Three ZMPs and two Co-ordination failures

"ZMP" stands for "Zero Marginal Product". It should really stand for "Zero Value Marginal Product". Can an additional worker produce no additional goods of any value? Is that why they are unemployed? Yes, but.

There are three types of ZMP. Two of them are based on two different types of coordination failure. The disagreement between macroeconomists is on what type of coordination failure is causing the ZMP of unemployed workers.


ZMP1. No coordination failure.

It is possible that some potential workers, perhaps because of severe disabilities, simply cannot produce anything useful, even in a perfectly functioning economy. Even the mythical central planner, who could allocate resources perfectly, wouldn't be able to think of anything useful they could work at, and would leave them idle. They have a Zero Value Marginal Product. There's no coordination failure. The problem simply can't be solved, given existing technology, tastes, and resources.

Nobody (I think) is talking about ZMP1.

ZMP2. Coordination failure 1. (Patterns of Sustainable Specialisation and Trade). (Thanks David and Wonks Anonymous).

The unemployed plumber wants his house re-wired. The unemployed electrician wants his pipes replaced. But the plumber doesn't know that there's an electrician in town; and the electrician doesn't know that there's a plumber in town. Given the current state of knowledge, both workers have Zero Value Marginal Product. Nobody is willing to pay for their labour. They would be willing to pay, if they knew of each other's existence, but they don't. The mythical central planner, who knows everything that anybody knows, would sort this one out immediately. All he has to do is introduce the plumber and the electrician, and both jobs are done.

Arnold Kling, I think (I'm not sure if I am representing his view correctly), is talking about ZMP2. (Of course, I have drastically oversimplified the coordination problem, just so we can understand it simply. In the real world it is much more complicated, and a real world entrepreneur might have to bring together many more people to interact in complex ways to resolve the coordination problem.)

There's an excess supply of plumbers' and electricians' services, and an excess demand for plumbers' and electricians' services, all at the same time. Both want to sell more of their own labour, and buy more of the other's labour.

ZMP3. Coordination failure 2. (Monetary Disequilibrium).

The unemployed hairdresser wants her nails done. The unemployed manicurist wants a massage. The unemployed masseuse wants a haircut. The hairdresser knows where the manicurist can be found. The manicurist knows where the masseuse can be found. The masseuse knows where the hairdresser can be found. But all three women are short of money, and won't spend any until after she earns some. Given the unwillingness of each to spend money, each of the three has a Zero Value Marginal Product. Nobody is willing to pay for their labour.

This one's a bit trickier for the mythical central planner to solve. Introductions alone won't do the trick. Each woman already knows where to find the service she wants. That's not the problem.

The central planner could simply order them all to provide the desired service, for no cash. That would make all three women better off. But if the central planner is mythical, and can only give mythical orders, that won't work.

He could try to get all three women together, and try for a three-way barter deal. But it's hard to cut someone's hair while your customer is giving a massage and you are having a manicure. Who's going to go first, and how will she know the other two won't break the chain?

The easiest solution is for the central planner to print more money and give each of the three women enough so they buy what they want.

ZMP3 is what the rest of us Monetarists and Keynesians (quasi or otherwise) are talking about.

There's an excess supply of each woman's labour. Each one wants to sell her labour and can't. In one sense (in Robert Clower's sense) there's also an excess notional demand for each woman's labour, because each woman would like to buy labour from one of the others. But she would only actually buy it if she could sell her own labour, and she can't. So there's no excess constrained or effective demand for labour.

73 comments

  1. Unknown's avatar

    Determinant: that makes sense to me. I always wondered why the United Church sounded so stuck in the past. Like many of that generation, they never got over the 1930’s. Socialism must have looked promising 80 years ago. They are the generals forever fighting the last war. Only, it’s not the last war, but the one before that. Not that I ever recollect the United Church focussing much of its attention on monetary theory, mind you, and the 1930’s, like the recent recession, was a monetary problem. But not all problems are due to monetary policy.
    Bill: agreed. The big problem with ZMP2 is just that: even if they don’t know about their highest VMP opportunity, is there nothing else useful they can do with their time, while waiting for the entrepreneur to discover the new opportunity?

