19 Jul 2012

Krugman, Karl, and Kalculus

Economics, Krugman 108 Comments

I want to follow-up on my initial thoughts on Krugman saying that rich people don’t add anything (net) to the economy, since I personally am seeing this whole thing much more clearly now, largely thanks to you guys and (believe it or not) my working through a mathematical model that is standard in grad programs. Later on in this post, I’ll even use basic calculus to show just how wrong Krugman has been on this issue. (Don’t tell Walter Block!)

In case you’re just joining the discussion: Paul Krugman for a while has been saying that standard price theory shows that right-wingers are crazy for thinking that entrepreneurs add anything to the economy, above what they take out. He did it here most recently, saying:

So, imagine a Romney supporter named John Q. Wheelerdealer, who works 3000 hours a year and makes $30 million. And let’s suppose that he really does contribute that much to the economy, that his marginal product per hour — the amount he adds to national income by working an extra hour — really is $10,000. This is, by the way, standard textbook microeconomics: in a perfectly competitive economy, factors of production are supposedly paid precisely their marginal product.

Now suppose that President Obama has reduced Mr. Wheelerdealer to despair…So Wheelerdealer decides to go…one-third Galt, reducing his working time to just 2000 hours a year…

According to marginal productivity theory, this does in fact shrink the economy: Wheelerdealer adds $10,000 worth of production for every hour he works, so his semi-withdrawal reduces GDP by $10 million. Bad!

But what is the impact on the incomes of Americans other than Wheelerdealer? GDP is down by $10 million — but payments to Wheelerdealer are also down by $10 million. So the impact on the incomes of non-Wheelerdealer America is … zero. Enjoy your leisure, John!

This is totally wrong. But the question is, what exactly is wrong? A bunch of people in my earlier post listed all sorts of great insights. Word-for-word, here was the best one, from Dean T. Standin: “I wonder if people in third world countries realize that food shortages aren’t bad for them, because they get to keep the money they wanted to spend on food.”

William was astute enough to point out that Karl Smith made (one of) my points back in November 2011, an earlier time that Krugman made this mistake on his blog. Here’s Karl, who was chiding his co-blogger Adam when he (Adam) had conceded too much to Krugman:

Yet we don’t actually need [as Adam seems to think] any deviation from standard neo-classical general equilibrium analysis [in order to prove Krugman wrong].

The problem was [that Paul] stopped with one person, one hour. However, most people suspect that we are dealing with more than a single man-hour here.

Let’s review.

The underlying assumption here is that the economy is an optimizing machine. And, we know that [at] the optimum, the marginal products of any factor are equal to the factor price and that the cross marginal products are equal to zero.

However, this holds only at the optimum. Any deviation away from the optimum will cause the condition to fail and prices and quantities will need to readjust to bring the economy back into line.

If that sounds [too] abstract imagine the following claim: Every factor of production is paid its marginal product, including crude oil. So, if crude oil imports to America are restricted the impact on real wages and income for everyone in America would be precisely zero.

That doesn’t sound right.

Well, it would be right if we were talking about 1 barrel. The effect of 1 barrel of crude oil on the US economy is about the price of the barrel. Restrict the barrel and we lose that positive [effect] but we also lose having to give up what we paid for it.

However, as you continue to increase the number of barrels you restrict the marginal product of each barrel rises and the marginal product of most everything else in the economy falls.

The way we experience this is that when there is a sharp restriction on imports of oil – because of a war or something – we see the price of crude oil rise and the real incomes of most Americans fall.

The same thing would happen with the “job creators.” [Typical Karl grammar mistakes fixed.--RPM]

Okay, so here Karl is making the point I handled under “consumer surplus” in my original post. And of course, Karl is just spelling out what many of you instantly realized too.

Let me pause for a minute and make sure we all see what happened here. Krugman took the mainstream approach of using infinitesimally small changes–such that in a competitive market, a factor is paid exactly what it adds, and thus the buyer is indifferent–and then erroneously applying this knife-edge result to all of the inframarginal units.

So to be clear, Krugman is wrong even on neoclassical modeling grounds. This isn’t so much a problem with “mathematical models,” I would say, as it is a problem with GDP macro models. This isn’t an isolated example, either. In a previous article I claimed that Krugman’s reasoning from national income accounts led him to an absurd conclusion regarding international trade (though I can’t find the article at the moment…).

Really what Krugman has done here, is akin to the fallacy underlying the water-diamond paradox. So back when Karl Smith and Daniel Kuehn were calling Krugman the modern-day Bastiat, they were right: Krugman writes very eloquent essays that are bereft of modern subjective value theory, just like the old Frenchman could do.

There’s something else going on here, though, and it’s the point I was trying to make with the labor/capital distinction in my first post. For specificity, let’s use a very simple example of a Cobb-Douglas production function, the workhorse of first year grad programs in mathematical economics. It looks like this:

Y = K^(@) * L^(1-@), where 0 < @ < 1.

The ^ sign stands for exponentiation; it means "raised to the power of." The @ is supposed to be an alpha, but I am too lazy to try to use better characters here. The * stands for simple multiplication.

Okay the neat thing about the Cobb-Douglas production function is that it's easy to work with mathematically, and yet it obeys lots of properties that make economic sense. For example, the first derivative of Y with respect to either K or L is positive, but the second derivative is negative. So adding more capital or labor gives you more output, but there is diminishing marginal returns.

The other neat thing is that if you assume a competitive market for capital and labor, so that each gets paid its marginal product, then the owners of capital and labor collectively get paid enough to buy the entire product. In other words, K times the first derivative of Y with respect to K, plus L times the first derivative of Y with respect to L, equals Y. (This is fairly easy to check, for those of you who are good with calculus but have never worked through the Cobb-Douglas production function.)

So let's ask the question: If we add an infinitesimal unit of capital to this economy, what will be the impact on workers' real incomes?

First let's calculate the wage rate. It's the first derivative of Y with respect to L, in other words:

w = (1-@) * K^(@) * L^(-@)

Since it's a competitive market (by assumption), we know every period that each unit of labor gets paid w, as defined above.

Now to find the impact of an infinitesimal increase of K on workers' wages, we just take the derivative of w with respect to K, getting:

dw / dK = @ * (1-@) * K^(@-1) * L^(-@)

Note that every piece of the above expression is greater than zero. Hence, their product is greater than zero, meaning that real wages rise with an infinitesimal increment of more capital.

But wait a second! We are assuming that the person who supplies that extra (infinitesimally small) unit of capital, gets paid the entirety of the increment in total output, Y. So how can it be that supplying this extra unit of capital, also causes the workers (supplying the same total amount of labor) to receive higher real wages?

The answer, of course, is that the other suppliers of capital get less. Specifically, here’s the rental rate of capital:

r = dY/dK = @ * K^(@-1) * L^(1-@)

NOTE: Mainstream economists will be tempted to call this “the real interest rate,” but no it isn’t. That is only true if you assume that the units of physical capital are the same thing as units of physical consumption goods. If you think that’s a harmless assumption to make, then I am going to start calling w “the real rate of interest” and justify this absurd statement by positing a model with reproducing robots. (For more on this pedantic but crucial point, see the Appendix of my dissertation.)

