Last week I blogged about my perplexity regarding the Keynesian notion of a liquidity trap.
In thinking about this harder, I’ve come to realize that a good part of my confusion has nothing to do with liquidity traps. It comes down to a very specific question about sticky-price models in general.
I expect this discussion will be interesting only to the most wonkish of my readers. The non-wonkish are invited to ask for clarifications, but please don’t jump in claiming to have “definitive” answers unless you’ve got a good grasp of the basics. I’d like to keep this discussion on track, and I’d like to learn something from it. Uninformed noise will be counterproductive.
For what it’s worth, I’ve discussed this offline, at considerable length, with several very good macroeconomists who eventually pronounced themselves as confused as I am. I really am hoping somebody with the right insight will pop up here and set us all straight.
By way of analogy, let me start with something I do understand — a world with flexible prices and (for simplicity) no inflation. (What follows is standard textbook material, which we all learned from Milton Friedman, who in turn probably learned it from Iriving Fisher. It is not controversial. If you think it’s wrong, the probability is 99.9999% that you’re mistaken.)
Let’s consider the supply and demand for money in this economy. Money is supplied at (essentially) zero social cost (the cost of paper and ink being essentially zero). However, the private cost of holding money — measured in forgone consumption — is positive. Whenever the private cost of an activity is greater than the social cost, people engage in too little of that activity. In this case, they hold too little money. Or in other words, they spend too much money. That means that each additional dollar you spend must hurt your neighbors more than it helps them. It remains to ask who, exactly, is hurt by your spending.
Answer: When you spend a dollar, you bid up prices. That’s good for sellers, bad for buyers, and bad for other people holding money (because it depletes the value of their dollars). The first two effects wash out, because every transaction involves both a seller and a buyer, leaving the moneyholders as the bearers of the net harm.
Note the logic: First we identify a discrepancy between private and social cost. This tells us that spending a dollar must (at the margin) do more external harm than good (“external” means “not felt by the decisionmaker”, the decisionmaker in this case being the spender). This in turn tells us that we ought to ask who bears that harm. The answer isn’t immediately obvious, but it’s clear once it’s pointed out.
Now I want to apply the same logic to a “Keynesian” world of fixed prices. In order to focus on one very specific question at a time, I’m going to assume this world is at full employment. (I eventually want to understand worlds without full employment, but one thing at a time!). Better yet, let’s follow Paul Krugman’s example and simplify things as much as possible by assuming that consumption goods just fall from heaven, so there’s no such thing as labor. They do, however, have to be purchased with money.
Okay, back to the money market. Once again, money is provided at zero social cost. Once again, it seems to me that the private cost of holding money is positive (that old forgone consumption again). Therefore, once again, people must hold too little money. Therefore, once again, they spend too much. Therefore, once again, an additional dollar spent must do more external harm than external good.
The problem, then, is to identify the bearer of that external harm. Well, what happens when I spend a dollar? Back in the old flexible-price world, I bid up prices. But in the fixed-price world, I can’t bid up prices, so I must bid up the real interest rate instead. That’s good for lenders and bad for borrowers, but that washes out because every lender is matched with a borrower. So where is the missing extra external harm?
To break this down further:
- Am I right that in the fixed-price world, the social cost of providing money is still zero and the private cost is still positive? These things are certainly true in the flexible-price world, and I can’t see any reason why fixed prices would change this part of the story. Maybe I’m missing something, but I’ll be very surprised if I am.
- Assuming the answer to 1) is yes, we know from the general theory of externalities that spending a dollar must cause net external harm at the margin. Who feels that external harm?
I understand that there are all sorts of Keynesian reasons why spending a dollar might cause net external benefits, but those reasons are all centered on unemployment. I want to know what happens in the simple no-unemployment world I described above. Once I get that down, then I can start thinking about the harder cases.
Help!
Edit: One could take a stab at an answer along the lines of “people expect deflation, which reduces the private cost of holding money, so they don’t hold too little after all”. But we can assume an economy with both zero inflation/deflation and zero expected inflation/deflation, and the same questions remain.
Once again, it seems to me that the private cost of holding money is positive (that old forgone consumption again)
What if deflation is expected? Is the private cost of holding money still necessarily negative? You exchange current consumption for more expected future consumption.
To start off, I don’t know the answer to this question (2).
What I imagine the answer to the question to be is those whose prices are sticky.
For starters, it seems intuitive to me, that if you move from flexible prices to sticky prices in a world where ‘the harm is done/escaped from’ by those with flexible prices, that when those no longer able to bid up their prices would suffer harm. Tax theory also tells you something similar, the person bearing the tax is the person least able to avoid paying the tax.
Now what I see when you move from flexible prices to sticky prices is that the person who’s holding money does not have his spending power depleted any longer when money is spent. Now there are two possible options remaining, the people involved in what was formerly a flexible price transaction: the buyer and the seller.
Considering you assumed that consumption goods simply fall from heaven, the answer is the seller. Why? Well if consumption goods were limited, the answer would be both buyer and seller as there would be shortages and eventually also the money holder as there would be no goods left to purchase. The answer is therefore the seller as the seller is now unable to increase prices.
Considering that the goods fall from heaven and are unlimited, this is probably a good thing as the (marginal) cost is zero.
Clarification needed. You say:
“The first two effects wash out, because every transaction involves both a seller and a buyer, leaving the moneyholders as the bearers of the net harm.”
There’s a problem with that. A sells an object to B. A is the seller, B is the buyer, the public is harmed.
B now turns around and sells the same object to A. B is the seller, A is the buyer, the public is harmed some more.
We can keep doing that for any arbitrary amount of harm we wish to cause to the public.
Ok, a possible answer is that the public is harmed because the price of X raises when A sells it to be (A has a lot of X’s). When B sells it back to A, the price of X goes down, so the harm is cancelled. I can buy that. What happens when X is a service, though? A sells a service to B, B sells another service to A (it won’t be the same service but that’s just fine). A and B together can harm the public for any arbitrary amount they choose.
