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As a choice condition, they are clearly equivalent.

I suppose the equations themselves are saying different things, but this is a pretty pedantic/pointless thing to ask, imo. After all, the following expressions are clearly equivalent, but are 'saying' different things:

1 + 1
2 * 1

I'd have said true as well. I don't see how the ordinal/cardinal point enters into it. If you redefine preferences by V(X,Y) = g(U(X,Y)) where g(U) is monotonic increasing, then you'd still get the same expressions when the g'(U) terms cancel.

Well, I voted "true". I have seen it taught both ways, and have taught it both ways myself. I can't figure out any devious reasoning why it should be false. And we don't (at least not deliberately) ask "trick" questions in ECON 1000.

Every so often, in every multiple choice test bank, and in study guides, I find the occasional mistake. I always do the test myself, then compare my answers to the "official" answers. I think this was a simple typo.

And the cardinal/ordinal thing doesn't work. As soon as you write "MUx" you are assuming cardinality. So both versions assume cardinality.

Gotta be a typo. Stuff happens. (Or I'm totally out to lunch, I suppose.)

I think I would contact the prof, and ask what we are all missing: I would certainly have answered "true". (b) can be generalized to more than two goods more easily.

And i didn't peek at Stephen's or Jared's answer first, honest teecher!

I would also add that I too can't see why anyone would see the point in asking this question.

Nick "I think this was a simple typo."

I don't think so, I was quite careful to try to get this right, and the solutions (which I don't have in front of me) do contain an explanation of why the answer is supposed to be false. But I will double check. And the question does say "equilibrium equations" when they are, in fact, optimization conditions.

Linda, I've always preferred formulation (b), too, and am glad to have a reason for this.

Jared, Stephen, Linda, I'll see if I can get some clarification on why false. Because I can't see it either.

In physics torque and energy both have the same dimensions but are not exactly equivalent. Torque is measured in Newton-metres (N*m) where the force (newtons) is perpendicular to the distance (metres).

Energy (Joules) is where the force and the distance are in line, it is force acting over a distance.

Torque can be converted to Energy by multiplying by the angle in radians (a scalar).

Thus the distinct notation of N*m and J.

This is a little more slip-shod as there is no conceptual difference like perpendicularity.

It seems to me to simply be a difference of interpretation of something which is dimensionally equivalent. For instance in Newtonian physics force and energy are interrelated and provide an equivalent solution through different mathematical operations.

Hmm, is there a math philosopher in the house?

Determinant: "Thus the distinct notation of N*m and J."

I think this is what the instructor was trying to get at.

I should also note that I never understood choice theory in terms of 'equilibrium', so the language used is strange to me anyway. Better wording: (?)

T/F: the following conditions are both utility-maximizing
i) MUx/MUy = Px/Py
ii) MUx/Px = MUy/Py

(but now maybe I'm the one being pedantic..)

Ah, Frances beat me to it.

Hmmm. If there are solutions, it's unlikely to be a typo. Oh well. I always end up proving England will export wine to Portugal.

I wouldn't worry much about the equilibrium/optimisation thing though. I would say it's both. Optimisation is a necessary condition for equilibrium, and it's expressed as an equation, so I don't see the problem in describing it as an equilibrium equation. Do others see it differently?

Determinant: I follow what you are saying about torque and force being different, even though they have the same units, but you lost me after that.

If x is leisure, and y is milk, then MUx/MUy has the units litres/hour, so we don't need to talk about utils. But that only works if we treat (MUx/MUy) as a whole, that you cannot unpack as one thing divided by another thing. But in that case, you would just write it as MRSxy instead.

Ok, then I didn't get the lesson. I also didn't take that lesson, I was busy in First Year Engineering and took two History courses for my electives.

Nick is also right when he says that if you asking a question about dimensionally identical units with different models/interpretations, then you ought to be very clear about the units and terminology you are using. Again first-year engineering profs are very clear about this.

This question is both obscure and insufficiently specified.

If you can directly derive the one from the other (which obviously you can) then they are equivalent. There really should be no debate here.

