Arnold Kling has a good "rant against monetarism", triggered by my saying "My position is that a general glut can *only* be caused by an excess demand for the medium of exchange."
Arnold's response:
"Most economists believe this, or something like it. I used to believe it, or something like it. I think that it is a horrible, horrible, confusion."
(I only wish he were right about the first bit, because I can find very few economists who believe it, and I've been trying hard to get them to believe it.)
Let's start with where I agree with Arnold.
"If you took money out of the picture, the construction worker and the college student would still be unable to solve their problem. When it comes to the failure of wants to coincide, the existence of money is part of the solution, not part of the problem."
Bingo! Yes, absolutely. It is hard to solve the economic calculation problem, of who should produce what, with whom, and how, and who should consume what. And without monetary exchange, solving that problem would be much, much, harder. Monetary exchange is part of the solution, not part of the problem.
With monetary exchange, I can concentrate on deciding what to produce, and on what to consume. I don't have to concentrate also on the chain of barter transactions that might eventually lead me from what I produce to what I consume, which depends on all the other things that all the other people might want to produce and consume. That's why we have a monetary exchange economy.
But it is precisely because money is part of the solution, and a very important part of the solution to a very real problem, that when something goes wrong with money, the solution falls apart. If it really were as easy to solve the economic problem with barter as with monetary exchange, it wouldn't matter if something went wrong with money. We would just resort to barter.
If barter were nearly as easy as money, then an excess demand for the medium of exchange would not cause a recession. People would just switch to barter, and the economy would carry on as normal, with a slight increase in transactions costs.
And I also agree with Arnold here:
"Perhaps my rant should be directed against Walras' Law, which says that excess supply somewhere implies excess demand somewhere else. Who the heck enforces Walras' Law? Nobody. Entrepreneurs are trying to figure out how to make a profit. Their aggregate groping is what discovers a viable pattern of comparative advantage and specialization."
Yep. Walras' Law is false. Yes, I know we learn it in micro, and it seems to drop straight out of the budget constraints, when you add them all up. But it's false, horribly false. And it's false because, as Arnold says, there's nobody to enforce it. More precisely, if there were a centralised Walrasian auctioneer, trading every good for every good in one big market, and not allowing trade to begin until he had found the market-clearing vector of prices, then Walras' Law would be true. But there isn't, so it's false.
That Walras' Law doesn't work in a monetary exchange economy is obvious, once we start to count up how many excess demands and supplies there are. Let there be n goods, including money. Walras' Law says that the sum of the values of the n excess demands must equal zero, for any price vector. Rubbish. In a monetary exchange economy, with n goods including money, there are n-1 markets. And in each market two goods are traded: money; and one of the other goods. So there are n-1 excess demands for the non-money goods, and n-1 excess demands for money. That makes 2(n-1) excess demands in total, not the n excess demands in Walras' Law. And each of those n-1 excess demands for money is chosen to maximise utility subject to the quantity constraints in the other n-2 markets. So they aren't even mutually consistent. If you actually succeeded in buying or selling what you wanted in one market, you would want to do something different in all the other markets.
Setting n=2(n-1), we solve for n=2. Yep. Walras' Law would work fine in a monetary exchange economy with 2 goods, one of which was money. But who the hell would need money if there were only one other good? If there are only 2 goods, apples and bananas, how could we even tell whether apples were used as money, or bananas were used as money? If n=3, and we saw carrots exchange for apples, and carrots exchange for bananas, but we never saw apples exchange for bananas, then we would know that carrots are used as money. But n=3 means n is not equal to 2(n-1). So Walras' Law is nonsense in a monetary exchange economy. It's not even false; it's nonsense.
Forget Walras' Law. What about re-calculation?
The calculation problem doesn't solve itself. It takes people to solve it. The price system helps them solve it. Monetary exchange helps them solve it. But it isn't easy to solve. And it never really does get solved, because there's always the chance another entrepreeur could come along and solve it better. And if technology, resources, and preferences are changing as well, people have to keep re-solving it. That's what I take to be the re-calculation problem.
But that re-calculation is happening all the time. What's it got to do with recessions?
Sure, sometimes a really big real shock comes along, like the rise in oil prices in the 1970's, or a war, and it takes a lot more re-calculation than it normally does. And OK, a financial crisis isn't exactly like a change in the underlying tastes, technology, and resources of Walrasian general equilibrium theory. But you don't have to try hard to convince me that it too would require a re-calculation. And maybe output would fall while we are trying to figure out how to re-solve the economic problem. Maybe even employment would fall too. "Hang on guys, don't commit to doing anything quite yet, while I try and figure out where you should best be working now that everythings changed". I'm sure every central planner or local manager has had to say that at some time or another.
[Added for clarity: this is the point at which I start disagreeing with Arnold.]
But I just can't buy it as a full story of recessions. It's the general glut thing that's missing. Stuff gets easier to buy in a recession, and stuff gets harder to sell. That's an essential part of what makes it a recession. To say that stuff is harder to sell and easier to buy is meaningless outside a monetary exchange economy. In a barter economy, selling stuff is buying stuff. When you are trying to sell you are trying to buy at the very same time. A thing can't be harder or easier than itself.
What makes a recession a recession, and something more than a bad harvest, or a re-calculation, is that most goods, and most labour, gets harder to sell and easier to buy. And I really want to call that an excess demand for money. Because it is money we are selling stuff for, and it is money we are buying stuff with. And if I've also got a theory as well, which says that an excess demand for money will cause a drop in output and employment, and an excess supply of goods and labour, that's just icing on the cake.
This probably won't convince Arnold. But it's why I believe that general gluts — recessions — are always and everywhere a monetary phenomenon.
Worthwhile Canadian Initiative 
Hello Nick!
With regards to my question about ease of selling and buying, it seems totally dependent on expectations and preconceived notions of worth.
For example with houses, it’s only a buyers market if people think the houses are worth more than the going market rate, and likewise, only a sellers market if people think houses are selling for more than the market rate. However, what concerns me, is that whenever there is a sale, there is a purchase, and whenever there is a purchase, there is a sale. Every time a buyer thinks they got a good deal, surely the seller thinks they also got a good deal (otherwise they wouldn’t do it). Sure there are exceptions, but we are talking about aggregate so I hope we can ignore them. It follows, that for every person who thinks it is a buyers’ market, there is another person who thinks it is a sellers’ market.
For example, if I think a house is worth 300,000, but I see it selling at 200,000, I will happily buy it, thinking it’s a buyers’ market. But the person who sold it to me (ignoring the exceptions) clearly thinks the house was worth 200,000 or less. If I own a house, and think it’s worth 300,000, but I could sell it for 500,000, I think it’s a sellers market, but obviously the person who bought it off my thinks the house is worth 500,000 or more.
