Thursday, October 06, 2005

Keynes, The Monetary Tract, and The Inflation Tax

Long before the General Theory was formulated, Keynes wrote a short book called "A Tract on Monetary Reform". The book was published in 1923 and was devoted to discussing the issues surrounding inflation, which at that time had engulfed Germany and Russia. The book shows the remarkable knack Keynes had for illustrating complicated problems with simple examples. The examples he chose were always highly germaine to the problem he was discussing and were not constructed merely to show his intellectual prowess. There is no better example of this than his discussion of the inflation tax.

To begin with, Keynes was interested in showing that while it is true that inflation is a tax on an individual's real balances, one could show that this is equivalent to a tax on transactions or a "turnover tax". Modern authors of monetary theory seldom if ever show this equivalence, despite the fact that it is highly illuminating. Let's take Keynes own words now on the subject and see what they mean.

" Suppose that the rate of inflation is such that the value of the money falls by half each year, and suppose that the cash used by the public for retail purchases in shops is turned over 100 times a year (i.e. stays in one's pocket for half a week on the average); then this is only equivalent to a turnover tax of 1/2 per cent on each transaction. The public will gladly pay such a tax rather than suffer the trouble and inconvenience of barter with trams and tradesmen." (from Chapter 2 of the Monetary Tract).

As was stated above, few authors of works on monetary theory use this device to discuss the burden of the inflation tax. Indeed, the inflation tax is often simply written as equal to the product (the rate of inflation)(real money stock), with the inflation rate being taken as the tax rate on real balances and the incidence being dealt with via consumer surplus and the demand for real balances.

Keynes goes on,

" Even if the value of money falls by half every month, the public, by keeping their pocket-money so low that they turn it over once a day on the average, can still keep the tax down to the equivalent of less than 2 per cent on each transaction, or more precisely 4d. in the pound. Even such a terrific rate of depreciation as this is not sufficient, therefore, to counterbalance the advantages of using money rather than barter in the trifling business of daily life. This is the explanation why, even in Germany and in Russia, the Government's notes remained in current for many retail transactions. "

What remarkable insight, but we have come to expect this of Keynes.

The two quotes above seem to indicate that Keynes was using a formula to compute the inflation tax as a "turnover tax". But what formula is being used? Also, he uses a now anachronistic term for English pence and this becomes a stumbling block for some students of the text.

The second of these is easier to deal with. Keynes says in the second quote that the turnover tax rate had become less than 2% per transaction. He then makes this exact by saying 4d. in an English pound sterling. Now, at the time he was writing this there were 240 pennies (or pence) in a pound. That is not true nowadays. There are 100 pence in a pound now. But, at that time 240d. = 1 pound sterling. It follows that 4d./240d. is 1/60, which is less than 0.02. This is why he says that the tax rate is less than 2%. He means it is exactly equal to 5/3% or roughly 1.67%.

Now, how does he come by these numbers in the above two quotes? What is the formula he is using to compute these things?

The formula he is using can be written as:

(Turnover Tax Rate)(Number of Transactions) = (Rate of Depreciation of Money)

For example, in the first quote, we have the Rate of Depreciation of Money is 50% which is equivalent to a doubling of the price level with a stable stock of nominal balances. The number of transactions is assumed to be equal to 100. This implies that the turnover tax rate is equal to 1/2% and this is what Keynes gets himself.

In the second quote, we need to think carefully. Keynes assumes that the Rate of Depreciation per month is 50%. He then assumes that each dollar is held on average one day only, which means that the number of transactions per month is equal to 30. Hence, the turnover tax rate is 50/30% which is what we got before.


At Friday, January 27, 2006 2:19:00 AM, Anonymous Anonymous said...

I agree completely.Notice,however,that Keynes essentially leaves it up to the reader to figure out the formulas.Keynes gives the reader all he needs in the examples.However,Keynes never ever would present all of his steps.He gives the reader what is necessary to figure it out on his own.


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