Where am I wrong?
Taking your advice, I’m going to assume there’s a 99.9999% probability I’m mistaken, so you could consider this a “request for clarification” :) But I can’t avoid thinking I found an error in the “uncontroversial” model — specifically, the statement: “When you spend a dollar, you bid up prices. That’s good for sellers, bad for buyers… The first two effects wash out.” When I crunch the numbers, the conclusion I keep getting is that when you spend a dollar, the benefit to sellers is MORE than the harm to buyers (because you increase the number of transactions, and increase the total surplus).
Suppose there’s an existing market for apples with 3 sellers, whose minimum selling price for an apple is as follows: A – $1, B – $2, C – $3 ; and 3 buyers, whose maximum buying prices are: D – $3, E – $2, F – $1. The market-clearing price is $2, at which two apples will be sold; the total producer surplus is $1 (to A), and the total consumer surplus is $1 (to D).
Now you decide you want two apples that you’re willing to pay up to $3 apiece for, so you take your $6 and enter the market. The new market-clearing price is $3, at which A, B, and C, each sell their apples, of which D buys one and you buy the other two. The consumer surplus is now $0, but the producer surplus is $2 to A and $1 to B. SO: total consumer surplus went from $1 to $0, but total producer surplus went from $1 to $3.
So that made me think there’s an error in the statement “The first two effects wash out, because every transaction involves both a seller and a buyer.” I keep thinking this omits the fact that by spending an extra dollar, you’re also increasing the number of transactions, which increases opportunities for extra surplus. This makes it possible for the increase in producer surplus to exceed the decrease in consumer surplus.
Take an intuitive example: Suppose Warner Bros starts offering “Pluto Nash: Ultimate Director’s Cut” DVDs at $50 apiece, at which perhaps one or two people in the world are barely willing to buy one. But then suppose thousands of buyers enter the market who love the movie and are all willing to pay up to $100 for a copy, so the price is quickly bid up to almost $100. There’s a tiny bit of harm to the old would-be buyers now priced out of the market, but Warner Bros makes out like bandits. Even taking into account the fact that the extra dollars slightly devalue everyone’s money, Warner Bros is still much better off than they were before. The benefit to the producers of that good is much greater than the harm to the consumers.
Now it’s still true that the spending is good for sellers, bad for buyers, and bad for money-holders, and that the net effect on the entire world (minus the spender) must be negative (otherwise you could counterfeit without hurting anyone!). But these examples seem to disprove the statement that the benefit to sellers and the harm to buyers must exactly “wash out”.
If this is wrong, why is it wrong?
(Feel free to suppress this comment — it’s just fwiw):
“Money”, in the sense of ink on paper, etc., is just a token — a thing that stands for something else. Yes, of course, the tokens can be supplied at negligible cost, but it’s not the tokens themselves that people value or want to hold, at the expense of present consumption — it’s the “something else”. And the value or cost — the social cost — of that “something else” is just exactly the value of the economy averaged over the number of token units. Hence, there is no discrepancy between the (average) private and social cost of money, and no need to seek out an “externality”. In particular, no one is “hurt” (on average) when a dollar (a unit token) is spent any more than anyone is hurt when goods are traded — the token is merely facilitating such trades across time and place.
The Keynesian world of fixed or sticky prices is certainly a complication, but on a much higher level than this.
@Marcel: I believe the explanation is that moneyholders are only harmed once, when someone takes money that they were previously hording, and spends it, thus the money enters the marketplace and devalues other money. (Same harmful effect if government prints more money, or if someone counterfeits it.)
However the money can only be “unfrozen” once. After that, it’s in circulation, and continuing to pass it back and forth does not devalue other people’s money any further.
The issue is that the net private marginal cost of holding a dollar is negative in Keynesian story.
So to be clear – because this wasn’t in your set up – money has private benefits as well as private costs. That is people desire liquidity, or there is money in the utility function, or a cash-in-advance constraint. Whatever, you want.
However, the fact that positive money balances exist tells us that they must have some private benefit or else everyone would attempt to spend down to zero.
Now, what is it that people want? Well, we assume they want real purchasing power. So, what they care about is not the face value of the money in their wallets but what it can buy.
No imagine that by some magical trick the amount of money in everyone’s wallet is cut in half, but prices remain the same. Real purchasing power is now less than what it was.
Because people were previously holding optimal money balances, they must be holding sub-optimal money balances now.
This means that the net private marginal cost to holding money is now *negative.*
So you get the exact opposite result, spending a dollar causes external benefit because it allows another person to build up their real money balances which makes them happier.
We don’t need inflation/deflation or expectations of either.
In regards to question 1, could the private cost of holding money be negative? If someone has available money, and they choose to delay consumption then they could lend to someone who wishes to consume immediately. Since real interest rates have increased, but prices remain fixed indefinitely, wouldn’t they be able to purchase more of a product at the later date. Therefore, their cost of delaying consumption would be negative?
I am assuming that “holding cash” implies that they will earn the real interest rate on their cash…
@Bennett: I don’t see how that can be the case; nobody spends the moneyholders’ money in my example. B spends his own money to buy from A, then A spends his own money to buy from B and so on. The rest of the public keeps hoarding the money.
Do you care about the cost of keeping prices fixed? Or to put it another way, is there such a cost? Are you postulating that prices remain fixed absent an enforcement mechanism, or that there is enforcement? Because in the second case you have more enforcing to do, which is a cost, and in the first might you have a reductio ad absurdem?
Karl Smith: I am just waking up and have only a moment here, but I want to thank you for your comment, which looks extremely helpful to me. I’ll come back to it later today when I have time to digest it more fully.
Others, including Marcel: I’ll respond to some other comments later today also.
Isn’t the real interest rate a price? How can that be moving in a fixed price world?
