Well, at least at a first glance, consumers get everything for free (if you don’t count being shown adverts). One can’t say that Google artificially restricts access to, for instance, Google Calendar for its potential consumers. It seems to be rather the opposite: they encourage consumers to use all these services by dishing them out for free. Obviously this is not how Google makes its money. How does Google make most of its money? They do this by auctioning off list spots after searches (see e.g., here and here for how the Google ad auction system works). All this is automatized, but whenever you or anyone else searches for something, let’s say “red sofa cheap”, you get a bunch of companies competing for first spot (or at least first page) on the list that appears on your screen. This way, probably billions of auctions are run each day. And this is where Google has some monopoly power. You, the searcher, are actually not Google’s customer, the companies outbidding each other to get your attention are Google’s actual and paying customers. These companies vying for your attention cannot control where you search for stuff online and if you choose Google then the only way to affect your choice (well, not quite the only way, but a very direct way) is that they “influence” Google (by bidding on list spots) as to what they show you. Now as Google is used for 70% or more searches, Google has a monopoly on very many searches and, thus, a monopoly on a bit of the attention of very many searchers.
How does Google use this monopoly power? What is the product that they “hold back” and price too highly? It is your attention for certain products in the form of what, after your search, you will most likely be looking at. Google, “artificially” structures their search page in such a way that there is a clear first option, a second one, and so on. The perhaps most crucial design feature is a first and then a second and then further pages. Remember, if you can, the old fashioned phone books. There everything was in super small print, but all companies were treated more or less equally. Well, actually, at least in those phone books that I remember, companies could also pay for a bigger mention in the phone book. I am just trying to say that one could imagine different formats of how to show searchers information and some other forms may lead to a more efficient result.
One could argue, and I believe Google does argue this way, that their bidding system is likely to lead to the best ranking of websites (or ads) for the searchers. But this is, of course, not necessarily true. It would be somewhat of a coincidence if the result of the companies’ bidding produces exactly the ranking of websites that you, the searcher, want.
If somehow Google could be forced to have many firsts spots there would be less competition for the bidding companies and they would all pay less. I am not sure this could be so easily done, but this, I believe, is the sense in which Google “holds back” its products (of list spots) to sell them at a higher price. In that sense there might well be an inefficiency in the way Google presorts websites and adverts for you the searcher and final consumer.
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I believe it is true that CocaCola and Red Bull have monopoly power. As we said this means that they do not produce and sell “enough” of their product. Actually in this case, however, I am in fact pretty happy that they sell less than what, supposedly, they could be selling of their product. Why? I don’t think it is actually such a good idea for people to drink these drinks. They don’t strike me as very healthy. In fact I do not allow my kids to drink them (as far as I can).
So what I am really saying here is that I think people have the “wrong” preferences and that’s why a Paretoinefficiency assessment based on “wrong” preferences does not worry me. If I impose my personal assessment of this on others – in short I am being paternalistic – I would then probably like people to drink even less of these drinks than the supposedly low monopoly quantity. Given my personal assessment I thus may have a problem with these drinks companies but not because of their monopoly status. I might not like the fact that CocaCola and Red Bull – I do like their adverts, though – make so much money with their products, as, in my mind, they prey on the foolishness (or myopia) of people. But I rather have that they make lots of money selling at high prices to a “few” people than almost no money selling at low prices to many more people. So I would personally certainly not advocate a more competitive market in this industry. Unless that is more competition in this industry would lead to people starting to drink water. But that seems unlikely.
]]>Die Formel kommt aus einem mittlerweile zum Standard gewordenen Modell bilateraler Handelsströme von Johnathan Eaton und Samuel Kortum. Dieses Modell ist im Prinzip eine Verallgemeinerung des „Ricardianischen Modells“, das wir alle im ersten Jahr VWLStudium gelernt haben (wir erinnern uns: England tauscht Tuch gegen Wein aus Portugal,…), nur eben mit unendlich vielen Gütern und beliebig vielen Ländern. Die Formel setzt das ProKopfRealeinkommen einer Volkswirtschaft w in Beziehung zum Inlandsanteil seiner Gesamtausgaben („home share“) h:
w = a*h^(b),
wobei die Konstante a die allgemeine Arbeitsproduktivität der Landes misst (je größer a, desto größer der „absolute Vorteil“ eines Landes) und der Parameter b die Streuung der Arbeitsproduktivität über die Länder hinweg bestimmt (je größer b desto stärker ausgeprägt sind die „komparativen Vorteile“ jedes Landes). Hier klicken, wer eine Herleitung sehen will. Eaton und Kortum und Krugman verwenden b=0,25 in ihren Berechnungen. Die Konstante a spielt für unsere Zwecke keine wesentlich Rolle.
