Home > Micro > A Conversation on Marginal Utility

A Conversation on Marginal Utility

Taken from the comments on an article on mises.org

Free Radical:

Well put. I’m actually interested in a true Austrian response to my marginal utility comment though. Doesn’t the entire notion of marginal utility hinge on cardinal utility and isn’t that a cardinal sin (can’t help myself) in Austrian economcs?

J. Giles:

Not at all. Ordinal utility works perfectly. Austrian theory asserts that it is impossible to measure how MUCH utility is lost or gained by any given person in any given transaction, since utility (or value) is entirely subjective and subject to sudden changes. But it is certainly possible to make general assertions about whether or not a certain thing is valued MORE than another, although it is not possible to tell how MUCH more. An example; A person is trapped in the desert with no water. He has a number of things he wants to use water for. If we could look into his head, we might be able to represent his priorities for the use of water by arranging them thus; 1st. A nice, big drink 2nd. Water this plant, maybe it’ll grow edible fruit or something 3rd. Take a bath, I’m filthy. 4th. Wet a cloth to wrap around my head and fend off sunstroke 5th. Fill a watering hole and attract adorable animal friends So now; if a container of water drops out of the sky, what’s our hapless desert-dweller going to do, given that his desires are ordered like this? Well, first he’ll chug it. Then, with what’s left over, he’ll water his plant. If there’s anything left, he might give himself a sponge bath; and if there’s still more, he’ll soak his cloth, wrap it around his head, and set to work digging a hole to fill up with the remainder. But what if there’s only a gallon? Well, then, he’ll take that nice big drink, and then water the plant. . . and then he’s out! He didn’t get to take his bath, or wet his cloth, or fill his watering hole. That’s marginal utility. The MARGINAL desires, or possible utilizations – the ones that are least important to him – get cut out if the supply isn’t sufficient to fulfill all his desires. The 1st priority gets satisfied first, then the 2nd, and so on until the supply is gone, in order of ordinal ranking. Cardinal utility is actually a useless concept. Think about it; look at the list up there. A cardinal ranking would require assigning a numerical value to each of those desires, upon which mathematical operations can be performed. The implications are unfortunate. If getting a drink is worth 1000 utils, and watering the plant is worth 500 utils, doesn’t that mean that it’s more valuable to water the plant three separate times than it is to have a drink? But that’s absurd; the plant doesn’t need that much water, and you’re still slowly dying of thirst in the desert. The fact that the plant is now drowning in an overabundance of water doesn’t do a single thing to solve the problem of your thirst.

Free Radical:

There are several issues with this, first determinnig marginal utility is a mathematical operation (derivative). Also, there’s no reason that if watering the plant one time generates 500 utils that watering it a second time must generate 500 more, this seems to deny the possibility of diminishing marginal utility in the defense of that very concept. Once you have the marginal utility of each of these things decreasing individually, then the example no longer works because the person can possibly do several or all of them to some degree. In this case he will do each thing until the marginal utility of each is equal. Once this is the case, it is likely that when he gets more water he will do more of many or all of them, and this may be the case even if the marginal utility of each thing is increasing. Now I am using an example that assumes cardinal utility but I am arguing thta you are doing this as well you just aren’t calling it that.

In order to argue with your example from a strictly ordinal perspective I would say that it is not enough to just rank each use, this is not a complete ranking of every possible way of using the water because the preference for each thing may depend on the quantities of other things being consumed. In order to construct an ordinal ranking you must rank every possible combination of uses (bundle). Once you do this there will be some optimal bundle for any given income (amount of water) and this will change when the amount of water changes but to say that marginal utility is decreasing is to say that the change in utils between the optimal bundle at one income and the optimal bundle at another level is getting smaller the more income you get and this requires cardinal utility. If you only have ordinal utility over all bundles you can only say that when he gets more income he gets a bundle with a higher utility but you can’t say anything aobut how much higher.