Larry: If what you were saying were on point, it would apply to the flexible-price world as well as the fixed-price world. Since it doesn’t apply to the flexible-price world, it can’t be right. (I’ve explained exactly what’s wrong with it multiple times in last week’s thread.)
Karl Smith’s argument, while superficially similar to yours, actually makes use of the fixed or sticky prices, and therefore, unlike yours, has a chance to be right.
Matthew: The usual Keynesian assumption is that the prices of goods are sticky but the prices of bonds (and hence interest rates) are flexible.
@Marcel, the issue is not that anybody is *spending* the moneyholders’ money, but rather when you “unfreeze” a dollar bill and spend it, it increases the amount of money in the world and everybody else’s money is devalued.
Consider the case of a counterfeiter. A counterfeiter isn’t spending the moneyholders’ money, but he’s still harming them, because adding more money to the world, devalues other people’s money.
However that only happens the first time a dollar bill is “unfrozen” (or counterfeited). It doesn’t keep happening every time the dollar bill is spent and passed back and forth.
Steven Landsburg is correct:
Keynesianism makes no sense in a world of perfectly flexible wages and prices. There is no way to get the purported Keynesian effects.
You can produce confusion models with the Lucas Supply Curve, but then monetary and fiscal policy would work in a totally different way.
[i]Better yet, let’s follow Paul Krugman’s example and simplify things as much as possible by assuming that consumption goods just fall from heaven, so there’s no such thing as labor. They do, however, have to be purchased with money.[/i]
With this hypothesis, we’re no longer dealing with a problem of scarcity, hence this could hardly be termed an economic problem.
Rather than thinking about it in terms of money, I find it becomes clearer when thinking about it in terms of available goods.
In the first example, we can assume that the buyer has consumed a unit of resource, thus leaving everyone else worse off, since they no longer have access to it. Hence why the prices are bid up.
In the second example, even if the buyer has consumed one unit of a resource, the assumption of zero cost means essentially that we’ve gone from an infinity of units to infinity-1 units, which is equivalent again to an infinity of units. Hence, everyone other than the buyer and seller are left exactly as they were before the transaction took place.
Holders of consumption goods in the present bear the loss in terms of decreased Net Present Value of their holdings.
In the world of fixed prices and flexible exchange rates, where the only price that moves is the interest rate (which rises), present consumption becomes more costly in terms of future consumption. Therefore demand for present consumption is decreased, and the value of consumption items falls.
In the world of fixed prices, the holders of goods with declining demand would realize a disproportionate share of the capital losses, since they can’t sell the quantity of goods they wish to sell at the fixed price.
I assume that the consumption goods falling from heaven are of a fixed quantity.
@Karl Smith: Can you explain how you get the conclusion in this bit:
“Because people were previously holding optimal money balances, they must be holding sub-optimal money balances now. This means that the net private marginal cost to holding money is now *negative.*” ?
I agree that the balances NOW are sub-optimal, because they are too low. So I want to hold an extra dollar. Doesn’t that make the marginal rate of SPENDING not HOLDING negative? What am I missing here?
If I spend an extra dollar, and the prices of consumer goods are stuck, but there are bonds with flexible price then I bid up the prices of bonds, and I bid down the real interest rate.
This benefits borrowers and hurts lenders and so is a wash. (The reverse of your argument, but the “wash” was the point.)
And so you are still left with you question about the external harm caused by spending.
Now, if you ignore this interest rate story, then the answer is obvious. You spend more. The price level is fixed. There is a shortage of consumer goods. Any consumption you undertake is at the expense of others. If you are the only one who suffers the shortage, you consume nothing and you have caused no harm. But if the shortages are spread out, your consumption is at the expense of their consumption.
If you assume that the _lower_ real interest rate story occurs, then the usual assumption is that the real interest rate falls until people are willing to hold the existing quantity of money. This is the liquidity effect. You consume more. Other people hold more money and consume less, because at the lower real interest rate, they don’t want to lend as much. Those who actually lend earn less and those who actually borrow pay less. That is a wash. But those who hold money rather than lend earn less without anyone paying less.
Now the result of this story is that the lower real interest rate causes people to consume more. In your model, I guess people borrow more to consume now and they are less included to consume less to lend. (There being only manna from heaven.) More generally, investment demand rises, and immediately reduces the production of consumer goods now to expand them in the future.
And so, we are left where we are at the beginning, shortages of consume goods. You consumer more by spending money, and they have less.
I would suggest reading Yeager.
Also, your basic framework for money–print it and spend it and who cares what happens to prices–really doesn’t do much to understand a world where the goal is to stablize some other nominal value like prices, inflation, or nominal GDP–the flow of spending on output.
Further, most money (checkable deposits) pays interest.
@KenB – note that Karl Smith said the “marginal COST to holding money is NEGATIVE”. Cancel out the double negatives and this means that the marginal benefit to holding money is positive, i.e. you want to hold money, which is what you are saying :)
@Bennett – let me see if I understand this correctly. You start from a world populated only by moneyholders. There are no transactions.
Now we change it: a transaction occurs – A sells a service to B. B “unfreezes” some money and gives them to A. This increases the amount of money in the world (what?) which hurts the moneyholders.
Well… 1) the amount of money in the world is not increased, and 2) doesn’t A “freeze” the money right back and thus undo the harm that was done to the moneyholders?
I mean, either A receiving the money undoes the harm, in which case there’s no overall harm done; or A receiving the money doesn’t undo the harm… in which case we can keep multiplying that harm. I guess I just can’t understand what this “freezing” and “unfreezing” means.
(I am asking these questions because Keynesianism is a weird world for me… I have a hard time thinking like this – I’m an Austrian – so thank you for your patience.)
I always thought it was self-explanitory, but maybe I’m looking at it too simply? Oh well, feel free to jump me intellectually.
