(Almost) every economist has learned the Keynesian Cross. (Almost) nobody (IMHO) understands it. (Or, less provocatively, we all understand it differently). Here is my interpretation of the Keynesian Cross model. This is how I understand it.
(This is inspired by Steve Williamson's post. I partly agree and partly disagree with Steve, but have decided to start from scratch anyway.)
1. The short side rule says that exchange is voluntary, and so Q=min{Qd,Qs}. Quantity actually bought and sold is whichever is less: quantity demanded or quantity supplied.
2. The Keynesian Cross asserts that Qd is a function of Q. If the relationship is linear, then Qd=a+bQ. That's the demand function.
3. The Keynesian Cross assumes that Qs is strictly greater than than Qd. There is always excess supply.
Putting 1,2,and 3 together we get:
4. Q=Qd=a+bQ or Q=a/(1-b) as the solution to the model.
Q means the aggregate quantity of newly produced goods bought and sold. GDP, for example. The normal symbol is Y. But I deliberately chose Q, by analogy with quantities in simple micro markets. People get awfully confused by that strange "AE" and "Y" notation. AE (aggregate desired expenditure) just means aggregate Qd; and Y (income, output) just means aggregate Q.
The short side rule is absolutely standard. Nothing weird or Keynesian here. That's exactly how Q gets determined in a partial equilibrium demand and supply model, if you impose a binding price ceiling or floor.
3 is a bit weird. There is no automatic adjustment mechanism that ensures that we get to where Qd=Qs. There is no supply function in the model whatsoever. There is no production function, and no market for inputs, and no real wage. The whole supply side of the economy is just ignored, other than to assume that Qs must exceed Qd for the model to make sense.
And so, despite what you hear people say, 4 is not really an equilibrium condition in the normal sense of the word. It's a semi-equilibrium condition. A full equilibrium condition has Qd=Q=Qs. This semi-equilibrium condition has Qd=Q<Qs.
But it's 2 that's really strange. That's a very strange form of demand function. There are no prices in it. And the quantity demanded is a function of the quantity bought and sold. Why, for example, would the quantity of apples demanded depend on the quantity of apples bought and sold?
It wouldn't. But if there's an excess supply of apples and pears, the quantity of apples demanded would depend on the quantity of pears sold, and the quantity of pears demanded would depend on the quantity of apples sold. Because an increase in the quantity of apples sold will increase the apple producer's income, leading him to demand more pears. And an increase in the quantity of pears sold will increase the pear producer's income, leading him to demand more pears. Add up all the fruit across the whole economy, and the quantity of fruit demanded will be an increasing function of the quantity of fruit sold.
The Keynesian Cross AE curve is a quantity-constrained aggregate Engel Curve. An "Engel curve" shows the relation between quantity demanded and income. A "notional" Engel curve assumes that income is equal to that generated when you can sell as much as you want to sell. A "quantity-constrained" Engel curve assumes that income is constrained because you cannot sell as big a quantity as you want to sell. That's how Qd=a+bQ should be interpreted.
To my mind, the Keynesian Cross only makes sense in a monetary exchange economy. It would be complete nonsense in a barter economy. In a barter economy, if the apple producer cannot sell as many apples as he wants, and would demand more pears if he could sell more apples; and if the pear producer cannot sell as many pears as he wants, and would demand more apples if he could sell more pears: then the two of them would just get together and do a swap.
There is money in the Keynesian Cross. But it's not there explicitly.
Whether the Keynesian Cross is a good or bad model is a totally separate question. This post is simply about my understanding of it.
Thanks for that info. I'll answer the question you allude to at the end. It's a bad model. As is any model that tries to explain nominal aggregates without modeling the medium of account.
Posted by: Scott Sumner | January 28, 2011 at 06:46 PM
To my mind, the Keynesian Cross only makes sense in a monetary exchange economy. It would be complete nonsense in a barter economy...
I reiterate my earlier criticism that you are conflating flexible prices and the (non-)existence of money; your model of barter is imposed in such a way as to generate flexible (relative) prices and so of course the economy behaves in a classical manner. Barter with price rigidities would entail apples being swappable for pears only at a fixed rate; the apple producer may prefer having marginal pears to having marginal apples at the flexible rate, but prefers to have apples over pears at the fixed rate, giving us excess demands and supplies.
The role of money would be to push all the excess demands onto one good (money), which, unlike apples, gives us no utility when held in excess. The distortion is still macroeconomic in size, even under barter, though.
Posted by: david | January 28, 2011 at 06:58 PM
"then the two of them would just get together and do a swap"
Only if they could find each other. And if they couldn't find each other, it would depend on whether they could find other goods to trade in the hope of being able to find each other's products indirectly. And their willingness to do such trades would depend on how many other people they expected to be doing such trades, which would determine the anticipated likelihood of being able to eventually find the good they want.
