With regard to folk songs, you're making it too complicated. Money is not poetic; beauty is. A song about someone who chose a wife based on her dowry would be dull and dry, even if it went on to point out how much better off the children would be because of the man's choice. Choosing a woman because of her virtue would be more poetic, but not as much so as beauty; you can write verses about long golden hair and unblemished skin, but writing about moral qualities in a few lines is harder.
There's a difference in emphasis between songs and folk tales. The latter often focus on qualities of character, especially hard work. Think of "Frau Holle" and "Cinderella." The poetic imagery is less of a factor in stories, so while beauty is still important, being a good person (as it was understood at the time) carries more emphasis. Choosing for wealth occurs in stories; it's generally paired with noble status. Marrying a prince is a good thing in a story; marrying a rich merchant's heir not so much so. It's probably because people distrusted merchants but were taught to respect royalty.
The sum of the marginal utilities of 1000 poor people who receive $1 is greater than the marginal utility of a single poor person who receives $1000. Therefore, according to Becker, the usefulness of the donor is greater to give them to a charity than to a single poor person. Margolis' critical argument could be made by the following experiment. If someone is asked: would you rather give $1 to 1000 poor people or $1000 to one poor person, they will answer (I think) that they prefer to give $1000 to one poor person. This contradicts Becker's prediction. The reason for this is perhaps the reward for the social prestige derived from this solution. Becker does not consider this prestige.
Becker's model doesn't assume that the altruism is towards random people but to a specific person or persons. It could be to a thousand people doesn't have to be.
>It is clear in such songs that marrying a woman for her money is bad but marrying her for her beauty is fine. It is less clear why.
Perhaps the idea is that, when you marry someone, you should marry them /for themselves/. A woman is not identical to her money or her beauty, but she is more identical to her beauty than to her money, and, arguably, she is not identical at all to her money (losing her beauty changes her, losing her money less so, if at all). So it is better to marry a woman for her beauty than her money, and, arguably, it is actually wrong to do so for her money.
>A more serious objection is that it is not clear how close the relationship is between "being in love" and altruism
We can take the above one step further. For a woman is more identical still to her /character/ than to her beauty (which is only "sink deep"), and so even better to marry a woman for her character than for her beauty. Best to marry a kind (aka "altruistic") woman. Best morally, if you wish, but more importantly best for you. But why should she marry you, if you are not yourself altruistic? (And she /will/ find out, if you live together.) So best yourself to be an altruistic person, if the other would be altruistic.
And this not just fine calculation—people fall in love with kind people just as much as they do with (objectively) beautiful people, with the added benefit that kindness is probably more stable than beauty, and certainly more than "being in love".
It appears Mr. Margolis is rounding 10 cents down to zero, and in doing so is ignoring the non-zero effect 10 cents can have when summed many times over.
I should like to extend his argument: "You currently have an income of a hundred thousand dollars of which you donate [zero] to the Red Cross. You are a Becker altruist...The Red Cross has, we may assume, ten thousand people it serves...[One dollar] is a very small part of their income...It follows that ten thousand donated, divided among ten thousand people, will have almost no effect on the (marginal) utility you get...It follows your [entire] income will go almost entirely to the Red Cross."
The preferences that led me to donating a tenth of my income to ten thousand people are likely to lead to me donating a tenth of my raise to them. If I have CES utility, given utility-weight parameters such that I donated a tenth of my income, the same parameters entail that I donate exactly a tenth of my raise.
The altruist equalizes his marginal utility for consumption to his marginal utility from the increase in beneficiary's utility from the donated money. That doesn't produce the behavior you describe.
In my attempt to show why you're wrong, I've illustrated of why I'm wrong.
Let the altruist have utility U[c,v_1(b_1),...,v_n(b_n)] across his consumption c and the utility of his n beneficiaries v_i(b_i) given by Cobb-Douglas: U = c^alpha * Π_i b_i^beta_i. For simplicitly, assume each beneficiary i is the same, such that: U = c^alpha * b^(n*beta). Normalize alpha and beta such that alpha + n * beta = 1.
Let the beneficiary consume b = d + K, where d is the donation he receives and K is his outside income. The altruist budget constraint is therefore: M = c + n*d --> M + n*K = c + n*b; note that the price of consumption is implicitly one.
IF K = 0, then we would obtain c = alpha * M and total donation D = Σd = Σb = n * beta * M, and I would be right -> consumption and donations scale linearly in altruist income M.
However, for K > 0, we obtain: c = alpha * (M + nK) and total donation D = n * b - n * K = n * beta * (M + nK) - n * K. If we plug in the initial conditions [c = 90,000; D = 10,000; n = 10,000], we obtain the income scaling factor alpha = 9 / (K + 10), which falls to zero as non-donation beneficiary income K gets large.
Since others' utility is not observable directly, one must use a proxy. But that makes the objection stronger, perhaps, as the proxy mostly will not respond to the actions of the altruist in the case of large charities like the Red Cross.
Is Becker incompatible with a signaling model? Maybe we could glue them together, with Becker providing the mechanism that determines which sorts of signals are considered valuable.