Now then, what happens to the rental rate of capital when we increase the stock of capital by an infinitesimal unit?

dr / dK = (@-1) * @ * K^(@-2) * L^(1-@)

Notice that this expression is negative, because 0<@<1.

So what this means is that adding one more unit of capital drives up workers wages, and drives down the rental rate of capital. Yet we know that competitive markets means that the change in total output must accrue entirely as payment to the owner of that last unit of capital. Thus, the total gains in real income to the workers must be exactly counterbalanced by the total losses to the capitalists (including the guy who supplied the latest unit, if we just focus on his supply of all previous units).

This is the element of truth in what Krugman was saying. If we just focus on an infinitesimal unit of output, then withdrawing it from production will not affect the total of incomes (and here I’m talking real income) earned by all other factors.

Now, Karl Smith (as well as you guys in the comments last time) pointed out that this breaks down once we start withdrawing more than an infinitesimal unit.

But, I want to make one final point: Even if we focus on just that infinitesimal unit, it’s not the case that every single factor owner’s income is unaffected. Rather, all Krugman could prove was that the total income to everybody else was unchanged.

As we’ve seen in the specific case of a Cobb-Douglas function, but which probably generalizes under most (reasonable) assumptions, adding a unit of Factor X will drive down Factor X incomes, while increasing payments to Factor Y.

Thus, to continue with Krugman’s analysis, we can say: Yes, if WheelerDealer cuts back one hour of his work effort because of Obamanomics, total incomes to the rest of the country are unaffected. However, there is a redistribution of this (constant) total away from middle- and lower-skilled workers, and into the pockets of the other fatcats. The competition the other tycoons faced from WheelerDealer just went down by one unit, so their services, on the margin, are now that much more valuable, and hence they command a higher real income.

I hope Keynesian bloggers like Karl continue to point out this problem respectfully. Krugman has been beating this drum for at least 8 months now, perhaps much longer. I would hate for the readers of the NYT to be misled on basic price theory.

108 Responses to “Krugman, Karl, and Kalculus”

  1. Major_Freedom says:

    Excellent post.

    For those of us more inclined to verbal analysis…

    In a division of labor society, invested capital is for the physical benefit of the end consumer. Capital such as office spaces, machines, factories, and the financial claims to them such as stocks and bonds, while owned by fatcats, are nevertheless physically bound for the consumer’s material enjoyment. The real wages of all workers depends on the productivity of labor, which is determined by the extent of capital invested per worker. Worker productivity and hence real wages go up when there is more capital invested, and worker productivity and hence real wages go down when there is less capital invested.

    Therefore, if there is a reduction in capital in location A, but there is not an increase in capital in location B, then there is a net reduction in capital, and thus a net reduction in worker productivity, and thus a net reduction in the worker’s real wages. This is the case even if nominal wages rise (what Krugman probably has in mind).

    It is better for a person to earn $100 with $10 million capital invested alongside his labor, then for a worker to earn $10,000,100 with no capital invested at all. Just consider earning $10 million on a deserted island, versus earning $100 in the US.

    What Krugman is doing, as most Keynesians are want to do, is conflating “nominal income” with “real income” and in so doing ignoring the phenomenon of capital consumption. He mistakenly believes that all incomes are equivalent in terms of their economic benefit, when in reality, a constant total “income” is quite capable of being consistent with economic impoverishment.

    ————————–

    In short, just imagine that starting tomorrow, every individual, capitalist and worker alike, started spending 100% of their nominal incomes on their own consumption. Wal-Mart’s owners for example take their entire $400 billion in annual sales revenues, declare a massive dividend, and they spend it all on their own consumption, and none on capital or labor. Imagine every company doing this. Imagine every individual consuming every dollar that comes into their possession.

    What would happen? According to DeKrugman logic, since “total incomes” didn’t fall (and probably rose substantially because no more cash hoarding!), we’re supposed to believe workers are just as well off. Clearly however this would be disastrous for workers. Why? Because the capital base of the economy would eventually disintegrate altogether, as factories wear down and rust, as inventory disappears and is not replaced, and so on.

    ——————————-

    If John Q Wheelerdealer brings about a reduction in net capital in the economy, then worker’s real incomes will fall in the long run, regardless if incomes don’t fall. People eat food, not paper notes.

    • Maurizio says:

      In short, just imagine that starting tomorrow, every individual, capitalist and worker alike, started spending 100% of their nominal incomes on their own consumption. Wal-Mart’s owners for example take their entire $400 billion in annual sales revenues, declare a massive dividend, and they spend it all on their own consumption, and none on capital or labor. Imagine every company doing this. Imagine every individual consuming every dollar that comes into their possession.

      Elaborating on what you said…

      you are saying that overconsumption implies capital consumption. which in turn implies lower productivity in the future.

      Given that current central bank policies induce overconsumption, this means that capital consumption is happening right now, so we should expect a noticeable drop of productivity in the future. But this means (even assuming constant money supply) we should expect a big increase in the prices of _goods_. Right?

      Question: should we also expect _commodity_ prices to increase?

      • Major_Freedom says:

        Well we have to be careful here, because capital consumption can take place even with absolute capital accumulation taking place.

        Think of capital accumulating at a rate of 2% instead of 5%, say, whereby there is roughly 3% rate of capital consumption taking place.

        Economics is more counter-factual than temporal, because human action does not operate according to constancy. We have to ask the question “What would have otherwise taken place had actions in the past been different?”, rather than the question “What would the temporal pattern of variable set X if we do action set Y?”

        So if there is a 2% rate of capital accumulation, which would have been 5%, and if future money supply growth is higher than the rate of goods production, then prices will rise. Yes, I know this isn’t saying much in the way of predictions, but I don’t accept the possibility of scientific predictions of human choices that are based on constancy, like the rate of goods production, or the rate of capital consumption.

    • Daniel Kuehn says:

      “What Krugman is doing, as most Keynesians are want to do, is conflating “nominal income” with “real income” and in so doing ignoring the phenomenon of capital consumption. “

      This has zero to do with nominal and real income. We haven’t even introduced money.

      • Major_Freedom says:

        I actually wasn’t talking to you directly, so I am not quite sure what you mean by “we”, but in any event, you’re as usual rather clueless.

        How in the world can you say that money is not even introduced, when Krugman said in black and white:

        “But what is the impact on the incomes of Americans other than Wheelerdealer? GDP is down by $10 million — but payments to Wheelerdealer are also down by $10 million. So the impact on the incomes of non-Wheelerdealer America is … zero. Enjoy your leisure, John!”

        Among other statements concerning money?

        Krugman is clearly saying that because the MONEY income decline for Wheelerdealer is offset by a corresponding MONEY income increase elsewhere ($10 million decrease here, $10 million increase there), that the net result to “incomes” is zero, and hence there is allegedly no net loss of any kind.

        Goodness gracious Daniel, I mean really? Zero to do with nominal income? Haven’t even introduced money? Come on!

