Truck and Barter

Sorry I'm converting this into a second post Kevin... I ended up typing fifty times more than I had intended to in my comment reply :-)

Kevin made a comment in my previous post that got me thinking:

"Isn't that a classic question economists have of charity? If you give, is it for your utility directly, or for the recipient's?
If for yourself, you might donate the whole amount even with doubling, because you just care to give.
But if you care for solely for the recipient's welfare, you'll give half with doubling, so the recipient winds up exactly where you wanted him....
This is poor economic analysis... and I doubt many people cut donations because of explicit matching contributions... but I'm just trying to get the general flavor of the argument..."

That definitely is the reasoning that needs analysis - and my take is it ends up being a very interesting game.

Assuming that you are a social 'charity' planner that wants to ultimately maximise the recipient's welfare... the only way that the recipient's welfare is maximised is by maximising the utility of the donor. (I assume that this would be a crude Nash equilibrium.)

The problem is compounded from the donor's side in one important way - the heterogeneity of the donor group. Utility for people in the 'passenger class' may be unconstrained at heart - but ends up being restricted by our budgets - i.e. our ability to give (poor students and their wallets... sigh). However, lets make an (unfair) assumption that this group has one additional characteristic - the budget constraint motivates them to derive maximum utility from the end value contributed - leading us to assume that if a matching fund exists, they may (inequality) be prompted to give less than what they intended to.

Assume that the 'upper class' donor's budget constraint isn't binding. Lets make another (unfair) assumption that the 'upper class' wants a more 'premium' way to donate -i.e. by being part of an endowment fund or to have their names lined up in a plaque. Now if they find that their status isn't upto the mark - then this psychological constraint may kick in and they may not give as much as they would have.

For purposes of simplicity (though this is probably a stupid assumption to make), lets say that the inefficiencies created by the two assumptions we have made for each class of people is unidentifiable. It could be one of four situations - a) matching fund causes more passengers to give less - b) absence of matching funds causes the elite to give less - c) there is an equal loss between the two - d) there is no loss. This then leads to a problem of how to design an optimal contract.

Kevin's point, that people wouldn't cut their giving because of the existence of a matching fund, is subject to doubt. A possible (and important) consideration is cultural differences. Many communities (many many Indian communities) are extremely frugal by nature. It is not to say that they have a bad heart - it is only to say that they seek to reach the original maximum utility they sought to derive and not be attracted to the lucre of a better maximum and the impact it will have on their wallet. This also applies to people who have a lot less to give. Many may have scraped through all kinds of cookie jars to come up with whatever they could, and this could imply that they have a few bowls of soup less over the weeks to come so that others may share the forgone bowls of soup. With the matching fund - they may give less. I was at the Albany temple when they made the announcement and I overheard atleast a handful of people arguing the matching fund when asked to improve on the value of their check.

So thats my take on things - I know there are many many many loopholes in this argument's design, but it's an attempt. :-)

More thoughts?