# Money Metric Welfare and "Economic Efficiency"

IN a comment to a post a while ago, someone asked me to explain the phrase “money metric welfare” and why I hate it so much. It is, in fact, the element of economic theory which I like least, at that is saying something.

A good explanation is given by a non Socratic dialogue reposted by Brad DeLong. He calls it “The Market’s Social Welfare Function.” This means he assumes the standard assumptions sufficient to make market outcomes Pareto efficient, rationality, perfect competition, market clearing, no externalities, symmetric information and complete markets.

My effort at explanation after the jump.

The idea is to choose a starting point A then evaluate changes from that starting point to a new point B in terms of the dollar (or numeraire) good value of the change to each individual and then add up these amounts. The advantage is that this gives a number so that if the number is positive one might have some reason to claim that B is better than A. The disadvantage is that no one who understands what is going on can seriously believe that claim.

The points A and B are social outcomes — complete descriptions of the world from now until forever. The sort of change one might assess would be say taxing CO2 emissions and dividing the proceeds equally among all citizens.

For each person one can imagine calculating (or eliciting) an equivilant variation EV_i an amount of cash such that the individual is indifferent between the reform (moving to state B) and receiving EV_i in cash. The is the money metric benefit of the reform. Obviously EV_i can be negative. If so the absolute value of EV_i is the amount of money metric cost to i of the reform.

Then the total money metric effect of the reform EV is the sum over all citizens i of EV_i.

It is clear that the choice of the initial state A is critical to this calculation. It is just not true that if the EV of a change from A to B is negative, then the EV of a change from B to A is positive. The choice of the initial state A is critical and always made very casually when attempting to calculate EVs.

EV is not a change in a function which depends only on preferences and technology. Only once an initial state is chosen is there anything like a social welfare function. We can say that state A gives the maximum money metric utility for initial state A if the EV for the change to all possible other states is negative.

We can understand EV by comparing it to another hypothetical function. Imagine that everyone has a utility function which describes how happy they are as a function of outcomes. EV_i says they are equally happy in state A and in (state B plus they get EV_i in cash).

If we thought that utility functions exist, a natural social welfare function would be just add up the utility functions to get to total happiness. This corresponds very closely (but not exactly) to the voice of my personal concience (I am very nearly a hard core add em up utilitarian). It does not correspond at all to money metric welfare.

If, as mentioned above, state A gives maximimum money metric welfare (for initial state A) then A maximizes a weighted sum of utility functions. The weights are the inverses of the marginal utlity of cash (the increase in happiness due to one more cent say). This implies a huge weight on the happiness of a rich person compared to the weight on the happiness of a poor person. It has no moral appeal.

One reason it is of some theoretical interest to economists is that if state A gives maximimum money metric welfare (for initial state A) then state A is Pareto efficient, that is, it is impossible to make everyone better off by changing to B. If such a Pareto improvement were possible, every EV_i would be positive so the sum would be positive . Also the free market outcome must be such a state such a state given the standard assumptions of rationality, perfect competition, market clearing, no externalities, symmetric information and complete markets, which imply that the result would be of no practical relevance (since all the assumptions are false statements about the real world) even if “money metric welfare” meant “welfare.”

One way of seeing this is to consider a change which has nothing to do with money or private consumption. Say we are deciding about whether to paint the Washington Monument pink (the paint and labor are both free by assumption). I’d guess this has a negative EV, but, in principle some people might like that.

Now let’s imagine a national lottery with a prize of say 100 billion (not optional) and use the state before the painting but after the lottery ticket is picked as our initial state A. If the winner is one of hte few people who wants a pink Washington moneument, it is entirely possible that painting it pink will have a positive EV. Someone with over 100 billion will be willing to spend billions on a whim and most people don’t care much. On the other hand, if the winner is someone who doesn’t want it pink, then the EV of painting it will be negative.

OK the right thing for society to do, the social welfare maximizing color of the Washington monument, can’t really depend on the blind chance of a lottery can it ?
I don’t think so, and so I consider the concept of money metric utility idiotic.
No one defends the claim that EV is social welfare.

Many people, however, pull a sneaky trick. They argue that social welfare and the right choice to make etc are inherently normative choices, statements about our values as well as about facts. EV sure isn’t a statement of anyone’s values (unless that person has deep respect for the God of chance). Therefore it is a positive statement.

So we can separate statements of fact and value as statements about EV and other statements about how things are good or bad. We can call EV efficiency and note that we also care about equity. All of this is based on the fact that a change can have positive EV even though it only helps a few super rich people and hurts everyone else.

OK just because something isn’t the function we should maximize and the guide to right choice that doesn’t mean it is a measure of efficiency. I can make as many arbitrary functions as I want all of which have any desirable property which EV with initial state A has.

The argument is, as always, look at this, it is not what we wish we had. Therefore it is a useful approximation to what we wish we had. I assert the argument is really just that, that I have left out nothing and been totally fair to the advocates of EV.

Fortunately, I think very few people have ever been convinced.