J. Giles:

No, I’m not using cardinal utility, although you are. I’m not sure where the confusion crept in, but I’ll try to resolve it. First off; Determining marginal utility is not a mathematical operation. The entire point of ordinal utility theory is that you CAN’T use math to deal with utility; utility is entirely subjective, changes every moment as the thoughts of the person in question change, and cannot be measured or mathematically manipulated. Second; Marginal utility cannot decrease ‘individually’, because ordinal numbers have no individual meaning. Economics uses the words ‘ordinal’ and ‘cardinal’ in the linguistic sense, NOT the mathematical sense; cardinal numbers are those numbers which denote quantities (1, 2, 3, etc), and ordinal numbers are those numbers which denote places relative to each other (1st, 2nd, 3rd, etc). Third; Yes, it’s possible that the person might do some or all of them ‘to some degree’, but that all depends on how he ranks his desires. When you try to give an example of ordinal utility, it is necessary to assume that you know the mind of the hypothetical person in totality, and are presenting an ACCURATE list of his desires; which means that the person up above does not want to partially fulfill any of his desires, he would rather fulfill the more important ones completely, and then move on to the next. That’s implied in the list I gave above. Fourth; To answer what you said in the comment below this one, you’re right, if we wanted to rank every possible use of the water at the start of the process, we would have to bundle them. But we don’t! We aren’t interested in every possible combination; we’re only interested in what HE, the person stuck in the desert, wants. Remember; utility is entirely subjective. Right now, at this moment, that list up there is an accurate representation of his desires. Now, after he gets the first drink of water, might they change? Absolutely! But we don’t know how, or to what, and there’s no way to represent it mathematically.

Free Radical:

“Right now, at this moment, that list up there is an accurate representation of his desires. Now, after he gets the first drink of water, might they change? Absolutely! But we don’t know how, or to what, and there’s no way to represent it mathematically. ”

This is my entire point!  So when he gets another unit of water you can’t say that his utility increases by less than it did from the first unit.  Also, having an accurate list of his desires doesn’t mean that the person doesn’t want to “partially fulfill any of his desires,”  I’m not sure how you come to this conclusion.  Your whole problem is assuming that some are “more important” than others and that this is independent of how much of each he is consuming.  Then you are assuming that there is some limit to each so the only thing determining the quantity of each is your arbitrary limit on each thing (assuming his income is high enough to make that constraint binding).  this is a very uninteresting model of consumer choice and utility.  However, even in this model I can demonstrate that you don’t get diminishing marginal utility from it.  I will simplify it somewhat by reducing the number of goods to 3

1. take a drink

2. water a plant

3. take a bath

Now, keeping with your convention assume that there is some unit of water and he can spend only 1 unit on each thing, no more no less.  Now assume that the above ranking represents his (ordinal) utility function over the three bundles which he can include with an income of one unit (to be complete we could include the possibility of doing nothing as number 4).    Now we can predict that if he has one unit of water he will drink it.  We haven’t said anything about marginal utility.

Now if he gets another unit of water we can rank his possible bundles (disregarding those which do not lie on the budget constraint)

1a drink and water

2a drink and bath

3a water and bath

Here I have assumed the most obvious ranking of these bundles in relation to his ranking when his income is only 1, however it is important to point out that this need not be the case.  It could be the opposite.

1b water and bath

2b drink and bath

3b drink and water

However, let us assume the first ranking (a).  In this case when he has 2 units he will choose to drink 1 and use the other to water the plant.  But if you want to claim diminishing marginal utility of water you have to compare the utility of a bundle on the 2 unit budget constraint (drink and water) to one on the 1 unit budget constraint (drink).  With ordinal utility we can say only one thing about these two bundles:

Bundle 1.a is preferred to bundle 1.

To say that marginal utility is decreasing is to say that utility increased by less between bundle 1 and bundle 1a than it did between nothing and bundle 1.  You can’t say this without having a cardinal measure of utility.  You are making an assumption about utility that inherently assumes cardinality:

Utility of drink and water = utility of water + utility of drink

Of course with ordinal utility this statement is nonsense because it includes mathematical operators (as you have pointed out).  However, even with cardinal utility this need not be the case to preserve the rankings as I have assumed them.  Consider the following cardinal utility function as an example of what I’m talking about.

