We will come back to the idea that people typically like more money over less (all else equal) – see last lecture, but let me now turn to another important idea, trade. Let me first talk about trade without money. I will (re)introduce money into trade a little bit later, but one key idea behind trade does not require money.

I here talk about (bilateral) trade and more general exchange, efficiency, and fairness. I do this in the context of a kid’s birthday party and follow, to some extent, chapter 3 of Ariel Rubinstein’s much more general treatment in “Economic Fables”.

I don’t know how this is done in other areas in the world, but in Graz there seem to be certain specific norms that one should follow when you host a kid’s birthday party. You invite roughly as many children as your child’s age in years. Children bring presents, but each child also goes home from the party with some little bag of goodies. As concerned parents we do not want to give the children too many sweets so we give them little presents such as little Lego or Playmobil figures or a car or something like this. We did this twice this year (we have two kids) and in both cases the first thing that happens after the kids finally find the treasure (there is often a sort of treasure hunt) is this: the kids start to trade. So, what is going on when kids are trading their presents?

To fix ideas consider a particular example with three kids. I call them Eva, Fritz, and Maria. They each receive one figure, Eva a pirate, Franz a nurse, and Maria a ghost. Assume that we are able to see inside their heads and see the kids’ preferences over these three figures. These are given in the following table.

$\begin{tabular}{c|ccc} & Eva & Franz & Maria \\ \hline present: & pirate & nurse & ghost \\ \hline 1 & nurse & pirate & pirate \\ 2 & ghost & ghost & nurse \\ 3 & pirate & nurse & ghost \\ \end{tabular}$

Please take a moment or two to think about which of these kids, in your opinion, would be interested in trading their presents.

Are you done? The answer is that actually every pair of them would potentially be happy to trade presents. Let me run through all possible sequences of trades.

Suppose first that Eva and Franz trade. This leads to Eva receiving her favorite figure, the nurse, and Franz receiving his favorite figure, the pirate. Maria is still left with her ghost. So what has happened? This is what we call a Pareto improvement. A Pareto improvement is a change in allocation that keeps everyone at least as happy as before and makes at least one person strictly happier.

A quick aside: The term Pareto improvement is named after a certain Vilfredo Pareto. He is no longer with us. You can google his name if you like. My policy with names in this course is this: I try to avoid them. I generally try to avoid talking about famous dead people, because I want you to judge concepts, ideas, and results for themselves. I don’t want you to “believe” in concepts, especially not just because the concept came from some famous dead person. This does not mean that you wouldn’t benefit from a course on the history of economic thought. One of the key things you learn in such a course, in my opinion, is to see how the times influence and constrain economic thinking. This allows you to appreciate how certain older “models” need to be adapted to fit modern times, but also how certain, perhaps forgotten, ideas from older “models” might still have relevance today.

Assuming for now that the three children only care about what figure they themselves get, we have that after Eva and Franz trade there are no more trades.

By the way, the different sequences of (bilateral) trade in the example led to three different possible Pareto efficient allocations. In terms of the kids’ preference ranking these allocations can be expressed in this table:

$\begin{tabular}{ccc} Eva & Franz & Maria \\ \hline 1 & 1 & 3 \\ 1 & 2 & 1 \\ 2 & 1 & 2 \\ \end{tabular}$

Can we compare these further? You might think that the second allocation, the 1-2-1 allocation (meaning Eva gets her favorite figure, the nurse, Franz his second favorite, the ghost, and Maria her favorite, the pirate) is better than the other two. But this is not clear. It could be that Franz really would like the pirate much much more than the ghost, while both Eva and Maria don’t care that much about which figure they get. Of course it could also be that Franz cares little about all this, and Eva and Maria care a lot. So we cannot really so easily compare two Pareto efficient allocations. This will be more interesting but also more radical, when we introduce money into trade, which I do in the fourth lecture.

Let me make another point. Suppose that instead of Franz we have Fritz at the party and suppose that Eva’s present is the ghost, Fritz’ is the pirate, and Maria’s is the nurse. Eva and Maria have the same preferences as before but Fritz’ are different from Franz’. The situation is given in this table.

$\begin{tabular}{c|ccc} & Eva & Fritz & Maria \\ \hline present: & ghost & pirate & nurse \\ \hline 1 & nurse & ghost & pirate \\ 2 & ghost & pirate & nurse \\ 3 & pirate & nurse & ghost \\ \end{tabular}$

Now, who would like to trade? Please think about it for a moment. Actually no bilateral trade is feasible, but they could all trade together. You could imagine that the three children sit around a round table, Fritz to the right of Eva, Maria to the right of Fritz, and Eva to the right of Maria.  Then they could all trade by handing their respective present to the child sitting to the right of them. Everyone should agree to this and all are happier than before. So what am I saying with this example? Bilateral trade, no matter how often this is repeated, is not sufficient to lead to a Pareto efficient allocation. Sometimes more people need to get together at the same time. Later in the course, when I talk about money, we will see that this latter case is probably much more common.

What I have to say next is very much taken from chapter 3 of Ariel Rubinstein’s “Economic Fables” and is a nice way to demonstrate that Pareto efficiency cannot be everything that we want from a good system of allocating things to people who want things. Let me go back to the first example of Eva, Franz, and Maria. Suppose that we now hand out presents with some alternative allocation protocols. Suppose, for instance, that I – the father of the birthday child and party organizer – put the kids in some arbitrary (or perhaps not even arbitrary – perhaps showing favoritism) order and tell the kids that they are allowed to choose one and only one figure in the order that I put them in. Suppose the order is Eva, Franz, and then Maria. Then Eva takes the nurse, Franz is lucky and his favorite, the pirate, is still available and so he takes the pirate, while Maria, finally, saw both of her more preferred figures disappear before it is her turn to take the only remaining and her least favorite figure, the ghost. Note that this also leads to a Pareto efficient allocation. Now change the sequence and you will see that in every case you will end up with some Pareto efficient allocation. Actually it is very easy to see that this procedure always leads to a Pareto efficient allocation. But different sequences will lead to different allocations. This was also true in the trade example. Different initial allocations (the presents) lead to different final Pareto efficient allocations. Instead of me, the party organizer, determining this order, we could have used any other way to come up with some order. We could have let the kids fight, or do a race, or play a rock-scissors-paper tournament. There are many possibilities.

One potential problem with, say, kids fighting over things is that such a system does not provide particularly strong incentives for especially weak kids to acquire something in the first place, if they know that it will just be taken away from them again. How incentives matter in the design of economic systems is the topic of another lecture, though.

Here is the video (in German):