If my example makes sense, surely only half or less the people could be considered rational.
Look forward to your thoughts!
James
James: If the housing market was clearing the price history would be a martingale. But it’s not. The market clearly trended downwards in what became a very predictable manner and housing forwards were in backwardation. There was no way to arbitrage it since you can’t short physical houses which is why the trend could persist. So liquidity collapses and bid/ask widens. A small number of buyers transact at the ask (every day another sucker…) but soon learn the meaning of buyer’s remorse as the market continues to trend downwards towards equilibrium. The fact that a few people momentarily felt OK about their purchase has nothing to do with market efficiency.
Nick:
I’m afraid that I’m having a terribly difficult time following your discussion of Walras’ law.
There are, of course, theorems that prove the validity of Walras’ law under a set of maintained assumptions. So when you say that the law is false, you obviously mean that one or more of these maintained assumptions is violated. Evidently, it is the assumption that prices are market-clearing that seems to be the problem. This assumption is, of course, nothing more than part of the standard solution concept that is applied to competitive market settings (centralized markets with price-taking agents).
Or, is it more than this? Do you also take issue with the assumed market structure; i.e., the idea that all trade occurs in a centralized market? The way your discussion proceeds leads me to believe that you have in mind some decentralized exchange process. Can you be more precise about the nature of this “monetary economy” that you speak of?
Perhaps you have in mind sequential pairwise meetings, as is the case in standard search models? But in those models, prices are determined not by an auctioneer, but by bilateral bargaining. And I’m not even sure that it makes sense to speak of Walras’ law in such an environment. (That is, telling us that Walras law is false is a nonsensical statement).
Anything you can say to clear my thoughts on this matter would be greatly appreciated. I am enjoying the general discussion.
Hi David: yes, I wasn’t as clear as I should have been.
Walras’ Law holds trivially in market clearing equilibrium, since all excess demands are zero. And so they must sum to zero.
Here’s a sketch of what I mean:
The standard proof of WL goes like this: a consumer with endowment vector E maximises U(X) subject to P(X-E)=0. Aggregate that budget constraint across all individuals, and you get WL.
The whole vector of demands X is determined in one decision. That makes sense provided: there’s one big market, where every good can be exchanged for every other good; the individual expects he can buy and sell as much of every good as he wants.
But:
1. Suppose he gets to market, and finds he can’t buy any apples, because there’s an excess demand for apples. His demand for apples is still determined as above, but he reformulates his demand for every other good by maximising U(X) subject to P(X-E)=0 AND a=0. So you get a demand function for every other good coming out of that second doubly-constrained maximisation problem, and a demand function for apples coming out the first problem. So when you add up all the excess demands, they violate the budget constraint. Simple example: I go to the store with $5 planning to buy $5 worth of apples, but there is none. So I buy $5 of pears instead. So I demand $5 of apples, plus $5 of pears, but only supply $5 of cash.
2. There is not one big market where all n goods can be exchanged for any other good, and n excess demands. There are n-1 markets, where each of the n-1 non-money goods can be exchanged against 1 good, which we call “money”. The apple market has an excess demand for apples, which equals the excess supply of money in the apple market. So there are n-1 little Walras Laws, one for each market.
There are n-1 excess demands for money, and if you add them all up, you will only get the sum of the excess supplies of all the other goods if no individual expects to be constrained in purchases or sales in any of the markets. But, if the price vector is not at market-clearing equilibrium, somebody won’t be able to buy or sell as much as he wants to, so will re-formulate his Utility maximisiation in all the other markets taking those quantity constraints into account.
Don’t know if that’s any clearer.
James: remember though, a house in Ottawa is worth a lot more to a person who wants to move to Ottawa because he’s just got a job in Ottawa, than it is to a person who wants to move away because he just got a job somewhere else. So both gain by the deal, in any market.
Nick: I see a crack in the clouds. Let’s see if I’m following.
Consider a standard choice problem, max U(x) s.t. p(x-e)=0. Suppose there is a unique solution x(p). We add up the demands and solve for p* in the usual way; x(p*)=e. We may without loss interpret x as a vector of time-dated commodities, and p as a set of intertemporal prices. The choice of numeraire is irrelevant. If there are n goods (n dates), then there are n-1 prices. You might want to say n-1 “markets,” but that’s not quite right. There is a single market; it opens at the beginning of time and clears immediately. As time unfolds, claims are simply redeemed as they come due. There is no need for a medium of exchange, obviously (which I define, btw, as an object that circulates as a means of payment).
You want to consider the following thought experiment. Imagine that an agent enters the world thinking that he has to solve the choice problem above. Consider some p that does not clear markets. At the given p, the guy was planning to buy x1(p) at date 1. To support this planned purchase, he has issued claims against his future endowments. But imagine that x1(p) is not available. Then what does the guy do?
Your assumption is that he re-optimizes from date 2 onward…subject to the same price vector (?)…and proceeding as if date 1 goods and prices never existed (it is now date 2, after all). The new solution to his choice problem (ignoring x1) is x'(p); which will generally be different that the original solution x(p). So, of course, if we add over all the x(p), x'(p), x”(p), etc…we get nonsense. In particular, Walras’ law does not hold. (Not too surprising, since we are no longer describing a Walrasian market structure).
Something tells me that I am missing a part of your argument. In particular, I’m not sure where money fits in here. I have assumed that people can keep their promises, so their time-dated claims can be used to purchase whatever they want as time unfolds. The problem arising above appears to have nothing to do with money, per se.
Also, I wonder what you assume about peoples’ expectations. Do they anticipate these trading difficulties? Sorry for all the questions. Let me know if they are peripheral to the main point you are making.
Nick and K:
Hello K! I am afraid your answer was too technical for me, and also suffers from a similar problem that brings me to…
Nick!
I was hoping to use houses just as an illustrative example, rather than specifically talk about problems associated with houses. Substitute in any good. The idea is that whenever a transaction occurs, both the buyer and seller think they got a good deal, making it difficult to characterize what exactly a buyers market is, or a sellers market.
This is all really a roundabout way of trying to illustrate that I really don’t see the difference between bartering and buying and selling within this specific context. (I obviously understand the general distinction).
You seemed to imply that this sort of idea of a buyers and sellers’ market was unique to a system using money, my feeling is that the situation is the same. The fundamental idea is that there is a buyer and a seller, whether they get a good or service in return or money in return shouldn’t really matter. My conjecture is that the idea of a buyer’s market and seller’s market is just in people’s heads about what they actually value the good at.
