Хюльсманн против мэйнстримовой микро
Мне кажется, что поняв смысл этого рассуждения Хюльсманна, ни один честный человек не будет использовать мэйнстримовое микро для анализа чего бы то ни было:
Caplan sets out to criticize Rothbard’s rejection of the theorem that
“in equilibrium the rate of the marginal utilities of the various goods equals the
ratio of their prices” (1999, pp. 826f.). But, astonishingly, Caplan gives no counterargument whatever.
He stresses that one can try to “represent” an agent’s preferences by a utility function, and that the same preferences can also be “represented” by any other function that leaves the order of preferences unchanged. This is true. But so what?
The crucial fact is that one cannot divide preference ranks by one another and then compare the result to a ratio of prices.
It is obvious that equality between the ratio of marginal utilities (preference ranks) and the ratio of the prices could only exist under two conditions. One, if preference ranks and prices had the same dimension (that is, if they were the same
kind of thing), then their ratios could undoubtedly be equal. However, this condition is not given since preference ranks and prices are different kinds of things. Thus we are left with two, if both preference ranks and prices were by their
nature somehow extended so that their ratios would be cardinal, then these ratios could be equal, too. However, this condition is also not given because preference ranks are non-extended entities. One can therefore simply not say how high a
preference rank is. One can say that a preference rank A is higher than a preference rank B and lower than a preference rank C. That is all. The expression “preference rank A divided by preference rank B” has therefore no cardinal dimension and, as a
further consequence, one cannot even possibly say whether it equals other ratios.
This is also evident from the problems that we encounter once we try to interpret the meaning of “preference rank A divided by preference rank B.” What precisely does the expression “to divide” mean in this context? We venture to submit that nobody can say what it means. It is just as meaningless as “a rabbit divided by a piano concerto,” or “a combustion engine divided by a prayer,” etc. All we can say about the dimension of “preference rank A divided by preference rank B” is that it is “preference rank A divided by preference rank B.” But this is obviously an idiosyncratic expression, and since idiosyncratic expressions by their
nature have no common denominator there is no possibility ever to ascertain equality between them.
The same problem appears on the side of price ratios. The common view that sees no difficulty in the comparison of price ratios is unwarranted. The problem becomes obvious once we recall that prices are themselves ratios. A price is not just “3 dollars” but rather “3 dollars / 1 hamburger.” Now consider the ratios of this price with two other prices, say, “1 dollar / 1 banana” and “2 dollars
/ 1 coke.” The ratio of the hamburger and the banana prices would be “3 bananas / 1 hamburgers,” and the ratio of the hamburger and the coke prices would be “3 cokes / 2 hamburgers.”
Caplan sets out to criticize Rothbard’s rejection of the theorem that
“in equilibrium the rate of the marginal utilities of the various goods equals the
ratio of their prices” (1999, pp. 826f.). But, astonishingly, Caplan gives no counterargument whatever.
He stresses that one can try to “represent” an agent’s preferences by a utility function, and that the same preferences can also be “represented” by any other function that leaves the order of preferences unchanged. This is true. But so what?
The crucial fact is that one cannot divide preference ranks by one another and then compare the result to a ratio of prices.
It is obvious that equality between the ratio of marginal utilities (preference ranks) and the ratio of the prices could only exist under two conditions. One, if preference ranks and prices had the same dimension (that is, if they were the same
kind of thing), then their ratios could undoubtedly be equal. However, this condition is not given since preference ranks and prices are different kinds of things. Thus we are left with two, if both preference ranks and prices were by their
nature somehow extended so that their ratios would be cardinal, then these ratios could be equal, too. However, this condition is also not given because preference ranks are non-extended entities. One can therefore simply not say how high a
preference rank is. One can say that a preference rank A is higher than a preference rank B and lower than a preference rank C. That is all. The expression “preference rank A divided by preference rank B” has therefore no cardinal dimension and, as a
further consequence, one cannot even possibly say whether it equals other ratios.
This is also evident from the problems that we encounter once we try to interpret the meaning of “preference rank A divided by preference rank B.” What precisely does the expression “to divide” mean in this context? We venture to submit that nobody can say what it means. It is just as meaningless as “a rabbit divided by a piano concerto,” or “a combustion engine divided by a prayer,” etc. All we can say about the dimension of “preference rank A divided by preference rank B” is that it is “preference rank A divided by preference rank B.” But this is obviously an idiosyncratic expression, and since idiosyncratic expressions by their
nature have no common denominator there is no possibility ever to ascertain equality between them.
The same problem appears on the side of price ratios. The common view that sees no difficulty in the comparison of price ratios is unwarranted. The problem becomes obvious once we recall that prices are themselves ratios. A price is not just “3 dollars” but rather “3 dollars / 1 hamburger.” Now consider the ratios of this price with two other prices, say, “1 dollar / 1 banana” and “2 dollars
/ 1 coke.” The ratio of the hamburger and the banana prices would be “3 bananas / 1 hamburgers,” and the ratio of the hamburger and the coke prices would be “3 cokes / 2 hamburgers.”