        • Daniel Kuehn says:

          Money is not introduced into the model

          There is no distinction between real and nominal values in the model, either the verbal one that Krugman presents or the neoclassical one that Bob does.

          Don’t write long posts about nominal and real values if you don’t understand what you’re talking about. The fact that a dollar sign came up in his post does not mean that money or real or nominal values have come into the discussion.

          You don’t know what you’re talking about here. Everything everyone has been talking about so far is in real values.

          • Major_Freedom says:

            Money is not introduced into the model

            I was talking about Krugman’s argument. What “model” are you talking about?

            There is no distinction between real and nominal values in the model, either the verbal one that Krugman presents or the neoclassical one that Bob does.

            False. It is quite obvious that $10 million refers to incomes, not capital goods.

            Don’t write long posts about nominal and real values if you don’t understand what you’re talking about.

            OK, then I’ll keep writing long posts then.

            The fact that a dollar sign came up in his post does not mean that money or real or nominal values have come into the discussion.

            Are you braindead? My whole point is that Krugman is only looking at nominal values, and ignoring real values. He says that because total incomes did not fall, there is allegedly no loss. But there is a loss, in REAL terms, which is what I explained.

            You don’t know what you’re talking about here.

            I do know what I am talking about here. You don’t know what you’re talking about.

            Everything everyone has been talking about so far is in real values.

            False. Krugman was talking about money incomes.

            • Daniel Kuehn says:

              re: “False. It is quite obvious that $10 million refers to incomes, not capital goods.”

              Right. REAL incomes.

              re: “My whole point is that Krugman is only looking at nominal values, and ignoring real values.”

              No his problem is that he can’t trouble himself to do the undergraduate exercise that Bob presents here and he can’t trouble himself to think through what’s actually going on in factor markets to make these changes in the output markets.

              That’s his problem.

              But so far all of us are working in real value space.

              • Bharat says:

                You say you’re not agreeing with Krugman. But you state that Krugman is talking about real income, not nominal income.

                MF is stating that if there is a net reduction in capital, total real income decreases although total nominal income stays the same.

                Krugman is stating that total income stays the same.

                Either you believe Krugman is right on this specific point and believe total real income stays the same with a net decrease in capital or you disagree with Krugman on this point and believe only total nominal income stays the same with the net decrease in capital. Which is it? Actually, I guess there is a third option. You believe Krugman was attempting to apply his analysis in real terms to more than just infinitesimal units, but because his argument only applies to infinitesimal units, it should totally be thrown out the window.

              • Bob Murphy says:

                Bharat wrote:

                MF is stating that if there is a net reduction in capital, total real income decreases although total nominal income stays the same.

                Krugman is stating that total income stays the same.

                I’m not sure if you are correctly describing MF’s position, but I am sure you are not getting Krugman right. Krugman agrees that if there is a reduction in labor input from a WheelerDealer, that total national income (real) goes down. But he’s saying that matches up exactly with the fall in WheelerDealer’s real income. Thus, the real output available to everybody else, is unchanged.

                This is actually an implication of a misreading of what free-market people mean when they say, “People get paid their marginal product.” If you think WheelerDealer makes the economy produce more total stuff than it otherwise would have, *and* if you think competitive labor markets give workers exactly what they add to the firm’s output, then Krugman seems to have a point. But alas, he is wrong because workers are actually only paid the marginal value for *every* unit of input they give.

              • Major_Freedom says:

                Murphy:

                Krugman agrees that if there is a reduction in labor input from a WheelerDealer, that total national income (real) goes down. But he’s saying that matches up exactly with the fall in WheelerDealer’s real income. Thus, the real output available to everybody else, is unchanged.

                Murphy can you parse this a little more? It doesn’t make any sense to me.

                You’re interpreting Krugman as saying that there is a reduction in labor input from Wheelerdealer and hence a reduction of national (real) income due to his reduction in output. To me, this is sufficient to show that non-Wheelerdealers are worse off.

                Before they paid Wheelerdealer the $10 million for his output, and whatever they have left they spend on their own output, and then after Wheelerdealer goes Galt, they pay themselves $10 million, but they have to do without Wheelerdealer’s output.

                So even though non-Wheelerdealers are commanding more nominal spending than before, $10 million more, the $10 million has a lower purchasing power, because there is less production.

                But you interpret Krugman as saying that while Wheelerdealer reduces his productivity, and thus reduces national production, there is an equivalent reduction of what others produce for his sake, on account of others making $10 million more nominal income than before. Thus, allegedly, there is an equivalent gain to non-Wheelerdealers.

                But that can’t be right, because there is still a net reduction in productivity on account of Wheelerdealer producing less. The $10 million in spending that Wheelerdealer originally made was due to his productivity. So he didn’t REDUCE the amount of goods that others can buy on account of him spending that money. He EARNED that $10 million by producing real wealth for others.

                So if Wheelerdealer reduces his productivity, then yes, he will make $10 million fewer dollars. But this doesn’t mean the idea that non-Wheelerdealers can now consume $10 milllion worth of goods more, that they are no worse off, is correct. They are worse off. They are worse off by precisely his productivity decline.

                To make what I am saying as clear as possible:

                Imagine everyone is equally productive and everyone earns $100 a day. Every time someone spends $100, they are making it impossible for others to spend $100. In this sense, they are “reducing” what is available for others. But each person’s $100 spending is due to them producing $100 worth of goods and earning $100 in money. So while they reduce other’s consumption by $100, they are adding $100 of consumption.

                If one person then produces less, say half, then they produce only $50 worth of goods, but they only consume $50 worth of goods too. This doesn’t mean that others can consume $50 worth of goods more, because there is a net loss of $50 worth of goods. So even though the others are spending $50 more amongst them, they are buying fewer goods, exactly to the extent the person in question reduced their productivity.

                So when you say:

                If you think WheelerDealer makes the economy produce more total stuff than it otherwise would have, *and* if you think competitive labor markets give workers exactly what they add to the firm’s output…

                I think that is exactly what refutes Krugman. The workers who used to buy Wheelerdealer’s output, now have to do with less of that output. Earning $10 million more dollars doesn’t make them more prosperous in real terms. Those dollars have a lower purchasing power.

              • Bharat says:

                Haha, well now I understand Krugman’s position but I’m not so sure I understand MF’s.

                Originally, I thought he was stating that value is subjective and that because exchanges are mutually beneficial, real income always goes down with the loss of a productive individual. Is that what you’re saying MF? I got confused by your last post.

              • Bharat says:

                Nevermind, I get what you’re saying now.

                If Wheelerdealer originally produces $100 in goods, he originally consumes $100 as well. If he reduces his production to $50 in goods, he reduces his consumption to $50 in goods as well. Total nominal income may stay the same to everyone else, but total real income cannot, because $50 in goods originally sold to non-wheelerdealers have disappeared.

                Non-wheelerdealers cannot buy that lost $50.00 in goods from other non-wheelerdealers, unless non-wheelerdealers start producing more. But assuming this is constant, $50.00 in goods originally sold to non-wheelerdealers is lost.

