Weekend Roundup

roundup2We had substantive posts this week on two of our recurring topics — economic efficiency and the foundations or arithmetic.

The former brought us the honor of an extended visit from Uwe Reinhardt, who, as far as I can tell, objects not to the concept of efficiency or to its usefulness, but to its name. But any crusade to change a well-established technical term is, I think, doomed to failure.

Efficiency, of course, is only one of the normative criteria in the economist’s arsenal. I pointed, for example, to an earlier post where I’d outlined a toy framework for evaluating some of the normative claims made by one of Professor Reinhardt’s Princeton colleagues. That toy framework employs a utilitarian criterion that goes beyond efficiency. It evaluates policies on the basis of “what an amnesiac would prefer”, which is very different than a pure efficiency criterion. This kind of analysis is perfectly standard in economics, so any allegation that we fixate exclusively on efficiency is a bum rap.

On the other hand, some fixation on efficiency can be an extremely valuable exercise, for reasons that I hope this week’s post made clear.

Re the foundations of arithmetic, I posted to dismiss the view that the natural numbers are fictitious. As one commenter pointed out, this was largely an attack on a straw man, because almost nobody believes otherwise. Indeed it was. This was intended as an educational post, not a contentious one, and attacking straw men can be a very effective form of education. When I teach students about continuous functions, I ask them to imagine a hostile party who insists that the function f(x) = x is not continuous, and we talk about how you could most effectively convince him otherwise. The hostile party is imaginary, but there’s a lot to be learned from thinking about how you’d refute him.

We also speculated on the defining idea of the next decade and the ideal reading list for a course on how economists view the world.

And then there was the probability problem: A woman has two children, one of whom is a boy born on a Tuesday. What is the probability they’re both boys? Several commenters explained the answer very clearly. In case you haven’t read the comments and don’t want me to give away the answer, I’ll just say that it’s greater than 45% but less than 49%. See the comments on the original post for the reason why.

We’re coming up on a long weekend, and I’m taking Labor Day off. I’ll see you Tuesday.

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7 Responses to “Weekend Roundup”


  1. 1 1 Todd

    I’ve just finished reading “The Big Questions” and I had a question about the Economist’s Golden Rule as it applies to charitable giving.

    You say that charitable giving is a neutral action as far as the EGR is concerned, as it is merely a transfer and neither creates nor destroys wealth–but is there nothing to be said for allocating resources efficiently? Giving money to a church which builds cathedrals and pays preachers is not making anyone better off; investing that money in a bank which lends it to an enterprising small business owner will likely create jobs and increase the general standard of living.

    Would the EGR not favor wealth-creating investment to charitable giving? Indeed, could it not be said that, according to the EGR, charity would be a slight negative, as it tends to be a more inefficient allocation of resources?

  2. 2 2 Neil

    “…Uwe Reinhardt, who, as far as I can tell, objects not to the concept of efficiency or to its usefulness, but to its name.”

    I don’t know if Professor Reinhardt agrees with your characterization, but to me “economic efficiency” seems a wholly appropriate term. It means getting the greatest *economic* value from a given stock of productive resources for a given distribution of ownership of said resources. One can argue whether the given distribution is the “right” one, but it doesn’t matter because you can apply the concept to any distribution. So if you prefer a different distribution, you still want economic efficiency.

  3. 3 3 Anonymous

    Todd: Money generally has decreasing marginal utility for most people, so when you transfer a dollar from yourself (relatively well off) to someone starving in Africa, you are increasing overall utility because that dollar is worth more to them than it is to you.

  4. 4 4 Steve Landsburg

    Anonymous: Money generally has decreasing marginal utility for most people, so when you transfer a dollar from yourself (relatively well off) to someone starving in Africa, you are increasing overall utility because that dollar is worth more to them than it is to you.

    This might be part of an argument for giving to charity (in fact it might be part of an argument for giving almost all of your income to charity) but it is NOT an argument based on the efficiency criterion or on the EGR. (The effciency criterion applies to public policies; the EGR is essentially the same criterion applied to our private behavior.)

    Todd: When I say that the EGR is neutral regarding charity, I assume that the charitable dollars are pure transfers to another person (it doesn’t matter whether that person is Bill Gates or a child starving in Africa). Insofar as charities might spend a dollar in a way that does only 50 cents worth of good, your argument is right on.

