Capping the price of frappe

I had been at the university for a couple of weeks and, while it´s fall, the weather still called for a frappe. I did not want to walk the 200 meters to go to the fancy cafe, however I needed an iced coffee desperately, so I decided to go to the canteen that I had only recently found out about.

So, I went in and ordered a frappe. The cashier, in turn, asked for €1.10. Really, that cheap? This canteen is in prime location (right in the middle of the university, which is full of frappe-thirsty students!!!), packed with young students, whose willingness to pay for a frappe is unreasonably high (as any visit to the fancy cafe clusterings would attest), and, with no real competitors around.1

This canteen is practically a local monopoly and it appears to be violating one of the basic economic principles. That is, that a profit-maximizing monopolist equalizes her marginal revenue (the change in her revenue from the sale of an additional unit) to her marginal cost (the change in her cost due to the production of an additional unit), so that the profit-maximizing number of frappes is determined. Then, the demand function will give the profit-maximizing price.

However, this canteen's behavior seems to be going against this principle. Even though, the quantity of frappes may well be at the profit-maximizing level of a monopolist, the price certainly is not. To see the intuition behind this claim, suppose for simplicity that the demand side of the market can be described by a representative agent with a linear inverse demand function of the form p=a/b - d/b, where d is the quantity demanded, b>0 measures the price sensitiveness of the consumer, while a>0 is the maximum number of frappes the consumer can have.

I postulate the assumptions that a=4, and b=0.5, without maintaining that these values fully describe the market, but I do argue that they are reasonable and help to get the main point through.  As claimed before, the willingness of a student to pay for cup of iced coffee is pretty high. Moreover, frappe is the "traditional" iced coffee to the point where most people order it without even checking the price first. Although, this might be because, in most places, frappe is the cheapest coffee, the crucial point is that Cypriot consumers are pretty insensitive to frappe's price. (Also, a=4 and b=0.5, suggest that at price of €8, quantity demanded is 0, and given that people were willing to pay €7.50 for frappe then I am pretty confident about the parameter values.)

We proceed by defining

 and, thus,

Equipped with the necessary tools from the demand side, we now move to the supply side, where we will examine the cost function of the canteen.
So, how much does a frappe cost? To answer this, we need to break down its ingredients. A frappe includes a couple of tablespoons of coffee and sugar, a bit of milk and a lot of tap water. Obviously, the cost of making an extra frappe is approximately zero, and indeed the equilibrium price will be lower, the lower the marginal cost (i.e., a higher marginal cost will only magnify the problem discussed below); consequently, for simplicity let's set the marginal cost equal to zero. 2

Hence, in equilibrium "Marginal Revenue=0". A bit of algebra would reveal that, in this simple model, the quantity a representative agent consumes is "d=a/2=2" (since a=4), while the profit-maximizing price is "p=a/b - d/b=8 - 4= €4".

How do these results compare to real life? The quantity demanded of two frappes seems about right; most students drink a frappe in the morning right before (or even during) classes, and one near noon.

The price, though, differs significantly from the price of €1.10 that is actually charged. This is €2.90 difference per frappe, and although the exact price deviation is not important, what is important is that the price differs from a monopoly price, and it differs greatly. What's also important is that the particular canteen has been operating under the current management for a while now, which reveals that it's, at least, covering its average cost (note: a (near) zero marginal cost does not imply a zero average cost).

As the price of most its products are also capped, one may wonder how is the canteen covering its costs, which are labour, rent and input costs.
The labour costs are pretty standard, and are determined by the labour market for coffee-house workers, and the same goes for the input costs (of course, the canteen management could choose to use expired raw materials, but she still has to buy the products).
This leaves us with the rent, which is the one the canteen can (partially) influence. Suppose, for  a moment, that the university when deciding to lease the space, it realizes that the canteen will be a local monopoly, and thus, the rent that will be charged should correspond to a local monopolist. Further, suppose that the university decides that the prices should be capped. As the rest of the (main) costs are beyond the control of the candidate canteen operator, then it's clear that no operator would be signing up the lease. Therefore, since prices are capped, it must be that the university is charging less than the monopolist rent.

In other words, the university is not getting the appropriate returns for its asset, and it is losing surplus. However, the said surplus is not a deadweight loss as it is transferred to the consumers (i.e., primarily the students) in the form of consumer surplus.This constitutes a transfer of welfare from the university towards the university community.

Since frappe is only one of the many products whose price is capped, we conclude that the transfer of welfare arising from the university's price capping policy is significantly more than argued above.
Indeed, this type of welfare transfer should struck as a problem to anyone, as it is an inefficient allocation of university funds. While the value in euros of the lost university surplus may not amount to the hundreds of thousands, it could still be a significant amount. An that could be used to aid the need-based funds, or the excellence-awards funds, or could be used in another way so that everybody is better off.

All in all, economists across the globe, more often than not, object to price caps, because the price as determined in the free-market provides vital information. In most occasions (and this one could not but be one of them), the free-market is able to aggregate economy-wide information and reflect all one needs to know in the price. Capping that creates market frictions in terms of information. However, it also creates another type of friction as the present passage argues. That is, there is an indirect transfer of welfare from the university towards (mainly) the students. This is indeed a friction as it is (weakly) dominated by a direct transfer of welfare by the university, which could be achieved by transferring either money to the students or improving its services towards the student population. Such an arrangement would benefit everybody.


