By Dan Kervick
Scott Sumner attempts to explain the so-called “hot potato effect” which has played such an important role in the theories and policy recommendations of the Market Monetarists. But the explanation contains two weaknesses. The first weakness is a muddle of inapt metaphors which seem to run together the concepts of diminishing marginal value and negative marginal value. The second weakness is more serious: Sumner and company refuse to take cognizance of the important institutional differences between the banking sector – an unusual and limited sector of the economy where only money and money-denominated financial assets are traded – and all of the other sectors of the economy where money is exchanged for everything else that can be bought and sold. As a result they seem to be incapable of distinguishing between realistic changes in the central bank’s patterns of doing business with the financial sector and imaginary changes in the central bank’s pattern of doing business with the rest of the world. And they mistakenly conclude that central bank statements about the former should have a major impact on beliefs about the latter.
1. The Hot Potato Metaphor
Sumner begins his discussion this way:
Many people continue having trouble with the “hot potato effect,” which to me is the sine qua non of monetary economics. You either understand it, or you understand NOTHING. They want explanations they can understand at the individual behavior level. But that just won’t work in this case.
Fair enough; he wants us to distinguish between the behavior of individuals and the behavior of the economy as a whole. He then goes to explain the hot potato effect:
Assume gold sells for $1200. Interest rates are low, so the expected future price is roughly the same, maybe a bit higher. Now assume a company discovers a gold hoard so vast that world output soars. Over a period of years the extra output causes gold prices to fall in half. But why? Because before the discovery people were already in equilibrium, they held as much gold as they wanted to hold at existing prices. The extra gold is a sort of “hot potato” that people try to get rid of. But obviously not by throwing it away! They get rid of it by selling it.
Let’s start with what I described as a confusing muddle of metaphors. I claim that the metaphors of “hot potato”, “trying to get rid of” and “willing to hold” are highly misleading since they appear to confuse negative marginal value with diminishing marginal value. Whether the explanation is intended to be applied at the aggregate level or the individual level, these metaphors make little sense in application to the types of scenarios Sumner is describing.
Consider a society in which everyone eats potatoes, all the time. They love how potatoes taste and they can barely get enough of their beloved spuds. They have perfected several hybrid varieties of potatoes that are not only exceedingly delicious and various in their flavors and textures, but satisfy all of one’s nutritional needs. And these hybrid potatoes have been genetically engineered to be free of all rot and decay. If you put one in your dry and cozy potato cellar, then 50 years hence it will be just as tasty and nutritious as it was the day you put it in your cellar.
Let’s suppose there is a steady annual supply of potatoes in the society, enough to provide each and every individual with 50 potatoes per year. Suppose also that people in the society frequently barter potatoes for all kinds of things. As in any economy, the rates at which people are willing to exchange potatoes for other services and commodities depends on the values they assign both to potatoes and to those other things. Let’s suppose people in this society tend to measure the market values of goods and services in terms of goats, and that the current market rate is 100 potatoes for one healthy young goat.
Now suppose the annual supply of potatoes increases. At first, people are really eager for more potatoes, so the marginal value of each potato added to their income doesn’t change much. If they had an annual income of 50 potatoes a year before and now have an annual potato income of 100 potatoes, they consider the value of their total potato income to be almost twice as great as before. Almost as great, but not exactly as great: you can still get a healthy young goat for 100 potatoes, but you now have to be willing to throw in a couple of tomatoes or a watermelon. So the marginal value of additional potatoes is beginning to diminish.
Now let’s suppose the annual potato income continues to rise even further. At some point the marginal value of adding additional potatoes to one’s income begins to decline very sharply. People now have enough potatoes to satisfy all of their annual needs and wants, and they don’t want to eat many more. They start saving more of potatoes in their cellars for the future. Notice that when we say that the marginal value of additional potatoes is going down, we don’t necessarily mean that the 200th potato that comes into your possession in a year is worth less than the 1st potato that came into your possession that year. Potatoes move around the market easily and are more or less indistinguishable. What we mean is that as you acquire more potatoes, each of your potatoes comes to have slightly less value.