  2. Determinant's avatar
    Determinant · · Reply

    The United Church is first of all a place of religion. We’ll tolerate most economics so long as there is a safety net for people. Call that socialism if you want. In practice we’d choose a free market with a guaranteed income over a state-controlled economy with state-guaranteed jobs. Make of that what you will.
    Stuck in the past? On economics, maybe, but we’ve never really seen a reason to switch. The free market Christ Right in the US has never caught on with us in the least.
    Besides, we spent most of the 1980’s on the Big Gay Question. It took up a great deal of our time.

  3. Unknown's avatar

    Determinant: responding now to your 9.17:
    “Perhaps too when you minister to people in a small open economy whose income is critically dependent on decisions taken in markets and boardrooms thousands of miles away to whom you are just a price point it is hypocritical in the extreme to preach that saving is a virtue and improvidence is a sin and a sign of your lack of grace. That point has been reinforced again and again and again over the years.”
    The risks people face now are far less than our ancestors faced, when a failed harvest could mean starvation. I would say the virtue of providence is less important now than it was in the past. But that doesn’t mean it is not a virtue.
    There is a difference between: justifying one’s economics by appealing to morality and religion; appealing to morality and religion: recommending that people follow, and encourage others to follow, certain rules of behaviour. Regardless of my religious beliefs, or lack thereof, I can recognise that in some cases religious movements have created cultural practices that were good ones.
    I think providence is a virtue. And if you are a preacher you ought to preach it. Do any preachers preach it nowadays? Or do they just blame the evil capitalists and sing kumbaya?

  4. Unknown's avatar

    I was thinking of blogging on this: http://www.aeaweb.org/aea/2011conference/program/retrieve.php?pdfid=477. It talks about the influence the intellectual debate on predestination v. people’s ability to make decision and control their destiny on Adam Smith’s thought.
    But fate intervened.

  5. Determinant's avatar
    Determinant · · Reply

    No, I am not a minister, I have not attended Divinity School nor do I intend to. I will be standing for election to the Session next week as an Elder.
    Nick, in the greatest respect, please don’t try to split hairs, your last post is nothing a teleological argument. You ARE justifying your economics by appealing to religion and morality. You aren’t making an economics argument anymore but a theological one. Which is fine, but a spade is a shovel.
    You are also looking at the past with rose-coloured glasses, or is the Irish Potato Famine just a fluke? Honestly, take a look at what happened. It wasn’t pretty. THAT was poverty.
    Societies can save in that they can invest in increased production and more productive technologies. However in a world with ever-increasing specialization there is an ever-increasing risk that that specialization won’t be profitable. Specialized farming like wheat is just as susceptible to booms and busts as the factory worker with a specialized set of skills or the trader dependent on derivatives.
    In a world where the frictional costs of changing careers (by which I mean income-earning activity) are substantial and entail substantial risk, technology and education make for high productivity standards in most industries relative to demand and with competition ensuring that no income is guaranteed, there will always be unfortunates who just don’t have enough money to meet their needs. We’ll get a macro result that a society can save but at a cost of creating a permanent set of people who are unemployed, have poor prospects and don’t have enough money to either provide for themselves or change their situation. There is also no implication that the existence of general saving means that individual saving will be sufficient in all circumstances. The two don’t follow each other.

  6. Determinant's avatar
    Determinant · · Reply

    Actually Nick reminds me of Margaret Thatcher’s “Sermon on the Mound” to my dear cousins the Church of Scotland.
    After she was done blustering they handed her a report on poverty in Scotland which was taken as a rebuke to her diatribe.

  7. Unknown's avatar

    Determinant: You are no longer arguing with me. You seem to be arguing with some figment of your imagination. To take just one example:
    “You are also looking at the past with rose-coloured glasses, or is the Irish Potato Famine just a fluke? Honestly, take a look at what happened. It wasn’t pretty. THAT was poverty.”
    What?! The whole point of what I have been arguing in the above comments is that people were much poorer in the past than they are today. And you come out with that!
    It would be like me saying: “Determinant: learn to do math, 2+2 is NOT equal 5. And workers are NOT all evil”
    Jeez!

  8. K's avatar

    Nick: Never mind the bollocks. Looking forward to your post.
    One thing I would consider though. I’ve been involved a fair bit with start ups and venture capital. Entrepreneurs are about the most improvident lot I’ve had the pleasure of knowing. They take huge risks, much greater than they generally realize, and they grossly overestimate their odds of success. Only about one in five vc investments are successful, but all of them think they have a 90% chance of success, and that includes the ones that don’t even get funded. Most telling of all, they happily borrow money at rates of that frequently exceed 10-15%, and often personally guarantee those loans. Hardly the picture of providence. They are however a big part of the reason for all our modern wealth, in many ways much more so than the providence of your grandparents.

