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It is typically asserted that on utilitarian grounds we can and should redistribute wealth from the richer to the poorer. On its face and all-alone the argument makes some sense. The argument goes like this: since there is diminishing marginal utility of wealth, a dollar to a rich person is worth less than a dollar to a poor person. Hence, taking a dollar away from a rich person will cause a small loss in utility while giving a dollar to a poor person will cause a large increase in utility – so the net change to society from a redistribution of a dollar from rich to poor is positive.

There is something wrong, mechanically, with this argument however. In other words, what about this implication of diminishing marginal utility is not quite right?

Yes, additions to my income may well bring me less satisfaction the richer I am … but this says nothing at all about how the next dollar adds to MY happiness as compared to how the next dollar adds to YOUR happiness.

For example, I am a millionaire and you have only $50,000. What diminishing marginal utility tells us is that the 100,000th dollar maybe added 50 utils to my satisfaction, and the 200,000th dollar added 45, and the millionth dollar added 30 … and so on. What it also tells us is that the 10,000th dollar to you added some amount to your happiness, the 20,000th added a little less and so on. But what the assumption CANNOT say, especially since we cannot do interpersonal utility comparisons, is how much satisfaction the millionth dollar gave me as compared to the 50,000th dollar you got. It could be the case that the 50,000th gave you 32 units of satisfaction while the millionth gave me only 10, but that does not at all follow from the theory. It could also very well be the case that the millionth gave me 25 units of satisfaction, which is of course less than the satisfaction that the 500,000th dollar gave me, and at the same time that the 50,000th gave you 20 units, which is less than the 40,000th gave you.

If you were a consistent utilitarian, then you would necessarily advocate for transferring income from the poorer guy to the richer if the assumption above is violated. I don’t know many people, self-proclaimed utilitarians among them, who would go that far. This is not, by the way, the only problem with utilitarian justifications for income transfers from rich to poor. But let’s keep things simple for now.

 

12 Responses to “Does Diminishing Marginal Utility Imply Wealth Transfers from More Wealthy to Less Wealthy?”

  1. Gabe Wittenberg says:

    Question for anyone who knows, including WC: Does Arrow’s impossibility theorem pose problems for utilitarianism (not that it would be the only problem)? Something I’ve wondered for a while.

    • ZT205 says:

      Gabe,

      Yes and no. Arrow’s theorem assumes ordinal utility– outcomes are ranked, but there is no meaningful distance between preferences. If I prefer A to B to C, we can say I prefer A to B and A to C, but we can’t say that I prefer A to B twice as much as I prefer A to C.

      Now, if we assume von Neumann Morgenstern utility– what we use to calculate expected utility, or anything involving probability– then we can get around arrows theorem. We can have a normative criterion where we ask ourselves “how would the average person behind the veil of ignorance, not knowing what position they will be born into, structure society?” Assuming all policies lead to the same population size, this turns into a utility maximization problem in the classic utilitarian sense, and does allow us to effectively do interpersonal comparisons.

  2. Harry says:

    By this logic the best wine should be shipped to France.

  3. Greg says:

    From what I remember, affine invariance is only implied for an expected utility maximizer, and we all know how that goes.

    • Greg says:

      I also suspect it would be possible to derive or observe bounds on relative utility improvements between individuals. For instance, it’s pretty clear that handing me a sandwich right now would do less for me than for someone who is starving. That is not borne out by the diminishing return argument alone, but diminishing returns are one way to make it so.

  4. Scott says:

    Does diminishing marginal utility of labor also have a role in current legislation? Specifically, the mandate for more overtime pay? By increasing requirements to provide ‘overtime’ compensation, we are being told that we must value one additional hour of leisure to be more valuable than the additional job security and/or the increased probability of long-term success in our professional endeavors that can be achieved in a hour’s worth of work. Perhaps I’m misreading the legislation.

    • Harry says:

      I believe that the proposal for overtime is for white collar salaried workers not on the clock; I am not sure this includes teachers. It is akin to a chicken-in-every-pot campaign promise designed to divert attention away from PAPACA problems, high energy prices, slow economic growth, Armageddon, etc.

      You can bet that BHO and Harry Reid have not thought much about marginal anything, except election margins, ever.

  5. Tim says:

    Taken to its extreme, would not the Utilitarian argument require that someone with $51,000 have to give money to somebody with $50,000? Isn’t it the same argument?
    Of course, somebody has to invest in the future or everyone sinks back into poverty.

    Along this line, there is horizontal “fairness”. Suppose there are 2 workers who get the same job on the same day with the same promotions throughout their careers. Worker A saves for his retirement, Worker B spends every cent he makes. Now, after retirement, along comes Mr. Utilitarian who says Worker A has “too much” money and Worker B has “too little” money. We can increase utility by transferring money to Worker B from Worker A. Does that strike anybody as “fair”? Of course, Worker A has already paid more taxes because he was taxed on his investments.

  6. Roger says:

    Further complicating matters is the well known cognitive bias of loss aversion. Basically, we tend to value losses double gains. Thus a dollar taken is equivalent to two dollars received.

    Add in the perverse effects on incentives for both the recipient and the victim of redistribution, and the utility arguments for coercive redistribution suffer greatly.

  7. Harry says:

    Thinking of your original question, what happens when interest rates are artificially pushed to zero? Forget all the policy problems for a moment, but remember that this is the river in which US people have swum for many years.

    When one gets hardly any return holding cash, that is, hardly any marginal utility, the choice is to spend it, perhaps for roof repairs or perhaps for a few cases of Thunderbird. The macro theorists will use the Rooseveldtian theory of trickle down, that it makes no difference if you decide to repair the roof, or drink the Thunderbird, as long as the money flows to the roofer drinking the Thunderbird, which eventually flows to the worker, the most important person in the Marxist chain of being.

    So, we screw everybody in the country, including poor widows, to promote the interests of condtruction workers, people with underwater mortgages, and creditors generally, in favor of debtors, killing them all with inflation, at $85 billion a month.

    I hope the Koch brothers, who have through their many enterprises have provided wealth and happiness to tens of thousands, keep up the good work. I would like to shske hands, and would pay for the lunch, and even for the jef fuel to ABE. As long as Wintetcow was along, and I would pay for his travel too.

  8. […] but then again, it is ONLY right as a theoretical matter and doesn’t take us very far. Here is one reason it does not take us very far – that even if we assume diminishing marginal utility it is not […]

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