I.e. if there is a bumper crop of rice, there is now a “buyers market” because the farmer is willing to accept less goods and services for his rice. The towns folk are happy because they valued the rice higher than what they can get it for now. However, maybe you weren’t ruling this out? I suppose that is my question.
Are you suggesting a barter economy rules out buyer’s and seller’s markets? (and thus the equivalent recession you implied)
Thanks, and look forward to both your thoughts!
“Simple example: I go to the store with $5 planning to buy $5 worth of apples, but there is none. So I buy $5 of pears instead. So I demand $5 of apples, plus $5 of pears, but only supply $5 of cash.”
So I’m allowed to post demand for $10 worth of goods when I only have $5? That’s not what is usually meant by a demand curve.
The whole reason it curves is to trace out the way you trade off more of one thing for less of another, and the trade-off comes from the fact you have a budget constraint.
How is your example different from this simple example?
I have $10, I demand 4 Porches (price $100,000 each). There is excess demand for Porches.
David: This is really good!
You have understood my objection 1 to Walras’ Law exactly. (That objection has nothing to do with money per se). Let me just add that if the price vector p is not at market-clearing, then the sort of problem your consumer faces (being unable to buy or sell as much of x1 as he wants) must happen for either the buyer or seller for at least one good.
Your x'(p) is called a “constrained demand function”. (Or sometimes an “effective demand function”). Your x(p) is called a “notional demand function”.
You have re-interpreted my thought-experiment as a of sequence of dated goods, where the market can re-open in period 2, which is interesting and entirely legitimate, though not the thought-experiment I had in mind. In my thought-experiment, if you found yourself unable to buy x2 for example, you might go back and buy some more x1 (if x1 and x2 were close substitutes), which you couldn’t do in your thought-experiment because it would mean going back in time.
What’s this got to do with money? Well, because once you recognise that people can re-formulate their plans, taking these quantity constraints into account, then the market structure really starts to matter. For example, suppose your consumer is rationed in x2. In your thought-emperiment, with a dated sequence of markets, he can’t go back and re-visit his demand for x1, because that would mean travelling back in time. But in my thought-experiment, he can go back and revise his demand for x1. So when you and I solve the same problem, we will get different answers, because we have assumed different market structures.
A monetary exchange economy has a different market structure from a barter economy. So, if the price vector is not market clearing, we will get different answers for a monetary and a barter economy, just as you and I got different answers above. With n goods, a pure barter economy has n(n-1)/2 markets, where all possible combinations of pairs of goods can be traded. A pure monetary economy will have (n-1) markets.
Take a simple example with 3 goods, where good 1 is money. There is a market 12 and a market 13, but there is no market 23. Assume U() is separable, for simplicity. Assume good 1 is also numeraire (it doesn’t matter, of course). Start with the equilibrium p2 and p3. Now double both p2 and p3. What happens? There’s an excess demand for 1, of course. So the markets 12 and 13 will both fail to clear. If we were in a barter economy, which had a market 23 as well, we would still get the efficient trades of goods 2 and 3, because the relative price p2/p3 is still correct (I assumed separability). But in a monetary exchange economy, where market 23 does not exist, we won’t get efficient trades in 2 and 3. Because to trade 2 and 3, you first have to trade 2 for 1, then 1 for 3. And you will be quantity-constrained in one of those two trades.
Let 2 be consumption, and 3 be labour, and you get an excess supply of consumption and labour, and low levels of consumption and employment, even though W/P is at the market-clearing level.
You ask how expectations of these quantity constraints are formed. Good question. It matters. My answer is “Dunno”. The old 1970’s literature implicitly assumed rational expectations, though they didn’t understand that that was what they were doing. It’s the expectations of future quantity constraints that are tricky. “Will I be able to sell my labour next year?” Expected future income may not be a choice variable. It may be determined by a quantity constraint.
Still not sure if this is clear.
This is on-topic, and important. I want to explain it to you.
Adam: the apple seller sees I have $5 in my hand, and I really do want to buy $5 of apples, and I would buy them if he had apples to sell. The pear seller sees I have $5 in my hand, and I want to buy $5 of pears, and I really do buy them. The Porsche seller sees me with $5 in my hand, pressing my nose against the window, and tells me to get lost, because he knows I wouldn’t buy it if he offered me one at $40,000.
Yes, the $5 demand for pears is in some sense a “false demand”, because I wouldn’t buy those pears if I could buy apples. But the pear seller doesn’t care about that. He might not even know it. And I can’t buy apples, so I do buy pears. Eventually, it is true, I might stop going to the apple seller, asking if he has any apples, so we would stop seeing the line-up at the apple store. I’m a “discouraged apple buyer”. just like the “discouraged worker” who stops looking for work because he figures there isn’t any, and is no longer counted as unemployed.
James: suppose there’s a bumper crop of rice, and the price of rice is sticky. In barter, the rice/wheat market would be a buyers’ market for rice and a sellers’ market for wheat.
In a monetary economy, we never talk about buying or selling money. We talk about buying or selling rice. So the rice/money market is a buyers’ market.
James: A price may be above or below equilibrium. Buyer’s market means above, seller’s below. That’s not just something in people’s heads. A Soviet grocery store is an example of a seller’s market. It’s easy to sell because the price is way too low, but nothing left on the shelves, the opposite of a glut (a buyer’s market). If you buy in a buyer’s market you are getting a lousy deal. The fact that it obviously was worth more than that to you at the time doesn’t change the fact that there’s a very real sense in which you are paying too much. And the price is probably going to drift down and you are more likely than you would have been in an efficient market to end up regretting it.
To be more clear about my comment above: a martingale is a process whose current value is it’s future expected value. A backwardated forward curve means that you can contract now to buy something in the future at a price that’s lower than the current price. Clearing means exactly all the supply is being sold; i.e. no neighbourhoods full of boarded up houses being used by no one; no line ups for bread.
Nick wrote:
The old 1970’s literature implicitly assumed rational expectations, though they didn’t understand that that was what they were doing.
I don’t think the hypothesis of rational expectations is defensible.
It claims that on average economic actors do not get ‘surprised’ irrationally, they act in their own perceived rational future interest on average.
In reality irrational “surprises” happen all the time. Some of the worst crashes in history were negative surprises snowballing – say the ’89 crash – with little ‘real economy’ basis in the magnitude of the crash. (The May 6 2010 ‘flash crash’ is probably in that category as well.)
Some of the worst bubbles in history were positive, irrational expectations snowballing.
These psychological phenomena, if they are large enough, if they last long enough, set a global sentiment and feed back on the real economy – and they do this all the time. They do not average out, unless your time scale is in the thousands of years.