Footnotes:

1. The only competitors being (i) the aforementioned fancy coffee house, and (ii) the canteen-type cafe in the senate house, which both, in fact, serve different types of markets --- i.e., provide different products, and, in the case of the senate canteen, serve mostly senate employees. 

2. Another reason for assuming a zero marginal cost is apparent when we consider the time period to be a day. In this case, the materials needed to make a frappe are already bought, and thus they are a fixed cost. As a result, the marginal cost in this case is 0.

Reciprocity in corruptio regionem

Imagine you are a resident of corruptio regionem.

You have always been an obedient citizen; prompt to your duties, paying your taxes and voting for representatives, who you know that were not reciprocating your righteousness. In particular, you always suspected that they were corrupted and taking side-payments, but only recently scandals broke out highlighting the extent of corruption.

In addition, your politicians exerted minimum effort governing the country and its economy which has led the country to the brink of economic collapse. (This is not to say that they were the only at fault for the state of current economic affairs, but let's take the assumption that the biggest share of the blame is attributed to them.)

Assuming there is still some margin for saving the country, how would you react to this crisis? Would you (as part of the people) sigh "bygones are bygones" and make your best to save the economy? Or, would you be bitter about the inability of those in charge, which would lead you to act in a way such that the collapse is unavoidable?

In other words, would you forget about the poor effort of those in charge and do your best? Or would you feel that you (as a citizen) were  treated unfairly and try to reciprocate "the love".

Let's simplify the analysis (by making it more complex). We have the following stage game, which is a modified Prisoner's Dilemma.

The row player is the Government, which can either exert "High" or "Low effort". The column player is the Citizen, who can "Cooperate" (for example pay his taxes), or "Don't cooperate" (for example cease filling his tax form, having dealings in the underground economy, and etc.).

It's immediately obvious that Low effort and Cooperate are dominant strategies for the Government and the Citizen respectively. So, the "best prediction" about the outcome a game theorist can make is that the Government will put minimum effort in, but the citizens will still cooperate. This is the unique Nash equilibrium of this simple game, where the Government has a payoff of 4X and the Citizen 2X. Indeed this a rational outcome, in the sense that a player should always be self-interested, and choose rationally the strategy that maximizes his payoff. 

The only problem with this prediction is that it exemplifies the omission from "traditional" non-cooperative game theory, the fact that in real-world people are not cold-blooded players who act without regard to the other's actions and how they deem those actions. Allow me to be more specific, all of us have emotions to which we act upon. For example, as Matthew Rabin (1993) argues if we deem the action of the other player as unfair and unkind then we might want to reciprocate with an action that is unfair and unkind, so that we will fell that social justice has been implemented. 

Such an implementation of social justice can bring about outcomes that are ex ante Pareto dominated by others (strictly speaking about the bi-matrix payoffs). Indeed in the simple game above, the outcome "Low effort, Don't" is a fairness equilibrium as per Rabin (1993). Although, ex ante the Nash equilibrium "Low effort, Cooperate" seems to Pareto dominate the "Low effort, Don't", it's possible that citizens feel that their politicians were unkind to them, and as a retaliation they responded with ceasing to cooperate.

Specifically, as with the Nash equilibrium, examination of Rabin's fairness equilibrium is concerned (only) with the strategies that occur with positive probability in equilibrium. More importantly though, in Rabin's world players are concerned with reciprocity. 

In particular, if a player perceives a behaviour as kind, then she might want to reward it by being kind as well, whereas an unkind behaviour might be punished. An unkind behaviour towards player i would of course lower i's material payoff. Retaliating unkindness often entails actions that lower i's material payoffs even more. Yet the satisfaction of "revenge" is possible to compensate i such that she finds it worthwhile to punish the unkind opponent.  With some (heavy) abuse of notation, the payoff function of player i is

where the first term represents the material payoffs (see table), the term outside the squared brackets is the perception of j's kindness by i (if it's positive then j is perceived as kind, if it's negative as unkind and if it's 0 then j is neither). Finally, the term is inside the brackets is i's kindness.

In this framework it can be shown if the citizens expect their politicians to exert low effort, and the politicians expect the citizens to not cooperate, then  "Low effort, Don't" is a fairness equilibrium.

This is far from thorough analysis of the above game, but merely a novel description. However, the main message is that behavioural game theory can help explain what traditional game theory cannot. This (extremely) simple game was devised with the "refuse" of Greeks to silently and blindly accept the idiom "bygones are bygones" to cooperate with their politicians and Troika to get out of the crisis in mind. Had they initially cooperated and avoided some costly strikes then the situation might have been better. Hence, to an outside observer not cooperating is a dominated strategy, and it seems inconceivable that the people refuse to count their losses and move on. However, as argued above behavioural game theory makes sharp predictions that it may well be that we get an equilibrium where the people just don't want to cooperate, because they want to punish the politicians; granted they do punish themselves as well, but they do punish the politicians as well.

All in all, even though the above passage by no means suggests that the simple game describes the real world, it says that there exists at least one fairness equilibrium which to my eyes seems to be pretty close to reality. 

References:

Matthew Rabin. Incorporating fairness into game theory and economics. American Economic Review, 83(5):1281–1302, December 1993.