1c drink and water U=30

2c drink and bath U=20

3c bath and water U=10

4c drink U=3

5c water U=2

6c bath U=1

Notice we have preserved the ordinal ranking but when the man gets his first unit of water his utility increases by 3 (assuming the utility of nothing is 0) and when he gets his second unit of water it increases by 29, in other words you have increasing marginal utility of water without violation any of the typical assumptions about the ordinal ranking of bundles (more is preferred to less, preferences are transitive, even diminishing marginal value can hold up in this scenario).

If you try to write a logical proof that utility must be diminishing you will find it impossible using ordinal measures because such a proof requires you to end with

U(1a)-U(1)<U(1)-U(0)                        (where 0 represents no consumption)

This can’t be done with ordinal utility because, as I said earlier, finding marginal utility is a mathematical operation.

This is important because diminishing marginal utility is a central justification for wealth redistribution among utilitarian types.

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  1. J Giles
    December 5, 2011 at 3:58 pm

    First off; thanks for having a rational, civilized discussion on the Internet. I see that so rarely that I like to call it out when I do. 🙂

    Secondly; I am using a highly simplified model; in fact, one taken from my memories of my basic microeconomics class, which I took at GMU from a very intelligent and libertarian professor. It requires several assumptions in order to make it simple enough to talk about easily. That doesn’t invalidate the model; it can easily be scaled up, or made more complicated by introducing several resources. This is just a simple thought-experiment used to outline the basic ideas.

    I’ll present my objections to your argument in bulleted list, going from top to bottom.

    -Why do we need units? Returning to the list of desires, remember that we assume that list is accurate in it’s entirety. Without that assumption, we can’t talk about this man’s utility in ANY way, because we don’t know what he wants. But those listed desires do not use the same amount of water, clearly. Our friend most likely isn’t going to chug as much water as he would use to water a plant, and still less is he going to drink a bathtub-full. Unit size is irrelevant; it’s unique to each desire, because each desire is unique.

    -When you start to talk about ‘bundling’, you’ve made another assumption. In order to have a worthwhile conversation here, we need to work under ceteris paribus; the only thing we’re changing is the amount of water available. But you’re also changing his desires! There’s no reason to do that; having a drink, watering the plant, and taking a bath are all separate desires, which our hapless subject wants individually. Why should they be linked together? They’re different things. Yes, it’s possible to represent them together, but you are unconsciously assuming that ‘water + drink’ is something other than ‘water’ and ‘drink’ are separately. That isn’t true. We don’t need to use ‘bundles’ at all; we already know what he wants, and we know which uses of a given amount of water he wants more than others. ‘Bundling’ is actually CHANGING the listed desires, and thus modifying the parameters of the thought experiment.

    -Now we get to the meat of the issue.

    “However, let us assume the first ranking (a). In this case when he has 2 units he will choose to drink 1 and use the other to water the plant. But if you want to claim diminishing marginal utility of water you have to compare the utility of a bundle on the 2 unit budget constraint (drink and water) to one on the 1 unit budget constraint (drink).

    Bundle 1.a is preferred to bundle 1.

    To say that marginal utility is decreasing is to say that utility increased by less between bundle 1 and bundle 1a than it did between nothing and bundle 1. You can’t say this without having a cardinal measure of utility. You are making an assumption about utility that inherently assumes cardinality: Utility of drink and water = utility of water + utility of drink”

    -I don’t have to compare any bundles at all. Absent the unit assumption this line of argument collapses immediately, because it isn’t relevant. Bundles don’t matter; the man doesn’t want ‘drink + water’, he wants a drink, and then he’ll think about watering the plant.