                But aren’t non-wheelerdealers now selling more to each other than they were before when they were selling $50.00 worth of goods to Wheelerdealer? And isn’t that amount precisely $50 in goods?

              • Bharat says:

                Let me know if I understand your position correctly.

              • Major_Freedom says:

                Bharat, that is exactly it.

              • Major_Freedom says:

                Actually, I responded with “That is exactly it” before I read this:

                But aren’t non-wheelerdealers now selling more to each other than they were before when they were selling $50.00 worth of goods to Wheelerdealer? And isn’t that amount precisely $50 in goods?

                This is the “main” confusion being made IMO.

                They are not selling more to each other than before, because before they produced X for themselves, sold an additional $100 worth of goods to Wheelerdealer, and BOUGHT $100 worth of goods FROM Wheelerdealer. Total for non-Wheelerdealers is X + $100 worth of goods.

                After, they produced X for themselves, sold an additional $50 worth of goods to Wheelerdealer, and bought $50 worth of goods from Wheelerdealer. Total for non-Wheelerdealers is X + $50 worth of goods.

              • Bharat says:

                Why would they only produce x for themselves after the fact?

                Let’s say Wheelerdealer produces $100 and reduces to $50. Originally he was producing and consuming $100, now he’s producing and consuming $50.

                Before, nonWheelerdealers were producing $Y (so they were both producing $Y and consuming $Y). Now, after Wheelerdealer’s reduction, why should anyone else choose to produce less total in real goods? The argument is that Wheelerdealer’s lost output is lost by himself equivalently through a loss in consumption. That much, I think you agree with. But why should nonWheelerdealers start producing less in real goods? Isn’t that the only way a reduction in their real production/consumption can take place?

                If originally they were producing $X for themselves, shouldn’t they now be producing $X+50 for themselves? $Y is what stays constant, not X.

                Hopefully I’m not arguing against something you feel like you’re already answered, seems like I’m late to the understanding lol.

              • Major_Freedom says:

                Bharat:

                The non-Wheelerdealers cannot be assumed as producing as much as before, because there is a reduction in capital on account of Wheelerdealer producing less.

                Wheelerdealer isn’t a producer of consumer goods. He is a producer of capital that increases the productivity of labor. With less capital, the non-Wheelerdealers will produce less for themselves.

                Try not to focus too much on the $50 worth of goods and $100 worth of goods. It clouds the difference between capital goods and consumer goods.

                If everyone just produced and consumed consumer goods, then Wheelerdealer’s reduced output and equivalently reduced consumption won’t have any effect on non-Wheelerdealers. But when Wheelerdealer is a producer/provider of capital, then he increases other people’s productivity, and so we cannot assume it’s just a loss of a consumer who consumes the equivalent of what he produces.

              • Bharat says:

                Gotcha, that makes sense.

          • Major_Freedom says:

            As expected, another Keynesian DK cannot distinguish between nominal and real, precisely because Keynes himself conflated the two and jumped back and forth haphazardly.

            To clue you in DK,

            “But what is the impact on the incomes of Americans other than Wheelerdealer? GDP is down by $10 million — but payments to Wheelerdealer are also down by $10 million. So the impact on the incomes of non-Wheelerdealer America is … zero. Enjoy your leisure, John!”

            Having fun yet?

            • Ken B says:

              This is the first time I learned that there can be no payments in a barter economy. Cool. So when my grandfather’s patients in the 30 left eggs for services rendered they weren’t paying him!

              • Major_Freedom says:

                Yeah, because Krugman was talking about a barter economy in his example of a Romney supporter named John Q. Wheelerdealer. the financial capitalist

                Geez you flies stick together against your ideological enemies, no matter what the depths of absurdity you’re willing to go.

              • Major_Freedom says:

                In what barter world are DOLLARS being used as a standard of measurement of incomes?

                Just askin’

              • Daniel Kuehn says:

                re: “Geez you flies stick together against your ideological enemies, no matter what the depths of absurdity you’re willing to go.”

                Dude, no one on the thread has agreed with Krugman yet.

                You’re the type of guy that sees enemies lurking around every corner, aren’t you?

              • Daniel Kuehn says:

                Barter is irrelevant.

                The question is are these dollar payments real or nominal?

                They are real.

                Nobody has brought money or the price level into the discussion.

                They are real.

              • Major_Freedom says:

                <i.Dude, no one on the thread has agreed with Krugman yet.

                I didn’t say they did. I was referring to Ken B and you.

                You’re the type of guy that sees enemies lurking around every corner, aren’t you?

                You’re the type of guy who makes enemies around every corner, aren’t you?

              • Ken B says:

                In what blogoverse does bolding the word ‘payments’ not mean you are emphasizing the word ‘paymentts’?

              • Major_Freedom says:

                DK:

                Barter is irrelevant.

                The question is are these dollar payments real or nominal?

                They are real.

                No, they are nominal. Payments in dollars for John Q. Wheelerdealer go down, and nominal incomes to others goes up, thus no alleged change.

                Nobody has brought money or the price level into the discussion.

                Krugman did.

                They are real.

                No, they are nominal.

                ———————

                You know what? Murphy is absolutely right about you DK. You will go to any level of outright absurdity and foolishness to defend Krugman when you know he got caught. This is the WORST attempt I have ever seen by you.

                This is bordering on intellectual dishonesty, I’m sorry to say.

              • Ken B says:

                You see DK M_F is a team guy. You defended PK from one charge, so despite your own blog posts slamming PK, you are supporting PK, ipso facto. I made a comment ridiculing one of M_F’s weak inferences, and so that puts me on the other team, so ipso facto I am defending PK.

                That’s life with M_F, and often enough just life on FA.

              • Major_Freedom says:

                You see DK M_F is a team guy. You defended PK from one charge, so despite your own blog posts slamming PK, you are supporting PK, ipso facto.

                I think you’re just a little sore from the whole bible thing in the last post, so that you’re now inferring something completely false on me.

                Slamming PK? Not when the slammer thinks PK is a moron. Then he turns into defend PK.

                I made a comment ridiculing one of M_F’s weak inferences, and so that puts me on the other team, so ipso facto I am defending PK.

                I am going by ideas, and I see clusters of them and noticable patterns. You’re not random when it comes to the advocates. You treat Murphy’s posts for example differently than you do others, despite the fact that he writes things that are on par with what others write in terms of content and position held.

                You should look in the mirror Ken B.

              • Major_Freedom says:

                Ken B

                In what blogoverse does bolding the word ‘payments’ not mean you are emphasizing the word ‘paymentts’?

                I don’t know, why do you ask? I didn’t bold the word payments to NOT emphasize the word payments. I bolded it to emphasize the fact that Krugman was talking about nominal incomes, not that the entire post wasn’t obvious enough.

              • Ken B says:

                “You should look in the mirror Ken B.”

                I look too much like Murphy to enjoy the experience.

              • Major_Freedom says:

                Try P90X. You can embarrass yourself in the comfort of your own home. I did.

              • Daniel Kuehn says:

                I’M NOT AGREEING WITH KRUGMAN. Krugman is wrong here.