So people are still willing to trade potatoes for goats, but now you have to give away substantially more potatoes to get a single goat. Let’s assume that the values people assign to goats and everything else haven’t changed. If you barter goats for squash, or squash for baskets, or baskets for goats, the price ratios are all still the same. Only potatoes have changed. You could say that the potato price of goats and everything else has gone up. Or you could say the goat price of potatoes has gone down. But assume at this point that potatoes still have a positive value, and that getting an extra potato for free still makes a net positive contribution to your potato income. It’s just that it isn’t received with as much joy as were previous potatoes.
Since the value of the average potato has now declined, then for any finite quantity of potatoes people are going to be somewhat more willing to part with them than before. On the other hand, people with things to sell are slightly less desirous of acquiring that same amount of potatoes than they were before. The total volume of potatoes changing hands may increase, or it may not. But at this point it makes no sense to describe people either in the aggregate or at the individual level as “trying to get rid of” their additional potatoes. They still like potatoes; they still positively value them. They are only increasingly willing to surrender them for other things they value, because the value of potatoes is decreasing relative to those other things.
Now suppose the annual potato income continues to rise, and things really start to change. The potato gods are raining potatoes down from the skies. People are surfeited with potatoes. They couldn’t possibly eat another bite of a potato. And they will never be able to eat all of the potatoes in their cellars. They are running out of storage room, and have to build or rent extra space just to hold them – which is costly. As the stocks grow excessively large, they begin giving off noxious fumes they never gave off before. They finally reach a point where the marginal value of adding potatoes turns negative, and the total value of one’s potato holdings actually decreases the more potatoes one has. For example, suppose for up to 20,000 potatoes the value of your potato stock continually increases, but at an increasingly small rate. But suppose that having 21,000 potatoes is actually worse than having 20,000 potatoes.
Notice that this still doesn’t mean that the average value per potato is negative, only that the marginal value of additional potatoes is negative. For example it could be that the value of having 15,000 potatoes is equal to the value of having ten goats; that the value of having 20,000 potatoes is only equal to the value of having 12 goats, but the value of having 25,000 potatoes is equal to the value of 11 goats. The average value of a potato is still a positive number, but if you have 25,000 of them, you would prefer reducing that number to 20,000. You are willing to give away 5000 potatoes.
What happens then? Well, at this point people with more than 20,000 potatoes really do want to get rid of some of their potatoes. They try to barter them, but find few buyers. They start dumping them in rivers; they burn them in bonfires; they shovel them into their neighbors’ potato cellars when the neighbors aren’t looking. And notice how hard it is now to get rid of them. People are eager to give them up, but that eagerness is equally matched by a disdain for obtaining them.
OK, now let’s bring things back from potatoes to money. Is money ever like this? No! In the modern world it costs virtually nothing to store money, and money doesn’t cause noxious fumes to rise from your checkbook or computer. Can you run out of room for money? No! It is equally easy to store $1 trillion dollars in an electronic account as $100. So as those dollars add up, do they become hot potatoes? Does your money stock ever reach a point where marginal additions to that stock pass beyond the point of having diminishing but positive marginal value to having negative marginal value? Does your growing money cellar become a money pit of declining value? It is hard to see how this could be the case. No matter what happens to the value of money, you will always prefer 50,000 units of it to 40,000, and prefer 100,000 units to 50,000 and prefer 100,001 units to 100,000 units.
A hot potato is a potato that is too hot to hold. Holding it in your hand hurts, and so even if you get nothing for it by throwing it to someone else, you are willing to throw it away just for the benefit of no longer possessing it. But money is never like that, since no matter how low the marginal value of incremental increases to one’s monetary holdings goes, it never reaches the point where having somewhat less of it is better than having the amount you currently possess. And so the Market Monetarist metaphor of increased supplies of money causing a situation in which the quantities of money held surpasses people’s willingness to hold it, and causes money to “hot potato” around the economy, makes little sense.