    Once you look at the model this way again, the proof of diminishing marginal utility is clear. The subject’s most important desire is for a drink. Once he’s gotten that, his next most important desire is to water the plant. The amount of water used to water the plant is NECESSARILY less valuable than the amount of water used to quench his thirst, regardless of what the amounts in question are. We know this a priori because the drink is his first priority, and the plant is his second; if it weren’t true, than his list of priorities would have been different. Once again, this is a tautological statement, and it was already implicitly stated when we ranked the values. To assert it requires no other assumptions or calculations.

    Your second paragraph quoted above is just a false assertion. I did not assume that “Utility of drink and water = utility of water + utility of drink”. The ONLY things I assumed with regards to relative utility were explicitly stated in the set-up; The value of a drink > the value of watering a plant > the value of taking a bath. It is entirely possible to claim that utility is diminishing at the margin without using any cardinal operators at all; I have just done so. I don’t know how much it diminished; all I know is that the water used to water the plant was less valuable to this man than the water that he drank was.

  2. J Giles
    December 5, 2011 at 4:03 pm

    Also, regarding your comment about wealth redistribution; all I can say is that anyone who tries to use DMU to argue in favor of wealth redistribution does not understand it at all. In brief, ‘value’ is an entirely subjective thing; it has no common denominator between people, if you want to talk in mathematical terms. That being so, it’s simply not possible to claim, EVER, that one person finds ‘greater utility’ in a good or service than another does. The only person whose evaluations you ever know about is you.

  3. Free Radical
    December 5, 2011 at 11:32 pm

    I agree about rational civilized discussions on the internet and return the compliment. I feel like everyone on mises.org is completely willing to argue about nonsense (like darwin inventing marginalism) to no end but whenever I ask a serious question I don’t seem to get many responses. So I appreciate you making an effort. And since we are friends now I will try to reframe the discussion a little bit. Hopefully you won’t take offense to this as none is intended and I think it may save us both some trouble.

    I am quite sure you are wrong on this and that you don’t have much formal training in consumer theory and that means probably not economics. This is not a knock on you, most people have better things to do than to study consumer theory. However, I don’t have anything better to do and as a result I do have this training. I’m not saying that that means you’re automatically wrong about everything and I’m automatically right or anything like that but it so happens that in this case you are and you are making some pretty major logical errors. You can disagree with me, that’s fine but what matters going forward is whether or not there is any hope of one or both of us getting anything out of continuing this conversation.

    For my part, even though I perceive a near zero chance of you convincing me that diminishing marginal utility is not a cardinal restriction, I still have some interest in the matter because I have a soft spot in my heart for Austrian types since morally and mostly intellectually we are kindred spirits. But Austrians make some serious economic errors and frankly, in my experience, they seem very difficult to reason with. So I am interested in what it takes to convince an Austrian that something they think is wrong and I sort of caught you in my trap.

    Now at this point it has become clear that what is required is at least pretty significant. It might be impossible, I’m not sure. So if it’s impossible–that is, if you don’t have any doubt in your mind that you are correct about this–then it’s probably best for both of us if I don’t bother trying. This point is pretty subtle and the errors you are making are pretty fundamental so it is going to require a lot of careful thought on my part to explain all the points necessary and if youa re determined to fight me on all of them it will be impossible and very frustrating.

    In light of this I will get started on it but if you are of the opinion that I can’t possibly know what I’m talking about then it would probably be best to just agree to disagree while we’re still buddies. Some immediately obvious points will follow and then after I organize my thoughts more some more detailed discussion and examples.

  4. Free Radical
    December 5, 2011 at 11:40 pm

    1. Simplified models are ok but you have to be careful about what you are simplifying. In the case of your model there is nothing wrong with it except that you don’t realize the restrictions you are putting on it. Adding more resources is not what it needs, it needs a more general utility function and since that is the heart of the debate this is of the uttmost importance.

    2. The units matter. It doesn’t matter what the unit is but it the relationship between how much water it takes to get a drink vs. water a plant matters. I think once you see the main thing you are doing wrong this will become obvious though so I will put off a more detailed discussion of the matter.