From 400 BC to 300 AD, greek mathematicians studied how to compute the surface of polygons through the method of exhaustion. But applying it to very complex shape was almost impossible and seeing only the geometrical application of that method made them completely miss out on inventing calculus.
It took 13 centuries for Newton and Leibnitz to reinvent calculus starting from new bases. And today we essentially use only Leibnitz approach.
Even though units may be the same, you need to know what you are looking for and understand whence you are coming when you build a model.
Even though Nxm and J are the same units, an engineer write them differently because it is very important to know whether a part is subject to torsionnal forces or not.
We should be as careful about what we ask our students to think and how to think about the what.

why did they ask this question in econ 1000? It is really not what matter...


I have been teaching first year class for some time now and would have pick A....

I would however never have asked such silly question though...

Nick is right that (MUx/MUy) does not require utils, which is the point of the question. Some principles texts--including Krugman's--use (MUx/MUy) as the notation for MRSxy, and in the context of a particular course this would not be confusing to students who had been paying attention and reading carefully. The choice of notation, although not precisely correct, is used to highlight that the condition is mathematically equivalent to MUx/Px = MUy/Py, but that economically the interpretations of the two equations are slightly different (ordinal vs. cardinal). I don't know of any books that clearly explain the distinction between diminishing marginal utility and diminishing MRS until intermediate micro; There are, however, professors making this distinction as part of the principles coursework.

Given Economics recent complete failure and given Steve Keen has shown it to be nonsense why would anyone want to pass Eco 101.

> (a) MUx/MUy=Px/Py (b) MUx/Px=MUy/Py

You can only get (b) from (a) if Px isn't equal to zero. So the statements are not identical from a mathematical point of view.

Wearn_and_worn,

Given that you're probably the only person on this thread who believes that, why would you ask such a rhetorical question?

Nick Rowe,

"But without thousands of first year students, how will they be able to pay for the graduate student teaching assistantships and "internationally competitive" salaries that are the basic prerequisites of a "research intensive" school?"

To avoid this problem for universities, perhaps Canada should move onto the Scottish system: universities get ample home undergraduate students at the taxpayers' expense (and those students can't get free higher education elsewhere) so they can focus on getting extra money through government research funds rather on that old-hat "educating" rubbish.

Nick: " If x is leisure, and y is milk, then MUx/MUy has the units litres/hour, so we don't need to talk about utils."

This is what the prof was getting at, and this is the reason that the answer to the question was supposed to be false.

John: "why did they ask this question in econ 1000?"

I can think of four explanations:
1. It's in the test bank, and someone is assigning test bank questions without thinking about them
2. To manipulate the grade distribution; without questions like this there would be too many As
3. To reduce the size of upper year classes; without questions like this people might major in Econ
4. The prof was trying to measure whether or not students really understood the units used in different types of economic measures, but picked a lousy way to do it.

Rather that focusing on the cardinal/ordinal business, suppose that the two ways of showing the expression reflect two different approaches to the problem described in class--allocating money income to different goods vs. indifference curves. The result immediately appears in one of those two forms. Each approach has advantages and disadvantages. The results are quite similar. Mathematically, the results can be expressed in a way that looks identical. But they come out of different traditions and different ways of looking at the problem.

By the way, my answer was "True." But you have to admit that with a true answer, it seems like an odd question.

You can say that the ratio of marginal utilities approach comes out of an approach that focuses on preference orderings (for combinations of products) and the ratio of marginal utilities to prices come from allocating income to different goods until the utils per dollar of income are equal, which suggests utils are measurable units of pleasures and was developed by people who thought along those lines, but I the mengerian approach is subjective and doesn't use indiffenence analysis.

If you were in class that day and paid attention to the discussion of the two different approaches brought to question by economists (and maybe cost of production theory too,) then the answer is obvious.

Bill "suppose that the two ways of showing the expression reflect two different approaches to the problem described in class--allocating money income to different goods vs. indifference curves....Mathematically, the results can be expressed in a way that looks identical. But they come out of different traditions and different ways of looking at the problem."

And I think that's why the phrase "in Eco 100 consumer theory" is crucial. Because in any other kind of consumer theory, the consumer's choice problem is max U(X,Y) subject to Px*X+Py*Y=M, and then the two equations given are simply alternative ways of writing the first order conditions. We're all saying true because we're not thinking in terms of Eco 100 consumer theory.

But it seems a bit tough to expect first year students to get that.

And also you have to think "in a typical exam situation, who is going to choose the answer false." It'll be three types of students
- people who are totally lost so just guess
- people who choose their answers strategically "i.e. the answer is obviously true therefore the answer must be false."
- people who reason as you suggest here

I would guess that the third group will be much smaller than the first two. So the question won't do a good job of differentiating between students who know the material and students who don't.

