and I should try lowering N’s price and increasing S’s price. This will take me closer to the pair of prices where marginal revenues are equal.” You won’t have perfect information on the relevant responses to price, but after some observation and trial-and-error you should be able to develop at least an educated guess, and when you have that, the math involved does not rise to the level of rocket science. Second: there are not simple correlations between income and demand for the arts, and so the willingness-to-pay by different groups is not quite as simple as saying “well, S are poorer, so they have lower willingness-to-pay for the arts.” For example, if your low willingness-to-pay groups are those without much experience in attending what you offer, then maybe your discounted prices ought to be directed at first-time visitors rather than to students. But suppose S and N truly do have different demands. A third complication is that I have assumed you can easily differentiate between S and N. Student cards are the most commonly used method. But recognize that the further apart the prices for S and N become, the more incentive N’s have to try to cheat, either by pretending to be S, or by buying from an S who bought from you at the discounted price. If cheating is a problem, you may need to modify your rule by pushing the S and N prices closer together than would otherwise be optimal (example from the headlines: the further apart the prices of prescription medicines in Canada and the US, the more Americans start looking to buy their drugs in Canada). A fourth complication lies in the psychology of consumers, who tend to get turned off if they think some other consumers are entitled to a better deal. As with the previous example, you might narrow the gap on prices between different segments to something

closer than would otherwise be optimal if the high-price group has a very negative reaction to seeing what is charged to the low-price group. For each of these complications, keep thinking at the margin: What is the marginal loss in departing from marginal-revenue-equalizing pricing compared to the marginal gain from reducing cheating? What is the marginal gain in increased demand from your high-price segment that you get from increasing the price to the low-price group (and so lowering the high-priced group’s sense that they are being ripped off) compared to the marginal loss from charging your low-price group a price higher than would otherwise be strictly optimal? Now let’s move on to a different sort of price discrimination, again a common one in the arts, where you offer different classes of service at different prices. Our previous examples have assumed a single quality of ticket, but now we will have better and worse tickets. The obvious example is charging people higher prices for better seats. I will draw from Sherwin Rosen and Andrew M. Rosenfield, “Ticket pricing” Journal of Law and Economics 40(2) (October 1997): 351-376, which you do not need to read. They design their problem as follows. There are two classes of tickets, high (H) and low (L). There are also complementary goods for sale inside the theater (food, drinks, programs, etc.) (Z). The seller must choose: how many of each type of ticket to offer for sale, how big to make the difference in quality, how to price the two types of tickets, and what to charge for Z. We assume the seller has an idea about the distribution of the population’s willingnessto-pay for high and low quality, and also about how ticket demand will respond to changes in the price of Z (more people will buy tickets at a given price the cheaper are the drinks inside), but the seller cannot know the preferences of any single individual. Thus, the same set of prices is offered to everyone, and people then sort themselves according to their individual tastes into who buys H, who buys L, who does not attend at all, and, for those who attend, how much Z they purchase. R&R break down the problem into steps. First, take as given the quantity available of H and L, and the difference in quality between them, and the price of Z, and based on that find the optimal prices to charge for H and L. After we have solved for optimal ticket prices we will look at quality differences. We’ll solve for the problem of what to charge for Z later. So let’s take on the first problem. Some notation: • ph and pl are the ticket prices of the high and low class seats. • An individual’s maximum willingness-to-pay for a ticket, also known as the reserve price, is denoted rh and rl. These will be different for different people.

