I’m going to dole out the answers to the first half of my honors exam slowly over the next several days. After that I’ll post the second half of the exam.
Let’s start with this one:
Question 3. Snidely Whiplash owns all the grocery stores and all the houses in the Yukon Territory. He charges a competitive price for groceries, and rents the houses at the highest price residents (who are all identical) are willing to pay. (If he charged any more, they’d all leave town). True or False: If Snidely raises the price of groceries, he’ll have to lower the price of housing, so he’ll be no better off than before.
Answer: It would be a great mistake for Snidely to raise the price of groceries.
Suppose you’re a customer who currently buys 15 bagels a week at a dollar apiece. Now Snidely doubles the price of bagels, and you choose to buy only 10 at two dollars apiece.
That’s bad for you in two ways: First, you’re paying an extra ten dollars for those ten bagels. Second, you end up with fewer bagels, which makes you sad. Since you were right on the verge of leaving town to begin with, Snidely’s got to make all of that up to you. He’s got to discount your rent by ten dollars plus compensation for the five forgone bagels.
So let’s look at both components. As far as the first ten bagels are concerned, you pay him an extra $10 and he gives it right back to you in the housing market. So far he’s even. As far as the remaining five bagels are concerned, he’s got to lower your rent by an amount commensurate with what you feel you’ve lost. Offsetting that, he saves the cost of providing those five bagels. But (and here is a subtle but key point) we know those five bagels cost him less than they were worth to you, because of the fact that he’s been willing to sell them to you in the past.
Therefore what he gives back to you in the housing market must exceed his savings from providing fewer bagels, leaving Snidely poorer than he was. He should never have raised the grocery prices in the first place.
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This gives me a chance to put in a plug for why you should take an economics class (at least if you enjoy this sort of puzzle). If you’re not used to this kind of thing, this reasoning probably looks convoluted enough to leave you thinking “Well, if you gave me an hour I could come up with an equally convoluted argument to prove the opposite”. And you’re right. You probably could. But your argument would be wrong, and mine is right. I know that because I didn’t just make it up; I discovered it by drawing a picture of the sort one learns to draw in economics classes. Once you’ve mastered the technique, these pictures force the right answer on you. It’s pretty cool, really. That’s why I like this stuff.
Just for the fun of making such a convoluted argument: If Snidely Whiplash is for whatever reason not in it for the long-term (he’s about to die and hates his children) than in the short term due to the inelasticisty of demand for housing he could profit for instance if housing is perfectly inelastic in the short-term then profit maximizing behavior maximizes is to maximize his grocery store profits.
I’m again left with the question of the word “competitive” in the pricing of groceries. Wouldn’t the answer be identical, no matter what price Snidely was charging for groceries, so long as it was a price high enough to make him a profit and low enough to allow the homeowners to eat?
Perhaps “competitive” means “at a price that would obtain in a competitive and successful market”, where “successful” guarantees that the grocers make a profit and the homeowners don’t starve.
Anyway. As a non-economist, I find that a clear and compelling answer. If there’s a diagrammatic way to arrive at such arguments, that sounds like a very useful tool.
He would not get me to stay in Yukon if all he has to sell is bagels.
What about Snidely decreasing the cost of groceries? was I correct in saying that he should sell groceries at cost (including the value of his time) or could he possibly earn even more by selling below cost?
Also, since you have drawn the picture, maybe you can share it with us, if it’s not too much trouble scanning it.
Steve Harris: Yes, “competitive” means the price that would prevail in a competitive market. And yes, the same answer applies as long as the price he’s charging allows him to make a profit on each bagel, which is equivalent to “competitive or higher”.
Snorri: You asked for a picture; I’m happy to oblige:
[Sorry, I can’t seem to get the picture to show here reliably. If you can’t see it, there’s a copy at http://www.TheBigQuestions.com/snidely.jpg .]
The curves illustrate the market demand for bagels and Snidely’s marginal cost of providing bagels. The competitive price is $1. Snidely earns a surplus of D+E+F in the bagel market. (I.e. D+E+F is the excess of his revenue over his variable costs.)
