I have an idea of what you think it means, but it actually cannot tell us anything about the person’s preference in a quantitative way.
It makes them bad academic economists. The idea of neoclassical mathematics was a rejection of new math. New math was a teaching method in vogue fifty years ago that introduced advanced mathematical theories into the teaching of basic mathematics to schoolchildren. It got a lot of criticism, much of it justified, because people felt that an understanding of these advanced theories was unnecessary for the average school child.
Neoclassical mathematics argued that schools should be teaching just the basics of math and leaving the theories for later. Some neoclassical mathematics advocates seem to go further and feel that abstract theories should be left out entirely and the only mathematics that should be studied are those areas which have practical applications.
But the main point is that this argument is supposed to be over how math is taught to school children. Once you leave high school, anyone who is still studying math is supposed to get into the heavy stuff. They’re supposed to be going beyond neoclassical mathematics and learning all those advanced theories that weren’t needed for a general school education. Somebody saying they have a PhD in neoclassical mathematics is essentially saying they have a PhD in high school math.
I meant neoclassical economics, sorry for the confusion.
OK, tell me what I think it means.
You think that it can tell us something about the person’s preference in a quantitative way.
Can you be more specific? If not, that’s fine, I’ll tell you what I think it means. I just want to make sure I’m starting this discussion in the right place.
My impression is that most of the people who subscribe to the Austrian school of economics do so less because of its theoretical underpinnings and more because they like the conclusions (i.e. less government taking their money to support the less fortunate). Any preference they have for the actual axioms are probably heavily influenced by confirmation bias. I also feel the same is true for Objectivism, which near as I can tell is mostly popular because it allows selfish people to justify their selfishness as being a good thing.
It probably would, but he might say it was ok as a transaction in which the you offered the child the food and shelter it needed to survive in exchange for sexual access.
I’ve been travelling. Running behind here…
Neoclassical is fine, if you don’t like “academic”.
I don’t closely remember or rely on “the Samuelson text”.
I rely on logical progression from the axioms, among which is the existence of a preference relation with certain properties. Do you know what a preference relation is? Do you know what a mathematical relation is, more generally?
I asked specific questions, because I don’t know what you don’t know. I can’t give “exposition” if I don’t know where to start. I don’t know if you know the axioms of neoclassical models. These models start with certain axioms. Among these axioms is a preference relation with certain properties.
Do you know what a preference relation is? Do you know what a mathematical relation is, in general?
I think that’s very likely accurate.
But every once in a while, it’s worth hashing out the logic in multiple ways. I actually used a Rothbard-like “preference scale”, as in Man, Economy, and State, in my own classroom explanation of micro, because it really is a nice clean way of getting across the idea of diminishing marginal utility in an ordinal sense. It’s just not the only way to express ordinal preferences, which is the issue here. I find it personally helpful to be able to “translate” between the different viewpoints. When we write words, we can skip logical steps. When we draw graphs, we can shift the wrong curve for the wrong reason. When we write out equations, we can forget to carry the one – or even worse, forget what the equations are intended to represent in the first place. But by working through every possible “language” of description, we can use one mode of thought to “double check” the others.
Most people don’t do this. (This is not limited to just “Austrians”. I mean most everyone.) But it’s a worthwhile way of trying to do this business. In my opinion.
Ok then in what text can I find the “logical progression from axioms” that you think adequately explains your viewpoint? I was under the impression that the Samuelson text was taught for decades and that many neoclassical economists learned from it. I see no point in you spending all your time explaining something when I could simply read what has been written. No need to reinvent the wheel.
https://boards.straightdope.com/sdmb/showpost.php?p=21131566&postcount=99
Do you agree with the bold statement in this post?
I don’t know which text you’re referring to, but if you want the axioms laid out clearly, you could try Mas-Colell, Whinston, Green. Very math-heavy, as most economics is nowadays.
I’m not sure asking each other questions will advance this discussion.
Well, this was overly snippy–I’m going to start the discussion with your question, which was how to interpret the bolded language
A utility function is a representation to define individual preferences for goods or services beyond the explicit monetary value of those goods or services. In other words, it is a calculation for how much someone desires something, and it is relative. For example, if someone prefers dark chocolate to milk chocolate, they are said to derive more utility from dark chocolate. A utility function of this relationship could look something like where is the utility of eating dark and milk chocolates. **In this example, a consumer derives half as much utility from milk chocolate as they do from dark**
OK, so let’s start with basics. First, when we say you can’t compare utilities, we mean across individuals. You can’t take 5 utils for one individual and compare it to 6 utils for another person. Ordinal rankings are specific to a single person (or “economic unit”) only.
But of course say you can compare utilities of market baskets for a single individual. Our axioms generally directly reflect that, such as the common axiom of “more is preferred to less”.
Now you seem to be asking about whether for an individual we can compare how much they like one good compared to another. Well, of course you can. You can do this yourself. Would you be willing to trade 1 m&m for 2 Skittles? If so, I think it’s fair to say you like M&Ms twice as much as Skittles (with the caveat here that people’s preferences generally change the more/less you have of a good. You might be more willing to make the trade if you had lots of M&Ms and no Skittles).
So the economics questions becomes: if you like M&Ms twice as much as Skittles, how much of each will you buy? Well, that will depend on the relative price of the two, right? In fact, there might be a simple relationship between the price ratio of the two compared to how much you like each of them, that will tell you how much of each you’d buy, right?