But suppose everyone holds inventories of various goods, so that they can buy things via barter without first (or simultaneously) selling the goods they produce. In that case, their willingness to buy (by trading from their current inventories) would depend on their anticipated demand, just as in the Keynesian Cross model.
So there do have to be "media of exchange" in the very broad sense of things that people are willing to hold merely for the purpose of trading them for something else, but it is not necessary that there be a single, preferred medium called money, and indeed, essentially all storable goods could be sufficient media of exchange.
What's critical to the Keynesian Cross model is that people hold inventories. Usually we think they're inventories of money, but they don't have to be, and they don't even have to be inventories of any medium of exchange. They only have to be inventories of goods that are reasonably easy to sell. If you see something you want to buy, you put some of your inventory up for sale, and when you've sold the inventory, you take your proceeds and buy what you want with it.
Posted by: Andy Harless | January 28, 2011 at 07:51 PM
To my mind, the Keynesian Cross only makes sense in a monetary exchange economy.
Try thinking about an economy where production takes time. Seeds are only planted if the crop is expected to sell. Ships are built to order. In such an economy you can have an equilibrium (of sorts) in which workers don't get hired because employers don't expect to get sufficient sales; and the employers turn out to be right, because high unemployment means depressed demand.
It's not fundamentally about money. If the shipyard workers were paid with beer and burgers the problem could still arise.
Posted by: Kevin Donoghue | January 28, 2011 at 08:22 PM
Scott: but Q is a real aggregate. It's real GDP (or whatever).
The KC model leaves a lot out (like prices), but the one thing it does have is something I like: the demand for goods depends on realised sales of goods. Actually, that's about the only thing in the model. And that important insight is either missing or hidden in most models.
david: I am not conflating flexible prices with barter. In the KC model, people want to buy, and want to sell, but will only buy if they can sell. The relative prices must either be unimportant to them, or else are at a level that doesn't hinder trade. So why don't 2 people get together and say "I will buy from you if you will buy from me"? They could use exactly the same prices whether it's a barter or monetary exchange.
Andy: "So there do have to be "media of exchange" in the very broad sense of things that people are willing to hold merely for the purpose of trading them for something else, but it is not necessary that there be a single, preferred medium called money,"
Agreed, I think. There has to be some sort of underlying trading friction that prevents them doing a simple direct barter, and that also motivates a medium or media of exchange.
You are losing me on the inventories though. I think the simplest interpretation of KC is that all goods are services, and the only storeable good is the medium of exchange. "....and when you've sold the inventory, you take your proceeds and buy what you want with it." But in what form are those "proceeds" held?
And remember, the distinction between "buying" and "selling" is a way of talking that presumes monetary exchange. "Buying" means "selling money". "Selling" means "buying money". Otherwise buying apples *is* selling pears.
Kevin: interesting. But what about a barter deal like this: "I will plant wheat for you if you plant oats for me"?
Posted by: Nick Rowe | January 29, 2011 at 04:54 AM
Nick:
'But what about a barter deal like this: "I will plant wheat for you if you plant oats for me"?'
You are right that this works for very small economies where you know all the actors. Each actor can enact mutually beneficial "we intend to grow, hence we will grow" fiscal policy in essence and break out of the stag hunt paradox and end the recession.
Real economies are much larger, with none of the participants large enough to break the stag hunt paradox. All of them know about the paradox, but they do not (and must not) trust each other, and they are forbidden to contract on pricing in large groups as well - as such contracts would be way too easy mediums for pricing/barter-contracting cartels.
Recessions as a phenomena need no money to occur.
And, as historic examples show it, medieval economies where there was a lot of barter were hit by recessions even harder than modern economies: mostly because barter concentrated an asymmetrically large proportion of economic activities into just a handful central 'liquid' products such as wheat, wood, wool or iron (money substitutes, if you think about it) - leaving 'specialists' producers and services way too exposed to fluctuations in demand, and leaving them out in the cold of the winter, so to speak. In those systems growth was sluggish, and the standard of living was sub-par, to say the least.
Historic versions of barter economies did not work that well in practice.
The invention of money and especially the invention of flexible, not fully collateralised credit did a lot of good in stimulating rare, weird, risky activities - most of which were just an irresponsible waste of money but some of which turned out to be key stepping stones to our civilization today.
Posted by: White Rabbit | January 29, 2011 at 07:28 AM
White rabbit: You misunderstand me. I don't blame recessions on monetary exchange. I blame recessions on the fact that barter is so difficult in practice that we need to do monetary exchange. If barter were easy, we wouldn't have recessions.
Posted by: Nick Rowe | January 29, 2011 at 07:44 AM
Nick:
I have read back my comment and indeed it gives the impression that you replied to.
What I wanted to articulate was that I think in practice barter economies are vulnerable to recessions just as much. (Mostly because often a recession is dominated by a post-shock 'collective/group state of mind' thing - which phenomenon is independent of the presence of money.)