Now he raises the price to $2. His surplus is now B+D+F. Consumers buy fewer bagels, reducing their surplus (that is, the excess of what they’d have been willing to pay for those bagels over what they actually paid) from A+B+C to A. (B is lost because they’re paying more for the bagels they buy, and C is lost because of the bagels they’re not buying.) Snidely has to make this up to them in the housing market by lowering rents by the amount B+C.
Bottom line for Snidely: He earns an extra B-E in the bagel market, and gives up B+C in the housing market, for a net loss of C+E. He never should have raised the price.
I don’t think this is quite right. Snidely doesn’t have to make up the entire cost B+C because consumers buy more than housing & groceries. Assume I’m a consumer spending $500 on housing, $100 on food and $100 on everything else (transportation, entertainment, etc.) If Snidely raises my rent to $510, I could choose to spend $95 on groceries and $95 on everything else. This makes me less happy than I was before, but not necessarily $10 less happy. Snidely lowers the cost of groceries as little as possible to get me to stay in town. That’s probably less than $10.
Thank you, Steve (Landsburg): using the same geometric reasoning, now I see that Snidely cannot sell groceries below cost and recoup the entire loss by raising the rent. Too bad for his customers.
What if Snidely has more houses than there are residents? (This possibility isn’t explicitly prohibited by the problem statement.) Suppose further that the residents greatly prefer to consume houses over groceries. In this case Snidely could put the residents each in a bigger house with the same rent they had before and also charge a more for groceries. This would result in more profit for Snidely, would it not?
You might answer that if Snidely had or could build more houses then he would already rent them at a price low enough to attract a new resident. But I’d respond that perhaps there isn’t anyone else who will live Yukon Territory territory at any price. There’s nothing to indicate an unlimited supply of potential residents who are identical.
Are you really claiming that someone with a double monopoly has no more power to abuse the market than someone with one?
In particular, isn’t there a net social benefit to lowering rent from its monopoly price to its competitive price? In your discussion, you seemed to say that Snidley can capture the entire social benefit, so I’d like to see you explain why he doesn’t benefit from raising grocery prices while cutting rent.
Don’t we need to consider A’, B’, C’, D’, and E’ in the rent market too?
PB: Yes, someone with a double (vertical) monopoly has no more power to abuse the market than someone with one.
The easiest way to see this is to consider a monopolist who owns two toll booths, one at each end of a bridge. You’ve got to go through both booths to get to the other side.
This monopolist is no richer than a monopolist who owns just one toll booth on an identical bridge. Either of them will charge you (in total) what you’re willing to pay to get to the other side.
There is in fact a net social benefit to lowering rent from the monopoly price to the competitive price. Snidely in fact captures that entire benefit. The reason he can capture that entire benefit is that every family occupies one house and they are (by assumption) all identical—so they all have the same maximum willingness to pay. Snidely captures all social benefits by charging that maximum.
You are on to the key intuition underlying the problem: Monopoly pricing reduces social gain. In this case, Snidely captures the entire social gain, so monopoly pricing is bad for Snidely.
Isn’t there a large marginal social gain from lowering rent, and a zero marginal social gain from adjusting the price of groceries? By adjusting one and compensating with the other, can’t he keep the consumers’ benefit fixed and increase the social benefit?
PB: If you start with groceries at the competetive price, any change in grocery price will result in a marginal reduction in social benefit. If grocery prices increase above the competetive price, residents end up not buying groceries that were worth more to them than it would have cost Snidely to provide them. This makes society poorer, because those groceries should have been sold. On the other hand, if grocery prices are lowered below the competetive price, residents purchase groceries that they value less than it cost to get them there- these groceries never should have existed in the first place. This also makes society poorer.
Once you have set groceries at the socially optimal price (the competetive price), lowering rent would have no impact on social benefit. If Snidely lowers rent, consumers will simply keep that amount as their benefit, and Snidely will lose exactly that amount. In total, society is neither richer nor poorer. The rent is represented on the graph as the area A+B+C. Lowering rent simply redivides A, B, and C so that some portion goes to the residents.