Sticky prices reflect a market with oligopolistic competition. A profit maximizing firm will set MC=MR, but new (yet few, oligopoly) firms will come in and try to undercut the competition. If they do this, their competitors will do it as well because demand for their goods are assumed to be elastic since consumers want to maximize their interest (even if this isn’t the case, the model *assumes* this is what business owners believe about their customers). This is bad because firms, in the long run, will compete eachother out of business since the price of their goods will be significantly less than the cost of producing them. Thus, they stay at a sticky price.
Now assume some competitor in that oligopolistic model tries to increase the price of their goods. Other firms won’t respond, because they know that if they keep their prices the same they’ll attract more consumers. Thus, in the long run the firm(s) that increased the price of their goods will have their prices return back to the original price of their competitors. Thus, again, a sticky price.
Thus, the external harm is placed upon the sellers because they may not be able to maximize profit due to other competitors and (either real or imaginable) demand elasticity of their potential consumers. They actually lose out in terms of consumer surplus.
@Bennett: Ahh, thank you. I shouldn’t have not missed to fail to not see that.
Bobby Jay: Sticky prices don’t have to involve oligopolies; Keynesians identify several sources of ‘friction’ in otherwise competitive markets. Menu costs is one that has been mentioned in this thread.
SL: Wouldn’t the losers in the scenario where the real interest rate is bid up again be the people holding cash for liquidity purposes etc. (i.e. they’re neither borrowers nor lenders?)
With the interest rate representing the opportunity cost of holding cash
Interesting — I was going to say much the same Karl_Smith, that the assumption of “net positive private cost to holding money” is wrong; I thought you had labeled that as part of the 99.999% probably correct part of your exposition. Okay, whatever.
Money carries option value — the option to redeem for an arbitrary good at prevailing prices. And you can’t assume this away for purposes of argument: if money doesn’t have option value, or people don’t value optionaality, there’s no point to money in the first place.
Silas:
I was going to say much the same Karl_Smith, that the assumption of “net positive private cost to holding money” is wrong; I thought you had labeled that as part of the 99.999% probably correct part of your exposition. Okay, whatever.
The “net positive private cost to holding money” is standard textbook fare and part of what I said is 99.999% sure to be correct in a world of flexible prices.
Karl Smith is pointing out that it might not be true in a world of fixed prices.
Producing goods has a cost to the seller.
With fixed prices and fixed demand there are static interest rates.
With an increase in demand, the seller now has to produce more goods–but to do so requires him to buy more equipment, labor, materials, etc in order to get to the new equilibrium point where supply = demand. This raises interest rates because this is an *additional* demand for investable resources to fund that production. There is more demand for investment money, so the interest rate goes up.
Karl Smith wrote:
“So you get the exact opposite result, spending a dollar causes external benefit because it allows another person to build up their real money balances which makes them happier.”
Who gets to build up their real money balances? When you spend your dollar, you give up some real money balance and the seller gains that exact amount. These effects wash, and we’re still left wondering where that extra cost (or benefit, in your case) goes.
In your explanation, the private cost is negative and the social cost is zero. There’s still a disconnect, and since the buyers and sellers still cancel each other out in transactions, we still don’t have any idea to whom that phantom cost (or benefit) accrued.
Either that, or I still don’t have any idea what I’m talking about.
I think there’s a missing component in the reaction of real interest rates to that extra dollar spent. Granted, if I understood that part better I’d probably be less suspicious of it.
I’d like to note that there is a typo in my last post. The last sentence should read ‘producer’ surplus, not ‘consumer.’
@ iceman
Okay, leave out the oligopolistic model. There was a fault in that reasoning anyway (producer surplus lost due to sticky prices is a consumer surplus gain. Another washout.)
Price stickiness can act as either a price floor or ceiling. Now assume a firm doesn’t change it’s prices due to menu costs when there is an increase in demand (people like Steve go out and buy, buy, buy.) This will cause firms to cut back production, and employment. Thus, every dollar that is spent may lead to unemployment and shortages of goods.
I’m not an economist by any measure (and accept freely the liklihood of being wrong), but when I see a question like this, I tend to go back to basics. Fortunately, basic supply/demand sheds light on this, I think.
If I apply what I’ve learned about supply and demand, here’s where I end up: given that price cannot move (because it is stuck) and demand has gone up (because you spend a dollar), it seems to me that supply must, necessarily, go down. If your universe doesn’t have goods falling from heaven, then you will find yourself with instances of non-supply–i.e. someone wanting good A cannot find it because price cannot signal the market to produce more of it.
So the cost of holding dollars in this system is the risk of not being able to spend them on the products you desire. Since shortages are paid for through time (queueing) or influence (political or social), the shortages will be paid for in the cost of acquiring goods through those methods.
To bring this back to your question of who is hurt, the answer, to me, is “future buyers of that product”. Specifically, those who must pay in time or influence to acquire the desired product (or shift to a poorer substitutes or any of the other supply-mitigating strategies people employ).
Karl Smith is pointing out that it might not be true in a world of fixed prices.
Oy. If prices are truly fixed, unresponsive to any changes in preferences or constraints, then all bets are off — literally and figuratively. You might as well ask what happens when people are indifferent between all alternatives.
I don’t think Karl’s solution is generally right. Here is a case where I think it is not.
Goods fall each day as heterogeneous manna from heaven. People have different preferences so they may not want to consume the bundle that falls in their front yard, so they trade. Without money, trade is barter and costly because of the double coincidence of wants.
With fiat money, these costs can be reduced or avoided. Suppose money takes time to circulate in exchange, so the more real balances people hold, the less they need to barter. The benefit to holding higher average real balances (which are not sitting idle in the bank but turning over) is the lower barter transactions costs.
Suppose people are holding a level of real balances at which barter is unnecessary. There are no bonds in this model, so this is the optimum quantity of real balances, which would be attained with zero inflation (zero real interest on money).
