Mas-Colell Chapter 1: Preference and Choice

As mentioned in a earlier post, I am working through Mas-Colell, Whinston, and Green's Microeconomic Theory1 (often shortened to Mas-Colell or MWG) as my introduction to modern Samuelsonian microeconomics. To help with the learning and teaching, I've decided to post a summary and analysis of each section. Jonathan Catalan did this with Keynes' General Theory and it was enjoyable. I hope to imitate that concept. Unfortunately, Mas-Colell is a textbook, compared to a treatise. This will bring about challenges, which I hope I can overcome.

While most casual readers might not be interested in a walkthrough of a textbook, hopefully some students will. I hope to give an introduction to those who are interested in graduate economics without the difficulty of the actual book. Also, I believe if I cannot write down my thoughts, they probably are not clear. Put differently, sloppy writing means sloppy thinking and I want to avoid sloppy thinking through practice, practice, practice. So I need to get it "on paper." While it might be dangerous to one's esteem to put ideas online after first reading, to steal the subtitle from Gene Callahan's blog- “Silence will save me from being wrong (and foolish), but it will also deprive me of the possibility of being right.” -- Igor Stravinsky.

Everyone is welcome (encouraged) to tell me where I am wrong. That is what comments are for and what makes blogging so enjoyable.

Note: I will attempt to avoid any commentary until the end or in the comments. That is where I hope to make comparisons with other authors. The most important step is to first understand what the authors are saying. Only then can I decide where the author is right and make counterarguments.

The first chapter begins with a complete abstraction of the consumer. MWG starts, like most of modern economics, with a decision. Every actor is faced with a set of possible alternatives, each being mutually exclusive to the others. If the actor chooses to do A, then he must forego B. To keep the topic abstract, the set of all possible alternatives is denoted by X. Each member of is a vector, meaning that it does not mean a choice of one "good", but of any number of goods. If one is shopping at a supermarket, the set denotes any possible combination of goods bought, while a member of X means a whole "basket" (5 apples, 3 bananas, a 6-pack, etc.) instead of any one good. This distinction between the whole set, X, the individual "baskets", and the individual items is important. The choice an actor makes is between members of X, not between individual goods.

From this framework, MWG explain two distinct approaches to modeling and understanding consumer behavior. The first is called a preference relation and the second is called a choice rule.

Preference Relation

The more common of the two models and the one emphasized throughout the rest of MWG is the preference relation. Without going into the formal math- I know this is almost blasphemous for some economists- a preference relation starts with an individual's internal preferences as given. The actor prefers an apple to a banana or prefers 3 beers and a sandwich to a shot and 4 tacos. The actor can be indifferent between two alternatives; he may not care whether he has an apple or a banana..

In order to turn these preferences into something that economists can use, MWG imposes rationality. While rationality can mean different things for MWG, in this abstract setting, it means two specific things.

  1. Completeness- Every basket is already compared to every other basket. The relation is given. Therefore, for every basket a, the actor has a ranking with every other basket, from b to z. a might be preferred to b, b might be preferred to a, or a might be indifferent to b. The actor has already compared everything.
  2. Transitivity- If one basket of goods, a, is preferred to another, b, and b is preferred to c, then a is preferred to c. The same idea applies for indifference. If a is preferred to b and b is indifferent to c, then a is preferred to c. This avoids any problems with the order the actor has to choose. While logically transitivity makes sense, it is does not always hold in the real world.

These are the two axioms  in MWG. They cannot be broken, otherwise the actors are not rational. It is hard to predict the actions of irrational people, so MWG avoids it. MWG cites proof the assumptions do not hold in reality, but insists on using them as a model. (Note: For a great introduction to some of the breakdowns of rationality and many other insights, check out Thinking Fast and Slow by Daniel Kahneman.)

Utility Functions

In order to better describe these preference relations, economists use utility functions. utility function assigns a numerical value to all choices in our set, X. The value does not matter, only the value relative to other baskets' value. If a is preferred to b, then with this new utility function, u(x), the number given to a, u(a), must be greater than the number given to b, u(b). Since we assume completeness and transitivity, a utility function is possible in theory. Mas-Colell emphasizes that the order of preferences is preserved when going from a preference relation to a utility function. Again, the numerical value of u(x) is meaningless.


Choice Rules

Since it is not stressed throughout the rest of MWG, I will be short here. The choice rule model of consumer behavior is similar logically, but different mathematically. The choice rules dictate what basket(s) of goods is picked given a choice between "many" baskets. For example, the choice rule will say that if the actor has a choice between baskets x,y,z, he will pick x and y. The rule dictates the choice. It starts from choice, compared to preference. The difference is subtle, but MWG stress this distinction.

Just as revealed preference required rationality, the choice rule requires a different assumption called the weak axiom of revealed preference. This is less demanding than rationality. Simply, if an actor is given the choice between x and y, and he picks x, then the introduction of more options, z, will not change his choice. He still picks x.

MWG goes on the explain how the two approaches are different. However, since MWG focuses on preference relations, I leave this part to readers if interested (see page 12).


While the difficult part of MWG is the formal math proofs of preference relations and choice rules, the logic is simple. All possible choices are compared with every other and the action picks a favorite. A utility function is then used to turn these preferences into a ranking on a graph or a numerical value for easier analysis and understanding. Although Austrians love to make fun of utility functions, MWG at least in the first chapter pays lip service to these concerns. If MWG follows through with the idea that the value of u(x) is irrelevant and does not try to add or subtract the utilities, utility functions will greatly improve our analysis and thinking.