As Landsburg said, monopoly pricing typically reduces social gain, because not enough goods are produced. However, since Snidely can capture the entire social gain, it is in his interest to ensure that social benefit is at its maximum. Pricing groceries competetively and charging the resulting surplus A+B+C achieves exactly this. Lowering rent from there just gives some of A+B+C to the residents, with no impact on the total social benefit.
If all moviegoers were identical, would this also be an argument that theatres should sell popcorn at the normal competitive price?
Phil: Bingo. Yes, it proves that if all moviegoers were identical, theaters should sell popcorn at the normal competitive price. The fact that they don’t do this proves (not too surprisingly) that not all moviegoers are identical. It also proves that the standard naive explanations for high popcorn prices at the movies (e.g. “the theater owner is exercising his monopoly power”) cannot be correct (or at best can only be pieces of a correct answer). There’s a chapter about this in my earlier book The Armchair Economist, and it’s something I dwell on at considerable length in Chapter 10 of my Price Theory textbook, because it illustrates multiple important points about pricing theory.
Right, I am a proud owner of “The Armchair Economist,” and I remember different popcorn preferences was part of the answer. I should go back and reread …
I remain unconvinced. As you said, it’s possible to come up with convoluted arguments for this in both directions. One such argument is right, while others are wrong. I’d like to make sure I understand this. Let’s leave aside, for the moment, vertical monopolies, popcorn, and your book. Instead, let’s try to establish what we are discussing.
Let’s assume that there is Snidley and the population of the Yukon, that groceries are produced and consumed as in your diagram, that housing is produced and consumed according to a similar diagram, with the exception that the monopoly owner has kept the price above the one that would prevail in a competitive market.
Thus, there are two diagrams, for groceries and for rent, to consider. On both, we can consider the initial situation in which Snidley keeps housing at the maximum the people are willing to pay, but allows groceries to remain at the competitive market rate. Secondly, we can consider the situation in which rents are lowered but grocery prices are increased. In the grocery diagram, we have regions A, B, C, D, and E, as you drew. In the housing diagram, we have similar regions A’, B’, C’, D’, and E’.
I tried to post the image earlier. It’s at http://www.victoria.tc.ca/~uq598/Snidley.jpg
The change in value to the people of the Yukon is L=-B-C+B’+C’. (I have -B-C, since this represents a loss to them.) Since the people are on the verge of leaving, Snidley cannot make this value, L, negative. However, as the double monopolist, he can make changes for which this change is zero. In this case, he is constrained by 0=L=-B-C+B’+C’. Applying algebra, we can see B-B’=C’-C.
The change in value to Snidley is K= B-E -B’+E’. (He gains B but loses E, so it is B-E as you said. The reverse occurs for rents.) From the earlier condition, it follows that Snidley’s gain is K = E’+C’-E-C = (E’+C’) -(E+C). If we look at the diagrams, we can see that C, E, and C’ are little triangles, but that E’ is a big rectangle with a small triangular piece on the bottom, so the total change, L< looks positive.
As you noted before, the fact that Snidley was previously willing to sell groceries implies that E+C is positive. Similarly, the fact that the prices are compatible with a competitive market means that both the consumers and producers are nearly indifferent to trading, so that E+C is positive, but small. On the other hand, the fact that Snidley is a monopoly producer keeping housing prices artificially high, means that the gain from lowering rents E'+C' is relatively large. Thus, Snidley gains by raising grocery prices, but lowering rents.
(Readers who enjoy calculus will recognise that in these arguments, triangles are small and rectangles are (relatively) big. Each is determined by the marginal change in social value. From the competitive value, the change, E+C, is small; from the monopoly value, the change, E'+C', is large.)
Perhaps I've made an error in my argument. It can be tricky to read through a convoluted argument and find the error. To be fair, let me start by saying that I believe the error in yours is the claim that "you pay him an extra $10 and he gives it right back to you in the housing market". This claims that the B'+C' that the Yukon residents gained in the housing market cost Snidley -(B'+C'), when it only cost him -(B'-E').