Now, assume nominal money balances are cut in half, so people are holding half the real balances they were before. Some barter is now required because of lower real balances, and people would be willing to pay to hold more real balances. But the price level is fixed, so for given nominal M this is not possible. We are in a sub-optimal situation.
You might say, as Karl Smith, if someone spends an extra dollar, he confers a benefit on others, but this is confusing the circulation of money with the level of real money balances. The right thought experiment is to suppose someone decides to spend a dollar not to exchange goods but to consume one more unit of manna than falls in his yard.This means that others have to consume one less unit of manna but they hold one dollar more money balances, so their barter transactions costs are lower. The first agent consumed one more unit of goods and his transactions costs go up. So it is a wash. there is no externality on the decision.
All:
There is always a wash. This was the point of Steven’s original post.
The question is if spending is a net benefit to the money holder who is it a net loss to. Who does it wash with
In an environment with flexible wages and prices it is the holders of other money. If this didn’t hold then you could simply improve overall consumer welfare by printing money. But, this is impossible in a world with full flexible prices.
So Steven asked who counter-balances that effect in a Keynesian world where there are not price changes.
The answer is that in the Keynesian case the externality is that people spending effects others real money balance. In the case where there is too little money then spending has a negative affect for the spender washed by a positive effect for the seller. In a world with too much money spending as a positive effect for the spender washed by a negative effect for the seller.
In other words the wash goes through being forced to hold a real money balance that is either too high or too low rather than through inflation.
Jacob Proffitt: I have very little free time today and still need to digest what several of the comments are saying —- but yours looks to me like it might be very useful. Thanks.
To all: I’ve not yet read all the comments, and a number of good answers might be lurking there. But I do have a reformulation of the question:
1) Suppose the govt can, at no cost, produce a magic substance that makes people look younger. Although it costs them nothing to produce this substance, they charge $5 an ounce for it.
2) At $5 an ounce, I buy 3 ounces a week. If it were free, I’d take 10 ounces.
3) Economists know that efficiency is maximized when people act as if private and social costs were equal. What that means here is that efficiency would be maximized if I could be forced to buy 10 ounces of this substance, paying the $5 per ounce. That would make me less happy, but it would generate an extra $35 for the govt which more than balances that unhappiness.
4) The govt can take that $35 and give it to whoever they want. That “whoever” is the recipient of the efficiency gain.
5) Now suppose instead that the govt can, at no cost, produce green pieces of paper that make people’s lives easier (by facilitating transactions). Although it costs nothing to produce these pieces of paper, holders must pay for them by forgoing the opportunity to earn interest.
6) Given the forgone-interest cost, I choose to hold three of these pieces of paper in my wallet. Absent the interest cost, I’d hold ten.
7) That tells us that if I were forced to hold ten instead of three, there would be an efficiency gain. I’d be less happy, but someone else would gain enough to more than offset that loss.
8) Who is that someone else? Well, the govt can create those seven dollars, use them to buy goods, and give those goods to whomever they want. That’s who gains.
9) Alternatively, the govt can *not* create seven new dollars. In that case, my (forced) decision to hold seven more dollars bids down prices, transferring the gains to other moneyholders. But the gains have to go somewhere.
10) Now suppose prices are fixed. If I am forced to hold extra dollars, the govt can create extra dollars, buy goods, and give those goods to somebody. That somebody is a winner.
11) Alternatively, if they don’t create extra dollars, the gains must go elsewhere. They no longer go to moneyholders (at least not in any obvious way) so they must go to someone else.
12) Who, exactly, gets those gains?
(The blog post asks who loses when I hold less money; this comment asks who gains when I hold more. These are of course essentially the same question, but maybe this way is easier to think about.)
Steve, an extremely interesting post. I don’t care so much about the answer, as about how we get there. (I think the same is probably true for you too?)
I have a request and then a possible money wrench:
THE REQUEST: Can you please elaborate a little bit on the thing that is 99.9999% right? You are bouncing around a bit. In the post you said the cost was foregone consumption, but now in the comments you are saying it’s interest. Then Silas said “net private cost” and you repeated the phrase, which doesn’t make any sense to me. (Why would someone do something that had higher costs than benefits?) I have my own views as to which way these switches should go, but I’m not sure how you’re thinking about it and it would probably help everybody if you spelled out the flexible-price case a little bit more.
THE MONKEY WRENCH: You are thinking about this in static terms. But in reality, when I add money to my cash balances, I have a long-term plan involving expectations of spot prices at t, t+1, t+2, etc. Think of it this way: Suppose at t=0 everyone in the world is shown a movie of the complete future of human history. They optimize their consumption and production decisions accordingly. Then we start watching human behavior unfold. Are you still sure that someone’s spending makes the dollar-holder worse off? I guess it might, but only back at t=0. I.e. that externality was already booked in the past. I’m not saying this changes the conclusion–obviously pollution from a smokestack is still inefficient, even if everybody knows it’s coming–but it’s hard for me to think through your analysis because you seem to be assuming that the dollar-holders are taken by surprise by the spending of others.
I’m not an economist, so some of this discussion is going over my head. However, I have a couple of questions. First, in a world of fixed prices, may I assume fixed wages? I don’t see how the world could work otherwise.
In a world of fixed prices and fixed wages, what happens when new prices are introduced into the market? Or, for that matter what happens if my business increases productivity, and I can sell more product. It seems to me that nobody could buy them. Let’s say I’m an apple seller, and I sell $3 worth of apples each week. I spent $1 on housing, $1 on clothes, and $1 on food.
Now, I have a great idea, and I determine I can produce $4 worth of apples a week. Can anybody buy them? Isn’t everybody’s money tied up in fixed purchases?
This sounds somewhat like the world of the medieval guilds, where craftsman were not allowed to increase productivity, and had to sell at fixed prices. Wasn’t the economy as a whole harmed by a lack of growth and innovation?
Bob Murphy:
You can view the cost of holding money either as forgone consumption or forgone interest (at the margin, the consumption you forgo to hold a dollar and the interest you alternatively forgo are equally valuable.)