Consumers choose the ticket that has the highest consumer surplus for them; in other words buy H if rh – ph > rl – pl, and buy L if rl – pl > rh – ph. The exception is if for both types of ticket p > r, in which case the consumer doesn’t buy a ticket at all. Let’s think through the effects of price changes. Suppose we hold pl constant, and increase ph. Of the people who were willing to buy H at the original price, they might (1) continue to find it worthwhile, or (2) find it better to switch to L, or (3) no longer buy at all (in other words, they were never interested in an L ticket, and now they don’t want an H ticket either). People who were previously buying L have no reason to change (buying H has become even less appealing as an option), and people who were previously not buying at all have no reason to change. Now suppose we hold ph constant and increase pl. People previously buying L might (1) continue to do so, or (2) switch to H, which is now a relatively better choice, or (3) stop buying (they are people who would never have bought H, and now L isn’t worth it either). People who were previously not buying have no reason to change. And finally, people who were previously buying H have no reason to change. With that in mind, let’s see if we can solve this pricing problem. We’ll do it in steps, and we’ll make some simplifying assumptions. As a first step, assume for the moment that all consumers have exactly the same tastes, and so they all have the same reserve prices rh and rl. Then the solution for our firm is easy: set prices for H and L equal to, or just pennies below (to be on the safe side), the estimates of rh and rl, and so capture all of the consumer surplus. Charge what the market will bear. But now let’s make it harder, and assume two types of consumer, where type 1’s have higher reserve prices for both types of tickets compared to type 2’s. But remember, while we know there are type 1’s and 2’s out there, we cannot tell whether any specific individual who shows up at our box office is a 1 or a 2. There are two options. 1. If type 1’s are very numerous relative to your capacity, forget about the type 2’s and just set ph and pl equal to the reserve prices of the type 1’s.You might have a few empty seats, but it is not worth lowering prices to try to get type 2’s in the door. 2. If type 1’s are not so numerous, it can be worthwhile to try to attract type 2’s into buying tickets. What is the optimal formula when there are lots of type 2’s and only some type 1’s? a. Set pl equal to the rl of type 2’s, and ph is above the rh of type 2’s. Thus, type 2’s only buy L seats, and you get all of their possible consumer surplus (you are charging them as much as you can).

b. Set ph less than the rh of the type 1’s. You cannot charge them their full reserve price for good seats, because they will flip to buying cheap seats. So you cannot grab all of their consumer surplus – the high price seats must remain a good enough deal for them to not switch to L seats. Let’s consider case 2 in more detail. Can we see why it makes sense? Why set ph equal to the rh of type 2’s? If we set ph any higher than that, we lose all the type 2’s: not good. There is no point in setting ph lower than rh: that would just hand them back some consumer surplus, and in addition in might even get some type 1’s to flip from buying H to buying L: not good. So, set ph equal to the reserve price of the type 2’s. For type 1’s, we want them to buy H. You must set the price low enough that they do not flip to buying L, yet as high as you can manage. The surplus that 1’s get from buying H needs to be at least as big as the surplus they could get from buying L, but no higher. Suppose you had the task of setting prices for H and L; how would you go about it? You might proceed by thinking about two numbers: pl, and ph – pl. In other words, a way to conceptualize the problem might be to ask “at what price can I still manage to fill lots of L seats, and how big a markup can I charge for H seats without inducing my highdemand patrons to purchase cheap seats?” For two classes of buyers and two classes of seats, price the lower-quality seats around the maximum willingness-to-pay of the low-reserve-price customers, but price the higher-quality seats at somewhat less than the maximum willingness-topay by the high-reserve-price customers, since you want to ensure they do not switch to buying lower-quality seats. Now let’s turn to quality. For the most part these are simple matters: there are seats with better and worse views, and that is not really something that in practice you can do much about. Tim Baker [“The bottom line? Using pricing to optimise sales and income” Arts Council England [pdf here, starting at page 23 of this file: http://www.artscouncil.org.uk/documents/publications/phpjHiIoa.pdf] gives an interesting example: “When the City of Birmingham Symphony Orchestra moved into Birmingham Symphony Hall, they priced a very complex auditorium in a logical way, but found that over the following seasons their yield fell. Customers were ‘learning’ the hall and finding that cheaper seats were just as good as more expensive ones. Detailed price demand analysis allowed the orchestra to identify which seats customers thought were best and re-price them accordingly. As a result, they were able to increase yield by 7.5 per cent.” Suppose you can adjust the quality of the good seats H. Improving quality will increase the reserve price, and the problem to be solved is whether the marginal cost of increasing

quality is less than the marginal revenue in terms of the higher prices you can charge. A problem you will face is that in practice people are not identical in their willingness-topay for improved quality. If you can have multiple quality levels you might be able to effectively target each type of consumer, but if your instruments are more blunt you face the problem of some people claiming they wish there was better quality (which they would be willing to pay for) and other claiming quality is too high (they would rather save a few dollars even if it meant losing a few frills). R&R note this is a classic problem in the government provision of public goods: quality costs money, and inevitably some people say they wish taxes were lower and others say they would be willing to pay more in taxes if it meant better quality. What about the quality of the L seats? Lowering quality deliberately has the following effects: • Some L-buyers drop out – it is no longer worth buying. • But, some L-buyers switch to buying H, now finding it a better deal. Sometimes firms will deliberately lower the quality of the L good in order to maintain demand for the H good. That sounds a bit evil, but if you are going to price discriminate there must be some significant quality difference. A classic example: Xerox ensuring that its printers aimed at the household market were slow, to keep business customers purchasing the more expensive, faster models. Shipping companies deliberately slow the delivery of packages mailed at cheaper rates, to maintain the demand for high-priced express delivery. Philip Leslie [“Price discrimination in Broadway theater” Rand Journal of Economics 35(3) (Autumn 2004): 520-541] explains that this theory tells us why half-price day-ofshow tickets to Broadway theater cannot be purchased by telephone or online, even though the mechanisms for buying tickets that way are already in place for other customers and could easily and cheaply be employed by the theater. Buyers are forced to go in person and queue because that makes these tickets less appealing to richer buyers who might otherwise wait for the day-of-show to buy them (which are in fact for reasonably decent seats). •