For the analysis of a vertical monopoly to apply, it would have to be that there is no gain to consumers to use one of the goods when the other is limited. For example, it does me no good to get on the bridge if I have to pay to get off. Similarly, it does me no good to get more oil from you for free if I have to pay you to move it through your pipeline. In Snidely’s Yukon, consumers do benefit from receiving more or better housing, and cinema goers do benefit from getting popcorn, regardless of whether they are identical.
PB: I am assuming that housing is in fixed supply, and that each household ends up with exactly one house. In the movie theater example, the analogue to housing is not the popcorn but the price of admission: Admission tickets are one-per-customer, and no customer has any use for a second one.
Regarding the comments about a “double monopoly” —
Just to be clear, this isn’t technically a “double monopoly” situation, is it? Snidely doesn’t technically have a monopoly on housing, since people can live in other towns, but once people choose to live in his town, he then has a monopoly on groceries. So it’s analogous to the movie theater / popcorn situation. Is there a technical term for that, like a “consequential monopoly”?
Or in terms of tollbooths, it’s as if there are multiple bridges competing for drivers’ business to get across the same river — once a driver chooses a bridge, the bridge owner could put another tollbooth at the other end of the bridge and they’d have a “monopoly” on getting off their bridge, but they wouldn’t make any more than if they charged the same total at the first tollbooth.
Steve Landsburg: I do not believe there is any housing supply curve which is consistant with both the demand curves we have considered and the situation you have described.
Are you confusing fixed supply with fixed demand?
PB: The assumptions are that in order to live in the Yukon Territory, you must have one house, that a second house is of no additional value, and that there are a fixed number of houses that Snidely provides at zero marginal cost.
Under the assumption you’ve given, which is fixed demand, I agree with the original conclusion.
In this model, the inhabitants are apparently completely indifferent to quality or additional space. Not only has Snidely managed to impose a monopoly price, but he has been able to do this without limiting consumption or total social value. However, we can’t say that he is holding the price above the competitive market price, since this model is so strange that there is no price which could be described as the competitive market price. All of these make the model seem weird to me, but I’ll concede that if you take this model, it has the behaviour you describe.
PB: I continue to claim that this is the natural baseline model, since any alternative introduces additional complications that don’t change the outcome and don’t illuminate the fundamental point. Of course that’s partly a matter of taste, so we can disagree about that.
But in pretty much *any* model, the point is this: Snidely has to give the residents some total amount of surplus; otherwise they’ll leave town. That means he gets to keep all of the social surplus, minus the constant amount he’s got to give the residents. To maximize (total surplus minus a constant) it is necessary and sufficient to maximize total surplus. Monopoly pricing fails to maximize total surplus, so it can’t be the right strategy.
PB: Perhaps your point is that with downward sloping demands for both groceries and square footage, there might be no way for Snidely to extract all the excess surplus—in which case some amount of monopoly pricing in each market might be optimal. If so, I agree, and a student who argued thus would deserve full credit and more. But it still seems to me that the natural vision is that nothing stops Snidely from offering a single standard (and optimally) sized home and chargint the amount that extracts all the excess surplus.
Of course, you could argue that he could do the same thing in the grocery market—offering a single standard sized package of groceries and extracting all his surplus there instead of in housing. But by posing the question as a choice between setting a high or a low grocery price, the problem implicitly rules out this kind of bundling.
In summary: It’s got to be optimal for Snidely to offer either a single standard-sized grocery package or a single standard-sized home; either way he gets all the surplus. . The wording of the problem seems to rule out the former, which leaves us with the latter.
“But (and here is a subtle but key point) we know those five bagels cost him less than they were worth to you, because of the fact that he’s been willing to sell them to you in the past.”
Prof Landsburg: People’s preferences change. Does it matter if the reason Snidely is raising the price of bagels is because his opportunity costs for bagels increased (say, because he found he had a greater hankering for bagels than in the past)?
RL: The solution I’ve given assumes that costs and preferences are stable over time. Students in economics classes know that these are always the default assumptions in problems like this. You are right that without those assumptions, the solution I’ve given would not apply.