  9. Unknown's avatar

    K. Hmmmm. You have a point. They aren’t improvident in the same way that dissolute celebs who blow the lot on consumption are. But you sure wouldn’t describe those over-optimistic risk-taking investors as “provident”.

  10. Unknown's avatar

    And yes. It needed both those risk-taking investors plus the provident savers to get us where we are now.

  11. Greg's avatar

    Nick: “K: I’m not sure. Pure theory of intertemporal utility maximisation says there should be no relationship between the scale of income and the savings rate. Everything just scales up.“
    This seems counter-intuitive to me. I cannot imagine the savings rate is constant across all levels of income. How to explain the increasing disparities in wealth and income? Let’s check: 2007, according to the FED in:
    http://assets.opencrs.com/rpts/R40647_20090901.pdf</a href>
    Table 1:
    -94.3___-13.6_____6.0____18.2____35.9 by quintile, after taxes. But that’s just one year.
    “People in the past were much poorer than us. But they saved, and invested. And it’s because they saved and invested that we are as rich as we are now…”
    Savings is usually with the expectation of spending in the future, (except for those who have saved so much they will never spend it.) Investment is with the expectation of increased consumption in the future. In a certain peculiar sense, our prosperity is built on improvidence as well as providence. Demand must grow along with supply.
    Nick: “Sure it’s hard to live within your means. But many poor people do it, and many rich people fail miserably. And we should stop making excuses. “They can’t help it; they are poor”.”
    I don’t know. Are you demanding of the poor higher standards than of the wealthy. Are you demanding that they take a lower discount rate, that they be more “provident” than the wealthy, when they must make greater sacrifices to do so? If the distribution of subjective rates of discount is the same among rich and poor, then statistically, it seems to me, it’s just going to happen: A larger percentage of poor will have, because a higher percentage of their income must go to ‘necessities,’ a higher realized discount rate than the wealthy.
    “Greg: “Only by continuously redistributing the money, can the system remain viable…”
    Nick: “And my grandparents reply: “Sure, reward improvidence…No!”
    I’m just being practical here. It’s really not a moral issue at all. (Well, it is, but in a different way.) Consider trade, with just a two country system. If they trade, with any difference in discount rates, the one with the higher discount rate will become impoverished, and the other will end up with all the money. And all the assets. And then what? And we are not talking ‘improvident’ here.
    The same with individuals, in a market economy. Take two. They trade. If one individual makes nine cents on the dollar, and the other ten, the one who makes ten cents will eventually come to possess everything the other owns. Should we punish the one who only makes nine cents with abject poverty? Is the one who makes ten cents so morally superior, that he deserves everything? He cannot be. Someone slowly inflicting poverty on his neighbor is- sick, so morally inferior, and undeserving of his wealth. Scrooge is not just mean, he is damaging to the economy.
    It is simply in the interests of the wealthy to keep “giving away” the money, and yes, rewarding a certain amount of ‘improvidence.’ My criticism of the wealthy is that they are not pursuing their proper self-interest.

  12. Unknown's avatar

    Nick: “People in the past were much poorer than us. But they saved, and invested. And it’s because they saved and invested that we are as rich as we are now…”
    The first two sentences are not at all obvious. Think about home ownership rates. In the US (the one place I could find info on), in 1900 less than half of male household heads were home owners, and less than one quarter of black household heads were. Since home ownership is far and away the largest asset most people hold, it would take a huge amount of non-home savings to put all of those 1900 non-home owners at a level comparable to 2011 average people. Here’s a paper a discussion of the history of home ownership: http://www.vanderbilt.edu/econ/wparchive/workpaper/vu00-w12.pdf. Or land ownership in England – historically 80 to 90% of land was worked by tenant farmers who didn’t own the land they tilled (sorry, can’t find anything ungated, I got that stat from the first page of this article: http://www.jstor.org/pss/2597481.
    The last sentence doesn’t follow from the first two, anyways. As you know, a very small fraction of the population own the overwhelming bulk of the wealth (is it 20% own 80% or 10% own 90%? I don’t remember). And that’s been true for a very long time.