With regard to folk songs, you're making it too complicated. Money is not poetic; beauty is. A song about someone who chose a wife based on her dowry would be dull and dry, even if it went on to point out how much better off the children would be because of the man's choice. Choosing a woman because of her virtue would be more poetic, but not as much so as beauty; you can write verses about long golden hair and unblemished skin, but writing about moral qualities in a few lines is harder.
There's a difference in emphasis between songs and folk tales. The latter often focus on qualities of character, especially hard work. Think of "Frau Holle" and "Cinderella." The poetic imagery is less of a factor in stories, so while beauty is still important, being a good person (as it was understood at the time) carries more emphasis. Choosing for wealth occurs in stories; it's generally paired with noble status. Marrying a prince is a good thing in a story; marrying a rich merchant's heir not so much so. It's probably because people distrusted merchants but were taught to respect royalty.
The sum of the marginal utilities of 1000 poor people who receive $1 is greater than the marginal utility of a single poor person who receives $1000. Therefore, according to Becker, the usefulness of the donor is greater to give them to a charity than to a single poor person. Margolis' critical argument could be made by the following experiment. If someone is asked: would you rather give $1 to 1000 poor people or $1000 to one poor person, they will answer (I think) that they prefer to give $1000 to one poor person. This contradicts Becker's prediction. The reason for this is perhaps the reward for the social prestige derived from this solution. Becker does not consider this prestige.
Becker's model doesn't assume that the altruism is towards random people but to a specific person or persons. It could be to a thousand people doesn't have to be.
But it's better to trust what people do than what they say. Your test is better.
>It is clear in such songs that marrying a woman for her money is bad but marrying her for her beauty is fine. It is less clear why.
Perhaps the idea is that, when you marry someone, you should marry them /for themselves/. A woman is not identical to her money or her beauty, but she is more identical to her beauty than to her money, and, arguably, she is not identical at all to her money (losing her beauty changes her, losing her money less so, if at all). So it is better to marry a woman for her beauty than her money, and, arguably, it is actually wrong to do so for her money.
>A more serious objection is that it is not clear how close the relationship is between "being in love" and altruism
We can take the above one step further. For a woman is more identical still to her /character/ than to her beauty (which is only "sink deep"), and so even better to marry a woman for her character than for her beauty. Best to marry a kind (aka "altruistic") woman. Best morally, if you wish, but more importantly best for you. But why should she marry you, if you are not yourself altruistic? (And she /will/ find out, if you live together.) So best yourself to be an altruistic person, if the other would be altruistic.
And this not just fine calculation—people fall in love with kind people just as much as they do with (objectively) beautiful people, with the added benefit that kindness is probably more stable than beauty, and certainly more than "being in love".
It appears Mr. Margolis is rounding 10 cents down to zero, and in doing so is ignoring the non-zero effect 10 cents can have when summed many times over.
I should like to extend his argument: "You currently have an income of a hundred thousand dollars of which you donate [zero] to the Red Cross. You are a Becker altruist...The Red Cross has, we may assume, ten thousand people it serves...[One dollar] is a very small part of their income...It follows that ten thousand donated, divided among ten thousand people, will have almost no effect on the (marginal) utility you get...It follows your [entire] income will go almost entirely to the Red Cross."
The preferences that led me to donating a tenth of my income to ten thousand people are likely to lead to me donating a tenth of my raise to them. If I have CES utility, given utility-weight parameters such that I donated a tenth of my income, the same parameters entail that I donate exactly a tenth of my raise.
The altruist equalizes his marginal utility for consumption to his marginal utility from the increase in beneficiary's utility from the donated money. That doesn't produce the behavior you describe.
In my attempt to show why you're wrong, I've illustrated of why I'm wrong.
Let the altruist have utility U[c,v_1(b_1),...,v_n(b_n)] across his consumption c and the utility of his n beneficiaries v_i(b_i) given by Cobb-Douglas: U = c^alpha * Π_i b_i^beta_i. For simplicitly, assume each beneficiary i is the same, such that: U = c^alpha * b^(n*beta). Normalize alpha and beta such that alpha + n * beta = 1.
Let the beneficiary consume b = d + K, where d is the donation he receives and K is his outside income. The altruist budget constraint is therefore: M = c + n*d --> M + n*K = c + n*b; note that the price of consumption is implicitly one.
IF K = 0, then we would obtain c = alpha * M and total donation D = Σd = Σb = n * beta * M, and I would be right -> consumption and donations scale linearly in altruist income M.
However, for K > 0, we obtain: c = alpha * (M + nK) and total donation D = n * b - n * K = n * beta * (M + nK) - n * K. If we plug in the initial conditions [c = 90,000; D = 10,000; n = 10,000], we obtain the income scaling factor alpha = 9 / (K + 10), which falls to zero as non-donation beneficiary income K gets large.
Since others' utility is not observable directly, one must use a proxy. But that makes the objection stronger, perhaps, as the proxy mostly will not respond to the actions of the altruist in the case of large charities like the Red Cross.
Is Becker incompatible with a signaling model? Maybe we could glue them together, with Becker providing the mechanism that determines which sorts of signals are considered valuable.
There are lots of possible explanations of human behavior. Becker is offering one.