Wie berechnet man den Inlandsanteil? Dazu müssen wir uns an die VGRIdentitäten erinnern. Das Bruttonationaleinkommen Y ist bekanntlich gleich den Gesamtausgaben eines Landes (Summe aus privatem und staatlichen Konsum und Investitionen) abzüglich der NettoExporte (Exporte X minus Importe M). Die Ausgaben auf inländische Güter erhält man indem man von den Gesamtausgaben die Importe abzieht oder wenn man vom Bruttonationaleinkommen die BruttoExporte abzieht. Das heißt wir können den Inlandsanteil wie folgt berechnen:
h = (YX)/(YX+M).
In einer geschlossenen Volkswirtschaft ist der Inlandsanteil gleich eins. Daraus folgt, dass das ProKopfRealeinkommen einer autarken Volkswirtschaft nur durch die allgemeinen Arbeitsproduktivität a bestimmt ist. Je offener die Volkswirtschaft, desto geringer der Inlandsanteil, desto größer sind die Handelsgewinne.
Nachstehende Grafik zeigt die Resultate meiner Berechnungen für die Österreich von 1995 bis 2017 (Daten von Eurostat). Warum 1995? Weil das das Jahr war, in dem Österreich zur EU beigetreten ist. Wie man sieht entfielen bei EUBeitritt noch fast 2/3 der österreichischen Gesamtausgaben auf heimische Güter. Heute liegt der Anteil bei unter 50%.
Laut unserer Formel stiegen dementsprechend die Handelsgewinne seit dem EUBeitritt von ca. 11% auf über 20% des ProKopfRealeinkommens. Sprich: würde Österreich wieder zur Handelspolitik von vor 1995 zurückkehren, wären wir um rund 9% ärmer. Würde Österreich alle Handelsbeziehungen kappen und von nun an in perfekter Isolation leben, müssten wir auf 1/5 unseres Einkommens verzichten. Oder in absoluten Zahlen ausgedrückt: Jeder Österreicher ist im Schnitt um 8.400 Euro pro Jahr reicher durch den Außenhandel. Eine Rückkehr zu VorEUHandelsverhältnissen würde jeden Österreicher ca. 3.800 Euro pro Jahr kosten.
Wie immer bei diesen Rechenspielchen sind die konkreten Zahlen mit viel Vorsicht zu genießen. Sie hängen stark von vereinfachenden Annahmen ab und bieten daher nur einen ersten groben Anhaltspunkt. Wie dem auch sei, ich mag solche PimalDaumenRechnungen einfach!
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Let us go back to the fundraising efforts of the student organization from the previous lecture. The setup is the same: the student organization wants to show a movie in a lecture hall that can seat up to 500 people and the demand function is such that at a ticket price of P (in euros) the number of people interested in a ticket is given by 700100P (that is 600 interested people at a price of 1 €, 500 at a price of 2 €, and so on).
But now suppose that instead of there being one student organization there are actually two with very independent interests. Each student organization is given 250 tickets which they can sell at any price they want. Suppose that they share the cost for cleaning and the movie equally before the whole thing begins. And suppose that you are in charge of exactly one of these student organizations. How should you determine the price of your tickets now? Should you charge the 3,50 that were profitoptimal when there was only one student organization or should you charge another amount?
In some ways “ideally”, for you and the other student organization, you would both charge a price of €3,50 and so roughly split the €1225 revenue that you would make together. You would get a revenue of €612,50 and from this you would have to pay €350 for the cleaning and the movie.
But what if the other student organization charges €3,50 and you charge slightly less, say €3. We first need to think about what we think the consumers would do in this case. Well, I guess if they see the two prices they would first try to buy your tickets, after all they are cheaper and a ticket is a ticket regardless of who they buy it from (and we believe that people prefer, ceteris paribus, having more money over less). So suppose this is more or less the case. Recall that at €3 the total demand for tickets is 400. You can only sell 250 as this is how many you have. So your revenue would now be 3 times 250 which is equal to €750. So this is €137,50 more than in the previous case! Undercutting the price would pay off for you!