2. Potato Banks
Sumner also asks us to consider what would happen if the hypothetical company he introduced in the passage I quoted above just makes various kinds of announcements. He asks us to assume:
… the company merely announces the big gold discovery, but it is credible. Now gold prices would plunge on the announcement.
… the company announces that radar has detected the vast gold deposit, but it will take 2 years to dig down and get it out. Again, prices will plunge right away, almost as much as in case 2.
To address this part of Sumner’s discussion, let’s turn to what I called the more significant problem with Market Monetarism and its hot potato story: the problem of distinguishing the behavior of the banking sector from other sectors. And let’s continue to press hard on our potato analogy – to the mashing point and beyond.
Imagine now that the government grows all the potatoes. And to get them to the public, it uses some very peculiar methods. One thing it has done is establish a nationwide system of potato brokerages, and the government supplies potatoes directly to those brokerages. It supplies those potatoes in a few different ways. Sometimes it lends potatoes to a brokerage, in exchange for a promise of a certain number of potatoes to be returned by the brokerage to the government in the future, and sometimes it just gives some potatoes to the brokerages. Sometimes the brokerages lend potatoes back to the government, and in return for the loan receive extra potatoes when the government repays them. Sometimes the government owes a brokerage some potatoes, and it gives the brokerage a promise for extra potatoes in exchange for the brokerage’s agreement to hold off on pressing its current claims for what it is owed. There are various such techniques that are used.
Assume also that the government doesn’t actually need any potatoes for its own direct use. All of these operations with the brokerages are carried out only to manage the supply of potatoes going into the brokerages. And the government keeps increasing the amount they loan out. This fact, in combination with the potatoes that are given away, and the potatoes that are given in exchange for loans of potatoes back to the government, serves to guarantee that the total quantity of potatoes in the possession of the brokerages continues to rise gradually over time.
The brokerages are regulated, and they are in a peculiar line of work. They don’t barter potatoes for goods and services. Basically they do most of the same things with their potatoes that the government does with its potatoes. They loan them for promises of more potatoes in the future. But whereas the government loans potatoes to the brokerages, the brokerages loan potatoes to the general public. The government doesn’t participate in the business of lending potatoes to the general public directly; all lending goes through the brokerages. But the government is also giving some potatoes away to the public on the side, outside of the brokerage system, and directly bartering potatoes with the public for things the government needs. These different governmental operations are distinguished administratively: there is the part of government that works with the brokerages alone, and the part which works with the rest of the society. The part which works with the brokerages alone is the National Central Potato Brokerage. The other part of the government is called the People’s Potato Agency.
Now here’s the twist. Imagine that the people in our hypothetical society have lost all intrinsic desire for potatoes. They don’t like them; they don’t eat them; they don’t need them for any primary purpose. But there is still a demand for them. Why? Well starting at Year One and continuing each year after, the government imposes a 50 potato tax on each citizen. Each citizen must deliver 50 potatoes to the government in each year, or else pay a heavy fine in goats, mules, bricks or something else. So the citizens make it their business to acquire 50 potatoes each year somehow.
Why would the government do something like this? Well for one thing, they have found that the circulation of something through the society that people never use up, never consume, never plant in the ground, never throw away, and never bend, fold or mutilate – but that is always in demand – is good for the promotion of commerce. But they have also found that maintaining this circulation of potatoes is a good and fair way to acquire things the government itself needs to run its various essential operations. Instead of taxing desk chairs from the office supply companies, and submarines from the submarine-making companies, and computers from the computer-making companies, the government can offer to buy these things with certain numbers of potatoes, and then tax everyone more or less equal numbers of potatoes. The existence of the universal tax means that goods and services exchange hands widely in the quest for potatoes, and everyone ends up sharing in the tax burden equally, instead of that burden being carried by just those who have to part with the goods and services the government actually needs to do government business.
