Irish Liberty Forum

Happiness Economics Butchers Marginal Utility Theory

with 9 comments

There’s a new wave of economic thought gaining popularity. It’s called Happiness Economics, and it attempts to place happiness at the centre of economics and public policy. Although it is replete with fallacies, I shall focus on the movement’s treatment of utility and value. I will attempt to highlight it’s theoretical misunderstandings and argue that empirical evidence does not support redistributive measures.

Here is one of the theoretical insights from Richard Layard’s Happiness: Lessons From A New Science:

In fact, the benefit from extra income is less the richer the person, so if money is transferred from a rich person to a poorer one, the poorer person gains more happiness than the rich person loses.  Thus a country will have a higher level of average happiness the more equally its income is distributed.

We can see where Layard is coming from if we consider the following propositions:

  • money has a diminishing marginal utility
  • a “rich” person values an additional € less than he values his previous hundreds of €
  • a poor person values an additional € very highly
  • therefore, we can increase overall utility/welfare/happiness by transferring money from rich to poor.

The above is a prime example of an economic non-sequitor. The conclusion does not logically follow from the previous statements. The first three statements are true however, for the following reasons:

  • humans value the first unit of an economic good more highly than they value subsequent units of  the same homogeneousgood. This requires no testing or validation; it is true a priori
  • it follows that a person with many €s will value a subsequent € less than the €s he already owns. As an aside, the rich person’s actions demonstrate that the person prefers the additional € to the leisure he sacrificed
  • similarly a person with few or no €s will value an additional € very highly

Now the problem is, where did Layard make the quantum leap of assuming that the poor person values the € more highly than the rich person? How does he know that redistribution will lead to increased overall happiness? Marginal utility theory simply descibes how a human values subsequent units of economic goods. How can we possibly compare the value scales of different humans? We simply cannot perform such an operation – unless someone has invented a utilitometer.

Diminishing Marginal Utility...?

Diminishing Marginal Utility...?

Layard’s statement reveals a level of ignorance of marginal utility theory. Humans’ value scales are ordinal, not cardinal. A human will place the first unit of a good toward the use he values most highly. The second unit will be directed to the second most valued end. And so on. It is for this reason that we cannot claim that the first unit gives us triple the utility of the next unit. We cannot add, subtract or multiply utilities, nor can we compare Smith’s value scale to Jones’.

Layard also falls into the “utility maximisation” trap. As utility is ordinal or cardinal, there is no concrete amount of “happiness” or “utility” to be maximised . For this I turn to Rothbard:

The chief errors here consist in conceiving utility as a certain quantity, a definite functionof an increment in the commodity, and in treating the problem in terms of infinitely small steps. Both procedures are fallacious. Utilities are not quantities, but ranks, and the successive amounts of a commodity that are used are always discrete units, not infinitely small ones. If the units are discrete, then the rank of each unit differs from that of every other, and there can be no equalization.

Many errors in discussions of utility stem from an assumption that it is some sort of quantity, measurable at least in principle. When we refer to a consumer’s “maximization” of utility, for example, we are not referring to a definite stock or quantity of something to be maximized. We refer to the highest-ranking posi­tion on the individual’s value scale. Similarly, it is the assumption of the infinitely small, added to the belief in utility as a quantity, that leads to the error of treating marginal utility as the mathe­matical derivative of the integral “total utility” of several units of a good. Actually, there is no such relation, and there is no such thing as “total utility,” only the marginal utility of a larger-sized unit. [Source]

Layard’s analysis is theoretically unsound. Even though empiricism is not the correct approach to economic science, it’s worth checking out the data. So what does it say?

All over the place

All over the place

The research conducted by the Institute of Economic Affairs claims that there is no correlation across time between the Gini coefficient and average happiness in the United States. In an excellent monograph, the IEA also argues that happiness isn’t correleated with violent crime, government spending, gender income inequality, life expectancy or unemployment either. So how can happiness be used as a basis for public policy?

Why start a New Economics if you can’t even get the basics right?

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Written by 20000miles

March 23, 2009 at 10:57 pm

Posted in economics, money, taxation

9 Responses

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  1. Or more simply the rich person may be rich precisely because he values his millionth pound more than the poor person values his tenth pound.

    Pat

    March 26, 2009 at 11:21 am

  2. This field seems like something that Rothbard would have invented to ridicule the empirical approach.

    Graham

    March 27, 2009 at 2:08 am

  3. “humans value the first unit of an economic good more highly than they value subsequent units …. This requires no testing or validation; it is true a priori”

    While I agree with the statement, in general, it is not automatically true (a priori).