I'd be willing to bet that the question also skews in favour of males educated in Canada, because they're more likely to try to out-psych the prof.

Sorry, for "Nick Rowe" read "Frances Woolley". The similar writing styles and the fact that the name isn't at the top of the article fools me time after time.

W. Peden "The similar writing styles" Really?

"the fact that the name isn't at the top of the article"

We're actually in the process of doing a minor blog tweak. Would you like to have the names of the authors more prominently displayed at the top of the article?

This reminds me of how calculus used to be taught. You would see the notation, dx/dy, but the student was cautioned not to treat it as a regular quotient, because it represented the limit of Δx/Δy as both go to 0. Later calculus texts dispensed with that notation.

In these days of non-standard analysis where infinitesimals are first class objects, it really does not matter anymore. And besides, IIUC, marginal utilities are not infinitesimals, anyway, right?

Now the term, "equilibrium", makes me wonder about psyching out the prof. In general, equilibrium requires continuity. Otherwise, we might get oscillation, for instance. As a practical matter the assumption of continuity is a mathematical convenience.

Now it may be that the prof is treating marginal utilities as infinitesimals in one equation, but not the other. In which case, he should be shot.

In any event, if I were grading the test, I would flunk the prof. ;)

Frances Woolley,

If there are differences in the writing styles, I haven't noticed them.

Yes, I think it would help a little to have the author name prominently displayed. Since neither of you always stick to a narrow topic or agree about everything, it would help to get a sense of who the author was before reading the blog.

If there are differences in the writing styles, I haven't noticed them.

Ouch. You sure do know how to hurt a blogger's feelings...

Laughing! Brett says he can usually spot who's writing the post in the first few lines, but then writing's his profession.

One bit of advice I tell my students: on a multiple choice (or T/F) exam, always choose the answer you think the prof thinks is right, not the answer you think is right. Essays are the place where you get the chance to argue what you think is right and against what the prof thinks is right. MC questions just aren't any good at letting you do this. MC questions have their role, but this isn't it.

Some other economics prof (John Palmer?) said he always gives the students the option to write him a short note afterwards arguing their case on an MC question he has graded wrong. Not a bad idea in principle. But few take him up on the offer.

Perhaps if one of you started off with a split infinitve, it would be easy to swiftly and unambigiously identify who is blogging...

For the record, I answered "FALSE" to the quiz, but only because of the technicality that the two expressions are not mathematically equivalent when MUx and Px are both zero. I am evangelical in teaching that utility is only ordinal, and that the assumption of diminishing marginal utility when teaching indifference curves is meaningless, but I still teach why optimisation at interior solutions requires MUx/pX=MUy/py and why that formulation is useful for constructing arbitrage arguments for the tangency condition.

Maybe in second year. But in Eco 100?

Update: I managed to obtain the "official" answer to the question:

"There is no difference between these two equilibrium equations in Eco 100 consumer theory as one equation can be transformed mathematically into the other
MUx/MUy=Px/Py
MUx/Px=MUy/Py

Answer: No.

There is a difference! First line above refers to Indifference Theory that does not require measureable utility; there are no units of measurement on the LHS or RHS of the equation. Second line refers to Utility Theory which does require measurement of satisfaction.

I don't get it. As I noted above, you get the exact same result if you apply a monotonic, increasing transformation to the original utility function.

"There is a difference! First line above refers to Indifference Theory that does not require measureable utility; there are no units of measurement on the LHS or RHS of the equation. Second line refers to Utility Theory which does require measurement of satisfaction."

So the variables in the different equations have different meanings. In which case summary execution is the merciful path to final equilibrium. ;)

Now see here Min I was taught that dy/dx should not be treated as a regular quotient and I'm under 30!

Though you can split them if you are differentiating or integrating you only do it under certain circumstances which require it. Otherwise you leave it alone.

I think we need the person who wrote that 'answer' to explain why it's not completely stupid, because that solution is - to say the least - unsatisfying. Any change in units of measurement on one side of the second equation will be cancelled out by the same change on the other.

Stephen; "I think we need the person who wrote that 'answer' to explain why it's not completely stupid, because that solution is - to say the least - unsatisfying."

I'm imagining the email "Dear Professor ____, One of your students has brought this question to the attention of this blog, and we were wondering if you could explain yourself."