How much would your opponent “make” in this case? This is actually a tricky question and we will need to make another assumption. We need to think about who the people are that bought tickets from you and who the people are that did not in order to determine what kind of people are still left with a desire to buy a ticket. In order to make sense of what I just wrote, we need to go a bit deeper into our demand function (in fact, very much as in the market experiment). There are two ways to think about a demand function. The one that I typically favor provides the number of tickets that people would buy as a function of the price. But we can also turn this upside down if you like. We can also think of the demand function as providing the price that is necessary so that a certain number of tickets can be sold as a function of the number of tickets. This is often called the inverse demand function, although many people also just call it the demand function. If you think of it this way, with number of tickets demanded on the xaxis and price on the yaxis, then how do we interpret the intercept, the value at which the (inverse) demand function intersects the yaxis? This is the price that is just so high that no one would want to buy a ticket. If we decrease the price we would get one person interested in buying a ticket. What characterizes this person? It is the person with the highest maximal willingness to pay for a ticket! Here this highest willingness to pay is €7. If we go down a Eurocent we hit the maximal willingness to pay for a ticket from the next most interested consumer, and so on.
So at a price of €3 we get 400 people interested but only 250 can buy (remember my post on rationing). So who buys? It must be some selection of all the 400 people with a maximal willingness to pay of €3 or higher. You can play with different scenarios if you like, but I will here assume that the people with the highest willingness to pay (that is all with a willingness to pay of €4,50 or higher) get a ticket. This scenario makes the profits to the other student organization as low as possible. But please do play with other scenarios: the other extreme would be that the people with a willingness to pay between €3 and €5,50 get the 250 tickets. In my scenario, what is then the demand “left over” for the other student organization at their price of €3,50? It is all the 100 people with a willingness to pay between €3,50 and €4,50. The other student organization then gets a revenue of 3,50 times 100 equal to €350 (just enough to cover their costs). If you played with the other extreme case, I believe you would have found that the other student organization would be getting 3,50 times 150 equal €525. This is the best they can hope for and is still considerably less than the €612,50 that they would have expected if both of you had charged a price of €3,50.
So if both student organizations really do choose prices independently and only care about the money that they themselves raise, then this starts a race to the bottom. I worked out the whole table of possible revenues for the two organizations for each possible price combination (assuming that only multiples of 50 eurocents are considered). Here you are:
€ 1,00 
€ 1,50 
€ 2,00 
€ 2,50 
€ 3,00 
€ 3,50 
€ 4,00 
€ 4,50 
€ 5,00 

€ 1,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 250,00 
€ 1,50 
€ 450,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 375,00 
€ 2,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 500,00 
€ 2,50 
€ 500,00 
€ 500,00 
€ 500,00 
€ 562,50 
€ 625,00 
€ 625,00 
€ 625,00 
€ 625,00 
€ 625,00 
€ 3,00 
€ 450,00 
€ 450,00 
€ 450,00 
€ 450,00 
€ 600,00 
€ 750,00 
€ 750,00 
€ 750,00 
€ 750,00 
€ 3,50 
€ 350,00 
€ 350,00 
€ 350,00 
€ 350,00 
€ 350,00 
€ 612,50 
€ 875,00 
€ 875,00 
€ 875,00 
€ 4,00 
€ 200,00 
€ 200,00 
€ 200,00 
€ 200,00 
€ 200,00 
€ 200,00 
€ 600,00 
€ 1.000,00 
€ 1.000,00 
€ 4,50 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 562,50 
€ 1.125,00 
€ 5,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 0,00 
€ 500,00 
The way to read this is as follows. The blue leftmost column has the possible prices that you could choose for your student organization. The green upmost row has the possible prices that the other student organization could choose. The euro amount in each cell is then your revenue if you choose your corresponding price in blue and the other student organization their price in green. So for instance, you can find your revenue of €750 when you choose a price of €3 while your “opponent” chooses a price of €3,50. I have marked your best “reactions” to possible opponent prices in red in the table. If you stare at the whole thing for a few minutes you will see that this setting gives rise to a certain repeated undercutting logic. If your opponent chooses a price of €5 you would optimally choose one of €4,50. To your opponent’s choice of €4,50 you would choose €4. To your opponent’s €4 you would choose €3,50. To your opponent’s €3,50 you would choose €3. To your opponent’s €3 you would choose €2,50. And, interestingly finally, to your opponent’s €2,50 you would still choose €2,50. [In fact, if we considered any multiple of 10 eurocents you would now optimally react with €2,40, and then all the way down to €2,10 both.] So, while a price of €2,50 each is not as good as a price of €3,50 each for both of you, the undercutting logic can easily lead you to €2,50 and this is much better for your consumers! In fact this is what economists tend to think and hope that competition does: it leads to lower prices and to an allocation that is thus much closer to the Paretoefficient allocation (with 450 sold tickets at a price of €2,50 we are not far from the Paretoefficient 500 sold tickets at a price of €2 – see previous post).