You can look at it this way: The nominal interest rate is effectively a tax on holding money. Like any other tax, this tax must create a deadweight loss. Somebody must feel that deadweight loss. In the flexible price case, I understand (thanks to Milton) who that is — it’s the other holders of money, whose money is worth less because I choose to hold less. My question is: In the fixed price case, there’s still got to be a deadweight loss, but I don’t understand who feels it.
Re your monkey wrench, I think you are right that this might be very important.
@Oliver :
In the scenario in Krugman’s paper, there is
* a good (manna)
* money
* a bond market
while the good may or may not be in infinite supply, there are limits on the supply of bonds and money, and money must be used to purchase manna. Hence, there is an issue of scarcity.
@Steve :
I don’t see fixed prices in the model in Krugman’s paper. It seems to me that the liquidity trap doesn’t depend on fixed prices, and isn’t even necessarily bad in the simple model – it’s just what happens when the bond market peaks out, and people hold cash instead of bonds since cash and bonds earn the same (zero) interest rate. Then, there is price deflation.
In the real world, price deflation in the labor market is accomplished via massive unemployment. And in the liquidity trap, since bonds are equivalent to cash, normal monetary policy can’t fix things. Hence the liquidity trap causes two things that are bad :
* long-term unemployment, along with attendant productivity losses
* confused policy-makers who make things worse with policies that work usually, but don’t work in a liquidity trap.
It seems the questions you pose in your most recent comment are unrelated to the model in Krugman’s paper. Maybe they are also unrelated to understanding a liquidity trap
Sorry, by “Your most recent comment” I meant the long one with 12 points, not the one that appears most recently before my post.
Regarding points 10-12 : you say “the cost of holding money is that I don’t earn interest”. You move from flexible prices to fixed prices without changing the interest rate. Is this realistic?
Bob:
There need not be any surprise. Expectations of future money creation (or release by private parties) will generate inflation – and hence a loss in the value of real money balances – along the path to the event date.
So if I know that either that Apple will unload some its cash in 2025. That will cause prices to rise not just today but each year (technically moment) from now until 2025.
That’s because there is a carrying cost of sub-optimal money balances. If the prices were to adjust immediately then I would be able to arbitrage away my carrying costs by selling out of goods and into cash now, and then out of cash and into goods once the money is actually released.
Why wouldn’t it be the money holders? I think it would have to be. There are only two possible sources of dollars – the government and money holders. If the government forces me to hold seven extra dollars and won’t supply them, I have to get them from somewhere. And my only option is another money holder(s). In order to induce another money holder to give up their dollars I would have to pay an above prevailing market interest rate. Isn’t that who gets the gains?
In the flexible price regime, when a dollar is created, prices today and prices tomorrow (via the interest rate) adjust instantly to reflect the increase in the money supply. In the fixed price regime, when a dollar is created, prices today cannot adjust but prices tomorrow can.
When a dollar is created in the fixed price regime, there is a wedge that distorts the intertemporal decision between consuming today and consuming in the future. This wedge does not exist when prices are flexible. The social cost of creating a dollar in a fixed price world is not zero but negative.
Typo: the social cost of creating a dollar in a fixed price world is not zero, but *positive*.
Indeed, I fear I’m not sufficiently wonkish to follow this.
I sense that Landsburg wants to treat the mechanism by which he “forced to buy 10 ounces” as exogenous to the analysis. I can’t tell if doing so makes sense within the context of this metaphor or not. Because if you internalize the cost of this mechanism, it becomes unclear that Scenario 3-4 creates a world that is more efficient than Scenario 2, let alone $35 more efficient.
To rephrase, gov’t has no marginal cost of production. Landsburg’s demand curve for this stuff passes through the points (Price $0, quantity 10 oz) and (Price $5, quantity 3 oz).
Scenario 2): Gov’t has a $5 sales tax/oz. Landsburg consumes 3 oz, paying $15. The tax causes society (and Landsburg in particular) to incur a deadweight social loss relative to a ceteris paribus world w/o any taxes.
Scenario 3-4): Gov’t replaces the sales tax with a $50 head tax. Landsburg now consumes 10 oz and pays $50, or $35 more than before. Landsburg’s utility from consuming the stuff increases, but the tax causes society (and Landsburg in particular) to incur a deadweight social loss relative to a ceteris paribus world w/o any taxes.
Analysis: Yes, Scenario3-4 produces more efficient consumption of the stuff, but it provides no basis for comparing the inefficiency of the sales tax to the inefficiency of the head tax.
To rephrase, gov’t has no marginal cost of providing liquidity. Landsburg has a downward-sloping liquidity preference function (?) passing through the points (Interest 0%, quantity 10 bills) and (Interest X%, quantity 3 bills).
Scenario 6): At an interest rate of X%, Landsburg carries 3 bills and invests the rest. Landsburg’s resulting lack of liquidity causes society (and Landsburg in particular) to incur a deadweight social loss relative to a ceteris paribus world with 0% interest.
Scenario 7): Landsburg is forced to hold 10 bills – by what mechanism? Perhaps gov’t lends unlimited money for free, driving interpersonal interest rates to 0%. Without an interest cost, Landsburg would hold 10 bills, or 7 more than before. Landsburg’s liquidity increases; he has cash on hand to pursue opportunities as they arise. But the loss of opportunity to earn private returns causes society (and Landsburg in particular) to incur a deadweight social loss relative to a ceteris paribus world with an X% interest rate.
Analysis: Yes, Scenario7 produces greater liquidity, but it provides no basis for comparing the inefficiency of constrained liquidity to constrained opportunity to earn private returns. Perhaps this analysis says something about the nature of risk. That is, I strive to maximize the utility I derive from dollars invested and dollars in pocket. The advantage of having dollars invested is that I seize an existing opportunity. The advantage of having dollars in pocket is that they’re available to spend on unanticipated opportunities/emergencies from which I might derive a greater return. In this sense, dollars invested provide greater certainty; dollars in pocket provide greater risk and the prospects of greater return.
