Saturday, November 20, 2010

More on the Deflationists

Suppose there is a $15 trillion economy made up of five equally sized industries, a through e. The demand for money rises, and those choosing to hold more money reduce their expenditures on the products of industry a. The output of industry a remains unchanged, and the price of the product of industry A falls in proportion to the reduction in money expenditures. Money expenditures on the products of industries b through e are unchanged, as are their prices and output. The price level has fallen, increasing the real quantity of money. The real quantity of money rises to meet the demand to hold money. There appears to be no decrease in real output. There appears to be no disruption at all to industries b through e. Only industry a, where demand fell due to the increase in money demand, suffers a loss of money expenditures. The price of that product did need to fall enough so that the lower money expenditures will purchase the unchanged quantity of real output. Real output is maintained.

Sounds plausible enough. However, add some numbers. The quantity of money is $1.5 trillion. The demand for money rises 20 percent, or $300 billion. So, expenditures on the product of industry a fall by $300 billion, which is 10 percent decrease in expenditures. The price of the product of industry a falls 10%, leaving the real volume the output of industry a unchanged.

The price level is now 2 percent lower. (That is, a 10 percent price decrease in an industry that makes up 20 percent of the economy.) This increases real balances by slightly more than 2 percent. Since the demand for money rose by 20 percent, there remains a shortage of money. Now, those who reduced their expenditures on the product of industry a, particularly those who provide resources to industries b through e have accumulated more money. As is the usual account of monetary disequilibrium, those in industry a, who are receiving 10 percent less money expenditures reduce their purchases of the products of industries b through e. While the decrease in the demand may initially have been solely for industry a, the rot spreads.

Reduced money expenditures for the products of industries b through e, and perhaps further reductions in money expenditures on the product of industry a, result in lower prices until the price level falls the approximately 17 percent needed for real balances to rise 20 percent. If there has truly been a shift in relative demands, so that industry a shrinks and one or more of the others grow, then such a change will occur as the real capital gain generated by the increase in real balances is expended on the products of various industries.

However, it would be possible for the initial reduction in money expenditures for the product of industry a to result in a decrease in the price of the products of industry a sufficient for the price level to fall the necessary amount. Suppose the income velocity of money is 1.25, and people hold money balances equal to 80% of income. In the example above, if the quantity of money was $12 trillion, the 20 percent increase in money demand would result in a $2.4 trillion decrease in expenditures on the products of industry a. With money expenditures in that industry falling in 80 percent, a proportional decrease in the price level would be 80 precent. With industry a making up 20 percent of the economy, the price level falls 16 percent. This raises real balances approximately 2o percent.

While the scenario of a very low velocity is possible, the notion that a reasonable decrease in the prices of a few products facing lower demand because of an increase in the demand for money will avoid monetary disequilibrium is implausible. The more likely consequences is spreading disequilibrium--difficulty in making sales--solved only by a general deflation of prices.


  1. Your model is peculiar. When the demand for A products falls (balancing the new demand to accumulate money), why would the output of A in physical terms remain the same initially, only the value of the output (in money terms) falling (because of falling price)? Don't supply curves slope upward? But let's accept that oddity.

    The figure $15 trillion (for the size of the national economy) is *per annum*--a flow, not a stock. But the $1.5 figure (the money supply) is a stock, not a flow. When you say that people increase their real holdings of money 20%, you fail to specify *over what time-period*. The time-period must be *one year*, if you can use it to calculate the simultaneous decrease in their real annual expenditure on A.

    "The real quantity of money rises to meet the demand to hold money." I take it this is your "second monetary institution" from the November 14 post: Changes in the Quantity of Money and Changes in Demand, in which the nominal quantity of money remains unchanged. So $1.5 trillion nominal amount of money increases in value from $1.5 real to $1.8 trillion real. (I am measuring "real" value in terms of the numeraire at the beginning of the year.) Accordingly the price level must have declined 20% (I missed your argument that the true figure is 17%) by the end of the year. I shall assume that this decline is steady throughout the year.