  5. 5 5 Steve Landsburg

    Neil:

    So if you prefer a different distribution, you still want economic efficiency.

    Yes, exactly.

  6. 6 6 Harold

    A slightly delayed comment on efficiency. It takes me a while to digest these things. I think I am at last getting the efficiency thing. Steve’s toy model optimises based on the amnesiacs point of view, and I don’t see how anyone could disgree with this as an objective. It relies on defining a utility function, which determines how much benefit each person gets from their buck. It would be easy to argue that this function is actually impossible to define accurately, but why not make the attempt?

    Efficiency is of different types. Assume policy A. If nobody is worse off, and some are better off, then this is Pareto efficient . In practice, this situation is unlikely, as some are likely to be worse off and some better off, so how do we asses if policy A is more efficient than the status quo? In comes Kaldor-Hicks, which says that if those made worse off would in theory accept as compensation less than the amount the benefits accrued to those made made better off by, then it is more efficient. This is effectively a cost / benefit analysis. Crucially, the compensation is never intended to actually be paid, it is just a method of measuring the different gains and losses. I think I am correct in saying that if the compensation payment were actually made, then this would be Pareto efficient, in that no-one is less happy and some are more happy. If the payment is not actually made, then we cannot say this. Using Steve’s Bill Gates example, Bill is allowed to have his music loud and pay me nothing.

    The Kaldor-Hicks efficiency on its own assumes each dollar is worth the same to everyone, thus ignoring the utility function. Steve says it is comnmon practice for economists to include a utility function. I have seen form a little reading that these concerns are well decumented in welfare economics. Steve even illustrates this with the following (in response to Asymptosis):
    “But you are (I am certain) majorly confused about the role of that utility function. Take again the Bill Gates example from my post. I assumed that your night’s sleep is worth $50 to you. I could just as easily have said “Assume that U(W-50,1)=U(W,0) where U=U(wealth, #of nights’ sleep) and W=current wealth.” So the utility function *was right there all along even though I didn’t explicitly mention it*. As it is, I am sure, in all of those 935 papers you tried to show me. ”
    I am not completely familiar with the nomenclature here, but I can notice a distinct difference between this utility function and the one in the “toy model”. This one is not logarithmic. I think this utility function is not flattened as income increases. If this is correct, then Asymptosis may have been wrong in detail, but he was right in essence. The utility function you include (and possibly is included in the 935 papers) is unrealistic, and ignores the well-accepted decrease in utility as wealth increases. The key here is the inclusion of a *realistic* utility function. I think that most people are concerned about the ability of economists to calculate these utility functions. I think people are even more concerned about the willingnness of politicians to include these in their discussions of policy.
    In Steve’s other example, the politician discussing the health subsidy for poor people, he could have reponded “from my calculation of the poor peoples utiliy functions, this 1/2 billion of benefit will provide more than giving 1 billion to all poor people” This does assume that the poor people will not choose or are not able to use their money in a way that will maximise their utility, which requires some justification.

  7. 7 7 Steve Landsburg

    Harold:

    A slightly delayed comment on efficiency. It takes me a while to digest these things. I think I am at last getting the efficiency thing. Steve’s toy model optimises based on the amnesiacs point of view, and I don’t see how anyone could disgree with this as an objective. It relies on defining a utility function, which determines how much benefit each person gets from their buck. It would be easy to argue that this function is actually impossible to define accurately, but why not make the attempt?

    Right. It’s important to realize that this “amnesiac criterion” is not at all the same as the efficiency criterion.

    The Kaldor-Hicks efficiency on its own assumes each dollar is worth the same to everyone, thus ignoring the utility function.

    Not exactly. The criterion makes no assumption at all about what a dollar is “worth” to anyone. It does measure gains and losses in dollars, but you can do that without any metaphysical assumptions about the “worth” of a dollar.

    I am not completely familiar with the nomenclature here, but I can notice a distinct difference between this utility function and the one in the “toy model”.

    You are dead on right here; I wish I had been clearer. Whenever we assume people have preferences (which is to say, always), we are implicitly assuming they have utility functions. But that’s not at all the same thing as *using* those utility functions to decide which outcomes we like best. The “amnesiac criterion” tries to do this; the efficiency criterion does not.

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