Will this really happen if we have two such firms in a market? Well, it all depends. In my class I managed to let my students play this game against each other in a slightly confusing way and a relative majority of them ended up choosing a price of €2,50. But I did not actually pay them any money, so I do not know how indicative this is of what would go on in the real world. In the real world firms sometimes manage to avoid this form of competition. In Austria fairly regularly big construction companies are caught colluding, that is they are caught meeting and discussing setting high prices. This is illegal in Austria and therefore punished in the form of heavy(?) fines. By the way, in the language of game theory, the theory of strategic interaction, what I have just described is called a “Bertrand game” (after some person Bertrand who wrote about this in 1883) with capacity constraints (you may want to look at a paper by Kreps and Scheinkman, Bell Journal of Economics, 1983) and the €2,50 would be the (not weakly dominated – whatever this means) “Nash equilibrium” strategy for both “players” in the game. A “Nash equilibrium” (after a person called John Nash who wrote about this in 1950) can here be defined as a price pair (one price for each student organization) such that no student organization would want to deviate to another price if they believe that the other student organization chooses according to the original price pair. Note that a price of €2,50 for both satisfies this definition. Actually, so does a price of €2 for both (but it is weakly dominated – as I said this is not so interesting at this point). Note that both choosing a price of €3,50 is not a Nash equilibrium exactly because if you assume your opponent really does choose a price of €3,50 then you do not want to do so, you want to choose €3 in this case.
To study collusion researchers have also considered what could happen in the “repeated game”. After all in most cases firms compete for the same customers not just once, but every week, day, month, hour, year anew (the frequency may depend, among other things, on how “durable” the good under consideration is or how often production decisions can be made). And it turns out that in the repeated game – meaning that the competition is a longlasting one, which after all often seems more plausible, it may be quite easy or at least possible for firms to collude without even speaking to each other. But I should really leave this for another lecture, probably in another course on game theory. But just briefly, how could this work in our setting? Suppose the two student organizations hold a similar event once every month. They could follow the following repeated game “strategy”: choose a price of €3,50 always unless at some point your opponent chose differently, in which case choose a price of €2,50 forever after. If both student organizations follow this socalled “grimtrigger” strategy, then both have no incentive to charge any price other than €3,50. In reality such “tacit collusion” is not always that easy because the demand function is probably not always the same over time and the two (or more) firms do not necessarily observe what the other firm’s prices are.
So you have seen the reason why economists tend to like competition. It tends to bring prices down and this is good for the consumers and (at least closer to) Paretoefficient. But whether or not the presence of two or three firms is enough to have proper competition is not always clear and should probably be investigated on a case per case basis.
]]>To fix ideas consider the following situation. You are in charge of a student organization and you are trying to do a bit of fundraising. You are thinking of showing a movie in a university lecture hall at reasonable ticket prices to students. You have convinced the university that they let you have a largish lecture hall with 500 seats for free. You only have to pay for the cleaning cost, which say amounts to €200. You also have to pay for the right to show a movie, which say amounts to €500. You have otherwise convinced some of the other members of the student organization to help with ticket sales, advertising, and other matters, for free. The key question for you is now, what to charge the students for the tickets?
To simplify matters let us assume that all seats are more or less the same, or perhaps better that you sell tickets without a particular seat number and people can choose their seat on a first come first serve basis. Do you have any idea on how to choose a ticket price yet?
Well, at this point, with the information that we are given, it is pretty unclear how you would identify a ticket price. You lack a key bit of information: what is your demand function? How would you know the demand function you are facing? Well, this is pretty hard sometimes. I guess in most cases firms learn their demand function from experience. Think of Lufthansa’s flight ticket pricing problem from a previous post, for instance. Suppose you look at the direct flight from Graz to Dusseldorf, which operates I believe three or four times a week. It may be hard for Lufthansa to work out the demand function for the very first such flight, but the longer they operate this flight the better they probably understand the demand function and how it changes on different days of the week and different months of the year and so on. Well, in fact, Lufthansa’s automatic booking system can automatically detect changes in the demand function. If the automatic booking system experiences a sudden increase in ticket requests (perhaps because of a conference staged in Graz – unknown to Lufthansa) then it automatically “infers” that the demand has risen and reacts accordingly. I am pretty sure that the real booking system Lufthansa uses is pretty sophisticated and pretty good at identifying any changes in demand for any flight.