Interesting: Leslie’s calculations suggest that these day-of-show booths are not a good business decision – there is too much switching as customers choose to rely on these booths. Profits would very slightly increase if they stopped selling tickets this way, and the optimum looks to be something like maintaining the booth but at a smaller discount, say 30%.

Paperback editions of books are deliberately delayed in their release, which is a way of ‘damaging’ them to maintain the demand for more expensive hardcovers (if paperbacks were released on the same day as the hardcover, what would the demand for hardcovers look like?). Two-part pricing

We face two-part pricing as consumers in many places: • • • •

We pay a fixed fee for telephone or cell phone service plus charges per minute of long distance; We buy printers and need to pay for ink cartridges separately; We buy a new Kindle from Amazon and then pay for each book we download; We pay an entrance fee to an entertainment attraction and then pay additionally for different exhibits within the attraction.

Here we solve the problem from the firm’s point of view: how do you set the two parts of the pricing in a coordinated way to maximize profit? The simplest case is given by Walter Oi, “A Disneyland dilemma: Two-part tariffs for a Mickey Mouse monopoly” Quarterly Journal of Economics 85(1) (February 1971): 7796. Suppose you are running a fairground. Suppose for now all consumers are the same. You will charge T for entering the fair, and P per each ride. Each person-ride has a marginal cost to you of MC. Consumers are told both prices before they enter, and if it doesn’t look worthwhile they will not come in. Thus, the less you charge for P, the more you will be able to charge for T. The two-part solution is: 1. Set P = MC 2. Set T equal to the total consumer surplus the customer will get from buying rides at P. Thus, if your MC is very close to zero, your optimal strategy becomes to give away the rides, but charge an entry fee that is as high as the maximum willingness-to-pay of our representative consumer. How do we know this two-part solution is correct? Let’s consider the alternatives. To keep the analysis general, let’s suppose MC is above zero. Why not set P > MC? Suppose MC = $1, and you set P = $3. Attendees will buy rides up to the point where their marginal benefit per ride has fallen to $3 (and by diminishing marginal benefits we know that the more rides they consume in an afternoon, the lower marginal benefit becomes…eventually it falls all the way to $3 for the next ride), but then call it quits. But this is inefficient, since they might be willing to buy a few more rides if the price were only $1.50, and it would only cost you $1 to give them a ride. In other words, there is a net gain from getting people on more rides – they would value them by more than it would cost you to provide them. So why not do it? Set the price per ride at $1 to maximize the overall benefits from going on rides. This will raise consumer surplus by more than it will cost you to provide it. And that is ok for you because you get that consumer surplus back on the higher entrance fee you can charge!

Why not set P < MC? That is wasteful: if your MC is $1 and you price rides at 50 cents, then at the margin people are getting rides worth less to them than it is costing you to provide them. The extra consumer surplus they get from these rides, which you can recoup in your entrance fee, is less than the cost to you of providing the additional rides. So P = MC makes sense. Now, once that is in place, consumers know the value of being able to attend your fair at those ride prices, and you can charge an entrance fee T as high as the market will bear for those anticipated benefits. Now let’s complicate things by assuming that consumers are different in their consumer surplus from rides (as is surely the case). Then we would bring in price discrimination on T, but not on P: 1. Continue to set P = MC…all consumers generate the same MC per ride, so charge them the same P; 2. Price discriminate according to willingness-to-pay on T. This solution depends on what instruments you have at your disposal to price discriminate on T. So, taking what we learned earlier, discriminate where you can either on quality of seat, or by giving discounts to students or other easily-identified lowwillingness-to-pay groups, and charge everyone the same price per ride, amenity, whatever, once they are in the door. Suppose consumers have different consumer surplus, but price discrimination on T is not feasible – you must set one value for P and one value for T that applies to everyone. What to do? If you set T equal to the consumer surplus for the high-demand customer (type 1, from before), the low-demand customer (type 2) will drop out, and you don’t earn any profit from him – not good. If you set T equal to the consumer surplus for the type 2, then everybody comes, but the type 1 is getting lots of consumer surplus and keeping it – good for him, but not for you since you would like to transfer some of that surplus to yourself. We can see the possibility that the solution might be to move to a P > MC. What are the effects? • Consumer surplus drops for each type of customer, so T must fall, but • You earn more per ride sold. It may be the case that type 1 is so keen on rides that he continues to buy many ride tickets, and the gain in revenue from charging a higher price per ride outweighs the losses from charging lower T. Oi, and Rosen and Rosenfeld provide a solution to the problem. Suppose we set admission price T and have P initially equal to MC. But there is different willingness-to-pay by consumers. Ask yourself “At these prices, how much Z (rides in Oi’s Disneyland case; drinks and souvenirs in Rosen and Rosenfeld’s theater case) will