And perhaps we can’t really compare youth cream and dollars. The utility you derive from youth cream is not closely related to the price of the cream. In contrast, the utility you derive from liquidity is arguably related to the utility you derive from prior investment – that is, you want to maximize your returns. But does it make sense to talk about maximizing private returns in a world in which the private return on investments is presumptively 0%?
I suspect I’m simply missing the point here. If so, well, never mind; I’ll catch you guys on the next topic.
I think Bill Woolsey has the right idea. If you start out at full employment and prices are fixed, then marginal spending results in a shortage, which hurts the people who end up unable to buy. (This is similar to what happens with flexible prices, except that, with flexible prices, “the people who end up unable to buy” is everyone who holds money, and the reason they are “unable to buy” is that they can’t afford to buy as much at the higher prices. Aside from a net transfer between buyers and sellers, the only difference is that, with fixed prices, the allocation of inability to buy is random instead of being proportional to ones money holdings.)
Keynesian economics isn’t normally used to study full employment, so it shouldn’t be surprising that the results it gets under full employment seem odd. Actual Keynesians generally don’t believe that the assumption of fixed prices is a useful one for studying full employment. I can imagine an L-shaped Phillips curve, but I can’t imagine a horizontal one: if it is possible to produce more by employing more resources, then by definition, you’re not at full employment. (I recall Keynes writing once that “we are never quite where we should be,” meaning that we never quite get to full employment, so perhaps he didn’t consider the case empirically relevant enough to be worth studying.)
“But in the fixed-price world, I can’t bid up prices, so I must bid up the real interest rate instead.”
As best I can tell, this is just a wishful thinking equilibrium condition. It would be nice if additional spending of money caused interest rates to rise, because that would lead people to defer other spending and thus offset the original increase and bring the goods market back into equilibrium. But I don’t see any mechanism in the Keynesian model by which additional spending of ones own money balances would bid up the real interest rate. You bid up the interest rate when you try to borrow more money, or when you try to lend less money, but if you are simply taking money that you already have and spending it, how would that bid up the interest rate?
If you ask a Keynesian what will happen if you start out at full employment and someone decides to spend more money, the answer you will get is that prices will rise, not that interest rates will rise. Unless this hypothetical Keynesian has already endogenized monetary policy, in which case we’re dealing with a completely different problem.
The 12-point reformulation doesn’t seem right to me. If prices are flexible, the government can, in a sense, force everyone to hold more money without printing any more, because the real quantity of money will go up when prices go down. If prices are fixed, however, and the government does not print new money, the only way to get one person to hold more money is by having someone else hold less. There is no efficiency gain in forcing me to hold more money, because someone else will have to be holding less. To equate my marginal benefit with the marginal social cost, you have to drive someone else’s marginal benefit further away from the marginal social cost. The only way there can be net gains is if the government actually creates the seven new dollars, and in that case we know who gets the gains.
After working through an example, it became clear that my answer is obviously mistaken.
The 12 point reformulation has only a few variables. It has the dollars, prices, goods and interest only. Taking the choice of the government NOT to create the extra 7 dollars, in the moveable price world, holding more money affected price, so the benefits can accrue with lower prices. In the fixed price world, this cannot happen. Goods are fixed, so the only thing already in the world is interest. Therefore, the gains must accrue through changes in interest, or something else must be introduced into the world.
In a fixed price world you cannot bid prices up ex hypothesis, so there cannot be a social cost to holding money.
Scrub that, sorry.
Quibble:
” the private cost of holding money — measured in forgone consumption — is positive. Whenever the private cost of an activity is greater than the social cost, people engage in too little of that activity. In this case, they hold too little money. Or in other words, they spend too much money. That means that each additional dollar you spend must hurt your neighbors more than it helps them. It remains to ask who, exactly, is hurt by your spending.”
By saying people engage in “too little of that activity”, you seem to be saying there are positive externalities of holding money. That is not true — the harm to other people is mediated entirely through the price system. So we have a pecuniary externality, which isn’t an externality at all.
It seems to me that your statements fall into three categories:
Things you’re 99.9999% certain of, such as “Whenever the private cost of an activity is greater than the social cost, people engage in too little of that activity.”
Things you are hypothesizing simply for the sake of example, such as “There is full employment.”
Things you think are implied by Keynesian economics
So,
Q1: Could you clarify what is in which category?
Q2: Is this quandary perhaps an aspect of the essential nature of fiat money? Fiat money is, in a sense, essentially worthless, so it is in everyone’s individual interest to get rid of it in exchange for actual goods. But it’s in society’s interests for everyone to keep pretending that it is worth something and keep the economy going.
Q3: If there is too much money being spent, does it follow that EVERY dollar spent is a net loss for society? “Too much money is being spent” means that the /average/ cost of dollars is positive. Does it follow that EACH dollar has a positive cost?
Q4: Does the fact that buyers are hurt and sellers are helped mean that they are helped/hurt by the same amount? As Bennett Haselton said, that is not self-evident.
Q5: Suppose I trade Good A for Good B with my friend. Is this bad? Does it depend on whether it’s analyzed as a direct barter exchange or two separate monetary transactions?
Q6: Why did you enumerate “buyers” and “other people holding money” as separate categories? Aren’t they the same set of people?
Q7: Similar to Bennett Haselton’s dispute as to whether the buyers/sellers cancel out, do borrowers and lenders really cancel? Is it possible that by bidding up the interest rates, a less-optimal investment situation prevails?