Or consider a bakery and their decision as to how much bread and how many bread rolls and other things to stock on any given day. I believe that experience, together with some knowledge of the calendar, allows bakeries to make these decisions pretty well on average and that these decisions are based on a pretty good understanding of the demand they face. But of course, one can also easily get this wrong sometimes. I remember one Sunday that was a day of voting for some general election in Graz when I found that the local bakery next to the voting booth was almost devoid of all food. When I asked them, they “admitted” that they underestimated the demand on that day. But, on the whole, I find it pretty amazing that I almost always get what I want (or a close substitute) from my bakery.
Sorry for the long excursions. Back to our problem. Where do you get the demand function from? Actually, let me not get back to our problem just yet, but let me add one last bit of excursion. I believe that correctly identifying (at least a good lower bound) for a product’s demand function is a key ingredient to the possible success of any startup. It is definitely something that an investor in your startup will want to be pretty sure about (or at least properly understand its risks – and perhaps demand a premium for such risks – see more on this in a future post).
But now let us really get back to our problem. Suppose in your case that the student organization has done similar things in the past and that you have a reasonably good idea of the demand function that you are facing. Let us assume it is roughly as follows. At a price of zero, that is if you give the tickets away for free, you would find that roughly 700 people would be interested in coming. At a price of €1 you would get 600 people interested, at a price of €2 you get 500 people, at a price of €3 this would be 400 people, at €4 there would be 300 people, at €5 we get 200, at €6 one hundred, and at €7 no one would come. With this information, what price would you, finally, choose?
Have you made your decision? When I asked my students in the class roughly 60% said they would charge €3, another 20% would charge €4, and another 16% would charge €2, with the remaining 4% going for €1 and €6 equally.
In fact both €3 and €4 give the same “revenue” (and thus the same “profits”) of 3 times 400 = 1200 € for revenue (and 1200 – 700 = 500 € for profits), and this is the best profit we can get if we only allow full euroamounts. If we actually allowed also eurocent amounts, we could do even better (assuming the demand function extends naturally (that is linearly) between prices of 3 and 4) profitwise by charging €3,50 per ticket and then get a revenue of 3,50 times 350 = 1225 € (with profits of 525 €). If all this is approximate, as it most likely is, then this is our best guess as to what price would be the best for your fundraising efforts. But perhaps this is not our (only) goal?
How about our “consumers”? If we compare prices €3 and 4 only, then consumers would of course prefer the lower price, after all an extra 100 people would prefer to come to the movie at the lower price and all those 300 that would come anyway have to pay less now and have a little bit more money to spend on other things. That’s probably why most of my students went for the price of €3 instead of €4.
But, even at a price of €3 per ticket, is the allocation of tickets (that is seats) to people, Paretooptimal? This is a tricky question, but it actually has a very clear answer. At first glance, and given what we have learnt so far, it seems that the allocation might well be Paretooptimal. After all we said that letting the price adjust so that there is not too much demand is the only way we get Pareto efficient allocations, when there is money that people could spend on other things. In fact, and maybe I did not stress this enough in a previous post (rationing) this is only a precondition for a Pareto efficient allocation. For a Paretoefficient allocation, when there is money which one could spend on other things, we need that the tickets go to those people who have the highest willingness to pay for these tickets. This is still true. And, of course, we have that here. But this is true for any price, as long as the price is such that the demand is less than the number of possible tickets we could have sold.
So why does a price of €3 (or any higher price, in fact any higher price than €2) not lead to a Paretoefficient allocation after all? Think of it this way: after you sold the 400 tickets for €3 each, there are still 100 empty seats and many people (300 in fact) who would be happy to take a seat (but for a lower ticket price). If you could somehow manage to sell another 100 tickets at a price of say €1 then we would get a Paretoimprovement [I am not saying that this is easily achievable!]. This is why the allocation with 400 tickets at a price of €3 is not Paretoefficient. Because both you (the student organization) as well as some consumers would be better off without making anyone worse off. But what then would be Paretoefficient? The only answer is a price of €2, which then leads to 500 tickets sold. [One should maybe add that it is possible that people do not like being in such a crowded lecture hall, in which case we would say that any ticket sold to someone else creates a negative externality on someone who already holds a ticket. Then this argument is not correct and a price of €2 is not Paretoefficient after all. See more about externalities in a future lecture and about this particular problem in this post here. On the other hand for football stadiums the externality is possibly reversed and it may be in the at least longrun interest of the football club to charge fairly low prices to make sure that the stadium is not half empty, which might lead to even fewer people interested in coming to the next game.]
