## Bidding War: The Quantity Theory of Money and the Price Level

I was going to run a blog on Hans Albert’s critique of the quantity theory of money but it appears that Lord Keynes has gotten there ahead of me. I just wanted to pull out one point that he raised as it proved to be one of the most difficult I encountered when trying to formulate a general theory of pricing.

Lord Keynes notes that some versions of quantity theory assume a linear, self-same relation between the increase in the quantity of money and the price level. So, if the quantity of money increases by, say, \$1,000 then the price level must increase by the same. The assumption here appears to be twofold. Firstly, that all the money is spent. And second, that prices are bid up by the same amount as the money spent.

I have outlined how such a bidding process occurs in algebraic form in the following post. In order to understand it we must imagine a market as an auction with a fixed supply of goods. Each buyer must bid up the goods using the cash reserves they have. The problems with the assumption that the price level rises in lockstep with the money supply increase becomes problematic straight away.

Imagine an auction with three buyers and one item. Each buyer is willing to spend all their money on the item, but they also want to get it for the minimum amount they can — a marginalist might place some utility maximising assumption here where money and the good both yield utility. Now, in equilibrium each buyer has \$1,000 of cash reserves. In such a situation only two things can happen: (a) the good sells for \$1,000 to the buyer who bids first or (b) two or more of the buyers engage in some sort of lending agreement with one another. Let’s pretend that (b) cannot happen because everyone is completely focused on getting the good.

Now, assume that a central banker walks into the auction with newly printed money. He gives and extra \$1,000 to the first bidder — call him Buyer A. Buyer A now have \$2,000 while the other buyers only have \$1,000. So, what does he do? Well, assuming that he has perfect information about the other buyers he would simply bid up the item by the smallest possible increment — say, he would make a bid of \$1,000.01.

In Keynesian economics the multiplier relieves us of this problem. In the above problem we would simply posit a marginal propensity to consume out of income. In the case above it would be 0.00001. The rest of the newly acquired money would be conceived of as savings — with the marginal propensity to save being the inverse of the marginal propensity to consume; i.e. 0.99999.

A modified version of the quantity theory could posit a fall in the velocity of circulation. This would especially fit in with the Cambridge cash balances version of the theory– from which, I think, Richard Kahn got the inspiration for the multiplier. But since many variants of the quantity theory — like monetarism in particular — assume a constant velocity they have very little to say about the above mentioned dynamics.