Any volunteers?

It's time for someone to summon up the courage to set up an anonymous e-mail account!

Determinant: "Now see here Min I was taught that dy/dx should not be treated as a regular quotient and I'm under 30!

"Though you can split them if you are differentiating or integrating you only do it under certain circumstances which require it. Otherwise you leave it alone."

Perhaps we are seeing the fruits of non-standard analysis. :) My college text, IIRC, did mention dy/dx, but only as an alternative way of writing d/dx(y), where d/dx(.) represents a function. Splitting was not allowed.

I now have sympathy for students complaining about marks.

d/dx(y)??? That's nonsense. Neither my OAC Calc textbook or my first-year calc book used that notation.

First, y=f(x).

Differentiating: dy = f'(x)dx The variable is reduced to infinitesimals.
So dy/dx = f'(x).

On more splitting, however else are you going to solve a 5% growth problem to project population:

If the growth rate is 5%, Population is P and t is time, then dP/dt = 0.05P

dt = dP/0.05P
=20*dP/P

Integrating, or anti-differentiating,

T = 20*lnP

P = exp(0.05t)+C, the initial population.

"We're actually in the process of doing a minor blog tweak. Would you like to have the names of the authors more prominently displayed at the top of the article?"

Most emphatically, yes. Seriously. As an amateur observer the name tells me alot. At the risk of overgeneralizing Nick Rowe = "trying to understand a grand model while arguing with Delong and Krugman and/or explaining better left wing ideas than what is in the NDP policy book". Frances = "applying the theory to a small-scale real-life event and/or musings on role of higher-ed in Canada". Livio = "nuts and bolts and data about Ontario". Stephen: "more businessy". The guy from Haute etudes who guest posts = "smart stuff on finance"

Now that I have offended all of you I will sign off by saying I enjoy it all even when I only understand to the third paragraph.

Chris J - thanks for the feedback. The only person you're likely to have offended is Mike Moffatt ;-)

My self-description on twitter is "I theorize about life" so your perception of me, anyways, is pretty much spot on.

"businessy"?!?

Determinant: "First, y=f(x).

Differentiating: dy = f'(x)dx The variable is reduced to infinitesimals.
So dy/dx = f'(x)."

Eminently sensible. And that's pretty much how people thought about infinitesimals in the beginnings of calculus. Later on, people began to worry about dividing by dx. In some ways, we treat infinitesimals as equal to zero, so dividing by an infinitesimal is like dividing by zero. In this case it gives us the right answer, but. . . . One solution to the logical enigma was to do the division to produce Δy/Δx, and then take the limit as they approach 0.

But then non-standard analysis provided infinitesimals with a sound logical basis. I suppose that some time later you had textbooks return to the previous style, as indicated in your post. :)

As for d/dx, check this out.

y = f(x)

dy/dx = d/dx(y) = d/dx(f(x)) = f'(x)

:)

Stephen - perhaps he was confusing you and Mike? Or perhaps he means that your posts are understandable and relevant to the real world?

Frances: "Stephen; "I think we need the person who wrote that 'answer' to explain why it's not completely stupid, because that solution is - to say the least - unsatisfying."

I'm imagining the email "Dear Professor ____, One of your students has brought this question to the attention of this blog, and we were wondering if you could explain yourself."

Any volunteers?"

Who is/are the author(s)?

Its ironic how the confusion here exactly matches the confusion in Nick's Volunteer army post, and for the same reasons people answer 'true' to that question and don't see that the volunteer army analysis depends on an unsubstantiated assumption, which is precisely the point of this question.

The notion of a unit "utils" has been discredited for fifty years in the US. Is it really true that the only professor in Canada who knows this is teaching your nephew's eco100 class?

Well you did say it was a top school!

Again, no. The ordinal/cardinal point doesn't apply in this context. It *does* apply when you use the expected utility criterion.

Jon: "The notion of a unit "utils" has been discredited for fifty years in the US."

Writing down MUx presupposes the existence of a continually differentiable utility function U=f(x). A one unit change in x will cause a change in U. We can use the word "util" to refer to the change in U with respect to a change in x without supposing cardinal utility, scalar measurement, or all sorts of other things.

Yes, utility theory not a literal description of human choice, it is only a model. People who find the assumptions of this model obnoxious can derive just about everything they need from revealed preference theory, which removes the need to talk about utility, marginal utility, or utils.