Does a price of €2 lead to a Paretoimprovement over a price of €3? Almost. A price of €2 is clearly better than a price of €3 for all consumers. Only one person (party) suffers: you, or the student organization, are clearly worse off at this price. So again, Paretoefficiency is a subtle concept. A price of €3 leads to a Paretoinefficient allocation of tickets, a price of €2 leads to a Paretoefficient allocation of tickets, but the latter case is not a Paretoimprovement over the former.
But note that, especially if we care mostly about the consumers, this is one major problem that firms with some monopoly power, such as an airline who is the only one offering flights from A to B, or the producer of Xboxes or PlayStations, or (interestingly and very upsetting to me) also some publishers of scientific journals, or producers of certain fairly unique drugs, or any other firm with a “flat” demand function, induce: that they charge too high a price and sell too little of their product. With “too high” and “too little” I mean that there are potential customers of this good who have a higher willingness to pay for this good than it would cost the firm to produce this good and yet these customers do not get this good.
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So how does it work? The program randomly declares 30 of the 60 students “buyers” and the other 30 “sellers” of some indivisible good. So the idea is that the 30 sellers each own some identical object (say all the same book, in the same condition) and the 30 buyers would possible be interested in buying this book. Each of the 30 sellers is randomly given a “value” of how much the object is worth to them. They can ever only sell their object at a price higher than their value. I, the experimenter, can choose the different values the sellers get. Each of the 30 buyers is also randomly given a “value” of how much such an object would be worth to them. Again, I, the epxerimenter, choose the range of values buyers could get. As all objects (that the sellers own) are identical it does not matter who the buyer buys the object from. Buyers can only buy an object at a price lower than their value.
Once the sellers and buyers are chosen and their values distributed, they can all make offers and can accept or reject offers made by others. While none of the buyers and sellers are informed about the distribution of values that others have, they do see some information on their screens. They see what offers are being made and they see the latest deals that were struck.
For the first two sessions I chose a value distribution that gives rise to a linear demand and a linear supply function. How does this work? I chose buyer values 10,11,…,39 and seller values 20,21,…,49. How do we get the demand and supply function from this? Give me a price, say 37. Then what is the demand at price 37? It is the number of buyers (as one person can only buy one object) who have a value above and possibly including 37. How many are there? There are three, those buyers with value 37, 38 and 39. What about the supply at this price? It is the number of sellers with a value of 37 or below. These are sellers with values from 20 to 37. So these are 18 people. At a price of 37 the supply far outweighs the demand. The software that Heinrich Nax and his colleagues have provided delivers the following picture of the demand and supply functions.
Note that in the experiment people can trade at any price. Here is the figure with all the deals that were made (over time).
Note that while the prices of deals vary a fair amount they fluctuate around a price of 30. What is so special about the price of 30? It is the market price. It is the price at which supply equals demand. There is one more thing you may want to note. How many deals have been made? The first session had two rounds and the supply demand diagram suggests that there should be 10 deals in each round. How many deals did we get? We got 21 in two rounds, one more than we “should have” according to the theory.
Here is the figure of deals over time in the second session with the same supply and demand functions.
Students played two rounds in the second session. Note again how the price fluctuates around a price of 30. In fact it looks like that the price fluctuates a bit less than before. This could be due to the growing experience students had with this problem. This time we got only 17 deals. This is now three short of what we “should have” according to the theory.
For the third session (with again two rounds) I changed the supply function. I left the demand function the same. I told the students that I am changing things, but I did not tell them how. Here is the supply and demand figure:
Note that the market price in this new setting, that is the price where demand and supply intersect, is now 35. Here is the figure with deals in this new setting:
Interestingly the first deal had a price of even less than 30, but then quickly after that the price fluctuates (not even all that much – except for two deals) around 35. How many deals “should” there be and how many were there? Well, we saw 30 deals this time, when the theory says that we “should have”, in fact, 30 deals.
A caveat: This is probably working almost too well. In many ways this is a pretty simple market, just one good and all potential traders are coming together in one central (here online) market. Financial markets, in fact, work very much like this and approximately so do many markets for basic agricultural products such as coffee beans and wheat, but not all markets do. Some markets are much less centrally organized – the market for holiday apartments for instance. Also often traders have to be active in several markets at the same time and if the price of one good is too high they would rather buy another good at another market (because the two goods are close substitutes). The theoretical literature in fact shows that, in principle, there could well be a collection of markets such that a dynamic trading process will not lead to the “market equilibrium”. See for instance the survey article by Franklin M. Fisher “The stability of general equilibrium—what do we know and why is it important?”, Chapter 5 of the book ”General Equilibrium Analysis”, edited by Pascal Bridel, Routledge, 2013.