    3. Utility has to rank bundles, it can’t just rank goods, this is basically your whole problem. It isn’t an assumption I am making, it is an assumption you are making. Your example fits just fine into my model but my model allows for all sorts of things which yours does not (like increasing marginal utility). This is because the utility of a good depends on the quantities of other goods consumed along with it. Once you realize that you have to rank bundles and not goods, I think things will start to fall into place so I will try to demonstrate why that is next. First, though I have to pick up a pizza and drive home.

  5. Free Radical
    December 5, 2011 at 11:42 pm

    Oh just for the record, I’m certainly not advocating for redistribution of wealth based on DMU nor arguing that DMU would justify it, hopefully it’s obvious that I’m on your side with regard to that stuff. But nonetheless people do use it as part of the justification. I really just added that for the benefit of any other readers that might stumble onto this and think “who cares about diminishing marginal utility” not so much for you.

  6. Free Radical
    December 6, 2011 at 6:02 am

    OK I’m gonna start by addressing the bundle thing. As I said once you get this point, I think the rest will be straightforward. As I have pointed out already you are assuming that the utility from consuming two things must be equal to the utility from consuming one plus the utility from consuming the other. You denied that you are doing this but I don’t know how to convince you other than to give you several examples that violate this assumption.

    As a first example let me exploit the very intuition that has led you into your present confusion. Imagine a man who is starving. You give him five dollars which he can use to buy one of these 3 things.

    A hamburger: Utility=100
    A slice of pizza: Utility=90
    A burrito: Utility=80

    He buys the hamburger of course. Then immediately upon finihsing said hamburger you give him another 5 dollars. Must it be true that the utility from a pizza must be 90 (in other words must it be the same as it would have been if he only consumed a pizza)? After all he is no longer starving. Obviously the answer is no. In fact this concept of utility depending on other goods consumed is pervasive in your original example. Notice that in this example if the utility of these goods wasn’t changing depending on how many hamburgers were consumed, then no matter how much money you gave him he would just keep buying hamburgers, he would never buy a pizza or a burrito. Similarly, if the utility of drinking, bathing, etc. wasn’t changing as the quantities of these goods consumed changed, the man in the desert would always just keep drinking and his marginal utility would be constant. So in assuming that he spends some water on drinking and some on watering a plant and some on bathing implies that at some point the marginal utility of drinking falls below the marginal utility of bathing. I presume in that example you would imagine that this is because the marginal utility of drinking is falling the more he drinks and the utility of the first unit of bathing is held constant until he starts bathing but here hopefully we have an example where the quantity of one good consumed (hamburgers) can plausibly change the utility from consuming another good (pizza).

  7. Free Radical
    December 6, 2011 at 6:25 am

    OK, if you have the utility of certain goods changing when you consume different amounts of other goods you can still get to diminishing marginal utility if these utilities are always decreasing as in the above example. But does this have to be the case? Consider a couple of examples.

    Again, a man is starving and you give him $5. He can buy one of the following things.

    a pound of hamburger
    1/2 lb. of sirloin steak
    2 oz. of filet mignon

    Assume that his preferences are ranked in the order above. Now if you give him another $5 does that mean that he will buy a pound of hamburger and a half pound of sirloin? Of course not. In fact it is quite likely that if he had $50 he may forego hamburger and sirloin all together and buy only filet mignon. Does this mean that the utility of the first unit of hamburger decreased when he got more money or that the utility of the first unit of filet mignon increased? The answer is that it’s not either one this is the wrong way to think about it you have to rank every bundle! These preferences could be represented as follows. (where > is read “is preferred to”)

    20oz. filet mignon>10oz.filet mignon and 5lb hamburger>1 lb. hamburger>2oz. filet mignon

    When you rank every bundle you don’t run into this problem. This is a case where hamburger is an inferior good and filet mignon is a normal good.