Gibberish. Unfortunately the 5-minute edit window has expired and my nonsense will lie there eternally for all to laugh at. :o
It was Evil Economist’s mention of chocolate M&M’s that reminded me I applied a non-monotone utility to a purchasing decision just two days ago. And I did so almost subconsciously without recourse to any textbook or calculator.
In the big city for other reasons I stopped at the bakery that sells large chocolate fudge brownies for $1.50 each. (Don’t you wish you could get then at that price? 
) I bought two brownies. With any naive utility function, I’d have bought all they had — in fact I’ve done just that in the past. But, since the rest of my family thinks brownies are not proper food, I’d have had to eat all the brownies myself. “Returns” would not only have diminished but become negative. Yes, electroconvulsive therapy might stifle my chocolate compulsion and let me feed excess brownies to the birds or such, but I don’t have health insurance and the cost of the shock treatment would dwarf that of the brownies. So … I intuitively and effortlessly applied a non-monotone utility function!!
Now I’ll return you to the on-going discussion of whether children would be sold as sex slaves in libertarian utopia.
That just means that your utility function was convex, not that it was non-monotonic. Your utility function for one brownie was greater than your utility function for $1.50, and your utility function for two brownies was greater than your utility function for $3.00, but your function for three brownies was less than your function for $4.50. You’d only have a non-monotonic utility function if you could get three brownies for the same price as two, but still only bought two.
This is fair.
A grad micro textbook will have the stuffs. (Samuelson’s most famous text was an undergrad book, which I wouldn’t think would have the same level of logical rigor, but I never owned a copy and I haven’t seen one in long time.) Which textbook depends on your comfort level is with the formalism. I’m travelling, my books are at home, so I can’t point to specific page numbers.
But your best bet is Advanced Microeconomic Theory, which literally starts with standard consumer theory and preference relations. If I remember right, the very beginning of Chapter 1 very briefly discusses how the notion of “measurable” utility was comprehensively ejected from (neoclassical) consumer theory. Then it goes on to demonstrate the existence of a utility function that represents a preference relation. I don’t recommend the whole book for the purpose of this discussion. Just stop not far past the point where the existence of a utility function that represents the preference relation is proven. Maybe finish that section, but that’s it. You said your calculus was fine? Then we can immediately go to Lagrangian multivariable constrained optimization problems without getting bogged down on stuff you don’t care for anyway.
Varian’s Microeconomic Analysis should have the same material, but I think Varian starts with producers rather than consumers. Mas Colell et al’s Microeconomic Theory is a monster book that has pretty much everything, but no need for all that jazz. Debreu’s Theory of Value is a comprehensive look at the maths from one of the peeps who actually invented this stuff (pdf here), but again, probably not worth the effort. Most of the material inside is not necessary here.
A used copy of a previous edition of Advanced Microeconomic Theory can be gotten for cheap. That’s the one to choose, I think. There might even be a PDF lurking on the internet somewhere. This discussion hinges on the beginning of chapter 1, in literally the first two sections if I remember right.
:smack: What in heaven’s name do I have to do to convince you I’m not innumerate? Do you want to look at my score on the Putnam?
My post was slightly tongue-in-cheek. The entire point was that I’d be better off getting two brownies than three for the same $3 price, because if I had a third brownie*** I’d feel compelled to eat it!***
Perhaps gluttony is not on your list of sins and you don’t know what I’m talking about, but if I had the third brownie, the best I could hope for is that I’d have the discipline to throw it away.
Capiche?
evil economist: “If so, I think it’s fair to say you like M&Ms twice as much as Skittles.”
I disagree with this statement. I think you are treating preferences as cardinal if you make this statement.
I think that all you need to get this result is the ability to compare two bundles of goods and know which one you prefer (and, more importantly, whether you are indifferent between two different bundles). If you add the additional constraint that “more is preferred to less”, then you end up with an indifference curve, which is the rate at which you are willing to exchange goods without feeling better or worse off.* The “rate at which you are willing to exchange goods without feeling better or worse off” is called an indifference curve. And, the way we’ve described it, the slope of the indifference curve is by definition, equal to the ratio at which you are willing to exchange goods.
Note that we can get the “indifference curve” without needing the ability to compare the utilities you get across market bundles that you are not indifferent between (did that sentence make sense?). We can give you more M&Ms without taking away any Skittles, so that (if “more is preferred to less”) you are better off. But we do not need to know “how much” better off you are.
So we can rank indifference curves by whether we prefer one over the other, but we don’t need to define this preference numerically. I.e., cardinality is not necessary.
*I think we also need to assume that your preferences are transitive, so that if you prefer A to B and B to C, then you prefer A to C.
I’m home, pulled Advanced Microeconomic Theory off the shelf.
This is the right book for this topic. It’s all there in the proper order, starting right at the very beginning with the definition of “preference relation” and related ideas and getting straight to the calculus – Lagrangian constrained optimization – in section 1.3. This shows why for an interior solution with certain friendly properties, it’s a necessary condition (and even sufficient, if the problem is friendly enough) for the “price ratio” to equal the ratio of the “marginal utilities”, as those two fractions are most often called.
One particular passage from the book I want to emphasize:
I can’t personally ever recall meeting an economist who refused to use the term “utility function” for fear of confusion. But I guess they’re out there.
You don’t need “more is preferred to less” (monotonicity) for an indifference curve, but you do need continuity of preferences. Monotonicity can make the math easier, tho, along with convexity (and of course differentiability, which is often an implicit assumption…)
Yes.
Non-transitive preferences would be… strange and unwieldy. The ordering of the real numbers is transitive, so no way a real-valued function could represent intransitive preferences.