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So did the demand for flights go up after Air Berlin went out of business? Look I do not know this fully, but I guess the answer is yes and no. Of course, Lufthansa’s individual demand function has gone up, but this is because the overall supply function has gone down. I would guess that the overall demand function for flights has not changed dramatically. And yes, while Lufthansa may not have changed the automated pricing system, automatically prices have gone up because the automated pricing system does already respond to an individual increase in demand for Lufthansa flights by automatically setting higher prices. I would be prepared to bet a fairly large amount of money that the total amount of money spent on tickets on a Lufthansa flight after Air Berlin went out of business was quite a bit higher than the total amount of money spent on tickets on the same Lufthansa flight before Air Berlin went out of business. I wonder whether Lufthansa could actually have done any better (in terms of profits) by changing the automatic pricing system.
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This is all interesting, you might say, but there is no such thing as a uniform price for holiday apartments. Each apartment is different and each apartment will have a different rental price. True. I guess what we did is a fairly rough approximation to the real situation. Far from perfectly correct. But recall that no model (or story that we can tell) is ever a perfect fit to any real life situation. The model we build always depends on the question we are trying to address. If we are only interested in explaining why holiday apartments in Upper Styria are, on the whole or on average, cheaper in summer than in winter, while at the same time fewer people actually rent them in the summer than in the winter, then the rough story of market supply and demand suffices for an explanation. If you recall, the simple rough idea that people are more interested in renting holiday apartments in Upper Styria in the winter, that is there is a higher demand (function) in winter, can explain these two observations. In fact, I believe this to be a very appropriate explanation. This does not mean that all apartments in Upper Styria will be cheaper in winter than in summer. There could well be some that are relatively more attractive in summer than in winter. For instance, take an apartment that is actually quite far away from a ski resort, and in winter always in the shadow of a mountain (because the sun does not climb that high), but is perfectly sunny and yet cool in the summer and close to the top of a mountain and what not. One could well imagine that such an apartment could have a higher rental price in summer than in winter. Our story was a rough one and probably true for the average apartment but not necessarily for all.
Now suppose that you own a house with a few (fairly typical) apartments in Upper Styria and you are interested in renting them out as holiday apartments (in winter or summer). Is the market demand for holiday apartments in Upper Styria also relevant for you? Well, yes and no. Yes, in the sense that the rental price that you will be able to achieve will be more or less determined by the market demand function but the market demand function is actually not the demand function you face. What am I saying? Suppose you have a few apartments. Then the demand function you are interested in is one that tells you how many of your apartments you can rent out as a function of the price. You will find that you have a very steep demand function. I mean that your demand function will look more or less like this: there is a price (in fact essentially the market price) such that for any price lower than that market price you will find it easy to rent out all your apartments and for any price above this price you find it virtually impossible to rent out any. This means that you as a small contributor to the total market of holiday apartments have very little discretion as to which price you could choose. It is more or less all or nothing for you. You may have more discretion with the price if you have a very special location or a very special set of apartments, but for most apartment owners their individual demand function will be very steep.
This is probably even more true for the market for apples (in Southern Styria). If you are one of really very many apple farmers and you grow more or less the same apples as many others, then you will find that you have virtually no discretion when it comes to the price of your apples. Your demand function is extremely steep around the market price. The market price is determined by the market supply and demand, but for you it is essentially simply falling down from the sky. If you follow news reports about farm products you will hear farmers complaining (or simply stating the facts) that “the price is so low this year, so that even though I have a higher apple crop this year I will end up with less income than in the previous year” or statements like these. For a farmer the price is just what it is. You would have to produce a very unique product to have an influence on its price. If you produce Xboxes, which are somewhat unique, even though there is a similar product called PlayStation, then you may well find that you have some discretion over price, meaning that you can sell more of the product for a lower price and less for a higher price and you can try and find a price that you like best overall (perhaps one that gives you the most income – or profit if we are talking about firms).
Let me provide you with a useful economic term, the term of “substitute”. A substitute for a product is another product that potential consumers of your product find somewhat similar to yours. A “close substitute” is very similar to yours; a “distant substitute” is only somewhat similar to yours.
One can explain the difference between market demand and individual demand in terms of substitutes. If we consider the market demand of all holiday departments in Upper Styria, then while there are substitutes for these they are perhaps not super close. There are holiday apartments in other areas in the world of course, but for some people driving so far may not be an interesting option. Well, I actually guess that even the market demand for holiday apartments in Upper Styria in winter is quite a steep function of prices. But if we look at a single house with only a few apartments in Upper Styria, then suddenly we have a lot more substitutes. Now all apartments in the same area are also substitutes. This makes the demand function for one house with few apartments probably extremely steep.