    If all you have are these rankings, is his utility increasing at an increasing or decreasing rate as he gets more income?

  8. Free Radical
    December 6, 2011 at 6:43 am

    Similarly try this one. A man has $5 and is deciding on what to have for dinner. He can buy one of the following things.

    Steak sauce
    BBQ sauce

    His utility of BBQ sauce and Steak sauce is relatively low at this point as these don’t make for much of a meal by themselves while his utility of chicken and steak is relatively high. Let’s assume the order of these preferences is as above so he buys chicken.

    Now this guy has $10. Does that mean he will buy chicken and steak? Again, no. He may not have the appetite to polish off both the chicken and the steak, it may be more desirable to have the chicken and spice it up with some sauce. So does this mean he will buy the chicken and steak sauce? Maybe not since he may prefer BBQ sauce with chicken. So does this mean that he will buy chicken and BBQ sauce? Again, perhaps not because he may prefer chicken to steak when unsauced and prefer BBQ sauce to steak sauce on chicken but prefer steak with steak sauce to chicken wth BBQ sauce. In other words, the utility function must rank all possible combinations. Such a function representing the preferences I just described would be (leaving out some other combinations assumed to be dominated):

    (steak and steaksauce)>(chicken and BBQ)>(chicken and steaksauce)>chicken>steak

    Here we have a case of compliments


    OK I think that should take care of the bundling issue, hopefully but let me know how this is going.

  9. J Giles
    December 6, 2011 at 3:37 pm

    You got me; you’re right in that I haven’t had an enormous amount of economic education. In the interest of full disclosure, I’m still a university student, only a few years into my education, and still taking economics classes. I’m very interested in discussing econ problems with other people, and if you think you have something to teach me, I’m glad to learn. That doesn’t mean, of course, that I’m going to take what you say without a grain of salt; but I try not to be close-minded. I’m certain that the way I think about these things can still use some refining; I don’t know everything, and I don’t imagine I ever will. However, I do have to say that I think it very unlikely that I’m wrong about such basic, fundamental laws as diminishing marginal utility. If you can provide a proof of your cardinality argument, that will certainly cause me to re-think my worldview.

    Now, as to your examples. Reading over those has given me some insight into our disagreement here, but not the one you were trying to create. I’ve realized that we’re talking past each other. You see, my original example did not include multiple goods.

    I used the example of the man in the desert precisely because there was only one good in question; water. That’s the only thing he can get; it’s the only resource he has to allocate. The discussion centered around how to use that single good to fulfill multiple desires. Your examples, by contrast, are all about something quite different. You are talking about using multiple resources – hamburger, sirloin, filet mignon, etc – to fulfill a single desire; the desire for food.

    The model that we are discussing is not a choice model. It is a RATIONING model. Questions of quality or complementary and substitute goods don’t enter in, because the input, the resource, is in all cases assumed to be identical. What I was representing was the basis of the human decision-making process; the determination of how to use any single given good. That model cannot be applied to multiple goods. Once you begin talking about multiple goods, a simple list of priorities is no longer an accurate model, because now there are multiple possible ways of fulfilling each priority.

    In brief; the issues that you are finding with the model are coming about because you’re taking the model too far, and applying it to the wrong problem. This thought-experiment is not concerned with finding the best of many possible ways to solve a problem; it is considering in what ORDER many problems will be solved, given a single possible method. It’s far more limited than you are claiming.

    At this point, I have to retract something I said before. I was wrong earlier, when I asserted that the unit was unimportant; in doing that, I accidentally removed cost from the model. The unit IS important, because the relative importance of a desire must be weighed against the cost of fulfilling said desire, and a more important desire may go unfulfilled if the cost is prohibitive. Even if a man in the desert wanted to take a bath more than anything else, if he only got a cup of water, he would likely drink it instead.

