Rothbard labor exchange demand for money

Carlos posted on Tue, Aug 7 2012 11:49 AM

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Hi, I'm trying to make sense of section 11.2 of "Man, Economy and State" but yet to no avail. What I find controversial are a couple of related propositions:

(a) man (labor factor) earns more money at the higher wage rate (this assertion is based on a reasoning concerning real wage rates and substitution and income effects, not an obvious nominal implication W'>W => W'xL>WxL -with W nominal wage and L hours laboured-).

(b) In the labor market, a higher exchange-value of money is translated into lower wage rates and a lower exchange-value of money into higher wage rates.

From (a) and (b) Rothbard logically concludes that:

"on the labor market [...]  The higher the exchange-value of money, the lower the quantity of money demanded; the lower the exchange-value of money, the higher the quantity of money demanded."

Although I don't think (a) can be deduced a priori I find it plausible enough (this point was already discussed in http://direct.images.mises.org/Community/forums/p/8153/161190.aspx).

But why (b)? First of all the idea of "a higher exchange-value of money" implies comparing different exchange-value of money and Rothbard was very explicit about that "there is no single price level or measurable unit by which the value-array of money can be expressed". But suppose, for the sake of the argument, that this value-array is greater or equal for every good and strictly greater for at least one good. And, to keep it simple, suppose there are only two goods in the economy (besides money): labor and -say- apples. The "price" of money is then a vector <#labor hours,#apples>=<L,A>.  Finally, suppose that this PPM changes to <L',A'> and that L'>=L and A'>=A and at least L'>L or A'>A, as stated before. Then we have 2 cases:

(1) Proportional increase of L and A to (1+c)xL and (1+c)xA. The wage in terms of apples is the same. If we abstract from non-monetary uses of the money commodity (which Rothbard seems to be doing at this point of the argument) the labor factor is not better or worse than before (she just uses money to buy apples and to increase her real balances in order to buy apples later) and I can't see any reason why she will be willing to provide more or less working hours. Obviously, in nominal terms she will need a lower wage to buy the same quantity of apples but there is no need of (a) or (b) to conclude that.

(2) Non proportional increase of L and A: then real wage can be lower or higher depending on the relation of L and A to L' and A'. So a higher exchange-value of money was not necessarily translated into lower (real) wage rates as stated in (b). Also, notice that this is not an equilibrium point if we believe that money is neutral in the long run or in the ERE (real wage can't be affected by PPM).

Briefly, if Rothbard is talking about real wages I don't see why (b) is necessarily true, and if he's talking about nominal wages something in the line "with constant real wage and constant hours of labor supplied, an increase in the PPM implies a decrease in nominal wage and so in total money bought by labor" would have been enough.

So what do you think?

Regards