A successful barter economy needs what you mention: "easy barter". Furthermore, a barter economy, to fight (or outright avoid) recessions successfully, would require a critical mass of actors commit to "future growth" collectively.
I.e. barter economies, to fight a shock induced slump, would have to 'believe' in higher future expected demand.
Unless I misunderstood your notion of how this would work for large barter economies I don't see the fundamental difference there: getting out of a production slump still needs a 'stimulus' in form of a critical mass of participants breaking out of the suboptimal local minimum represented by the paradox. In a barter economy that 'stimulus' would be something like an agreement by thousands of corporations to mutually increase production - against current observed trends of (slump-depressed) demand.
Unless such a collective (basically centrally planned) 'barter agreement' can be fundamentally automated and made mechanic, I don't see how it's fundamentally different from current large stimulus and easing programs: the role of 'trillions of dollars' is taken over by 'thousands of barter contracts created on a mutual understanding'.
Especially considering that most non-trivial production facilities today would need hundreds of barter agreements themselves, to function - think car production, computer production or even construction. Each and every one of those hundreds of agreements would have to be revved up in lock-step unison to break out of the paradox - and this would have to be done for thousands of large producers on a potentially global scale.
QE looks really easy in comparison! But I might be missing something about how you think this would work out.
Thanks.
Posted by: White Rabbit | January 29, 2011 at 08:08 AM
How do you interpret aggregate demand, in theory, when Q = 0?
Posted by: anon | January 29, 2011 at 08:09 AM
anon: in the context of the KC model, if Q=0, the way in which Qd could be greater than 0 would be if people planned to sell their stocks of: bonds; old goods; land; and money, to finance purchases on newly-produced goods. I would put the emphasis on money.
White Rabbit: assume barter is easy. A 2-way barter deal is the apple and pear producer doing a deal in which each agrees to increase production and give the increased production to the other. A 3-way barter deal brings the plum producer in too. An n-way barter deal is what you are talking about. Or, there could be n 2-way barter deals: apple and pear, pear and plum, apple and plum, that could do the same thing (in a simple economy). But yes, I see your analogy between 1 n-way barter deal and fiscal policy.
Posted by: Nick Rowe | January 29, 2011 at 09:51 AM
And it's a good analogy.
Posted by: Nick Rowe | January 29, 2011 at 09:52 AM
But what about a barter deal like this: "I will plant wheat for you if you plant oats for me"?
Fine, let’s suppose the market in cereals works wonderfully. But that doesn’t help the guys who are turned away at the gates of the shipyard because orders for ships are way down. They can compete with the farm labourers of course. So there will be downward pressure on the wage, just as there is in a conventional Keynesian model. Once we take wage movements into account we need something more in the way of a model than a simple Keynesian cross. But as long as the wage is exogenous we can construct a simple Keynesian barter model which is no more objectionable than a simple Keynesian monetary model.
AFAICT, to bake the simplest kind of Keynesian model the two key ingredients are: (1) a non-produced asset of some sort, since if agents choose to abstain from consumption they must be trying to accumulate wealth; and (2) wages which are sticky in terms of that asset. Money makes the story more plausible, but you don’t actually need it. Also, if money is the non-produced asset that agents seek to hoard, notice that the problem arises because this filthy lucre is a store of value, not because it is a medium of exchange.
One way to see what I’m getting at is to isolate the store-of-value function of money from its role in trade. Imagine a central bank which prints money so recklessly that annual inflation ranges between 60 and 80 percent. Can we have involuntary unemployment? Of course we can, but not because there is excess demand for money. Excess demand for land will do the trick. Why doesn’t the price of land adjust sufficiently, relative to labour? Because people know that, in the past, the price has never gone much above one year’s labour per acre and buyers are reluctant to bid it up above that level. A sticky land-wage will perform the same role in this model as a sticky money-wage does in the usual introductory model. You hardly need to change the equations at all.
Posted by: Kevin Donoghue | January 29, 2011 at 10:31 AM
"[...and when you've sold the inventory, you take your proceeds and buy what you want with it.] But in what form are those "proceeds" held?"
They are held in the form of money, but only for long enough to conduct the subsequent purchase. So in this example, people only hold money while they are in the process of using it, while it is providing direct transaction services; they don't hold inventories of it. My point is that the critical feature of money (in the real world, not in my example) is not that it is the formal medium of exchange but that it is a store of value. That store of value could be something else, and as long as that store of value is freely exchangeable for money (and as long as goods prices are fixed in terms of the store of value) you get Keynesian effects that depend on the store of value. (Inventory holding is essentially what defines a store of value, I think.)