                I’m DISAGREEING with you on a really stupid, tangential point.

              • Major_Freedom says:

                I’m DISAGREEING with you on a really stupid, tangential point.

                Ah, so now it’s stupid and tengential? Sounds like an admission to me.

                That “stupid” point is key to the entire argument of why PK is wrong to assume that unchanged nominal income does not mean unchanged prosperity.

                PK has AD on the brain.

  2. Tel says:

    This may sound nitpicky (probably because it is) but you seem to automatically presume that John Q Wheelerdealer is himself equivalent to capital (i.e. the K part of the equation). I can imagine various scenarios, for example John is a CEO of an important factory and just decides one day to resign and learn to surf and so the factory doesn’t stop production it just gets a different CEO (presumably promoting up someone not quite as good as John, but probably someone OK). In that case the economy lost John’s labour, but didn’t lose the capital itself.

    In a different scenario, maybe John owns the factory and decides to shut it all down because it isn’t economical to run anymore. Then the economy does lose capital, and also loses John’s labour.

    I think we should give Krugman the benefit of the doubt on which scenario he might have been talking about (not because Krugman deserves any benefits, just because we are all nice guys here).

    Also, with regards to units, it seems that Y and K and L all need to have the same units (i.e. $ per time period) which would imply that both dL/dY and dK/dY are unitless (the units divide out). That doesn’t quite fit the narrative. I’m seeing dL/dY and dK/dY as some sort of efficiency factors, but maybe an example with good honest numbers might help (coconuts perhaps).

    • Bob Murphy says:

      Tel wrote: This may sound nitpicky (probably because it is) but you seem to automatically presume that John Q Wheelerdealer is himself equivalent to capital…

      Well, that’s what I meant in the part where I said you could generalize. If you had Y = f(K, L, W), where K is capital, L is regular labor, and W is the effort of Wheelerdealers, then I think you’d get similar results.

      • Tel says:

        You generalized by jumping a 2 dimensional function into a 3 dimensional function. Did you know that something special happens when you step from 8 dimensional space into 9 dimensional space? Not many people know this.

        I quote Martin Gardner’s Mathematical Circus, page 39, Spheres and Hypershperes:

        David Singmaster, writing “On Round Pegs in Square Holes and Square Pegs in Round Holes” (Mathematics Magazine, Vol. 37, November 1964 pages 336-37), decided that a round peg fits better in a square hole than vice versa because the ratio of a circle to a circumscribing square (π/4) is larger than the ratio of a square inscribed in a circle (2/π). Similarly, one can show that a ball fits better in a cube than a cube fits in a ball, although the difference between ratios is a bit smaller. Singmaster found that the difference continues to decrease through 8-space and then reverses: in 9-space the ratio of the n-ball to n-cube is smaller than the ratio of n-cube to n-ball. In other words, an n-ball fits better in an n-cube than an n-cube fits in an n-ball if and only if n is 8 or less.

        Is this important?

        Let’s consider an economy with only one production factor, or if you like:

        Y = f(L)

        Kind of stupid right? Only one dimension, must be linear. What you get out is what you put in. Boring as bro. So we generalize by adding dimensions, and after thinking a bit, we could add various kinds of labour to the picture. I mean, that’s the whole idea of division of labour, you have specialists in particular fields, who can achieve more than what a generalist would do, but only useful when other specialists are doing their part.

        So to capture this, the number of dimensions has to keep increasing, as the various types of speciality labour keep sub-dividing. However, we run into the problem that higher dimensional spaces behave intrinsically differently to low dimensional spaces (turning around at the crossing from 8-space to 9-space) and what makes sense with a small number of variables no longer fits together with large numbers of variables.

        Just saying there’s a pitfall waiting for you… not pretending I know the way around it.

        • Ken B says:

          That’s pretty cool. And no, I did not know that.

        • Major_Freedom says:

          Are different individuals performing different labor a multiple spatial dimension scenario?

          There’s around 140,000,000 million workers in the US. I don’t think anyone would say that the intuition that gains through division of labor can be increased going from 2 people to 3, and 3 people to 4, and so on, suddenly “intrinsically” changes going from 8 people to nine.

          • Tel says:

            There’s a kind of difficult transition from micro economics (where everyone is an individual) into macro economics (where you just have to classify people because million dimensional problems are intractable).

            So, if you have thousands of agricultural labourers with no particular skills and they dig dirt then it’s not entirely unreasonable to add up their total efforts into an aggregate and no one really cares if you swap two of them around or anything.

            However, a modern economy is made up of many specialists. Let’s suppose all forensic accountants are the same, but experts on accounting ethics are sufficiently different to require their own category. Maybe one software engineer is as good as any other, but a network specialist is a different animal.

            You see how rapidly the problem expands?

            I don’t think anyone would say that the intuition that gains through division of labor can be increased going from 2 people to 3, and 3 people to 4, and so on, suddenly “intrinsically” changes going from 8 people to nine.

            What I’m pointing out is that the mathematical behaviour of high dimensional systems cannot easily be inferred from low dimensional systems. If we have reason to believe we are dealing with a high dimensional problem, then we are stuck with statistical methods rather than transfer functions. Consider the approach that particle physics adopted: Maxwell–Boltzmann statistics, Fermi–Dirac statistics and Bose–Einstein statistics.

            The link between microeconomics and macroeconomics seems to me more closely linked to particle statistics than it does to the traditional aggregates.

            • skylien says:

              What you are essentially saying is that the economy is a bit like the climate, which is a dynamic complex chaotic non-linear system.

              Except the economy is additionally adaptive and doesn’t even have any constants that well stay constant.

            • Major_Freedom says:

              Let’s suppose all forensic accountants are the same, but experts on accounting ethics are sufficiently different to require their own category. Maybe one software engineer is as good as any other, but a network specialist is a different animal.

              You see how rapidly the problem expands?

              I don’t even see a problem.

              What I’m pointing out is that the mathematical behaviour of high dimensional systems cannot easily be inferred from low dimensional systems.

              Well then don’t use mathematics to understand the economy of acting man, and you won’t run into such problems.

              If we have reason to believe we are dealing with a high dimensional problem, then we are stuck with statistical methods rather than transfer functions.

              If it isn’t a high dimensional problem, but a problem of epistemological approach, then we don’t have to remain stuck.

              Consider the approach that particle physics adopted: Maxwell–Boltzmann statistics, Fermi–Dirac statistics and Bose–Einstein statistics.

              Consider the approach that economists have adopted: Mises-Praxeology.

              The link between microeconomics and macroeconomics seems to me more closely linked to particle statistics than it does to the traditional aggregates.

              Humans aren’t particles. Humans act.

          • Tel says:

            Mathematics is nothing more than the formal process of starting with axioms and building a symbolic representation of the implications of those axioms (constrained such that the system as a whole is self-consistent and the results are repeatable). If you build any sort of knowledge representation in this axiomatic way (and Praxeology does appear to be built this way) then that is mathematics. You can express it verbally if that suits your taste, words are after all a set of symbols that represent concepts.