I’d also expect this to get worse in the future. People are more connected to each other than than they used to be, communication and propagation of information is faster and more global than ever before. This, considering that we have fundamentally unstable feedback loops, sets us up for higher volatility.
And yes, acknowledging this also means that ‘big actors’ like governments or central banks adaptively ‘smoothing’ out these irrational cycles should be considered as a response: to reduce human suffering – to ‘buffer’ positivism when it’s in over-supply, just to feed it back into the system when negativism rules.
And, given that the phenomenon is human and partly irrational in nature, measuring and controlling it via the money supply alone is not enough.
Nick- Thanks for the answer to my question. It seems both more understandable and plausible to claim that it is the desire of people to ‘hoard’ a store of value in the face of future scarcity and the dual role of money as a store of value and MOE contributes to demand short falls.
One other question that I think I get from your writing, but want be sure. Is it not only the MOE role of money but price ‘stickiness’ that is necessary to cause rescessions? Or are those possible in your model even if with perfectly flexible prices as long as there is an MOE (that also serves as a store of value) both necessary and sufficient?
And as a follow up, does your model assume flexible pricing under a barter system? I am not sure that completely makes sense if it does. If the source of price stickiness is search costs or coordination problems, real barter economies might have higher stickiness issues.
OGT: I assume that prices would be equally sticky under monetary exchange as under barter. In practice, they might be more or less sticky in one case than in another. I’m not sure.
Is price stickiness also necessary for recessions? The safe answer is “yes”; an instant fall in the price level would increase the real stock of money to whatever it took to eliminate the excess demand for money. But we can imagine cases where expectations were de-stabilising, so that a fall in prices caused people to expect a further fall, and so increased the demand for money. Not to mention the consequences of increased real value of debts. So the answer might be uncertain. I just assume price stickiness because I think most prices are in fact sticky.
Nick,
I think we can stick to my intertemporal formulation. All we need to do is to assume that the decision-maker, at date 0, goes through thought-experiments concerning what is likely to transpire in the future. (I.e., suppose I get to date t and that no date t goods are available?) We are in the realm of game theory here; not conventional competitive analysis.
What’s this got to do with money? Well, because once you recognise that people can re-formulate their plans, taking these quantity constraints into account, then the market structure really starts to matter.
Hmmm. What do you mean by “reformulate plans?” Are people prohibited from formulating a state-contingent plan? I mean, if I understand the environment, I understand that for a given p, my plan to purchase x may not materialize. If I can anticipate all possible future contingencies, then I come up with a state-contingent plan that maximizes my expected utility, subject to those pesky “effective demand” constraints.
Of course, everyone is playing the same game; and they formulate their state-contingent strategies accordingly, taking as given the play of everyone else (standard Nash assumption).
And now, to close the model, we need a solution concept. A Nash equilibrium, I guess.
Not sure what this has to do with needing money. If people can commit, as I have assumed all along, then claims to their endowments will be acceptable for payment.
Let me now move on to your example (sorry, I am thinking on the fly here).
You have a three good example. Let us imagine an intertemporal Wicksellian triangle. Good j=1,2,3 represents output at date j. There are three agents, j=1,2,3. Agent j wants to consume good j. But agent j has an endowment of good j-1 (modulo 3). There is a complete lack of double coincidence of wants here.
Despite the lack of double coincidence, money is not necessary (this is contrary to Kling’s assertion–he obviously does not know monetary theory). In particular, an Arrow-Debreu market with 2 relative prices will do the trick. For that matter, cooperative exchange will do the trick too.
Imagine now that agents 2 and 3 lack commitment, but that agent 1 does not. Agent 1 is the person endowed with the asset that pays off in the “long run,” date 3. It is natural here to let a claim to this good serve as money, and that agents meet in sequence over time: 1 acquires good 1 from 2 in exchange for money (good 3). Then, 2 acquires good 2 from 3 in exchange for money (good 3). Then agent 3 redeems his money for good 3. This is a monetary economy.
Let’s see, instead of 3 agents, assume a continnum of 3 types of agents. Then we can speak of a sequence of competitive spot markets. We use good 3 (money) as the numeraire; so price vector is (p1,p2,1).
OK, you say to start in a competitive equilibrium. Fine. Now, double both p1 and p2. OK, do that. What happens?
Your claim is that in barter (AD market), we’d still get efficient trade in goods 1 and 2 because the price ratio p2/p1 remains unchanged. I am not sure I understand/agree with this statement. The demand for good 1 here depends not only on that relative price, but also agent 1’s wealth. And if p1 and p2 double, the purchasing power of agent 1 is diminished (recall, he owns good 3).
I think that I’d better stop here. Remember your post: Why Blogging is Hard? It sure is.
David: “The demand for good 1 here depends not only on that relative price, but also agent 1’s wealth. And if p1 and p2 double, the purchasing power of agent 1 is diminished (recall, he owns good 3).”
Agreed. It changes the distribution of wealth in your model, because one person owns all the money.
Here’s my model, which gets around that problem:
There are 3 goods: backscratching services, leisure, and gold (worn as jewelry). Separable Utility function U(Y,L,G). Gold cannot be produced.
All agents are identical, except: half the agents only enjoy backscratches on odd days, and the other half only on even days. You can’t give and get a backscratch on the same day.
All agents are anonymous, so will only trade backscratches for gold, not for promises of a future backscratch. So gold becomes money. Let gold be numeraire. Price of a backscratch is P
Monetary equilibrium:
1. “Goods market”: Marginal Utility of receiving backscratch/P = MU of gold.
2. “Labour market”: Marginal disutility of giving backscratch/P = MU of gold.
(“MU of gold” really means the MU of one extra bit of gold jewelry worn forever).
With flexible prices, P adjusts to satisfy both 1 and 2, so we get efficiency, where the MU of receiving a backscratch = the Marginal disutility of giving a backscratch.
Now suppose the government raises P above equilibrium (or, suppose P stays fixed and half the gold vanishes).
We get an excess demand for gold, and an excess supply of backscratches and leisure.
Equation 1 still holds, but at a lower quantity of backscratches. (exchange is voluntary, so the short side of the market determines quantity traded, and that’s the demand side of both markets.
Equation 2 no longer holds. There is an excess supply of labour. Involuntary unemployment, even though the real wage stays at 1 (i.e if you give one backscratch today you get enough gold to buy one backscratch tomorrow).
Now suppose we drop the assumption that agents are anonymous, so we allow barter. “I will scratch your back this period if you scratch mine next period”. We get the efficient quantity of backscratches again.
(I have ignored time preference in the above, for simplicity. This is fine if the “day” is short).