Another example I think I've brought up before is this: what if goods are priced in terms of oil but purchased with money? In other words, when you want to buy something, the seller looks on her Bloomberg terminal to see where WTI is trading and charges you some fixed multiple of that price. Money is still the formal medium of exchange. (People don't carry barrels of oil around with them.) But I contend that this economy will behave (except for the nominal price level in terms of money) like one in which the central bank fixes the price of oil. It's the store of value, not the medium of exchange, that matters. Changes in the money supply will have only small effects (making transactions more or less convenient), but changes in the supply of oil will have dramatic effects.
Another way to put the example above: suppose the dollar floats against the euro, and people use dollars for transactions, but goods are priced in euros, and transactions are made at whatever is the current exchange rate. Which central bank controls nominal spending?
Or what if cash floated against bank deposits but goods were priced in terms of bank deposits and purchased with cash? This actually describes the real world to some extent: as Frances' coin machine example makes clear, the bid and ask prices for certain forms cash are not the same as the official unit of account. In fact, as I understand it, the Fed (and the mint, too, I believe) has a policy of fully accommodating the demand for cash. In this sense, the Fed doesn't actually control the quantity of the medium of exchange (cash); it controls nominal spending by controlling certain stores of value (bank reserves).
Posted by: Andy Harless | January 29, 2011 at 10:40 AM
"To my mind, the Keynesian Cross model only makes sense in a monetary exchange economy"
You mean like the type of economy we ACTUALLY LIVE IN!!!
My my, your primary critique is that Keynes actually tried to explain reality not something existing only in the minds of economists. Now I know why orthodox economists are absolutely no help in either explaining or prescribing a remedy for this crisis.
Posted by: Gizzard | January 29, 2011 at 05:49 PM
Gizzard: Jeez! OF COURSE it's the type of economy we actually live in. That was NOT my "primary critique". It was NOT a critique at all!
I'm a "quasi monetarist" for crying out loud. I'm a "monetary disequilibrium" guy. Of course I think that money and monetary exchange matters. I spend half my time on this blog arguing that money and monetary exchange matters. That the fact we do not live in a barter economy matters.
God only knows how the hell you came up with that interpretation of what I wrote!
Man, you wouldn't recognise an orthodox economist if you......were one yourself!
Sometimes I really wonder
Posted by: Nick Rowe | January 29, 2011 at 06:09 PM
White Rabbit's analogy is a very good analogy. Was thinking about it while skating the canal. If barter were easy we wouldn't need monetary exchange, and we would easily get out of a recession by switching to barter even if we did normally use money.
But barter is hard because of (e.g.) double coincidence of wants. In a very complex economy, you might need 3, 4, 5, or n people involved to work a Pareto-improving barter deal. And the transactions costs and enforcement problems get bigger and bigger. Fiscal policy is an n-person barter deal, enforced by the government.
The Keynesian Cross has fiscal policy explicitly, but monetary exchange only implicitly. And the demand for money only implicitly.
(Here's my critique of the Keynesian Cross: it is a model of a monetary exchange economy, but does not model money explicitly. It should be built into the AE curve explicitly.)
Posted by: Nick Rowe | January 29, 2011 at 06:18 PM
Kevin: "Fine, let’s suppose the market in cereals works wonderfully. But that doesn’t help the guys who are turned away at the gates of the shipyard because orders for ships are way down."
If barter were easy, they would take payment in ships, which they would swap with the farmers for cereals, etc.
(Of course that's ridiculous, but that's just to say that easy barter is ridiculous).
If Qd is less than Qs, it must be the case that MPL exceeds W/P exceeds MRS so that firms could profitably hire extra workers if the demand for output increased.
Posted by: Nick Rowe | January 29, 2011 at 06:30 PM
"If barter were easy, they would take payment in ships, which they would swap with the farmers for cereals, etc."
If barter were easy, *and* if production was instantaneous, then they could be paid in ships.
But if it requires time as well as raw materials to make ships, and if the labor and raw material sellers need to be paid when they supply their own goods as inputs into the production process, then barter is not possible. Say it takes a year to build a ship, but you pay workers every two weeks. And you pay your raw material suppliers, landlord, and energy suppliers every month.
Then there is nothing to barter with, so at best you pay your workers with IOUs, to be redeemed when the ships are produced and sold.
But if the interest rate on the IOUs is higher than the expected profit rate of the firm, then the workers still wont be hired, the intermediate goods sellers wont find a buyer, and both Q_d and Q_s will decline.
Q_d will decline first, so Q_d < Q_s, because the factors of production are paid prior to production, which requires time, and Q_s will decline later (with the delay being the production time).
Posted by: RSJ | January 30, 2011 at 01:37 AM
If barter were easy, they would take payment in ships, which they would swap with the farmers for cereals, etc.