As Nick said earlier, if you rewrote the question so that MUx/MUy was replaced with MRS (marginal rate of substitution) *then* the professor's answer might make sense, because you can have a MRS without a utility function - just use revealed preference theory. And it would, in this case, be a really great question - if the students had in fact been taught revealed preference theory.

Frances: I don't follow the distinction you're drawing. If the preference relation cannot be represented by a continuous utility function, then the ratio of marginal utilities isn't defined, but neither is MRS. Similarly, if behavior satisfies the weak axiom but is not rational, neither the ratio of marginal utilities nor MRS is defined. What am I missing?

The answer seems very wrong to me. There's a distinction drawn between "utility theory" and "indifference theory" which doesn't exist (the latter is a pedagogical approach to teaching the former), the word "measurable" is abused, the claim that price and marginal utility ratios are unitless is wrong (presumably what is meant is "the units don't involve `utils'"), and, as many have pointed out, neither way of expressing this equation implies that utility is cardinal. I think we can even dispense with the technical problem that arises when p_x=0 because the question tells us to invoke Econ 101 assumptions, which include non-satiation.

Chris: "I don't follow the distinction you're drawing. If the preference relation cannot be represented by a continuous utility function, then the ratio of marginal utilities isn't defined, but neither is MRS."

It's between (a) postulating the existence of a utility function and from that deriving predictions about consumer behaviour and (b) postulating certain assumptions about consumer behaviour and from that deriving a utility function. If you start with the MRS and then go on from that to derive the existence of a utility function that's approach (b), and that's the distinction I'm drawing.

I agree completely with what you say in your second paragraph.


Francis, I don't like the professor's wording either, but it seems to me that the point of the question is that two theories can have different epistemology even when they appear to have some mathematical equivalence.

That's a VERY important point when discussing models from which we intend to draw inferences. For instance, we might agree on the meaning of probability--such that we can compute probabilities in a finite space by enumeration, but then interpret probabilities differently: i.e., frequentist vs baynesian interpretation. (Are there any frequentists still !?!?)

"True or false: There is no difference between these two equilibrium equations in Eco 100 consumer theory as one equation can be transformed mathematically into the other (a) MUx/MUy=Px/Py (b) MUx/Px=MUy/Py."

What does "no difference" mean that's what this matter hinges on. If you insist on thinking about "no difference" in purely mathematical terms, you get one answer, but as Bill Wooley explained earlier MUy/MUx is a notation, not a quotient. In particular the theory in question states that the only the relative prices reveal the relative utility). MUy/MUx is a direct rejection of that calculus of utility implicit in MUy/Py; MUy and MUx cannot be known as individual quantities. Only their ratio can be observed by the manifestation of Py/Px. That's the whole point the notation is making...

The question appears to take as given the terms are mathematically convertible, so it somewhat hints that it isn't asking about mathematics. Its asking about the epistemology.

Your best friend's son is going to a good school.. but I find the the solution in the "Update #2" to be quite rather muddled in making the point.

Jon: "two theories can have different epistemology even when they appear to have some mathematical equivalence."

Yes, that would be true of revealed preference theory and utility theory.

That is *not* true of "utility theory" and this so-called "indifference theory".

You write: "MUy/MUx is a direct rejection of that calculus of utility implicit in MUy/Py"

How could "MUy" be a direct rejection of the calculus of utility when MUy is defined in terms of utility calculus, i.e. dU/dy?

"Your best friend's son is going to a good school.."

That is totally and utterly irrelevant. The variance in the quality of instruction within universities is much greater than the variance between universities.

Min:

I learned the basis of calculus using limits. Besides, most of the interesting questions are actually related to integration or the solving of differential equations where you use Laplace Transformations or weirder things like the Method of Froebenius. And you have to use limits when you integrate to infinity anyway so it serves a double purpose.

Then there is complex number calculus, in which we get interesting results like any integral over a closed path being zero (Cauchy's Theorem).

Speaking of limits, a certain economist on this blog got caught short by not invoking L'Hosptial's Theorem when he should have.

Francis,

The the point is that you can define a concept of MU, and a concept of MUy/MUx but MUi is unobservable, and not computable (neither is MUi/Pi). That's what there being no calculus of utility means. In this line of thinking, MUy/MUx cannot be calculated directly, but happens to be observable by inspection of the relative prices, i.e., from Py/Px.