What’s in it for the brokerages? The potato brokerages have owners, and if brokerages have surpluses of potatoes, because more potatoes come into their possession than they need to repay the government and the public, they give them away to the owners. Potatoes are valuable for the purposes of exchange, so the owners want some. And it’s nice to be able to get some without doing any work.
The potatoes are now like money. If they were the kind of money that needed to be stored, the society might actually reach a point where an overabundance of potatoes pushed them into negative marginal value territory. But that never actually happens. Since potatoes are not actually used for any industrial process or consumed to satisfy health and nutrition needs, a reliable IOU for potatoes is just about as good as actual potatoes. So fewer and fewer real potatoes change hands, and the society increasingly does its business with different kinds of virtual potatoes. The government’s IOUs for potatoes are traded among the brokerages to settle their inter-brokerage debts, and the brokerage IOUs for potatoes are traded among the public.
Now suppose the public is not doing so well economically. Investments start to yield small and even negative returns. Given the number of potatoes the brokerages have to deliver when they repay the government for loans of potatoes, they increasingly find themselves in a situation where they lose potatoes by lending to the public. The borrowers of potatoes spend their potatoes, but often don’t get enough potatoes back to repay the loans. The brokerages ask for lower rates from the government, and the government complies, but it doesn’t help much because the public is in dreadful shape collectively. The price of borrowing potatoes declines as the government injects potatoes into the brokerages, until at some point the brokers will have so many potatoes that the potato rate for borrowing potatoes is so low that holding onto a potato is no less profitable than lending one.
Still there is not much of a market for loaning potatoes. Some people are willing to borrow potatoes, to be sure. But many of these people have been judged unlikely to pay back what was borrowed. Other people are unwilling to borrow potatoes at all, because they already have a lot of them and given the poor returns on investment, they can’t think of anything better to do with them than hold onto them. The brokerages can increase the lending rate, but then fewer people will want loans and many of those who foolishly still want those loans will never be able to pay back. And the brokerages can’t make the rate go negative, because the potatoes are now a modern form of money, which as we have seen can’t have negative marginal value. So holding onto one potato is always better than giving it away, no matter how low its marginal value gets, given that the value is always positive. The expected value of loaning potatoes at any positive rate is lower than the expected value of holding onto the potatoes, and the positive marginal value of holding potatoes means the rate can’t go negative.
Now suppose the National Central Potato Brokerage makes a big speech. It announces that it will be injecting even more potatoes into the brokerages. It announces that it will buy back promissory notes for potatoes and give out potatoes in exchange. It makes all sorts of predictions about how this is going to impact things such as the potato price of goats. But the lending rates are already as low as they can go, and the only way the National Central Potato Brokerage interacts with the public is through the brokerages and the lending system. People who understand the phenomena described in the last paragraph will not be impressed. The brokerage sector is in the business of lending potatoes, not distributing them for free, and the lending market can’t be expanded unless something from outside the lending sector changes conditions in the broader economy.
If the National Central Potato Brokerage could inject potatoes directly to the public, they might be able to accomplish something. More potatoes would circulate and people would be able to repay their potato loans more easily. More brokerages would then lend to them. Things might get moving again. But the National Central Potato Brokerage can’t inject potatoes directly to the public, only to the brokerages, and we have already seen that injections to the brokerages are unavailing. Until the People’s Potato Agency announces a way of delivering more potatoes directly to the public the National Central Potato Brokerage can’t do much.
Now the National Central Potato Brokerage might try to bluff their way through all of this by pretending that they can do things they can’t. Nobody can say for sure what kinds of effect those announcements will have, since people might have all manner of crazy beliefs about what the National Central Potato Brokerage does. Maybe if the brokerage announces it is going to cause rain to fall, people will go out and plant gardens, and the upsurge in human industry and zeal will get the economy moving. But governing by rain dance doesn’t seem like a very enlightened way to run a society.
Cross-posted from Rugged Egalitarianism
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