Barter is easy, by assumption. It's a barter economy! But no, they will not take payment in ships because there is no excess demand for ships, land or cereals and there is an excess supply of labour. (I won't be surprised if somebody now tells me that can't be the case because it violates Walras' Law. Of course it does. It's a Keynesian equilibrium in a model without money.) Given current prices for land in terms of labour, there would be excess demand for land if the economy were operating at full employment. But it's not. Income is at a sufficiently depressed level to ensure that the market for land is clearing.
Posted by: Kevin Donoghue | January 30, 2011 at 04:59 AM
Nick are you arguing that Keynes was making his arguments assuming a barter economy? Because as I understand it Keynes most certainly was NOT.
I understand that your entire post was illustrative and not a critique but your last paragraph belies where your critique would be focused and was a criticism of sorts. Saying that a model only works for a set of conditions not set forth in the model is criticizing it, and justly if its true. I just have always understood Keynes to be basing all his models on monetary economies.
Posted by: Gizzard | January 30, 2011 at 05:58 AM
Nick: "But what about a barter deal like this: "I will plant wheat for you if you plant oats for me"?"
and if oat output comes out lower than expected, say due to the weather in oat growing country? Does the oat grower still get the wheat?
Posted by: Adam P | January 30, 2011 at 06:58 AM
Gizzard:
There are two types of macro models:
1. Those that only make sense in a monetary exchange economy
2. Those that makes sense in both monetary and barter economies
plus maybe 3. Those that only make sense in barter economies.
I interpret Keynes as saying "This General Theory is a type 1 model".
But:
1. Keynes could be wrong in his interpretation of his own model.
2. The Keynesian Cross isn't Keynes' model. It's an interpretation of Keynes.
So it's an interesting question to ask of the KC model, whether it's type 1 or type 2. It helps us understand the model better. And some economists say it's type 2 (or 3). I say it's type 1. And that is not a critique.
But, it is a critique to say that if it's type 1, it needs to explain explicitly where money fits in. For example, if money were modelled explicitly, you might find that Qd=a+bY would have to be replaced by (e.g., just for illustration) Qd=a+bY+c(M/P). In other words, it's not *consistently* a monetary model. Implicit assumptions should be worked through explicitly, to see if they are being applied consistently. And it would also stop all the confusion people have about how to interpret the model.
Posted by: Nick Rowe | January 30, 2011 at 08:22 AM
Adam: dunno. I expect they would really be swapping *shares* in wheat and oat production. If the crop fails, your shares are worthless.
Same answer to RSJ: the workers will be paid shares in ships.
Kevin: don't worry about Walras' Law. Walras' Law is wrong. Rather, it is only right for "notional" demands. There is a *notional* excess demand for ships and cereals. If people were able to sell their inputs, they *would* demand ships and cereals. They *want* ships and cereals, but only if they can sell their labour and other inputs. There is no *constrained* excess demand for ships and cereals. But a barter swap lets them sell their inputs and buy output at the same time.
Posted by: Nick Rowe | January 30, 2011 at 08:29 AM
Andy: I gotta come back to your comment. Off skating this morning, while the ice is good.
Posted by: Nick Rowe | January 30, 2011 at 08:31 AM
... don't worry about Walras' Law.
Rest assured I don’t. I was merely trying to forestall a possible objection.
There is no *constrained* excess demand for ships and cereals. But a barter swap lets them sell their inputs and buy output at the same time.
I think you may be confusing barter swaps with wizards. If nobody wants more ships, a general willingness to swap ships for cereals, cereals for labour and labour for ships does the shipwrights no good at all.
I interpret Keynes as saying "This General Theory is a type 1 model".
GT, Chapter 17 is hard to reconcile with that interpretation (emphasis mine):
“That the world after several millennia of steady individual saving, is so poor as it is in accumulated capital-assets, is to be explained, in my opinion, neither by the improvident propensities of mankind, nor even by the destruction of war, but by the high liquidity-premiums formerly attaching to the ownership of land and now attaching to money. I differ in this from the older view as expressed by Marshall with an unusual dogmatic force in his Principles of Economics, p. 581: —
Posted by: Kevin Donoghue | January 30, 2011 at 09:00 AM
For me, the question Nick’s post raises is this: what is the simplest model we can construct which captures the essence of a Keynesian underemployment equilibrium? The model which I think Nick has in mind (Barro-Grossman) has the awkward feature that (w,N) is typically to the left of both the labour supply curve and the marginal product curve. So what’s the simplest way to justify calling such a position an equilibrium?
I haven’t worked out the details, but I think the best way is to think in terms of a game with two players: an entrepreneur and a household. The firm pays wages while the product is being made and receives proceeds if and when it is sold. The marginal increase in output doesn’t happen because the entrepreneur rightly calculates that a dollar of wages will only produce (1-c) dollars of revenue. The problem essentially is that we don’t have a futures market such that the household can commit to buying the finished product. Nick says barter would solve the problem; I think he should say that a suitable futures market would solve the problem.
