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Tuesday, March 15, 2005

Something Brad DeLong explained to me which is not totally obvious

In standard general equilibrium theory, the market outcome is Pareto efficient. One of the standard assumptions is that people are totally selfish and care only about their own pleasure minus pain due to consumption. One might wonder if the result can be generalised to the case of people who care twice as much about their own pleasure minus pain due to consumption as that of others. I think that, decades ago, I guessed that assuming that people could give to others would imply the result that free trade and free giving would lead to a Pareto efficient outcome. If I did, I was wrong. The assumption of total selfishness is required for the conclusion that Laissez Faire is Pareto efficient.

If people are altruistic but not 100% selfless then coercion in helping the poor is Pareto improving (Brad explained this to me by the way). Let's say we care about strangers one half as much as I care about people in my family. This is an immense degree of atlruism (my poor kids would be living at lower third world levels if I did). However, at the point when I am indifferent about giving more, you would want me to give more to the poor. The reason is that you don't care any more about me than a poor person.

This is true even if one of the reasons I want to give to the poor is that I know it will make you feel better (and I care about you too).

This means that we would both be happier if we were both coerced to give more than we want. The poor, needless to say, would be much happier.

If people are altruistic, then there is an externality from giving (you give to the poor so I feel better because the poor are less poor). This means that the amount of giving optimal for the rich is more than we would choose acting as individuals.

Charity with no is Pareto efficient only if people are totally selfish or if they are totally selfless caring no more about their flesh and blood than total strangers.


Anonymous said...

Im not completly sure I understand the intuition. Isnt the above implying that there there are mutually beneficial trades left undone?

That is; suppose we have firm 1, which will give to the poor whatever youd give in the goverment coercion case, if and only if everyone who is not poor buys the charity product. If there is even a single non-poor not buying the good (I guess the right term here would be sining the contract) then everyone gets their money back and we give it another shot.

So at the margin I should sign the ocntract since if everyone does it is a pareto improvement, and if everyone doesnt then I still get my money back.

what is wrong with the logic above?
or rather, do you have a proof of why I need either complete selfishness or selflessness for the first welfare theorem to apply?


Robert said...

Thanks for the interesting comment nik.

Technically, the reason the first welfare theorem doesn't apply without 0% of 100% selfishness is that general equilibrium models do not allow fancy contracts. Agents can only buy or sell. They can't invent a contract like the one you propose, nor can it be implemented. I mean that is part of what makes them models, that is simple.

In practice there are things along the line of the contract you propose. For example, corporations agree to match small individual donations. This is better for the recipient group than just giving money and much better for the corporation's public image because the recipient group must advertise the corporation's generosity to take advantage of it. Also sometimes corporations donate based on participation (number of donors even if some give very little).

Your proposal might or might not solve the public good problem. Given the contract you propose two outcomes are consistent with full rationality (there are two Nash equilibra). In one Nash equilibrium everyone gives so I know that if I don't the poor suffer a lot. In the other no one gives and I know that if I give then the money will come back with a delay inconveniencing me and helping no one.

Standard economic theory offers no hint as to which outcome would be more likely. Still it is worth a try.

This is a very common theoretical result when there are public goods especially if someone like you has a clever idea.