The inventor of this theory is none other than one of the founders of marginal analysis in economics... Carl Menger, so please lets not call it a "so-called indifference theory". Indeed, in fact this is what we know as Marginal Utility. "Utility" as a quanity is something entirely different--something that does not exist, and therefore there is no calculus of utility.

Or in Menger words:


Value is thus nothing inherent in goods, no property of them, nor an independent thing existing by itself. It is a judgment economizing men make about the importance of the goods at their disposal for the maintenance of their lives and well being. Hence value does not exist outside the consciousness of men. It is therefore, also quite erroneous to call a good that has value to economizing individuals a "value", or for economists to speak of "values" as of independent real things, and to objectify value in this way.

Jon: "The inventor of this theory is none other than one of the founders of marginal analysis in economics... Carl Menger, so please lets not call it a "so-called indifference theory"."

I'm afraid history of thought is not my area. This is from the UK edition of Dick Lipsey's text:

http://www.oup.com/uk/orc/bin/9780199563388/01student/interactive/lipsey12e_extra_ch05/page_02.htm.

So perhaps this idea is out there some places. It's certainly not one that's in common currency, as you can see from the comments on the blog.

If you want to get some idea of how widely used the term is, this is what Wikipedia says on the subject:

"The page "Indifference theory" does not exist. You can ask for it to be created, but consider checking the search results below to see whether the topic is already covered."

And again, it's a restatement of the ordinal/cardinal utility point. And again, it's a point that doesn't matter here. A monotonic transformation of U(X,Y) will change units, but you still end up with both expressions.

Stephen,

not sure that the ordinal/cardinal point doesn't matter. I think the issue is that for a given set of prices, which are observable, one of the expressions is invariant to choosing a different cardinal representation of the preference ordering, the other isn't.

If you start with a choce of utility function that represents the preference ordering and is consistent with observed prices, then apply a monotonic transformation to the utility function in order for b to be true under the new utility function you need to multiply all prices by the derivative of the transformation.

On the other hand, a is true for *all* representations of the preference ordering.

I matters because prices are observed, thus should be invariant to the utility representation. Thus you want to work with the invariant expression, that's (a), not (b).

Adam P "Thus you want to work with the invariant expression, that's (a), not (b)."

The thing is, you never actually "work with" either expression. All you observe are prices and quantities demanded. Both (a) and (b) are ways of representing a consumer's state of mind and, together with the budget constraint, define the consumer's demand function.

I have to say, I find expression (b) much easier to think about - in fact the only way I can ever get to expression (a) is to derive it from expression (b).

The idea that expression (a) is a concrete expression of reality somehow divorced from utility theory makes no sense. When you ask people to think about their own personal marginal rates of substitution you're asking them to set U=K i.e. keep their own utility constant. Indifference as a concept is meaningless without reference to a preference ordering. (If you want to draw a distinction between preference orderings and utility that's fine, we're back in the world of revealed preference, but in that case *don't talk about marginal utility in the first place*).

I don't like the MRS much because it involves this weird thought experiment - how much of this could you give up for how much of that and be just exactly as well off as you were before. It's extraordinarily difficult for people to conceptualize *because in real life no one ever makes these kinds of trade-offs.*

Expression (b), however - allocate resources so that the value to you of the last dollar spent is the same for every purchase you make - just makes total sense.

And as Linda says about 60 comments ago, expression (b) is much easier to generalize to a multi-good case.

"True or false: There is no difference between these two equilibrium equations in Eco 100 consumer theory as one equation can be transformed mathematically into the other (a) MUx/MUy=Px/Py (b) MUx/Px=MUy/Py."

Based solely on reading the question I would have said true. In the context of intro micro (bear in mind I'm not an economist, I only play one in blog comments) don't you write down a budget constraint, you write down a utility function, you assume the functions are well behaved, maximize utility subject to the budget constraint, and presto? So by definition and assumption both expression are describing the same thing (given well behaved utility and budget constraint functions).

The cardinal/ordinal thing seems like a stretch, especially since the question wasn't something like "which expression is still valid if we mess around with cardinal representation of the preference ordering".

-1 to the Prof for asking an unfair question.