“All agents are anonymous, so will only trade backscratches for gold, not for promises of a future backscratch. ”
How is gold not a promise of a future backscratch? It seems that you are imposing a condition on your model that says that there is zero debt — no one can buy and sell “back-scratch coupons”, but they can buy and sell gold. Now given that the market structure is important, shouldn’t your market structure be a plausible model of the world?
Suppose you changed your model to allow people to borrow gold from each other. Then, you can imagine someone that wants a backscratch, but does not have gold from performing a previous backscratch to get one today. I.e., they can pull consumption forward, just as the storage of gold allows them to defer consumption.
In your model, it is possible to defer consumption, but not possible to pull it forward. That is why your model has a market disequilibrium. If you allowed people to borrow gold (i.e. go short) as well as to store gold (go long), then the disequilibrium goes away.
Moreover, then you would ask — do we live in a world in which no one can go short money? The answer is no. They do not have a cash in advance constraint, they have a credit constraint. There is still a constraint, and you still have recessions, but not because of the medium of exchange per se.
This is not to say that you can’t formulate models in which an increase in the desire to save in the form of the medium of exchange causes recessions, even if the overall desire to save does not increase.
But I don’t think you can formulate such a model in an economy with a financial sector in which you can go both long and short the medium of exchange.
Once you allow that, all that matters is the interest rate, and in an zero-rate context, the last thing that there is an excess demand for is the medium of exchange.
RSJ: That model is not about money vs, bonds. It is about money vs. barter. So adding bonds would merely be a totally unnecessary complication.
If I were talking about money vs. bonds, I would do a different model.
Here’s a similar model with bonds in it as well: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/the-is-curve.html
Nick, I will look at the post — thanks for the link.
But in the specific case of the model presented here, the only reason why there is recession is because it is possible to defer consumption, but not possible to pull forward consumption.
Therefore any non-zero increase in the demand to defer consumption must result in lower output, since this demand cannot be balanced by households pulling forward consumption.
If you had bonds, then households could sell bonds and use the proceeds to buy backscratches and all the markets would clear (assuming the bonds were always correctly priced :)) The households would not be constrained by their gold holdings.
RSJ wrote: “Once you allow that, all that matters is the interest rate, and in an zero-rate context, the last thing that there is an excess demand for is the medium of exchange.”
That depends on what the real interest rate is. If the real interest rate is -4%, if output is shrinking (or not growing as much), if prices are deflating (or not inflating as much), then there can still be plenty of rational demand for the medium of exchange as well: both individuals and corporations find no better place to put their cash into.
(Not to talk about irrational demand when unemployment is high and the economy is in trouble: the desire for safe, government-guaranteed deposits. That kind of sentiment can catch corporations as well and can induce them to keep more in deposits and bonds than they really should. “Be safe financially” is a strong survival instinct.)
RSJ: “In your model, it is possible to defer consumption, but not possible to pull it forward. That is why your model has a market disequilibrium.”
That’s not right. everyone has a stock of gold. Each individual can bring consumption forward by reducing his stock of gold. In equilibrium the representative agent is neither increasing nor reducing his stock of gold (except doing one on odd days and the other on even days). It goes into market disequilibrium because I put it there, by fixing prices at the wrong level, and not letting prices fall in response to excess supply of haircuts.
Nick:
Alright, let’s take your example. The structure, by the way, is very similar to Townsend’s turnpike model. As such, there is no need to stick gold (money) in the utility function; a medium of exchange will be necessary if agents are anonymous.
And, by gosh, can we not just consider a standard OLG model? Of course, in this case (as in Townsend’s), we have n = infinity (the number of prices, or markets). Hope this doesn’t cause a problem for Walras’ law.
So let’s consider an OLG model. If agents are not anonymous, then we can support efficient trade; say, by relying on trigger strategies for noncompliance. No money is needed.
But if agents are anonymous, a monetary instrument is needed. Consider a stationary equilibrium; there is a constant price level, P1 = P2 = P3 = … = P.
Now, imagine that the government (or whatever) to lower P1 < P (a transitory shock). Or, for that matter, consider some arbitrary and random pattern P1, P2, …
The statement you seem to want to make here is that: [1] given a non-market-clearing price system in a monetary economy, we have excess demands and corresponding excess supplies all over the place. I agree; though I’m not sure what this has to do with the complaints about Walras’ law. [2] in a non-monetary (credit) economy, efficient trade is still possible. I agree.
So the basic lesson is that when the value of an economy’s medium of exchange is somehow screwed up, this screw up affects all markets–in a way that would not happen in a pure credit economy. If this is the basic idea, then I’m fine with it. Though, now I’m not sure why we talking about Walras’s law.
Perhaps you can tie it all together for me?
David: we are on the same page.
Let me relate it to Walras’ Law.
In an economy with one centralised market, and n goods, there are n excess demands.
In a monetary exchange economy, with n goods, there are n-1 markets, in each of which one good is traded against money. Let me propose “Nick’s Law” for a monetary exchange economy. Nick’s Law is trivial, but true.
Nick’s Law says that in each of those n-1 markets, the excess demand for the non-money good must equal the excess supply of money in that market. P1X1=M1. P2X2=M2, etc. So there are n-1 excess demands for non-money goods, plus n-1 excess demands for money. And those 2(n-1) excess demands sum to zero trivially, since each pair sums to zero in each market.
And Nick’s Law has nothing to do with anyone’s budget constraint. It follows simply from the fact that people pay for stuff they buy. To answer Arnold Kling’s question “Who enforces Walras’ Law?”. Well, nobody enforces Walras’ Law, because it’s false. But who enforces Nick’s Law? Answer: the cops!
“That’s not right. everyone has a stock of gold. Each individual can bring consumption forward by reducing his stock of gold.”
What happens when enough people run out of gold?
What happened to my reply(ies) to RSJ?
TMF: they won’t, in my model.
I unpublished your other comments because they were off-topic. This post is about money, not debt.
Nick @7:53
“Each individual can bring consumption forward by reducing his stock of gold.”
They obtained the stock of gold in period n, by deferring consumption in that period. In period n+3, they reduce their stock of gold and increase consumption. The entire operation is a deferral of consumption by 3 periods, in which households consume in period n+3 what they could have consumed in period n.
If the only way to obtain gold is to sell a good (your hypothesis), then the only way to obtain a positive stockpile of gold is to sell goods and not spend all of the proceeds. So in this model, you must first save before you can dissave.
If you start the model of with a helicopter drop of 100 coins in period 0, then there can be 100 gold coins of savings and 100 coins of pulled forward consumption at any point in time. But that’s it. You have an arbitrary constraint on savings and dissavings constrained by the quantity of coins. In general, the savings and dissavings desires wont have anything to do with the quantity of coins.
