But once again—just because you’re doing something reasonable does not mean it’s useful to change the meanings of standard terms. One policy is preferred by an efficiency criterion; a different policy is preferred by your sum-of-utilities criterion. I can easily write down a different sum-of-utilities criterion, with different utility functions, that disagrees with yours. One criterion endorses one outcome; another endorses another. That’s not paradoxical, but it can get confusing if you hijack vocabulary from one criterion to another.

A world can me dreamed up whereby the second situation has a greater social welfare after the transfer than before; where social welfare is defined as the sum of all utility functions, i.e. Jack and Jill’s utility functions.

You are not dreaming up a different world. All you are dreaming up is a different way to decide between outcomes.

There has been a “social gain” and this policy is now good under this reanalysis.

The fact that a policy is good under your (perfectly reasonable) criterion does not mean that it creates a social gain.

Of course you can define “social gain” any way you want, but since it already has a perfectly good meaning, and since what you’re talking about can be perfectly well described as a “sum of utilities”, it only muddies the water to hijack an existing term and use it in a nonstandard way.

I am interested in what Asymptosis had to say about the use of utility functions that have declining marginal utility of money. For example the Ln function. Dollars are a very good at measuring value but there is something to his point about Lamborghinis and a college education.

“In applications, the Kaldor-Hicks criterion and the efficiency criterion amount to the same thing. When Jack gains $10 and Jill loses $5, social gains increase by $5, so the policy is a good one. When Jack gains $10 and Jill loses $15, there is a deadweight loss of $5, so the policy is bad.”

A world can me dreamed up whereby the second situation has a greater social welfare after the transfer than before; where social welfare is defined as the sum of all utility functions, i.e. Jack and Jill’s utility functions.

Let utility (U) be the Ln of the persons wealth in dollars. At time (t) 0 Jack (K) will start off with $1 and Jill $100 (it does not say how much money either had initially so I have taken liberties). At time 1 there will be a transfer of $15 from Jill (J) with $10 going to Jack and $5 will be thrown into the sea where an evil sea creature eats it up (somehow $5 dollars of real wealth is thrown into the sea and we do not care about the monster’s welfare).

t=0
U of K=Ln(1)=0 — U of J=Ln(100)=4.6 —- Social Welfare= 4.6

t=1
U of K=Ln(10)=2.3 — U of J=Ln(85)=4.4 —- Social Welfare= 6.7

There has been a “social gain” and this policy is now good under this reanalysis. It all depends on how you measure what can broadly be called social welfare. Asy’s point is that the first bit of consumption is probably more important to people that the last bit. I recognize it is impossible to really measure this stuff so we have to pay attention to dollar signs. But, there is some important information in this experiment that think think Asy was trying to get at.

I would like to be able to quote it, Steve. It is a crisp statement of the issue, and you have a penchant for crisp clarifty — also, by the way, on the economic case for the voluntary army. No one has put this as crisply as you have.

Best,

Uwe