Frances Woolley: "I don't like the MRS much because it involves this weird thought experiment - how much of this could you give up for how much of that and be just exactly as well off as you were before. It's extraordinarily difficult for people to conceptualize *because in real life no one ever makes these kinds of trade-offs.*"

Gee, I thought I made that kind of trade-off while grocery shopping.

OC, I have a different equation in mind:

Px*Δx = Py*Δy = Δ$

where Δ$ is small.

Min: "Gee, I thought I made that kind of trade-off while grocery shopping."

This comment just illustrates how few people really understand the notion of indifference - the "equilibrium equation" described in (a) above is not something you would have experienced while grocery shopping, unless you are the type of person who takes time out from your grocery shopping to ponder the nature of choice.

In the grocery store hardly anyone, ever, thinks to themselves "I could take an apple out of my shopping basket and replace it with a mango and be just as well off as I am right now because the relative price of apples and mangoes is just exactly equal to my willingness to substitute the two goods."

People think "I'm going to buy apples instead of mangoes because they're equally delicious and apples are cheaper." Or people think "I'm going to buy mangoes instead of apples because even though mangoes are more expensive, they taste better." (Unless they're in a tropical climate, where mangoes are cheaper than apples).

In other words, people in terms of how to make themselves better off, how to move from one indifference curve to another. People rarely if ever think in terms of indifference, i.e. "I could do this, or not, and it would make absolutely no difference to me." When they do think in those terms, often they're talking about a good that gives them no utility at all, i.e. MUx=0.

Frances Woolley: "People rarely if ever think in terms of indifference,"

Who said they have to do so to make trade-offs? Thinking in terms of indifference is for theorists.

Frances:"In the grocery store hardly anyone, ever, thinks to themselves "I could take an apple out of my shopping basket and replace it with a mango and be just as well off as I am right now because the relative price of apples and mangoes is just exactly equal to my willingness to substitute the two goods."
It simply means that ,in our socio-economic class, have no budget constraint in the grocery store,only satiation. The process is so fast and automatic we don't ever realize it took place.But a welfare mom will have to judge both how to attain her highest indifference curve and how to stay on it.
As a did last time I bought a car. And my ex,on a disability pension, who took to year to choose her new car.
If you are in the 1% though( better yet the 0.1%), I agree with you. Except that the MU of buying a bigger megayacht than your neighbour is priceless.

Min: "Who said they have to do so to make trade-offs? Thinking in terms of indifference is for theorists."

All of the alleged advantages of the MUx/MUy formulation rely upon the notion of indifference - only by keeping the consumer on a single indifference curve can we eliminate any need to talk about the gain in utility from moving from one indifference curve to another.

If you're coming around to the point that the difference between "indifference theory" and utility theory is an obscure distinction unsuitable for Eco 100 then, good, I agree.

If all we're interested in is the conditions which define consumers trade-offs then, fine, expressions (a) and (b) above are equivalent - which is what I've been maintaining all along.

Jacques Rene - "It simply means that ,in our socio-economic class, have no budget constraint in the grocery store,only satiation."

Not at all. If you are a welfare mom, you are *of course* thinking about how to get onto the highest possible indifference curve.

What you *don't* do is waste time thinking about various combinations of goods that are alternative ways of obtaining that highest possible level of indifference. Imagine saying to a welfare mom "right now you have 2 boxes of pasta and 1 bag of potatoes in your shopping cart. I'm going to take away 1 box of pasta. How many more potatoes would you need to have to be just exactly as well off as you were before."

She would - rightly - say to you - "Give me back that box of pasta and quit asking me stupid questions."

We think in terms of making ourselves as well off as possible. We do not think in terms of indifference. It's a really really unnatural way for animals focussed on survival to think.

AdamP: ". I think the issue is that for a given set of prices, which are observable, one of the expressions is invariant to choosing a different cardinal representation of the preference ordering, the other isn't."

Start with MU_X/P_X = MU_Y/P_Y. Apply a monotonic transformation g() to the utility function and you get:

g'()MU_X/P_X = g'()MU_Y/P_Y,

which is the same expression since the g'() terms cancel. There is no sense in which one of those equations requires cardinality and the other does not.

I actually use the formulation: MUx/(Muy/Py) = Px. The LHS is willingness to pay; the denominator is Marshall's Marginal utility of money in a 2-good world. This is how I get from the consumer equalizing MU per dollar to demand for x.

Jacques René Giguère: "Except that the MU of buying a bigger megayacht than your neighbour is priceless."

