[QUOTE="airshocker"]
[QUOTE="chessmaster1989"]
If he benefitted more from donating the money than he did from keeping it, he would already have donated it. Therefore, under the law, he will donate (including taxes) at least as much as he did before the law was passed, while his utility gain will be non-positive.
chessmaster1989
I don't see where utility comes into play in this instance. This has to do more with philosophy than microeconomics, I think.
But I'll bite regardless, even though you'll destroy me: We would first have to determine what his total utility gain would be corresponding with the amount of money he gives.
Utility comes into play as the idea of measuring an individual's 'happiness' or well-being. A selfish action, in terms of utility, would necessarily increase one's utility. Therefore, if an action does not increase one's utility, it cannot be selfish. I'm not entirely certain what you mean when you say this has more to do with philosophy than microeconomics, could you elaborate?
You don't have to determine anything about total utility gain. Let's assume that u(G) is a certain individual's utility function, dependent on both how much money he keeps (M) and how much money he gives (G). Assuming total income is fixed (to I), M+G=I, so utility can be expressed as a function of how much money he gives.
Now, without the law, he maximizes u(G), choosing the optimal quantity G* (for the sake of argument, assume that such a maximum exists (although it is not necessary to assume it is unique) - if the maximum does not exist, this optimization will not necessarily be well-defined anyway). He then contributes G*.
Now, with the law, he pays an amount G** in taxes, and then reoptimizes. For the sake of simplicity, let's that G* is the only local maximum (this condition is not necessary in terms of measuring the impact on his utility, but is convenient). Then, he either contributes exactly G** (if G** is greater than G*) or contributes exactly G* (if G** is less than or equal to G*), due to the same optimization as above. As G* is the unique local maximum, and is also the absolute maximum, u(G**) is less than or equal to u(G*). Thus, he has a non-positive gain in utility.
I think math/econ would be a fun duo.
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