    There are cases where it isn’t true, due to networking effects. For example, if I had a lego set, the second piece potentially has a higher marginal utility than the first. With the 2nd piece I get both “a piece of lego” and also “the ability to make a 2-piece combination”. Ofc, there will come a point where I have so much lego that more pieces don’t really increase the flexibility of what I can make.

    “Humans’ value scales are ordinal, not cardinal.”

    Again, not true. The point about utility theory is that interpersonal comparisons are problematic.

    For example, I might ask you “which would you prefer an apple or a 50% chance of an orange”. If you feel both options are equally good, then it can be said that your utility increase from been given an apple is half of your utility increase from been given an orange.

    This allows internal personal utilities to be compared. However, it doesn’t allow you to compare utlities between people. In effect, for every possible ‘universe’ you can calculate a person’s utility (the so called utility function).

    Rescaling and changing the zero point of a utility function don’t have any effect on it.

    To compare utilities between people, you need a reference. You can use money for this, i.e. rescale all personal utility scales so that everyone value an additional dollar as 1 unit of utility (and also considers “have no property whatsoever” as their zero point).

    However, that makes a marginal dollar equal for everyone by definition, so it doesn’t really help with the topic at hand.

    The main point about utilities is that you can multiply a person’s utility function by a scaling factor and it is still a valid representation of their utility function. Likewise, you can change the zero point (i.e. add an offset) and it is still a valid representation of that person’s utility.

    ivnryn

    March 27, 2009 at 1:20 pm

  4. Greetings, ivnryn.

    “There are cases where it isn’t true, due to networking effects. For example, if I had a lego set, the second piece potentially has a higher marginal utility than the first. With the 2nd piece I get both “a piece of lego” and also “the ability to make a 2-piece combination”. Ofc, there will come a point where I have so much lego that more pieces don’t really increase the flexibility of what I can make.”

    I think that the lego refernce is incorrect. A counter example: eggs have a marginal utility, the first egg will be used to satisfy my most highly valued end, my second egg will satisfy my second most valued end. And so on. But what if it takes 10 eggs to bake a cake, and that cake is what I value most highly? Does the 10th egg become more valued than the others, thus violating the law of DMU? No. One egg no longer becomes the relevant unit of supply, and 10 eggs becomes the homogenous unit. A cake then becomes the the most valued use for “a unit of 10 eggs”.
    More on this here: http://mises.org/story/3100

    “For example, I might ask you “which would you prefer an apple or a 50% chance of an orange”. If you feel both options are equally good, then it can be said that your utility increase from been given an apple is half of your utility increase from been given an orange.”

    But I can never say that both options are equally good. When I choose one option over another one I demostrate that I don’t value them equally, so we still cannot quantify anything about my utility. We can only say I prefer A to B to some extent.

    You might have guessed that since the Austrian framework doesn’t permit quntifiable utility, then the use of utility “functions” and calculus is incorrect when approaching the subject.

    20000miles

    March 27, 2009 at 5:05 pm

  5. On further reflection, we can praxeologoically compare individuals’ value scales. For instance, in an auction, where one person demostrates he values the object more highly than another.

    Am i correct in saying this?

    20000miles

    March 28, 2009 at 4:44 pm

  6. […] a comment » I was going over my post on Happiness Economics and Marginal Utility and I had a few more ideas. Perhaps I was wrong in saying that “We simply cannot perform [a […]

  7. Very insightful! Recently I had my own shot at defining happiness, which aims to be more “scientific” and “objective” (as much as this is possible for a subjective feeling such as happiness):

    “A person can be considered to have experienced a “happy” moment if the person chooses to re-live it as an end in itself if offered at no cost.”

    For the detailed derivation of this conclusion please have a look at What is happiness? ; What do you think about this definition?

    Thank you,

    Nick

    Nick

    December 11, 2009 at 2:41 pm

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    Pr0ffkr

    December 3, 2014 at 6:31 am

  9. You are arguing against the simple fact that a £ is more valued by one who needs it than it is by one who does not need it?

    And your argument is ‘because every person is different’ … but the claim is ‘all other things equal: A poor person will value a $ more than a rich person’ – it’s the only way to do comparisons on single issues and the proponents of the marginal utility do it all the time.

    Of course you could find a hungry, poor person who would frown at your dollar and toss it, and you could probably also find a rich person who got over joyous by hamstring yet another dollar … but those would be marginal cases, and I challenge you to prove otherwise.

    acebone

    April 2, 2015 at 7:54 pm


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