;) ;) ;)

Frances Woolley: "If you're coming around to the point that the difference between "indifference theory" and utility theory is an obscure distinction unsuitable for Eco 100 then, good, I agree."

Well, that's in part why I suggested summary execution. ;) In part it is because if you want to make that distinction, comparing those equations is a lousy way to do so.

In response to you I was just thinking about experimentation. As I said, that actually led me to a different equation, not in terms of infinitesimals, but in terms of small differences. A supermarket does offer many choices involving small differences in both quantity and price. Some people find that paralyzing. ;)

As for the, ahem, utility of talking about utility, I doubt if that is an experimental question. Assuming that you can dispense with it, does that make things more complicated or less complicated?

Oh, this thread makes me so weary! I HATE the way we (well, many of us) teach this material in Principles, and I think the question in question is simply horrible. Students (in my experience) understand cardinality versus ordinality without much trouble at all (until we confuse them with "tricky questions" such as this, that is....). And the very simple idea that one will always spend an extra dollar on whatever good yields the greatest happiness is blindingly obvious to 99% of first year students. It is just a couple of simple steps to get them from this point to utility maximization, and you can do it without EVER using the dreaded words "marginal utility. Finally, its not that hard to convince them that diminishing MU is a total red herring: we give them too little credit to assume otherwise.

I think the way we teach consumer theory in Principles is the single biggest reason that many students flee econ in droves after first year. That and the fact that we drag them through weeks of cost-curve tedium.

All IMHO, of course

I blame Paul Samuelson and his incompetent attempt to create "science" -- see Stanley Wong's devastating analysis in his important book.

Did Hicks use "utils" in his original indifference curve work?

Hayek directed Hicks to Pareto and suggested he develop the indifference curve mechanics using Pareto's work as a model.

Hayek would be appalled at the destruction to thinking competently these constructions have so often unintentionally produced.

"Utils" indeed.

No one has had this thought:

"If you are a welfare mom, you are *of course* thinking about how to get onto the highest possible indifference curve."

Well said:

"We think in terms of making ourselves as well off as possible. We do not think in terms of indifference. It's a really really unnatural way for animals focussed on survival to think."

Emma "I HATE the way we (well, many of us) teach this material in Principles"

Agreed. It's just so easy, though, to go on doing things the way we always have done and never step back and really think about what we're doing. And coming up with a different way of doing things is so much like hard work...

Greg "I blame Paul Samuelson"

I wonder how the marginal value of time devoted to improving first year texts compares with the marginal value of time devoted to cutting edge research?

Frances: "I wonder how the marginal value of time devoted to improving first year texts compares with the marginal value of time devoted to cutting edge research?"

I think we need to distinguish between the social and private marginal values here: seems to me the social value is huge for the former, and small for the latter (on average). However, significant improvements to a first year text would not be recognized for a while, and would likely have little impact on salaries.

Frances: when I said "our socio-economic clas", I meant the participants to this blog. We are in the 75-90 ( mostly). A welfare mom must think whether she will buy pears or apples.

Greg: Samuelson wrote for future professionnal economists when economics began to suffer from physics envy. Physicists were beginning to understand the weird implications of quantum physics. So we tried to stomach purely intellectual constructs like indifference curves.
Then we try to expand economics to people who had not intention nor interest in professional economics. No wonder they are confused.

There are very good discussions about "utils" ans " indifference curves" and even "demand" and "supply curves" in
Alfred S. Eichner ed. "Why economics is not yet a science" from 1983, still relevant.

http://www.amazon.com/Why-Economics-Not-Yet-Science/dp/0873322495/ref=sr_1_1?s=books&ie=UTF8&qid=1322161447&sr=1-1

Linda: in the early '80's ,still young and foolish, I was explicitly told that no work I would do on authoring a textbook would be recognized by the econ. dept. But I could apply for credit at the Education Faculty ( is that a real faculty?). Professionnaly, I couls also put a bullet in my brain.

Linda: "I think we need to distinguish between the social and private marginal values here" True, so true!

As you say Jacques Rene, the professional equivalent of a bullet through the brain...

I think the issue here is that Econ 100 isn't completely standardized; terminology, definitions and even assumptions vary, even though the analytical methods are relatively constant. The question in question isn't analytical - it's just a definition, one that someone who was studying from the textbook/lecture notes it was based on would have been able to answer.

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