  13. Mike Moffatt's avatar
    Mike Moffatt · · Reply

    “Mike Moffatt thinks I’m a lefty and I’m fine with that.”
    I wouldn’t read too much into that. George Carlin has a bit where he says that anyone that drives slower than you is an idiot, and anyone who drives faster is a maniac. Same principle applies here.

  14. Unknown's avatar

    Frances: Hmmm.
    All assets must be owned by someone. Someone must have done the savings. A couple of differences I can think of:
    1. In the past, since people were poorer, their labour supply was much greater, so they worked till they died. No retirement savings motive. Standard permanent income hypothesis. You save when your current income is above your permanent income.
    2. In the past, land + houses were a much larger share of the total stock of assets. For example, if land and houses were the only form on non-human wealth, you would expect to see the distribution of ownership of land and houses as unequal as total distribution of non-human wealth is today.
    3. Total inequality of income and wealth was greater in the past?
    Reminds me of that book you lent me. Biography of that women living in very poor hamlet in England late 19th century. The one couple in the village who had financial savings were childless. The rest saved and invested in their kids. The kids were the retirement plan.

  15. Unknown's avatar

    Greg: “In a certain peculiar sense, our prosperity is built on improvidence as well as providence. Demand must grow along with supply.”
    Agreed. But that demand can come from either consumption or investment. We can have a higher or lower share of savings (=investment) in GDP.
    “If they trade, with any difference in discount rates, the one with the higher discount rate will become impoverished,..”
    Yep. This has always been something that bothered me. Take the simplest example of what you are talking about: 2 infinitely-lived agents, identical except that one has a slightly higher discount rate than the other. Each with a constant stream of income (before interest payments). The equilibrium rate of interest will be between the two discount rates. So one saves, and the other dissaves. And there is no long run stationary equilibrium. The impatient one starts out with higher consumption, but has declining consumption over time, with consumption asymptotically approaching zero, which means in the limit the patient one consumes both their incomes.
    The only way out of this nasty conclusion is for the discount rate, at the margin, to increase with permanent consumption and wealth. The poor need to be more provident than the rich. And saying it’s OK for the poor to be less provident than the rich just makes things worse.
    And I don’t think that transfers from rich to poor will prevent it either. Because you take those future transfers into account when you make your savings decision. The person with the higher discount rate will save even less in anticipation of those future transfers.
    So, what would work? Something like a TFSA (for non_Canadians: where each person can save $5k tax free) would maybe help? Because that $5k is a bigger percentage of income for the poor than the rich. So, the after-tax return on savings is greater for the poor than the rich, at the margin? I think that’s right.
    Yep. I think (not sure) that the only policy that could work in the long run is one which gave the poor a higher marginal after-tax rate of return on savings than the rich.

  16. Unknown's avatar

    These comments are good, by the way. Helping me get my head clearer on it all. Thinking about the policies that would and would not work is what’s important.
    By the way, I hate Dickens for what he did to Scrooge. Scrooge (in the dream) died having spent much less than he earned. He gave it all away on death. Scrooge was much more charitable than all those other useless improvident self-satisfied idiots. We are rich now because of Scrooge. And that bastard Dickens does a ritual humiliation of Scrooge worthy of the Red Guards in the Cultural Revolution. Christmas Carol is hate literature. We join in the annual hate-fest while consuming the wealth that the object of our hate created.
    Scrooge did not impoverish anyone. He enriched us.

  17. Unknown's avatar

    WCIers – book Nick refers to at 9:56 is Lark Rise to Candleford.
    Nick:
    “All assets must be owned by someone. Someone must have done the savings.”
    Isn’t the traditional method of land acquisition (a) taking it by brute force and then (b) passing it one to one’s children? (see, e.g. the Americas, Africa, India, etc.) Given your point (2) above, this means implies that historically savings haven’t been particularly important for many people.
    The problem a tenant farmer faces in attempting to buy his/her own land is that to acquire the capital to do so, he has to produce more than the rent on the land, but why would a landowner set rents that low?
    1. “In the past, since people were poorer, their labour supply was much greater, so they worked till they died.
    They worked until they reached the point of ZMP (1 or 2, don’t remember which). Which could, especially for women, be a fair time before they died. Hence the 1960s stories of old women eating catfood.
    3. “Total inequality of income and wealth was greater in the past?” Depends when/where.
    Am very much looking forward to your post on this, Nick.
    One of the most forceful attacks on 19th/early 20th century religious preachings on the virtues of thrift etc comes from George Bernard Shaw. He articulates it well in An Intelligent Woman’s Guide to Socialism and Capitalism. It’s in my office, I’ll pick it up for my response to your post, which may come before your post at this rate!

