The Optimal Quantity of Money
The trick to getting an optimal outcome from a decentralized system to have things arranged such that each actor receives the net benefit, positive or negative, of his actions, the benefit summed over everyone affected.1 A competitive market system does this, although not perfectly. You pay the cost of your inputs, either the cost of making them or their value to someone you bid them away from, when you buy them in a voluntary transaction. You get the value of what you produce when you sell it to the person who consumes it. The costs and benefits to other people of your actions are transmitted back to you by the price system, so it is in your interest to take an action only if its net effect is positive. A full explanation, including the imperfections, requires a semester or two of price theory or my Hidden Order, a substitute I wrote for people who prefer a book to a class.
To see how that approach can be applied to a monetary system, consider the decision of how much of your wealth to hold as cash. The cost to you is the interest you could collect if you instead held that wealth as an interest-bearing asset. The benefit to you is that the more cash you have, the less precisely you have to match income and expenditure. Your cash balance is, in effect, a shock absorber, letting you buy something today when it is available or when you want to use it without having to sell something today to pay for it.
What is the social cost of your cash balance, the cost summed over everyone in the society? The answer is roughly zero. Due to the Law of Large Numbers, on average total consumption and production are almost always equal, the individual differences averaged out. The society as a whole does not need a shock absorber.
It follows that individuals will hold the optimal stock of money, the stock that maximizes economic efficiency, only if the nominal interest rate is close to zero.
It is possible that a few of my readers, not being economists, are not familiar with the distinction I am making between real and nominal, hence a brief digression.
Real and Nominal
The problem with measuring changes over time in money prices is that the value of the money you use to measure them may change — you are using a rubber ruler. Lending someone a thousand dollars today and getting back two thousand next year sounds like a great deal, but not if the two thousand next year buys less than the thousand this year. A job where your income goes up by ten percent a year sounds pretty good, but not if the annual inflation rate is twenty percent.
In dealing with those issues it is useful to distinguish between nominal and real, where nominal values, such as the nominal interest rate, are based on money prices, real values on purchasing power.2
If banks pay an interest rate of ten percent that is a nominal interest rate — give them ten dollars and in a year you get back eleven. If prices are rising at ten percent a year the real interest rate is zero, since eleven dollars next year is the same value, will buy the same goods, as ten dollars this hear.
On our world inflation is almost always positive so the real interest rate is almost always lower than the nominal, but it does not have to be.
Ways of Producing the Optimal Incentive
The obvious way to get a zero nominal interest rate is deflation, a money whose value is growing at the real interest rate. Seen in real terms, both cash and other investments bear interest; holding either results in increasing value over time. Seen in nominal terms, neither bears interest.
Either inflation or deflation makes it harder to keep track of prices. From that standpoint, the ideal money keeps a constant value. There is, however, a simple way of getting both the optimal incentive and stable prices — interest bearing money. If your money is not currency, bank notes, but a deposit in a checking account, the bank can pay you interest on it. If it pays the same interest that other investments pay we are back with the optimal incentive to hold money.
If a bank pays interest on checking accounts it can no longer fund its operations with the interest it collects on the interest bearing assets it bought with your deposits, but that need not be a problem. The cost of your account to the bank depends not on how large it is but on how many transactions you make, how many checks it has to clear. Following the approach to optimizing a decentralized system that started this essay, the bank supports itself by charging per transaction instead of by the difference between the interest it collects and the interest it pays.
My Addition
The analysis of the optimal quantity of money from the standpoint of the incentive to hold wealth as money is not original with me; I lifted it, and the title of this post, from an essay and book of my father’s. I have, however, an addition to the analysis which links it to the two previous posts.
Suppose money is provided by competing private issuers. Further suppose a fractional reserve system with a reserve ratio near zero, as in the commodity bundle system I sketched. If the bank issues a million Friedman dollars it can use them to buy a million F-dollars worth of interest bearing assets, producing an income of a million F-dollars times the interest rate.
That sounds like a great deal for my bank but this is a system of competing private issuers; there are other banks. They too would like the business of my customers. To get it they offer my customers a better deal — interest. If the money consists of bank notes that means that the bundle it is redeemed in, and so the value of their notes, increases year by year. If the money consists of bank deposits, they keep the value of the money, the definition of the bundle, constant and simply pay interest on deposits.
In a perfectly competitive market, economic profit is competed away. In this market, that means that all the banks end up paying interest on their money. If they have no costs, the market for money produces precisely my father’s optimal incentive for cash balances.
What if they have costs? What if, for example, the reserve ratio, now in silver instead of commodity bundles, is 25%? Their return from issuing a note is only 75% of the market interest rate since a quarter of their money has to be used to buy silver. That, assuming no other costs, is what they end up paying their note holders once their profit on note issue has been competed away.
My father’s analysis assumed a fiat money, which costs nothing to produce. With a fractional reserve system that is no longer the case. With the numbers I assumed, maintaining a cash balance, summed over the entire population, of a million ounces, requires someone to mine a quarter million ounces for bank reserves. The resources that mined that silver could have been used to produce something else, an interest bearing investment, so the annual cost of having a million ounces of money is a quarter of the interest on a million ounces.
The individual cost of holding wealth as money is again equal to the social cost. The market yields the efficient outcome.
My web page, with the full text of multiple books and articles and much else
Past posts, sorted by topic
A search bar for past posts and much of my other writing
How to add people up is not obvious. The concept I am using is economic efficiency, explained in a previous post.
The definition of purchasing power is a little fuzzy, since prices change differently for different goods. It is usually based on the price of an imaginary market basket of good and services representing roughly what the average individual consumes.
This is off-topic, but I see that Vietnam has offered zero tariffs on U.S. goods if the Trump Administration will hold off on the new tariffs on Vietnam. It won't be sufficient for the Trump people, because they want an equal balance of trade in goods. But couldn't Vietnam simply use the cash from its sales to the U.S. to buy, say, platinum from U.S. producers and then use the platinum to buy the autos it really wants from China, thereby achieving the balance?
1) All your analysis shows is that the optimal nominal interest rate is zero in the same sense that the optimal sales tax on coffee is zero --- you are minimizing deadweight loss in the money market (or the coffee market).
2) But in a system where the government must raise some amount of tax revenue, the optimal sales tax on coffee is probably not zero, because any reduction in the coffee tax requires an increase in some other tax. So in that sense you have not proved that the optimal nominal interest rate is zero. We might want the government earning more revenue through inflation so that it can lower taxes on other things.
3) There is, however, this: Even if we take it as given that the government needs to raise some revenue through taxes, and therefore the optimal sales tax on coffee is non-zero, it remains the case that the optimal tax on capital income is zero (for Chamley/Judd reasons). [Note: We know from the work of Werning and others that there are important mathematical gaps in the Chamley/Judd analysis. It seems to me that these gaps are unimportant in the sense that the fundamental intuition underlying the Chamley/Judd papers remains clear.] So at least *some* taxes should be zero, and perhaps the implicit tax on holding money is one of these taxes. That, however, remains to be argued.
4) So the question now is: Is money more like coffee or more like capital income from the point of view of optimal taxation analysis? I'd very much like to see a clear answer to this.