I do, however, feel uneasy about indifference. I can imagine a rational actor. I cannot picture an indifferent actor. How does a scientist observe indifference? If I buy an apple, clearly I prefer the apple to money. If I do not, I prefer the money. What do I do if I am indifferent? Do I just stand with a look on my face of confusion? While indifference does not make sense to me, I will see of MWG uses it in future chapters before I decide whether the modeling shortcut is worth it.

It is also unfortunate that time is ignored. MWG does not reject the importance of time, but ignores it. Again, time is a vital part of economics which is introduced too late. Hopefully, MWG avoids this problem.

Just as Euclid starts with definitions of lines and points and Rothbard with definitions of action, MWG stars with formal definitions. It is not the most thrilling topic, but necessary to understand the rest of the work. Hopefully, this little summary makes it a little easier.

  1. Mas-Colell, Andreu, Michael Dennis. Whinston, and Jerry R. Green. "Chapter 1 Preference and Choice." Microeconomic Theory. New York: Oxford UP, 1995.

Also see Chapter 7 of Hal Varian's Microeconomic Analysis for a similar, but more intuitive, introduction to revealed preference.

For a short critique of revealed preference see Rothbard's Toward a Reconstruction of Utility and Welfare Economics.

15 thoughts on “Mas-Colell Chapter 1: Preference and Choice

  1. Lovely blog and initiative. Myself, I'm reading Mas-Colell on its own but am soon embarking on a joint reading of von Neumann & Morgenstern's 'Theory of games' and Luce & Raiffa's 'Games and decisions'.

    In regard to your - may I suggest - Austrian-induced frustration with non-observable indifference: there is a fine paper by Edna Ullmann-Margalit & Sidney Morgenbesser, 'Picking and Choosing' (1944, Social Research, 44(4), 757-785), which brings the notion downer to earth and examines it in a very straightforward way. With the preponderance of the scarce references on the topic in place.

    • I greatly enjoy joint reading. It is forces you to challenge things that would otherwise go unexplored. Good luck with vNM and Luce/Raiffa.

      Thanks for the recommendation. I don't buy their construction of "picking" cans. Those two cans are not the same, regardless of the chemical makeup question. They are in different locations and the actor knows this. I don't see how the actor can be indifferent between two locations. The authors just switch the choice between a physical good to a physical location. A reductio ad absurdum would show that different locations clearly have different "utilities."

      Now this is getting beyond my level, but I do not see that article as a refutation. Even their point of choosing A "rather than B" vs choosing A "to the exclusion of B" is not convincing.

      For my interests, it is not a huge deal though. Indifference can be a worthy concept if it improves our understanding of the world.

  2. Thanks, yes, looking forward to that.

    I've had a similar objection but I think it arises out of a resistance to grant the full power of the argument. The can soup example might not be ideal (though, having recently moved to a new country where most of the stock I'm familiar with is simply absent, I've had an occasion to feel the force of the underlying reasoning), but it points to an important point about indifference. The point being that chemical composition, location, package traits - all these characteristics are treated as exogenous. A fully reflected upon indifference (the one Mas-Colell, for example, assume for the weak preference relation) is already to be conceived as an indifference over the goods themselves, their location and any other property they may posses and that the agent might consider relevant.

    The implication is that if the agent is truly indifferent (all properties considered), a repeated choice sequence would reveal a random 'picking' of the goods. If the the choices are not random and location is indeed a salient feature, one can take two approaches. On the one hand, one can re-define the preference ordering, denying indifference, and treating the preference for a good on the left, say, as given. Or, one can fix indifference over all the properties of the goods except for location as given and treat location as a dependent variable. If over a repeated sequence holding other properties fixed, a choice pattern emerges (for choosing the can on the right, say), location can be inferred as a salient feature.

    It seems to me the second approach is more operational, at the very least in the sense of paving a way for making an inference. And I suppose that's what marketers have been doing all along! Indifference - where appropriate - then amounts to a mechanism of isolating potentially endogenous variables.

    • I get what indifference means in a repeated interaction. I also understand why indifference is constructed from a theoretical point of view. It makes everything much nicer. Also, indifference must be the possible if we assume that goods are infinitely divisible.

      That was not my original point on this post. My original point is that from a more "realistic" point of view, what does indifference mean? I can prove when something is preferred by the actor. I can't prove that someone is indifferent, because people do not face repeated identical choices. Since I can never point and say, a ha, that is indifference, I don't know it means in reality.

      However, I've warmed up to indifference curves over the last few months, even if I do not understand the underlying mechanism.

      • Yes, I understand. It's a tricky thing. Yet very much similar to context independence in this respect which one hardly ever faces. Yet despite that it's somewhat fairly easy to strip an ordinary context-dependent choice into a preference, in general as it were. I suppose one can think of and understand indifference the same way: as the step of stripping the disinterested "I'll just pick this can (whatever it's location and so on)" choice into an abstracted disinterest.

        The uneasiness is vexing indeed though. It would make a logical positivist deny any meaning to claims about indifference. Economics has gone a long way away from positivism.

        In any case, best of luck on finishing the joint reading! Will be following the progress.

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