            If you start with the axiom that the world of statement consists of true statements and false statements, then you are doing boolean algebra. If you want to do that in words or in algebraic notation or some other notation that suits you then be my guest.

            If you want to start introducing additional truth values beyond “true” and “false” then you get into 3-value logic or fuzzy logic or a lot of other areas that have also been extensively studied and mapped. You might as well take advantage of the work other people have done in these areas.

            Now you say that humans are different to atoms, because humans act. Well as far as I know humans are made of atoms, so anything a human is doing is also being done by atoms.

            Of course humans are more complex than individual atoms, because humans are an emergent being consisting of mind-bogglingly large numbers of atoms put together in a very particular manner. Intellectually, it is more convenient, and efficient to conceive of a human as a single entity rather than trying to keep track of where many atoms are going. Most of the time you don’t need to worry about exactly how much blood is in someone’s big toe in order to have a conversation with them. We ignore a lot of irrelevant details simply because they don’t concern us.

            • Major_Freedom says:

              There is a difference between recognizing an epistemological affinity between praxeology and mathematics, and trying to force mathematical concepts like continuous functions into economics simply because they make sense in mathematics. Not even physicists accept continuous function phenomena anymore. Quantum mechanics is discrete.

              ——————

              Now you say that humans are different to atoms, because humans act. Well as far as I know humans are made of atoms, so anything a human is doing is also being done by atoms.

              I am more than the atoms of which I am composed.

              Of course humans are more complex than individual atoms, because humans are an emergent being consisting of mind-bogglingly large numbers of atoms put together in a very particular manner. Intellectually, it is more convenient, and efficient to conceive of a human as a single entity rather than trying to keep track of where many atoms are going.

              More convenient, or necessary? Even if you had a supercomputer than can know the exact locations and speeds of every particle in my body, there’s still uncertainty because you don’t know the exact locations and speeds of every particle in the universe that I might utilize.

    • csentropy says:

      Wouldn’t the capital that would have been accumulated had John Q been the CEO vs the “less good” replacement CEO be considered capital lost? If so, what is lost is not just John Q’s labor but the capital accumulation as a result of the loss of his labor. Am I missing something?

      • Tel says:

        I’m tempted to think that this would apply to anyone’s labour… presuming that somehow they produced more than they consumed, or at any rate produced more than they would have produced if they were unemployed.

        I’d better stop now before I start making excuses for some government jobs guarantee.

  3. Gienon says:

    So much for the Murphy-Krugman debate after this kind of annihilation ;/

    • Daniel Kuehn says:

      Don’t be so pessimistic. There’s PLENTY that Bob still gets wrong :)

      • Major_Freedom says:

        He doesn’t hold a candle to you in that respect.

      • Bob Murphy says:

        I’m kind of backed up with being a wheelerdealer right now, Daniel, but I skimmed the stuff at your blog and I don’t see what your deal is. We are assuming a healthy market economy with no problems of AD or whatever. In that context, the economy re-optimizes when WheelerDealer removes the infinitesimal unit of capital. So total (real) income to everybody else really is unchanged. I mean, we can measure it with the Cobb-Douglas function if you want to use a specific model.

        Obviously we can bring up all sorts of real-world complicating factors, saying how my story in this post is leaving all kinds of stuff out–you and MajorFreedom would surely come up with a different list of omissions. But I think in the context of what Krugman was doing–where he was trying to say, “These idiots right-wingers don’t even know the implications of their own faith in Chicago-School markets”–then he is correct to say total income to everybody else remains unchanged, if we limit Krugman’s point to an infinitesimally small reduction in WheelerDealer’s contribution.

        • Bob Murphy says:

          I’ve got it: Krugman made a legitimate point, but it was infinitesimally small. In the limit, Krugman’s position shrinks to zero.

          • Ken B says:

            Isn’t that an inframarginal argument?

          • Major_Freedom says:

            If you’re talking real terms, I think it’s not even true in the infinitesimally small scale.

            Strictly speaking, if the change in real incomes for an infinitesimally small change in capital is zero, then two, three, four, five, a hundred, a million, etc, infinitesimally small changes in capital should also bring about a zero change in real income.

            An infinitesimally small unit of good not going to Wheelerdealer, but to Joe Plumber instead, is net zero to “national real income”, but there is still the infinitesimally small reduction in production FROM Wheelerdealer that did not take place because he went 1/3 Galt (3000 hours down to 2000 hours).

            Regardless of what others not John Q Wheelerdealer are doing when it comes to the shifting and moving of the goods they produce and sell, society as a whole still goes without 1000 hours of Wheelerdealer’s real productivity.

            Krugman is just looking at incomes, rather than real productivity.

            • Major_Freedom says:

              I think Krugman is tacitly assuming the Marxian idea that the productivity of capitalists accrue to the capitalists only, and nobody else. It is the only explanation I can think of that would lead him to believe that less (earnings) and thus productivity from the capitalists, the more is available for others who are not a Wheelerdealer, and then construct a silly scenario post hoc to for his readers.

            • Bob Murphy says:

              MF wrote:

              Strictly speaking, if the change in real incomes for an infinitesimally small change in capital is zero, then two, three, four, five, a hundred, a million, etc, infinitesimally small changes in capital should also bring about a zero change in real income.

              MF, rather than me argue this with you, I just want to point out that you are here attacking differential calculus, not just Krugman. Are you prepared for that battle, this Thursday July 19, in the year 2012 of our Lord?

              • Ken B says:

                Differential calculus has a lot to answer for. Now integral calculus, there’s something that really adds up.

              • Bob Murphy says:

                I can’t remember Ken B., are you still on my embargo list? If not, I will chuckle.

              • Ken B says:

                Oh I doubtless am Bob, but I’m willing to hug and make up, like RPLong suggests we do.

                No kissing though.

                At least, no deep kissing.

              • Major_Freedom says:

                You want to battle my attack on differential calculus? In an economics discussion?

                OK, but just to preempt things, I will set a ground rule of my own and reject every “infinitesimal” change in physicality that is not an object of subjective valuation such that they are not something relating to economics, but to chemistry or physics.

                Other than that “tiny” caveat, haha, let’s do this.

              • Tel says:

                Apologies for trying to be serious for a moment :-)

                Differential calculus only works with things that can reasonably be approximated to be smooth, continuous variables.

                Integral calculus works with “lumpy” variables. In a nutshell: differentiating amplifies measurement noise, but integration attenuates the noise.

              • Bob Murphy says:

                BTW something seems to be screwy with my WordPress interface. It’s showing me that my reply to you was posted in the Yield Curve thread, but of course, I am trying to question you in the Krugman Kalculus one…

              • Ken B says:

                @Tel: If you want to be analytic the situation is complex.

        • Daniel Kuehn says:

          My deal is not to criticize your arguments here. As you can see, I repeated a lot of them for my readers.

          But when I think you can go even harder on Krugman than that I like to point it out :)

          I didn’t intend it as a “see how Bob’s analysis is wrong” post – more of a “here’s an addendum of what’s wrong with Krugman”.

