marginal utility : price = constant??

Economics Economics Questions
1

I was reading “Why I am not an Austrian Economist” (http://economics.gmu.edu/bcaplan/whyaust.htm) which says:

“Rothbard goes on to dismiss the standard intermediate micro theorem “that in equilibrium the ratio of the marginal utilities of the various goods equals the ratio of their prices. Without entering in detail into the manner by which these writers arrive at this conclusion, we can see its absurdity clearly, since utilities are not quantities and therefore cannot be divided.” What initially appeared to be a slight difference in nomenclature yields serious disagreement about some fairly basic issues. As plausible as Rothbard sounds on this issue, he simply does not understand the position he is attacking. The utility function approach is based as squarely on ordinal utility as Rothbard’s is.”

The author doesn’t make any sense. Either utility values are cardinal quantities that one can divide by, or they are ordinal rankings (subject to arbitrary monotonic transformations) that one cannot divide by.

Anyway, the theory he mentioned - “the ratio of the marginal utilities of the various goods equals the ratio of their prices” - must be incorrect. Entertain cardinal utilities for a moment. Suppose having an extra orange would give me twice as much pleasure as having an extra apple. I would pay 100 pennies for an apple. But I would not pay 200 pennies for an orange, because the marginal utility of the last penny is too great. I have a certain amount of money in my pocket and consider 200 pennies too wasteful. Doesn’t the quoted theory break down here? The problem is that it elevates money to a special status compared to the other goods and doesn’t take into account the fact that units of money have marginal utilities too.

All one could say is that the marginal utilities of different things (apples, pennies, etc.) are in various ratios. But essentially nothing can be said about ratios involving an integral of my utility function over some number of pennies. It is not a constant function.

Any other opinions on this “marginal utility/price ratio” theory?

2

Thanks for coming up with an interesting topic.

Your approach is obviously right. You can also look at this issue from another angle.

Lets take the same example you’ve given, where you pay 100 pennies for an apple and 200 pennies for an orange. Apart from the fact that, as you’ve already mentioned, this doesn’t mean you can say the orange is valued twice as much as an apple in marginal utility terms; you can also see that you exchange 100 pennies for an apple because you value an apple more than 100 pennies. Similarly, you value an orange more than 200 pennies.

So you actually can’t match the utilities of apples and oranges on the one hand; and 100 pennies and 200 pennies on the other hand to say that equality of marginal utility values can be derived from the equality of prices; and that’s simply because in terms of marginal utility, 100 pennies is not equal to an apple nor is an orange equal to 200 pennies.

3

You also can’t match utilities between different amounts of the same good. People get discount rates for buying in bulk. It also doesn’t even work for the same amount of the same good. people are less price sensitive the higher the amount of money people pay for goods. Ask people if they would travel 20 miles extra to get $50 off of a $200 ipod, and many say they would. Ask the same thing about getting $50 off of a $1000 Television, those same people would not. Why not? It’s the same $50, it’s the same distance. The cardinal utilities don’t even match up there.