The key here is that the only way to obtain gold is to sell a good and not spend the proceeds on another good.
That is the channel by which demand for gold spills over into disequilibrium in the goods market why you believe that OMO have an effect other than expressed in interest rate effects.
But once you can obtain gold without selling goods — by selling bonds — then it becomes possible to both defer and pull forward consumption by amounts far greater than the stock of gold.
As soon as you introduce a financial sector, then is no such thing as an excess demand for money that is not equivalent to an excessively high interest rate.
But in barter markets, you can also have excessively high interest rates (e.g. with corn bonds) that have the exact same effects.
The only place where money is “special” is when you assume both a monetary economy and remove the financial sector — e.g. no money markets or banks. Or equivalently, you impose a cash-in-advance constraint, so that no can sell a bond and then spend the proceeds in the same period. Or equivalently, you assume that bond holdings are always zero.
But unless you somehow remove the financial sector from your monetary model, you aren’t going to get recessions just from an increase in the demand for the medium of exchange in which overall savings demands are held fixed. What is important is the overall savings demands and whether the interest rate clears those demands.
RSJ: A stock of gold exists. All individuals are identical (except for the odd/even timing). Therefore they all have gold.
You can introduce bonds into the model, but if barter is allowed, you can’t get a recession. Unemployed backscratchers just scratch each others’ backs, even if there is an excess demand for gold, bonds, whatever.
Right, introduce barter and the recession goes away. Introduce bonds and the recession goes away, too.
The recession is only there because you don’t have enough gold to meet savings demands.
As soon as you de-couple the ability to save from the (fixed) quantity of gold, then savings demands will be met and the recession goes away.
So the recession in your example was “fake”, in the sense that it only existed because you required monetary exchange but didn’t allow for money markets. Relax either assumption and the recession goes away.
Or perhaps you changed the model? The gold stock is not fixed, and everyone is not the same; their preferences are the same but their state, in terms of endowments, is alternating.
You have two generations, with those who cannot scratch backs on odd days, and these have more gold on odd days, with which they buy backscratches. The scratching switches some of the gold stocks back and forth between these two groups, in equilibrium.
The general equilibrium is not a micro-equilibrium, in the sense that the gold holdings are constant for each person across time. They alternate. The source of the recession is the assumption that you need gold in order to buy a backscratch, and you don’t have it. Introduce money markets, and you can borrow it, buy a backscratch, and the next period you can sell a backscratch and repay the debt (or roll it over). No recession, unless it it due to the interest rate being too high.
OK, the above may have been a little incoherent. Let me try another tack.
In an economy in which half the group can produce output on odd days, and the other half can produce output on even days, and the output cannot be stored, then if you were in a pure barter situation with no bonds, then only those who can produce output would do so, and 1/2 of the actors would go without any output at all times.
Now if you assume diminishing marginal utility, that means that overall utility would be lower than if those who can produce output are able to somehow “sell” their output to those who have nothing to give in return in the current period. Therefore, for a given disutility of labor, overall output would be lower in the no-bond situation.
Now, if you add the ability of people to issue IOUs that can be redeemed for future backscratches, then overall output and employment would go up due to the gains in trade.
Similarly, if you convert this economy to a monetary economy, then “money” in this economy is nothing more than an IOU for a future backscratch, Output would again go up.
But gold isn’t a particularly good substitute for an IOU, because the total stock of gold is fixed, whereas the stock of IOUs needs to be flexible in order to respond to changing savings preferences. If you only have gold, then a decrease in the demand for consumption goods in the current period could be because people prefer leisure, or just don’t want consumption, or it could be because they do want more consumption, but only in a future period. In the former case, it’s not a recession. But you don’t which unless you have a bond market. The bond market channels the decrease in the demand for present consumption goods into an increased demand for present capital goods, so that the economy does not experience an overall decrease in demand in the present period if there is a general shift away from present consumption and towards future consumption.
So gold satisfies the role of allowing intertemporal substitution, but it doesn’t send the right price signals when there is a shift in demand, which is what you expect since your economy is missing a money market.
So the source of the recession is that gold is only a good substitute for bonds if everything is fixed. When preferences or demands change, then gold stops effectively playing the role of bonds, and then you get the recession and you start reverting the lower levels of output and employment that you would see in the no-bond situation.
But given the economy that you described, what is important is that people can create and sell a non-produced good in exchange for the produced good when they are unable to produce. Anything that interferes with this will cause a recession. This has nothing to do with the transaction technology, but with intertemporal substitution, so it is fundamentally all about bonds, at least in the example you described.
RSJ: You have misunderstood it.
In the context of this model, “barter” means “If you give me a backscratch today, I promise to give you a backscratch tomorrow”. And the reason they can’t barter, and have to use money, is that they are anonymous, so that promise would be unenforceable.
It’s a simple way to get monetary exchange into the model. I could have used other ways, like assuming there’s a taboo against giving a backscratch to anyone from whom you have recently received one from. These are all just ways to make sure there is no double coincidence of wants, without having a very complex model with multiple goods. The temporal sequence isn’t essential. Though we do in fact observe people’s money balances rising and falling day to day. But this is very high frequency stuff, not like the much lower lifecycle frequency at which we see people save and dissave.
Now, one picky point: I know that finance people and business people frequently use the words “money market” to mean the market for short term bonds/loans. But when you are talking about models of monetary exchange, it is a really bad idea to use the words “money market” in that way. What you really mean is “bond market”. Because in a monetary exchange economy, all markets are money markets. Apples are bought and sold against money. But we call that market the “apple market”. Similarly, we should call the market where bonds exchange for money the “bond market”.
Now, suppose I introduced one extra agent into may model who was not anonymous (say, “the government”). The government could then make enforeable promises, i.e. issue bonds. Depending on the rate of interest offered on those bonds, and whether it would compete with gold, those bonds would be used as money. If I wanted to change the model, so that bonds weren’t used as money, so we could distinguish money from bonds, I would need to change the model again. I could assume, for example, that bonds could only be exchanged once a month, when the government office opened to record ownership changes.
Hmm, are you saying that I misread the model, or your intentions of the model? A model is there to enforce consistency; you can’t say “well, even though the money holdings are not constant, I’m going to assume that they are.” If the model says that they aren’t, they aren’t.