Moving on to your 12-point formulation:
Q8: You examine an example of a cost (the magical substance) and then switch to an opportunity cost (interest rates). Is the analysis really the same? Suppose we turn the first situation into an opportunity cost situation. The government is providing it for free. However, a rich Saudi businessman looking for some amusement offers to pay you $5 for each ounce you’re willing to forgo. You take him up on the offer, and buy less that you would otherwise. Is your overall utility decreased? Is the overall utility of all Americans decreased? It seems to me that if there’s any cost, it must be borne entirely by the Saudi businessman. If we then look at borrowers paying people to forgo consumption, any cost must be borne by the borrowers. And the borrowers wouldn’t be borrowing money unless they were benefitting from it, so they must not be bearing a cost. Furthermore, the borrowers are borrowing money so that they can spend it. So do rising interest rates really decrease consumption?
Q9: In this imaginary world, is counterfeiting cost-free?
In a fixed price world, you bid up the nominal interest rate. The external effect is that a higher nominal interest rate reduces consumption demand, and production. (This is a Keynesian world with consumption determined by the Euler equation, and production determined by consumption). You do not take into account the effect on production. That’s the externality.
I’m still thinking that on net, there’s no externality. If you want to say that printing money has zero social cost but positive private cost, okay, but then you should also consider that holding money balances has zero social benefit but positive private benefit. I elaborate here.
“When you spend a dollar, you bid up prices.” Incorrect. Tunnel vision will identify that the price of a good will increase upon sale of a unit. While that is correct, peripheral vision will identify that the choice to purchase one unit of product/service A also results in a choice not to purchase product/service B (and C and so on). The price of good A goes up while the price of all goods not purchased goes down. In the forward production economy (goods are produced prior to the purchase by the consumer), sellers (assume the manufacturers are the sellers) must either save on their own to produce the goods or take a loan. The sale of good A allows a return to the savings or payment of loan. For sellers of goods B, C, etc., the prices will drop in hopes of a return to savings or payment of loans. On the large scale, products desired by consumers will yield sellers with profit. Products not desired will not have sellers with profits (loss of savings/loan default). This is the evolution of products (record, 8-track, cassette, CD, MP3). There exists no demand for 8-tracks, therefore there are no producers. The last of the producers likely were not profitable.
On to the moneyholders: they can either consume or save. If they choose to save (place money in the bank and expect small yields), the money is lent out. This money is available for potential producers. Some potential producers succeed, some producers fail. Small yields should be expected in this type of investment. If moneyholders consume, less is available for loans. Less loan availability will result in less production of goods (rationale for TARP, right?). Fewer goods produced will cause fewer choices for consumption (only good A exists) thus an increase in prices. At a tipping point, moneyholders will no longer perceive value in the consumption of good A and prices will stabilize. Future moneyholders will not consume and will build up savings and undo the aforementioned situation resulting in more loans/production/choices of goods and lower prices.
Depletion of the value of the dollar occurs when more dollars are put into the money supply, not when consumption patterns are changed. When more Nike shoes are available (greater supply) prices drop. When the price drops, has the value of the dollar changed? Prices of goods naturally decrease due to innovations in manufacturing, process improvements, and abundance of supply (if I see someone selling good D at a profit, I will develop a business model to determine if I can produce good D at a lower cost and therefore still sell the good at a profit while depleting competitors’ customer base). This reduction in price is an increase in buying power, not a reduction in the value of the dollar. I would state that because of naturally reducing prices, the dollar value goes up.
Government intervention in this process occurs when the Federal Reserve changes interest rates. Interest rates are changed to encourage consumption/lending (Greenspan, Bernanke), but is the new consumption/lending made by funds saved, or are the new funds “printed”? The government also intervenes via regulations. More regulations cause consumption choices to change (incandescent light bulbs). Regulations can also cause entry into production difficult, which will alter availability of products. Why have no new American automobile manufacturers come into existence in the past few decades? The government can also intervene by subsidizing certain types of products (ethanol, green energy). Cash for Clunkers typifies the government entry into the free market. The subsidy increased sales, but the natural reduction in supply the following year or years likely won’t occur now. Since the cars weren’t sold to begin with, I would expect a similar situation in the future, assuming no further government intervention.
Craig Reynolds:
While that is correct, peripheral vision will identify that the choice to purchase one unit of product/service A also results in a choice not to purchase product/service B (and C and so on).
The choice here is to purchase product/service A instead of holding money. That’s why there’s no corresponding choice not to purchase B or C.
My answer, to this, and to your previous question:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/10/my-answers-to-steven-landsburgs-two-questions.html
Short version. There’s no deadweight cost triangle of an externality (or tax) if the supply curve is perfectly inelastic. In the Keynesian case, with P fixed and M fixed, the supply of M/P is perfectly inelastic. Therefore no deadweight cost triangle.
Steve Landsburg, You say “However, the private cost of holding money — measured in forgone consumption — is positive.” I don’t agree: there is no private cost, indeed there is a private benefit as long as the money supply does not exceed what the private sector wants for the well known precautionary and transaction motives. Money brings benefits both social and private as compared to barter.
But once the money supply exceeds that level, then “holding money” becomes a cost as viewed by the private sector: so it tries to get rid of the stuff which is liable to boost inflation.
Your next few paragraphs deal with a hypothetical world where prices are fixed. That is plain unrealistic, and I don’t see what this hypothesis achieves.
To summarise, in the “no unemployment” world (or as I would put it in the “unemployment at NAIRU” world) the external cost kicks in when the money supply goes above the “precautionary and transaction” level. Inflation is the result, and EVERYONE suffers from excessive inflation.
Now what have I missed?
Ralph Musgrave:
Now what have I missed?
Pretty much the entire point.
If there is no private cost to holding money, why don’t you hold more of it than you do?
Nick Rowe: Thanks for this. It’s exactly right.
Considering how fast prices change from day to day at the store, I do not think we live in a fixed price world. However, debt payments do not change over time with changing interest rates.
When I buy something on fixed credit (say a house), I am “locked in” paying at that intrest rate for a very long time.
What would this mean then? What if interest rates are sticky and prices are flexible?