          • Bob Murphy says:

            DK right, I get that. And I’m saying, I think you are being too hard on Krugman. (Butt-head: Heh heh, he said hard on.) In the context of what he was trying to do–namely, deploy Chicago School price theory against right-wingers who worship the “job creators” among the upper .1%–I think Krugman’s only real mistake was the marginal/inframarginal one. Beyond that, he wasn’t wrong but was very misleading (perhaps unintentionally) when he didn’t point out that this constant “total income of everyone else” would redistribute away from regular Joes and into the hands of the fatcats.

            Then I took you to be saying, “Ah, but yet another mistake is that actually, because of withdrawing an infinitesimal unit of capital, total real income of everybody else really does go down.” And I’m saying, no it doesn’t, not under the ground rules we’re using.

            • Daniel Kuehn says:

              Well it’s everyone’s price theory, isn’t it? Anyway, I still think it does. No matter.

              • Bob Murphy says:

                DK wrote: Well it’s everyone’s price theory, isn’t it?

                No, some people don’t think every factor gets paid its marginal product; it’s how theorists get around objections to minimum wage laws, for example. Some people think that cooperative game theory might be a better approach to particular issues.

              • Bob Murphy says:

                DK hang on a second here. Of course total output goes down (by a teensy bit) when you reduce one of the inputs by an infinitesimal amount. But, if factor markets are competitive, that reduction in real output matches up exactly with the loss in real income by the owner of that infinitesimal unit. So the total income accruing to all other units of input is the same.

                This isn’t open to debate, if you agree that factors get paid their marginal product in equilibrium.

            • Scott Angell says:

              So the total income accruing to all other units of input is the same.

              This isn’t open to debate, if you agree that factors get paid their marginal product in equilibrium.

              Wow. Every time one of these debates get this technical, I feel a little bit more retarded.

              I could’ve sworn that loss of participation in the division of labor would’ve impacted everybody else negatively & reduced total income. I never would’ve thought of the redistributive effect, either.

              Pretty cool.

              • Bob Murphy says:

                Scott Angell,

                Just be careful that you don’t draw too much from this. Yes, in general because of the division of labor and other features of the real world, someone withdrawing his labor from society will make everyone else poorer. Your intuition was right.

                However, Krugman thought that this insight contradicted another tenet of free-market economics, namely that workers get paid the full marginal product of their labor.

                So if you think about those two things, they do at first seem contradictory. I.e. if John joins society and makes everybody else richer, even if John spends all of his paycheck at the bar every week, then it seems as if John isn’t being paid the full marginal product of his labor.

                There actually isn’t a contradiction, but it has to do with what we mean by “marginal.”

  4. joeftansey says:

    It would have been funnier if the blog post were titled “Krugman, Karl, and Calculus”, because we’d realize you could have gone with calculus, then realize that you are probably aware of this, and then laughed at what you just made our brains do.

    • joeftansey says:

      *kalculus

      • Bob Murphy says:

        It would have been funnier if you didn’t put “*kalculus.” Then we would have wondered if you intentionally did a Triple Lindy.

    • Ken B says:

      Spell bolour with a ‘k’?

  5. christopher fisher says:

    You invoke Bastiat, but does anyone else see the parable of the Broken Window with Krugman’s claim:

    Now let us consider James B. himself. In the former supposition, that of the window being broken, he spends six francs, and has neither more nor less than he had before, the enjoyment of a window.
    In the second, where we suppose the window not to have been broken, he would have spent six francs on shoes, and would have had at the same time the enjoyment of a pair of shoes and of a window.
    Now, as James B. forms a part of society, we must come to the conclusion, that, taking it altogether, and making an estimate of its enjoyments and its labours, it has lost the value of the broken window.
    Whence we arrive at this unexpected conclusion: “Society loses the value of things which are uselessly destroyed;” and we must assent to a maxim which will make the hair of protectionists stand on end—To break, to spoil, to waste, is not to encourage national labour; or, more briefly, “destruction is not profit.”
    -Bastiat

    Basically, when you take production out of society, society is worst off by that amount. Although this model might break down if you switch the hypothetical rich person job with the job of Mr Krugman.

  6. JoshArizona says:

    Math has letters now?

  7. Kevin Donoghue says:

    “In a previous article I claimed that Krugman’s reasoning from national income accounts led him to an absurd conclusion regarding international trade (though I can’t find the article at the moment…).”

    Try the link below. My impression is that you are making the same mistake now as then, i.e. attributing an error to Krugman which he isn’t actually making, because he isn’t reasoning from national accounts as you suppose. In this case all he’s doing is applying the Envelope Theorem.

    http://mises.org/daily/3945

    • Bob Murphy says:

      Kevin Donoghue, are you saying Krugman is correct in what he’s saying about WheelerDealer? If so, you are the first person to do so. And yet, on Daniel Kuehn’s blog, you listed 8 different things you thought were wrong with Krugman’s analysis, such that you said you doubted Krugman was actually serious when he wrote the post.

      So what gives? Are you doing something really nuanced here, like saying “Yes Krugman is wrong, but because he is incorrectly applying the Envelope Theorem, not because he’s incorrectly applying national income accounting, as you seem to think Bob.” ?

      • Kevin Donoghue says:

        Maybe I’m the first to say Krugman is correct in this thread, but that doesn’t make him or me wrong. Krugman is applying the Envelope Theorem correctly: the difference between the income which WheelerDealer foregoes by going Galt and the reduction in national income is approximately zero. Not exactly zero, because there’s a small ‘triangle’ under the marginal productivity curve with area 0.5 x dL x dW, where W is WheelerDealer’s real wage and L his input.

        On DK’s blog, I didn’t say Krugman’s analysis was wrong; it’s perfectly standard theory. What I said was that Krugman: (1) doesn’t adhere to standard theory in his own research, where he uses increasing returns to scale; (2) doesn’t believe it should be applied to WheelerDealer in any case (it’s like talking about the marginal productivity of a pirate); (3) knows very well that the likes of Sarah Palin and Paul Ryan don’t go in for this marginalist stuff; they have quite different reasons for wanting to further enrich the rich.

        • Bob Murphy says:

          Kevin D. wrote:

          Not exactly zero, because there’s a small ‘triangle’ under the marginal productivity curve with area 0.5 x dL x dW, where W is WheelerDealer’s real wage and L his input.

          Kevin, that sounds dangerously close to saying, “If the reduction in input from the super rich is close enough to zero, then Krugman is right.” That’s what everybody has been saying. You can also say, “Krugman is wrong.”

          Krugman has been talking about right-wing claims that tax hikes on the rich hurt “the economy,” and he has been using this analysis to say that’s nuts. He’s not talking about an epsilon reduction of labor input, he’s talking about a possibly substantial reduction too.

          • Kevin Donoghue says:

            Obviously if the rich all emigrate to Australia that’s a whole different story. Enough already. I think we understand each other. On the off-chance that a picture really is worth 1,000 words, I drew one here:

            http://anyoldbullshit.blogspot.ie/2012/07/a-picture-for-bob-murphy.html

            • Major_Freedom says:

              Kevin the envelope theorem only applies to continuous functions.