You have complete freedom in picking what you want to put into the model, but you don’t have any freedom in adjusting the outcome. Besides, how hard would it be to say that “aggregate money holdings are constant, but individual money holdings are periodic”. The word periodic only has a few more letters in it 🙂
More seriously, what OLG models tell you is that equilibrium for the economy does not equal equilibrium (in the sense of constancy across time) at the level of the individual. Now this poses a problem when you are constructing a representative agent, but not an insurmountable problem — your representative agent will not behave the same way as an individual, that’s all. The micro individuals (and firms) will have a lifecycle, whereas the representative agent will not. The overlapping lifecycles will lead to emergent effects due to interactions between individuals and firms in different states, and this should be the focus of macro, right? I.e. an individual borrows and repays, but the representative individuals merely maintains a certain debt to income level, in equilibrium. Similarly, government does not “repay” debt, but maintains some debt to GDP level. And firms do not repay debt, but maintain some capital structure of equity/debt. Total debt is not zero, in equilibrium.
About money markets, yes, you are right. But now I get to point out how non-sensical the treatment of bonds is 🙂 Basically, in a model when you say “bond”, you mean any financial claim that can be purchased in order to obtain a return across time.
But that includes equity, so you cannot impose a market clearing condition that bond holdings = 0. That is like saying that all financial asset holdings = 0, when we know that even without household borrowing, bond holdings would grow with the market value of the capital stock, and once you add household lifecycles, then you can have additional levels of debt. So you cannot argue that the interest is such that bonds = 0.
That, too, is an example of improperly using a representative agent to model transactions between actors in different states. The firm sells bonds (or equity) and households acquire them, and young households purchase a house on credit, going into debt which they repay when old, and the savings necessary to repay the debt come from the younger generation of borrowers. Similarly, firms that dissave by purchasing capital supply savings to firms that have already invested in previous periods and now need to earn a return on their investment, etc.
I would argue that the most basic models should take this transactional approach, and then accept what the various outcomes can be, in terms of the quantity of bonds and interest rates at any point in time; i.e the aggregate quantities (e.g. total output, total bond holdings, total employment) are derived from a proper accounting of transactions between individuals in different states, rather than imposing wierd ansatz without micro foundations (such as assuming that there is some aggregate “supply” of loanable funds which is an increasing function of the rate of interest), and then deriving the dynamics of the model based on the ansatz, rather than based on what the micro interactions predict.
About running out of gold, I think I need a model with workers and corporations and something “bank like”, which does business in currency.
Let’s say in year 1 the amount of money is just right vs. the amount of goods. The next year productivity rises 4%, and there are 4% more goods.
Does more money need to be “produced”? If so and the way the system is set up now, is all new (emphasize new) “money” demand deposits?
I’ve been trying all morning to figure out what’s bothering me about this post, and I think I’ve finally figured it out. What we have is an excess demand for savings. Because our economy is monetized and money keeps well, this generally manifests itself as an excess demand for money; however, one could easily picture a similar outcome in a barter economy.
Let’s say in this barter economy, for whatever reason people become convinced that next year’s harvest will be much smaller than this year’s. They want to save in order to smooth consumption. Obviously, the most obvious solution is for people to keep producing what they’re producing, but stockpile it. This doesn’t work because some goods are much more perishable than others. Some have higher carrying costs than others. Services could be considered to be instantly perishable. Now, the ultimate impact is not totally unlike in a monetary economy. Overall consumption falls, which means producers of rapidly perishable goods and services suffer, while durable items that could be bartered at a future date continue to be produced. (If you look at historical precedent, it might be hard to find given that most barter societies did not exhibit today’s degree of specialization; in most of those people would just shift their own production and most of the output loss would come from people producing goods they’re less skilled at producing.)
In a monetized economy, the set of durable goods used to save is much more restricted (generally just money and other financial assets), but the principle is the same.
Victor: “What we have is an excess demand for savings. Because our economy is monetized and money keeps well, this generally manifests itself as an excess demand for money; however, one could easily picture a similar outcome in a barter economy.”
I like your comment. You have addressed the key issue. That’s what many/most economists think. I think they are wrong.
Let’s take a barter economy, with 2 goods: wheat (perfectly storable), and berries (can’t be stored at all). No money or bonds or loans or anything else. There is only one market, where wheat is swapped for berries.
Start in equilibrium. Then, as in your example, people expect a bad wheat and berry harvest next year. So everybody wants to save more.
But notice, in this economy, desired savings is desired investment. Stores of wheat are both saving and investment. We could equally say that everybody wants to invest more. The demand for wheat, in terms of berries, has increased.
If the price is flexible, the price of wheat rises in terms of berries, but the market still clears.
Now suppose instead that the price is fixed (by law, or whatever). So there’s an excess demand for wheat in terms of berries. One produced good (berries) is in excess supply. But the other produced good (wheat) is in excess demand.
As always, if the relative price of two goods is fixed, and there’s a shift in relative demand, bad things will happen. But, there is no general glut of produced goods.
Furthermore, we would get similar problems if people suddenly expected a bumper harvest next year (and so want to store less wheat than they normally do). Desired savings = desired investment would fall. The demand for wheat in terms of berries would fall, and we would get an excess supply of wheat and an excess demand for berries.
“But notice, in this economy, desired savings is desired investment.”
I think this is the key point of dispute. Suppose that there was a barter economy in which desired savings was not automatically desired investment. This would require some form of bonds, of course.
Now, are you saying that
1) Such a situation is impossible in a barter economy
2) Such a situation is possible, but it would not lead to a general glut
?
RSJ: “Suppose that there was a barter economy in which desired savings was not automatically desired investment. This would require some form of bonds, of course.”
Or, it could be a durable, non-produced good, like land, rather than bonds.
OK, a simple model with berries, peaches, and land. No money, so each of the 3 goods can be traded with each of the other two.
Start in equilibrium. Then people expect a bad harvest of berries and peaches next year, so everyone wants to save (i.e. buy land). The price of land should rise, relative to berries and peaches, but can’t, because prices are fixed. In the land/berry market, there’s an excess demand for land/excess supply of berries. In the land/peaches market, there’s an excess demand for land/excess supply of peaches. But in the berries/peaches market, there can be market-clearing. Berry producers swap their berries for peaches produced by peach producers. There’s nothing to prevent the optimal production of berries and peaches, since there’s no reason for their relative price to change.
But if land were used as the medium of exchange (i.e. if there were no berry/peach market), then there would be underproduction of berries and peaches.
To give you the intuition, suppose there were a durable good that everyone wanted to buy, but it didn’t exist, so they couldn’t buy it. Venus dust. There’s an excess demand for Venus dust. But that doesn’t prevent full employment. Land is like Venus dust. Sure, it exists, but you can’t buy it, because everybody wants to buy and nobody wants to sell (at the fixed price). Same with bonds, in a barter economy.
Nick, I agree with your example, but this isn’t the only possible model of a barter economy, and in particular your example does not have a forward looking economy with long-lived capital goods.
Suppose that the bonds are not used to finance the purchase of land, but for the production of capital goods which themselves add to demand.