If this makes sense then presumably someone has published a paper decades ago which works out the details. If so I’d appreciate a pointer. If it doesn’t make sense I’d like to know what’s wrong with it.
Posted by: Kevin Donoghue | January 30, 2011 at 01:51 PM
Sorry that should be $c of revenue, not 1-c, where c is the MPC.
Posted by: Kevin Donoghue | January 30, 2011 at 01:55 PM
Andy: "My point is that the critical feature of money (in the real world, not in my example) is not that it is the formal medium of exchange but that it is a store of value."
I think it's critical that it's both.
Start in equiilibrium, where money is changing hands once a week. Now suppose people decide they want to hang on to it for twice as long. Money now changes hands once a fortnight (V halves). If M and P stay the same, Y halves. Money here is a "warm potato"(?) on a cold night. But because it's the medium of exchange, it disrupts all markets. If it weren't the medium of exchange, the only market disrupted would be the market for the potato itself.
If money were not the medium of account (as well as medium of exchange), then it would be much easier for the price of money to double when V halves. But since it is the medium of account, the only way for the price of money to double is if all other prices halve. Which can't happen easily, and won't happen quickly.
Posted by: Nick Rowe | January 30, 2011 at 02:57 PM
Kevin: "I think you may be confusing barter swaps with wizards. If nobody wants more ships, a general willingness to swap ships for cereals, cereals for labour and labour for ships does the shipwrights no good at all."
If no goods were scarce (i.e. if an omniscient central planner would not increase the production of any good), then why would there be an excess supply of labour? Why would people want to work longer, if there were nothing they would want to buy with their incomes?
"GT, Chapter 17 is hard to reconcile with that interpretation (emphasis mine):"
Hmmm. Good point. Sometimes I feel like Joan Robinson (quoting, no doubt incorrectly, from memory) "Sometimes Maynard doesn't understand what he's really saying, and we have to remind him to be more Keynesian".
I vaguely remember some part of the GT, where he talks about Say's Law being correct in barter??
But yes, Maynard does go a bit wobbly sometimes.
"..what is the simplest model we can construct which captures the essence of a Keynesian underemployment equilibrium?"
I think n players is easier than 2. With 2 players, if one increases his demand, he knows that some of it will return to him. With n players, only 1/n will return to him. As n get's large, each player takes macro variables as exogenous wrt his own choices.
"The problem essentially is that we don’t have a futures market such that the household can commit to buying the finished product. Nick says barter would solve the problem; I think he should say that a suitable futures market would solve the problem."
Start in equilibrium. Then increase desired savings. If all the extra savings were spent in the futures market, no problem. If it's horded as money, we get a recession.
Posted by: Nick Rowe | January 30, 2011 at 03:09 PM
Nick: I don't believe that Gizzard understands you are implicitly debating Steven Williamson, or so was my impression. Hence his confusion with your statement about the economy we live in.
I'm not sure that I understand the importance of framing the background as either a monetary exchange economy or a barter economy. For sufficiently low transaction costs, how would barter be different? I don't see prices hiding in the KC framework, or playing a role in shocking the model, though I suppose one could assume price level shocks drive aggregate expenditures shifts.
Posted by: westslope | January 30, 2011 at 08:29 PM
"the workers will be paid shares in ships"
Yes, that's my point. But "shares in ships" is not shares of actual ships -- it is equity shares of the economic surplus provided by ships that do not yet exist, but will exist after 1 year of production. This is the only way the firm can pay the workers today, and this payment then allows the workers to consume today, and buy output from the cereal maker even though they have no present goods to exchange for cereal.
This additional demand for cereal in the present period allows the cereal maker to pay back it's own IOUs in the present period. When the creditors of the cereal maker come knocking, the cereal maker hands over the ship-building IOUs, and as all these are fungible (anything can be bartered for anything else), then the cereal-maker's creditors are happy and the market clears.
But in a leap-frogging system such as this, if the "market" believes that the ship-building IOUs are no good, or equiivalently if they discount them too highly, then the ship-builder cannot hire workers, and the cereal maker can't repay its own debt. There is less demand for cereal, and less demand for ships, but Q_s will not fall until inventories are depleted.
The difference is not monetary exchange versus barter, but between an economy in which the exchange is primarily across time rather than one in which the exchange is not across time (e.g. presents goods are sold for IOUs for future delivery of goods, and present goods are bought with these IOUs as well.)
From the point of view of money as any form of debt, then it really is about money.
But from the point of view of the existence/use of legal tender, then the Keynesian Cross has nothing to do with it.
It's all about inventories/time-shifts, not the exchange mechanisms. Once you think in these terms, the model doesn't seem "weird" -- it seems light years ahead of the paleolithic models that assume instantaneous production.
Posted by: RSJ | January 31, 2011 at 01:18 AM
Westslope: "I don't believe that Gizzard understands you are implicitly debating Steven Williamson, or so was my impression."