my average customer buy, and how much will my marginal customer buy, where the marginal customer is the low-demand person who barely finds it worth paying T to attend at all?” If the average customer buys more Z than the marginal customer, then it is worthwhile to increase P and decrease T: you will earn a lot from those average customers who buy lots of Z, and the decrease in T will allow you to attract a few more marginal customers in the gate (since they won’t care about the increased price for Z…they don’t buy it so much anyway). If the average customer buys less Z than the marginal, then subsidize Z by lowering P below MC, and increase T. This increases the number of marginal customers who will buy an entrance ticket (good), but it won’t break the bank having P < MC, since your average consumer doesn’t buy so much anyway. Applications. Why is popcorn at the movies so expensive? It must be that theater-owners have determined that the average customer buys a lot more popcorn than the marginal attendee does. So, keep T (the price of a movie ticket) low and set P (the price of popcorn) > MC. [This seems counter-intuitive – surely your real cinephile, who goes to see everything, is not loading up on buckets of popcorn? But research has shown that in fact it is true – your high-demand movie-goer is also a high-demand popcorn eater; theater owners know what they are doing]. Why is wine so expensive in restaurants? Wine is priced at P, your dinner costs T. Wine is like popcorn – your average customer is more likely to buy wine than your marginal customer, so keep the price of meals down and the price of wine up. Why so many lunch buffets? In this case P = 0, less than MC, but T is high. We expect then that the marginal customer is someone with a big appetite, while the average customer is more moderate. Lure the marginal customer with all-you-can-eat (which, after all, is still going to hit a limit as marginal benefits of another helping fall to zero), but you won’t lose that much, because the average customer will eat a smaller amount, and you are charging everyone a high T. Matt Yglesias the other day writes on his blog “I love gadgets and I like books and I don't really like carrying books around or go in for nostalgic reveries about the scent of paper on my fingertips. So basically, I'd like a Kindle. But at $399 it seems a bit pricey. Or, rather, at $399 the books should be cheaper. After all, distributing a digital text is way, way, way cheaper than manufacturing, storing, and shipping a hardcover book.” Why are Kindle books $9.99, far above marginal cost? Again, it must be that your average customer is going to buy more individual titles than the marginal customer. He finds the combination of $399 for the reader and $10 per book too much, and of course some people will decide to forego the thing altogether (as I have – I like paper books).

But Amazon’s strategy is not necessarily unreasonable. [Side note: with a product so new Amazon is in “nobody knows anything” territory, so prices may start to change]. [Further side note: on the other hand, iPods have been around for a while now, and persist in a P > MC strategy]. Why are printer cartridges so expensive, and printers surprisingly cheap? Because businesses drive up the average level of ink consumption, and households, who are your marginal customer, do not use much ink. So, for cartridges, P > MC. Printers have a low price, T. Notice that this only works if the printer manufacturer can ensure that a competitive market does not develop for cartridges – they need to keep some monopoly power, insisting that you buy from them or a licensed dealer. Major league baseball teams charge a lot for a plastic cup of Bud Light, or, as they call it, “beer”. But on “bat day” they give away bats to children. Why have P > MC for drinks but P < MC for bats? Disneyland sets P = 0 for rides, and P way above MC for food, drinks and souvenirs. Explain. Finally, keep in mind (and Rosen and Rosenfeld remind us) that the more you can price discriminate on T, the more you should do so, and keep P equal to MC for things on the inside. Setting P different from MC is a consequence of customers with different willingness-to-pay where you have no good way of price discriminating.