Imagine an economy of planters and harvesters. Land is free, but it’s jungle. You have to pay people to clear the jungle and plant it, and this requires 1 period of time. Once the land is cleared and planted (to keep things simple and avoid depreciation) assume it produces a harvest every period forever.
During the planting period, workers still need to be paid and they still need to eat, but they are not producing anything other than cleared land. You cannot take a piece of cleared land and pay someone with it. You can only pay someone with a claim on the future output arising from the use of the land. If you want, you can think of this as the “missing market” in your barter model.
Enter bonds — the firm sells consols for corn and uses the proceeds to pay wages (in corn) during the planting season, in which case it creates 1 unit of planted land. When the firm is in harvesting mode, it pays interest (in corn) to its creditors and pays wages (in corn) to its workers.
You have an arbitrage condition that says that the market price of the consols can’t be any different than the costs (in terms of wages) of creating more planted land in a given period. Suppose it takes 1 unit of labor to create planted land. Let corn be the numeraire. Instead of assuming that a single firm increases it’s own capital stock, assume that each firm has exactly 1 unit of planted land, and the number of firms increases.
Therefore the current period wage, w_n, is going to be equal to the price of consol owed by harvesting firm:
w_n = P_n/(1+R) + P_(n+1)/(1+R)^2 + ….
where R is the rate of interest and P_n is the expected corn profit delivered each period to bondholders. Note that P_n is a function of n, but R is not, because that would allow arbitrage. The interest rate on the consol cannot be expected to change from period n to period n+1.
And this means that if the firms expect low profits in the current period, but higher profits in the next period, then neither the current period wage nor the current period interest rate can adjust to allow the spot markets to clear.
Now you can argue that over the long term, P* and R* will be such that w* is the market clearing rate. But there is no reason to believe that over the short term this would be the case, as both w and R are not determined by the spot markets.
If the consol rate is too high, then the fact that there are a lot of people lining up, willing to be hired for cheap isn’t going to lower the wage rate in our model, because the same fact means that the enterprise value of all existing firms is plunging relative to that discount rate, and therefore the surplus value that the firm believes it can obtain from hiring the worker is falling just as fast as the asking wages — i.e. demand for labor does not increase as a result of a decline in the wage rate if the reason for unemployment is an excessively high discount rate, rather than an excessively high wage rate.
Oops — the last paragraph should read “the fact that there are a lot of people lining up, willing to be hired for cheap isn’t going to lower the unemployment rate in our model”, the rationale being that if w is falling, then so are the expected P_n’s.
Nick: “But in the berries/peaches market, there can be market-clearing. Berry producers swap their berries for peaches produced by peach producers. There’s nothing to prevent the optimal production of berries and peaches, since there’s no reason for their relative price to change.”
I think your argument is incomplete here. The berries/peaches market only pins down the relative prices of berries and peaches. Let’s say it’s 2 berries for a peach. How does that say anything about the total aggregate level of production of fruit?
All we know is that we should produce 2 berries for every peach to clear that market fine. That can be done with 2 berries and 1 peach or 4 berries and 2 peaches or…
You’ve still said absolutely nothing to explain why the barter economy can’t have a general glut of the fruit if the land is in excess demand.
Adam: OK. But I thought my “Venus dust” analogy explained why you still get the efficient output of berries and peaches.
Let’s see, in the berry/peach market, we have the following equilibrium conditions:
MRT berries into peaches = Pb/Pp = MRS berries into peaches
MU berries = (Pb/Pp)MPL in peaches x MULeisure
MU peaches = (Pp/Pb)MPL in berries x MULeisure
The price of land doesn’t appear in these conditions. If both Pb and Pp both double in terms of land, it doesn’t affect the equilibrium.
In order to affect those equilibrium conditions, you would need to assume that being unable to buy extra land affected the MU of leisure or MU of consumption differently for the peach producers than the berry producers. You would need some sort of asymmetry between berries and peaches.
If the utility functions were separable in berries, peaches, land and leisure, for example, everything should be unaffected.
RSJ: I think I am more or less following your model.
Here’s a simplified version.
There are two classes of people: rentiers, who own cleared land and can either consume the wheat it produces, or use that wheat to buy more land; and workers, who clear land and sell it to rentiers, for wheat, and consume the wheat. The only market is where land is swapped for wheat.
In this model, the price of land in terms of wheat is the very same thing as the real wage. It is also the very same thing as the inverse of the (infinite horizon) real rate of interest.
So yes, if the government by law fixes the price of land too high, then it is also fixing real wages too high (and the real rate of interest too low), and capitalists will choose to consume rather than save/invest, and the workers will be unemployed. There’s an excess supply of land (and labour), and an excess demand for wheat.
But this is really just the same story as unemployment caused by a binding minimum wage law.
Notice also that even though there’s an excess supply of land, it’s not a general glut of newly-produced goods, because it’s matched by an excess demand for wheat.
Notice also that the unemployment has been caused by the government setting the rate of interest too low, not too high.
“In order to affect those equilibrium conditions, you would need to assume that being unable to buy extra land affected the MU of leisure or MU of consumption differently for the peach producers than the berry producers. You would need some sort of asymmetry between berries and peaches.”
That’s easy to get, you assume that the bad harvest is only for one of the fruits. Suppose it’s not a generally bad harvest that reduces peach and berry output by exactly the same amount.
Suppose it’s only peaches that are expected to have a bad harvest. Then peach producers want to buy land instead of berries. Thus berry producers can sell their land to the peach producers but not their output. So that’s what happens, we get a glut of berries. Berry producers respond by contracting their output and taking more leisure today (this is also their optimal response).
Tommorrow the extra land the peach producers have allows the berry/peach market to clear at 2berries/peach (though less aggregate output as must happen with the bad peach harvest).
Adam: Peach producers will want to sell their peaches for land, not berries. Agreed. But if all prices are fixed, the berry producers will not want to sell their land. So peach producers won’t be able to buy land with their peaches. So, facing this additional quantity constraint, they revise their plans, and sell their peaches for berries instead. They do the second best thing. It’s better than letting the peaches rot.
But, in general, your point is correct. If prices are fixed, any change in the relative demands or supplies of peaches and berries will cause an excess demand for one and an excess supply of the other, in the market where they are swapped.
Things can go wrong in a barter economy. My point is that in a monetary exchange economy, more things can go wrong. You get all the things that would go wrong in a barter economy, plus some other things that cannot go wrong in a barter economy. Introducing (hypothetically frictionless) barter into a monetary exchange economy (even with prices fixed at the same level) is like opening up an additional set of markets, and those additional markets will sometimes allow additional mutually advantageous trades to be made.