    If during that year people maintain their nominal spending on B, C, D, and E (call this "Case 1"), the real value of that spending at any moment will increase--I am assuming gradually, steadily; on the last day of the year it will be 20% higher than on the first day. For the year as a whole it will be 10% greater than it was the year before. But perhaps you meant that *real* spending on B-E remains constant at the old level (call this "Case 2"), in which case nominal spending will be 20% lower right at the end of the year, and 10% lower for the year as a whole.

    Over the year in question, people spend 2% less in real terms on the products of A-E, while the real value of their money holdings rises 20%. They spend (Case 1) 10% more in real terms on B-E; therefore they spend 50% less in real terms on A. Or they spend (Case 2) the same amount as before in real terms on B-E; therefore they spend 10% less in real terms on A. Since they buy the same physical quantity of A, its average price in real terms must be half (Case 1) or 90% (Case 2) of what it had been in prior years and at the start of the year in question. (Two cases is one too many to handle; henceforth I'll just go with Case 2.)

    Suppose As had been selling for $100 each. When the sudden enthusiasm for holding money appears, at the beginning of the year, the price will immediately fall to $90 each. From this point the overall price level will decline 20% (17%?) in nominal terms; at the end of the year As will be selling for $72 apiece (and B-Es will fall from $100 to $80 apiece).

    Then, at the end of the year, people suddenly become sated with money; they engage in no further accumulation. The real demand for As returns to what it had been historically, and, under your strange assumptions, the price of As will come back to equality with prices of B-Es: it will suddenly jump to $80. Our $15 trillion-dollar economy (nominal and real) with $1.5 trillion dollars of money (nominal and real) will have become a $12 trillion-dollar economy (nominal = $15 trillion real) with a $1.5 trillion-dollar money supply (nominal = $1.8 trillion real).

    You conclude that an increase in the demand for money will cause a general fall in the price level, not one affecting just "a few products facing lower demand because of an increase in the demand for money." You label this "monetary disequilibrium," and your tone suggests that it is bad. This is a very plausible suggestion, but exactly why it is bad has not been articulated.

  2. This comment has been removed by the author.

  3. While I realize there is a difference between flows and stocks, I don't think the change in the demand for money necessarily must be continuous. Perhaps it all occurs in one month. The reduction over the year would be the same as in the continuous case. However, this point does show that the example, and in particular, income velocity, depends on the choice of period. The demand for money might be very large relative to daily income.

  4. The 17 percent figure is rounded. Suppose the price level is 100 and drops by 20 percent to 80. If the quantity of money was $1000, then its real value is now $1000/.8 or $1250 (with the first year being the base year.) But the real demand for money increased 20 percent, so it should be $1200. The price level that results in a 20% increase in real balances is 1/1.2 or 83.33 (repeating.) To go from a price level of 100 to 83.33 is a 16.66 (repeating) decrease. That rounds to 17 percent. If you use small numbers, (like derivatives) the differences in base don't matter.

  5. My post is in response to some arguments by what I think is an amateur Austrian. It was from a comment thread at The Coordination problem.

    I think the pattern of demand with the extraordinary decrease in the relative demand for good a is taken to be permanent. That there is no further increase in demand for money simply means that the demand for a, and so the price of a, doesn't have to decrease any more. In the next period, there is no recovery in the real demand for a. It think it is possible, and implicit in the scenario. that those producing b-e spend less on product a and more on b-e. Those producing a are much poorer and spend less on a-e. The net effect is no change in real or nominal spending on b-e and a permanent decrease in spending on a. The purchasing power of money has risen enough to meet the demand to hold money. Equilibrium though price changes only.

    As for the supply curves have positive slopes, that seems likely to me as well. Those earning lower incomes in industry a will shift to the production of the products of industry b-e, and this will result in reduced production of a and increased supplies and lower prices of b-e. Through this process, the result should be similar to the scenarios described my previous posts. Though it is not obvious that the real capital gain exists with the real balance effect and that it could be spent in a way different than the usual flow of income.