  18. Unknown's avatar

    Frances: “Am very much looking forward to your post on this, Nick.”
    Thanks. But I’m not 😉
    Realising: first, just how touchy a subject this whole thing is (not just religion plus neoclassical economics plus debt plus inequality plus “How dare you blame the poor for their improvidence!”; and second, because getting my head clear, and then writing it clearly, is going to be bloody hard.
    Yep. Lark’s Rise to Candleford was a great read.
    GBS (I haven’t read it) was probably pushing the vulgar Keynesian savings-glut line. I wonder. Nice pubs around Ayot St Lawrence, where he retired. Often used to go drinking there.

  19. Unknown's avatar

    There are two parts to land acquisition: getting the raw land, which usually means stealing it from someone else; clearing, draining, getting rocks out, etc. People always underestimate the importance of the second. It’s the second that is savings and investment. Productive land is mostly capital, in other words. There is almost always an extensive margin, where raw land is not scarce.
    In a simple model land rents should equal VMP land. So the tenant farmer must use savings from his own labour and return on capital if he wants to buy land. In a more complex model there’s a problem of asymmetric information between landlord and tenant farmer. Because it is hard for the landlord to observe the tenant’s investment in the land. The tenant can exhaust the soil, or improve it. It’s tricky to write this into the lease and monitor. So the VMP of land farmed by an owner can be higher than the VMP=rent of tenanted land. So if a tenant farmer can save enough for a downpayment, he can sometimes afford to pay off the mortgage partly from the difference between the two VMPs.
    “They worked until they reached the point of ZMP (1 or 2, don’t remember which). Which could, especially for women, be a fair time before they died. Hence the 1960s stories of old women eating catfood.”
    That’s ZMP1. But isn’t inflation what impoverished those retirees? Plus increased tax rates on “unearned” income?

  20. K's avatar

    Nick: “They aren’t improvident in the same way that dissolute celebs who blow the lot on consumption are.”
    Maybe. Providence is a loaded word. Krugman uses the word “patient,” which strikes me as a lot more objective and relevant. As far as being “impatient” I don’t see a big difference between the entrepreneurs and the celebrities.
    The biggest differences between the entrepreneurs and the poor are:
    1) Nothing. Some entrepreneurs end up poor.  It’s just risk.
    2) Work ethic.
    3) Innate skill.
    4) Luck (monopoly). This one is by far the biggest. Numbers 2 and 3 can effect income by an order of magnitude. This one accounts for the next six zeros. There are millions of people with the skills of Bill Gates. None of them lucked upon an emerging natural monopoly for operating systems. Bryn and Page happened to be working in fields relevant to an emerging monopoly on search. Most brilliant grad students aren’t.
    I don’t agree with your premise that the principal consideration in evaluating redistribution is effectiveness. You ignore the extent to which wealth is the result of monopoly, ie the natural wealth of the earth plus aggregate demand alone. This is the case for a citizen’s dividend. Entitlement, not welfare. And if you want to figure out how to prevent that income from being appropriated by, eg the banks, due to their lower discount rate (which results principally from their seignorage monopoly), I think you should look at the state refusing to enforce claims against that income. Or maybe refusing to enforce any loans over and above handing over the collateral. Then we could get rid of the incredibly wasteful bankruptcy process at the same time. 

  21. Determinant's avatar
    Determinant · · Reply

    Nick:
    Frances really made my point for me in her post. I was trying to find the words but didn’t make it. K drove the nail home.
    It is a fallacy to think of everyone in the past as poor, provident savers.
    For example, on clearing land Nick, Peterborough, ON was settled in 1827 by the Canad Company. They had Crown grants galore, brought the settlers over from Cork and the deal even included most farm implements, provisions, even a cow. The race was against time to get crops in and yourself set up.

  22. Unknown's avatar

    Thanks all commenters. I’ve now posted. Let’s stop this discussion here and switch this discussion to the new post. Because we were all way off-topic here (my fault).
    From now on, only comments about ZMP here.

  23. Unknown's avatar

    By the way (breaking my own rule) feel free to re-state any of your comments here on my new post, if you think they are still applicable after reading it. Because otherwise people might not find your critiques.

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