    Now, let me present the same model in a different way, as a logical statement;

    *When a person has multiple desires which can be fulfilled by using a given amount of a resource, they will uniformly choose to fulfill those desires which they consider most important first, and only afterwards proceed to fulfill those desires which they consider less important.*

    That statement says everything which my list of priorities says, or at least what it was trying to say. Perhaps I have presented the model incorrectly, but what I’ve written here is what I’ve been trying to get at. That statement also logically necessitates the idea of diminishing marginal utility; if the highest-priority desire has been fulfilled, then logically whatever amount is used to fulfill the second highest priority must be less valuable, because it is being used to fulfill a less important want (or, to use Austrian language, to remove a less important uneasiness). And in addition to all this, it encapsulates the concept of ordinal utility; desires are ranked in order of importance, and the most important one fulfilled first.

    In order to argue against ordinal utility or DMU, you have to reject that statement as false and substitute a different one. Is that what you want to do?

    • May 16, 2013 at 8:37 pm

      2 فبراير 2010 12:49 م بواسطة mohammed amin moohgb شكرا علي هذا الموقع الممتازاتمني ان تراسلوني من بعض المواضيع الانجيلزية مع ترجمتها وشرحها جزاكم الله خير انا من السودان

  10. Free Radical
    December 6, 2011 at 8:36 pm

    Yes that statement is fales. Also (this is very important) I am not arguing against ordinal utility, I am arguing thta ordinal utility doesn’t allow a restriction on marginal utility (namely that it’s diminishing). The statement is false because the ranking of desires that they consider most important can change when they have different amounts of the resource.

    My model is no different from yours. Water is not the good in your model it is income. The goods are drink, bath, water plant, etc. which he can “spend” water on. I can do the same thing with this example, it’s no different.

    A man is stranded in the desert, there are several things he could do if he had some water. He can drink it or he can bathe or he can water a plant. The plant if watered enough (5 gallons) will produce a large bounty of fruit that are delicious and provide both hydration and nourishment. If he waters it less than this it will produce no fruit. His preferences over what to do with the first gallon are as follows

    1. drink
    2. bathe
    3. water plant

    When he has 4 gallons he chooses to drink 2 and bathe with 4.

    But if he has 5 gallons he chooses to use all 5 watering the plant. He doesn’t have to still spend 2 on drinking and 2 on bathing! Furthermore, it is not difficult to imagine that his utility increases by far more with the 5th gallon than it did with the 4th gallon which he probably used for some amount of drinking and bathing.

    As a side note, if your conclusion about DMU holds up only in a model with one good but falls apart as soon as you have more than one good (this is not the case because as I said your model has more than one good, and frankly even if it did have only one good it wouldn’t hold up there either) then is it of any use to us? Where are these people who consume only one good? In the desert? Economics, after all is the study of choice. If you were really just pondering how much happiness someone would get from getting more and more of the same good when there were no other goods, this would be a purely psycological endeavor. Of course this is not what you are doing you example has choice in it and as I have said, this is because it has more than one good. Saying it is one good with multiple uses would be like me saying that in my models the man only has one good–money, but can use it on multiple things. If I substituted gold (a good) for money it wouldn’t change anything. If I substituted wheat that he can trade for different things, or corn that he could feed to either a pig or a chicken, or labor which he could use producing different things, it wouldn’t change anything. It’s still about choosing between some number combinations of goods, and an ordinal utility function must rank every combination individually.

    • May 18, 2013 at 12:36 pm

      Thanks very much Floss XXI think your blog deserves all awrdas – dont put yourself down.Never heard of Vide Grenier – what are they?

  11. Free Radical
    December 6, 2011 at 8:39 pm

    OH! If you are a student there may be a shortcut here. Obviously I’m not expecting you to just roll over and take my word for it, that would defeat the purpose for me. But if you have access to another econ professor ask him/her whether a utility function has to rank all bundles or can just rank goods, I am sure they will tell you the same thing. Of course you shouldn’t just take their word for it either but it may help to add some doubt in your mind (plus maybe they can explain it better than me).

  12. July 3, 2013 at 3:01 am


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  1. December 20, 2011 at 2:37 am
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