]]>Man beachte die Ausreißer rund um Änderungen in der steuerlichen Behandlung von Ehepaaren in der Zeitreihe. Fazit: Österreichische Pärchen reagieren auf monetäre Anreize. Keine Überraschung für Ökonomen, aber immer wieder schön zu sehen.
Dasselbe gilt auch für Studierende:
Man beachte den Knick nach unten bei Wiedereinführung der Studiengebühren 2001 und den Knick nach oben bei der (DeFacto)Abschaffung derselben ein paar Jahre später.
Die ganze Präsentation ist äußerst lesenswert!
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If I recall this correctly, Styrian white wine became quite a bit more expensive between the second half of 2016 and the beginning of 2017. In my private recollection prices (at least of the wines I was interested in) increased by something like 20%. Why? Well, in principle there could be many reasons. Perhaps, for instance, the 2015 wine (which was sold in 2016) was of better than normal quality. This would be a demand function argument. Higher quality means higher demand and, assuming the supply function stays the same, this leads to higher prices. Now suppose that you also learn (which I believe to be true here) that the amount of Styrian wine sold in the latter half of 2016 and in 2017 was actually lower than in previous years. Can the demand function explanation “explain” this as well? The answer is “no”. And all we need to see this is what we developed in the last lecture (and the one before that) about supply and demand.
Let us start with a depiction of the pre 2016 market for Styrian white wine with price on the xaxis and number of wine bottles on the yaxis. Let us put in a somewhat arbitrary but downward sloping demand function and a somewhat arbitrary but upward sloping supply function. The equilibrium price is the price (on the xaxis) at which both functions intersect. The value on the yaxis at this intersection point is the equilibrium quantity of wine bought and sold at this equilibrium price.
Now suppose that we shift the demand function (the whole function) upwards. Because, for instance we think that the quality of wine has suddenly increased in 2016 and 2017. Let us stick with the same supply function (after all we are trying to see if a change in the demand function alone can be responsible for our observed changes in the wine price and the wine quantity bought and sold). Now suppose we get a new equilibrium with the new demand function and the old supply function. Then note that indeed we do get a higher price than before. But note also that we get a higher quantity of wine bought and sold. So this is not a good explanation of our empirically observed phenomenon.
In fact I believe that the real reason for the increase in wine prices and the decrease in bottles (bought and sold) in the second half of 2016 and in 2017 is a decrease in the supply function. In fact I believe that the supply function decreased suddenly because of the late April frost in 2016 which destroyed a fair amount of the grape harvest. Because of this, wine farmers in 2016 and 2017 (smoothing their supply immediately I believe) were not “able” or willing to supply as much as before at the same prices, simply because they didn’t have as much wine as before. Let’s see if this is a feasible explanation of our two observed phenomena of a price increase and a decrease of bottles (bought and sold).
So suppose that we shift the supply function (the whole function) downwards and let us stick with the same demand function (after all we are trying to see if a change in the supply function alone can be responsible for our observed changes in the wine price and the wine quantity bought and sold). Now suppose we get a new equilibrium with the new supply function and the old demand function. Note that indeed we do get a higher price than before. And note also that we get a lower quantity of wine bought and sold. This does not mean that this is the true story, but it is a plausible story (especially when you learn about the frost) that provides theoretical implications that are consistent with the observations we made. [Another story that would also be consistent with the observations could be that Styrian wine makers in 2016 and 2017 suddenly managed to be more collusive. I do not believe this to be the case, but it could also “explain” the increase in prices and the reduction in wine bought and sold.]
This was an example of a price change quite possibly because of a change in the supply function.
Let me now turn to the price of holiday apartments and hotel rooms in the Upper Styrian region. Roughly speaking I think you will find, if you look at the posted prices for these apartments or hotel rooms, that they are higher in the winter than in the summer. I also believe that when you check with e.g. Statistik Austria you will find that there are many more overnight stays recorded in the winter than in the summer. This cannot be explained with different supply functions in the winter and the summer. A possible explanation is that the demand function for such apartments and hotel rooms is substantially lower in the summer than in the winter. Upper Styria is a skiing area in winter and a hiking area in summer, but I guess skiing in winter is more popular than hiking in summer.
So this is an example of a price difference that is quite possibly driven by a difference in demand.
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