You are probably right. Though I'm implicitly debating a number of people, I think. And even if every economist agreed with me, it would still be worth saying, so that people who were new to the model could understand it better.
"I'm not sure that I understand the importance of framing the background as either a monetary exchange economy or a barter economy. For sufficiently low transaction costs, how would barter be different?"
I keep trying to make this point in different ways, but seem to be failing to get it across. Let me try again.
The apple and banana producers would both be better off if A bought more bananas and B bought more apples. But A would be worse off if he individually bought more bananas, and B would be worse off if he individually bought more apples.
That's because if A buys more bananas he has more bananas and less money. But if both buy more apples and bananas both have more apples and bananas but the same amount of money. It's a prisoner's dilemna. A coordination failure. And the way out of a coordination failure is to do a deal: "You buy my apples and I will buy your bananas in return". But that is essentially equivalent to a barter deal. 100 apples and 100 bananas change hands. And $100 and $100 change hands. But swapping $100 for $100 is irrelevant. They might as well just swap the fruit.
RSJ: Assume a representative agent barter economy in which labour is the only input. Labour produces output, but with a 1-year lag. Suppose people are not prepared to wait 1 year before being paid in output. Everybody wants to eat now, but there's a 1 year lag between planting and harvest, and there are no stocks of food. That economy is screwed anyway. No central planner or government can fix it. It's not a coordination failure.
Posted by: Nick Rowe | January 31, 2011 at 06:57 AM
'But what about a barter deal like this: "I will plant wheat for you if you plant oats for me"?'
That's fine, you now have a barter economy with credit but still without money. But if that's your line, then you have to amend your summary: "to my mind, the Keynesian Cross only makes sense in a credit economy.
Posted by: Phil Koop | January 31, 2011 at 09:29 AM
Phil: But if you could do those credit/barter deals, the Keynesian Cross model would NOT make sense. Output would immediately rise to where Qs=Qd.
Posted by: Nick Rowe | January 31, 2011 at 10:58 AM
Yes, Nick, that economy would be screwed, but that's not our economy. There is inventory -- there are stocks of food, even if the food itself is non-storable and perished after 1 day.
Suppose that there are 365 agents, each agent requires 1 year of production before they produce any output. Still, at any point in time there would be enough output for them to consume in exchange for their IOUs.
Nevertheless Q_s will generally lag Q_d, and this economy can have two sources of failure: it could be an idiosyncratic crop failure on the supply side ("productivity shock") or a coordination failure on the demand side, as the agents whose crops have come to harvest come to rely on the demand arising from those still producing, but not harvesting. Now you could argue that the demand failure is just a supply failure with a time lag, and I'm fine with that characterization, but it will appear with the same characteristics as a traditional demand failure. I think this is what Keynes was describing when he pointed to insufficient investment as causing a demand failure.
Does that make sense?
Posted by: RSJ | January 31, 2011 at 11:58 AM
I vaguely remember some part of the GT, where he talks about Say's Law being correct in barter??
You may be thinking of Chapter 2, where he says: these [Classical] conclusions may have been applied to the kind of economy in which we actually live by false analogy from some kind of non-exchange Robinson Crusoe economy, in which the income which individuals consume or retain as a result of their productive activity is, actually and exclusively, the output in specie of that activity.” (my emphasis)
But if that’s the passage that you have in mind, I’m not convinced it puts Keynes in your camp, even for a flying visit. What you call a barter economy is something between a Robinson Crusoe economy and a monetary economy. Actually what you call a barter economy looks to me like a textbook Walrasian, or Arrow-Debreu, economy in which any coordination failure is impossible. (If that’s not what you mean, in just what respects does your barter economy differ?) In Chapter 17 Keynes refers to a barter economy, but he means an economy in which cigarettes or something like that play the role of money:
It’s pretty clear that Keynes wouldn’t say that “Say’s Law is correct” in such an economy. But if Keynes were the only great economist to disagree with you, you wouldn’t have a problem. He was notoriously cavalier about some aspects of theory. He admitted that himself; as he put it, there’s no harm in being wrong as long as you’re found out quickly. What I think ought to bother you a bit more is that Frank Hahn (who tries harder to avoid being wrong) sides with Keynes on this one: “Of course in actual economies it makes sense to study, say, money wages and not land wages. Keynes, however, knew that for very purely theoretical purposes it made no difference.” (Microeconomic Foundations of Macroeconomics, ed. GC Harcourt.)
Posted by: Kevin Donoghue | January 31, 2011 at 01:19 PM
Kevin: I just found my GT. Yes, that is very close to the passage I had in mind. But look just a little earlier (page 19/20):
"The conviction, which runs, for example, through almost all of Professor Pigou's work, that money makes no real difference except frictionally and that the theory of production and employment can be worked out (like Mill's) as being based on 'real' exchanges with money introduced perfunctorily in a later chapter, is the modern version of the classical tradition. Contemporary thought is still deeply steeped in the tradition that if people do not spend their money in one way they will spend it in another."
I interpret Keynes, when he says "real exchanges", to be talking about barter. Given the context, that means that supply creates its own demand in a barter economy, but not in a monetary exchange economy.
I think that what Frank Hahn is talking about is money as a medium of account, not as a medium of exchange.
Posted by: Nick Rowe | January 31, 2011 at 02:21 PM
I think that what Frank Hahn is talking about is money as a medium of account, not as a medium of exchange.
Minor linguistic quibble: shouldn’t that be unit of account? The trio I always heard of were store of value, unit of account and medium of exchange. More usefully, here’s the context for Hahn’s remark:
If Hahn is in agreement with you then I have completely misunderstood at least one of you. Which is only too likely, so many thanks for providing these learning opportunities. As a student I didn’t get many chances to argue with professors.
Posted by: Kevin Donoghue | January 31, 2011 at 03:15 PM
Correcting typo: "It also has one special property amongst assets, namely that it has no uses other than its exchange use." (Restores the missing 'e' and 'namely'.)
Posted by: Kevin Donoghue | January 31, 2011 at 03:22 PM
Kevin: Thanks.
Picky quibble squared: this is the correct way to use those words (I only learned this myself recently): "Silver was the medium of account, and one ounce of silver was the unit of account". There are only two modern cases I can think of: Sterling is the medium of account, and pound the unit of account. Remnimbi is the medium, and yuan the unit.
"If Hahn is in agreement with you then I have completely misunderstood at least one of you."
I strongly disagree with Hahn there. So I think you understand us both.
Hahn is wrong. An excess demand for land, bonds, or antique furniture cannot cause a general glut. God, I think Hahn is so muddled in that passage!
Now, I vaguely remember some passage where Keynes says the same sort of thing about land. Arguing against Gessell.
Posted by: Nick Rowe | January 31, 2011 at 03:44 PM
Proof! David Laidler agrees with my interpretation of Keynes:
"Say's Law, Money and Sticky Prices
To put the same point less obliquely, today's dynamic general equilibrium models can generate variations in the levels of real activity and employment, but by their very nature they must treat
these as reflecting voluntary behaviour in markets for goods and services that are continuously clearing. In this respect they embody an up-to-date and extreme version of what at one time was commonly referred to as "Say's law", the proposition that a general glut - excess supply in modern terminology - of goods and services is impossible.10 Keynes, of course, argued that "Classical economics", citing John Stuart Mill among others as its representative, relied on this proposition, and claimed his refutation of it in the case of a **monetary, as opposed to a barter economy**, to be a critical innovation of his General Theory, thus helping to originate today's misleading but standard view about the essential continuity of modern equilibrium modeling with the economics of Adam Smith and his Classical successors."
Posted by: Nick Rowe | January 31, 2011 at 04:08 PM
"If it weren't the medium of exchange, the only market disrupted would be the market for the potato itself."
I don't think this is true. I repeat my "pricing in barrels of oil" example from above. Oil is not the medium of exchange, but if everything is priced in terms of oil, then changes in the demand for oil will disrupt all markets.
Posted by: Andy Harless | February 01, 2011 at 05:21 PM
"Oil is not the medium of exchange, but if everything is priced in terms of oil, then changes in the demand for oil will disrupt all markets."
The big bang comes from whatever you use as the unit of account in nominal contracts. That then becomes the thing which disrupts all markets.
But the excess demand is for the store of value function of money, not the medium of exchange.
Posted by: Jon | February 03, 2011 at 01:04 AM
I don’t know if this has already been addressed, but it seems to me that the point of the Keynesian Cross model was (basically) that, in the aggregate, spending=income. (Thinking about stored wealth in this context, would it be possible to increase aggregate expenditure by running down stored wealth? Or would the act of liquidating the asset to increase A’s expenditure require that B reduce expenditure sufficiently to purchase the asset? Of course, credit could increase expenditure in the short term). Consequently, AE must equal Y – and this would be a stable equilibrium, in the absence of external changes.
If all that can be purchased is (Everything), and the only way income can be earned is by selling some (Everything), there would be no way to signal that more (Everything) would be purchased, because the income to signal a desire for more (Everything) could only be obtained if people bought more (Everything).
This would then suggest that, in terms of Nick’s 2 (or 3) types of economic models, the Keynesian Cross is a Type 2, that works in both monetary and barter economies. It would, however, not work in small economies – the driving force seems to be that, if informal co-ordination is not possible, then the model makes sense.
I suppose the point is how you can have a non-full-employment equilibrium that is stable; recessions would, presumably, then be caused by factors outside the model, but endure because of the features of the model?
Posted by: Luke | February 03, 2011 at 05:28 PM