              The pitfall of using mathematical concepts to explain economic phenomena is that you end up having to forcefeed the mathematical assumptions into the real world where they are not even applicable, such that you end up making the claim that a decline in a single individual’s productivity leads to an “infinitesimally small” reduction to net output, that can be ignored.

              Yet in the real world, the relationship between labor and output is not a continuous function. A reduction in a single individual’s productivity will result in a distinct, positive, significant net loss to national income that is (or course) exactly identical the drop in productivity of that single person.

              Please note that Krugman did not even use the envelope theorem correctly, because he said there would be NO change to the aggregate, that the $10 million fall is accompanied by a $10 million gain. There is no “small triangle” implied in his article. He was reasoning incorrectly from the concept of “national income”, and inferred from an unchanged nominal spending that there is no net loss to anyone. Wheelerdealer gets $10 million less, others get $10 million more, hence no loss.

              He didn’t take into account that the second $10 million (the offsetting increase) will have less purchasing power, to the exact extent of Wheelerdealer’s decline in output.

            • Bob Murphy says:

              Kevin D. wrote:

              Obviously if the rich all emigrate to Australia that’s a whole different story. Enough already. I think we understand each other. On the off-chance that a picture really is worth 1,000 words, I drew one here:

              Yes, the picture was helpful in that you are drawing exactly what Karl Smith and I said in words. :) Our point was, “Krugman is right for a marginal change in labor supply. But in the context of his argument, he leads his readers to think that the point would hold in general.”

              You are not defending Krugman from our critiques, by pointing out that an infinitesimal change in labor supply will yield Krugman’s answer. Right. Karl and I both said that, upfront.

              If you want to defend Krugman, you will have to quote from his discussions and show why he was telling his readers that this only works if just one guy restricts his input. But if more than one WheelerDealer starts doing this, his argument collapses.

              • Major_Freedom says:

                If you want to defend Krugman, you will have to quote from his discussions and show why he was telling his readers that this only works if just one guy restricts his input. But if more than one WheelerDealer starts doing this, his argument collapses.

                Why does it work with one person but not more?

                Even if one person reduces his productivity FOR OTHERS, doesn’t that mean the other’s real income declines, even if they make more nominal dollars?

              • rob says:

                If you take a very simple economy with 2 farmers. Farmer A produces 20 apples and farmer B produces 20 Bananas. Suppose they trade 10B for 10A and both have maximized their utility.

                Farmer A retires and Farmer B then can only produce 8 apples and 7 Bananas.

                Farmer A produced 20unit of fruit and consumed 20 units so his contribution was neutral as Krugman says. Except without his contribution Farmer B loses 5 units of consumption that came from division of labor and trade.

                If you added in more farmers then the contribution of one farmer to total productivity diminishes but never goes away.

                A very small number is not zero and the sum of all these small numbers adds up to the benefits we get from division of labor and trade.

                Which I think is what Bob’s model also shows.

            • rob says:

              The “small triangle” is actually quite big and illustrates why Krugman is wrong.

              • Major_Freedom says:

                This is my assessment too.

                Even if a single individual doesn’t go to work one day, then output for others declines, however small his addition to the total pie happens to be. If his employer doesn’t pay him for that day, and they have more money to spend, that money will still have a lower purchasing power.

                Anyone who says one person’s reduction in productivity has no effect on others, but somehow, when an unstated, fuzzy logic, faded out middle is passed, after which we get to “many people” reducing their productivity, that now real incomes decline, these people are just wrong.

                Each individual who earns money is boosting other people’s standard of living. It might be small in the grand scheme of things, but it is still positive.

                It’s this pernicious infiltration of unjustified mathematical concepts of continuous functions, and notions of “infinitesimally small” changes, that has corrupted this discussion, and, I think, leading people to say Krugman “has a point.”

                I hope it’s not just a question of Murphy jealously defending his PhD thesis.

  8. Seth says:

    Perhaps Krugman could go all-the-way Galt to give us a test sample. I’m sure NYT would still continue his column space as a blank, which I might be more willing to pay for.

  9. Kaj Grüssner says:

    So in Krugman’s view, all entrepreneurs could stop working completely. All corporations could shut down and fire all their workers, and that would have no effect on the economy.

    We can all drop dead, in other words, and the economy won’t change one bit because all the money we don’t give to the dead entrepreneurs and shut-down corporations will be spent on other things by…well…the other DEAD people.

    Howcome this man can’t open his mouth without sounding like a complete moron?

    • Bob Murphy says:

      We can all drop dead, in other words, and the economy won’t change one bit…

      Actually let’s just be careful here. Krugman is acknowledging that “the economy” will change; after all, there are fewer people working, so clearly less total stuff is getting produced.

      What Krugman is claiming is that the total amount of stuff available to everyone else won’t change one bit. So e.g. if a guy who made $1 million drops dead, then there is $1 million less stuff produced. But, that guy himself consumed $1 million of stuff when he was alive, so now the total amount of stuff available to everybody else is unaffected.

      (I’m assuming the guy consumed 100% of his income just to make sure you see the “logic” of Krugman’s argument. He’s still wrong, but I don’t think some of you guys are seeing exactly what he’s claiming.)

      • Tel says:

        You must admit, under Krugman’s system murder would not be a crime, or at the very least the only reason murder would be a crime under such a system is because of the theft of tax revenue (with the implication being every person is an asset owned by government, and exists only for the purpose of paying up tax).

        I’ll hasten to add that I disagree with this conclusion, but it is just another of the absurd results you get when you presume that no positive kickback exists when people work together.

        As ever, economic discussion drifts into moral discussion, but it is Sunday.

        • P.S. Huff says:

          “You must admit, under Krugman’s system murder would not be a crime, or at the very least the only reason murder would be a crime under such a system is because of the theft of tax revenue.”

          Huh? Replace “be a crime” (both instances) with “have adverse economic consequences for other people,” and I see what you’re saying. But I don’t know how you leap from that to the conclusion that Krugman’s system would not get in the way of murder.

      • Kaj Grüssner says:

        Bob,

        I think you’re being too kind to Mr. Krugman.

        A million less produced and a million less consumed means no change for the rest of us. Taken to its logical conclusion, that means that if production stops, so does consumption, which according to Krugman is a-okay.

        That was the point I was making, albeit not too clearly. It also illustrates Krugman’s fallacy, which is seems akin to the zero-sum-game argument. I should like to hear Krugman explain how growth occurs in a world in which everyone consumes 100% of what they produce.

        It is amazing how one person can be so wrong on so many levels and in so many ways in such as short text. It really takes a Keynesian, doesn’t it?

  10. Kevin Donoghue says:

    The latest from Krugman bears out my claim that he knows conservatives don’t really base their thinking on orthodox microeconomics:

    … it’s wrong to think of conservatives as having a single argument for their preferred policies. What they offer instead is more like an onion, with layers inside layers; every time you strip away one excuse there’s another one inside.

    He concludes:

    This onion structure is why you should never believe reasonable-sounding conservatives who say that you’re attacking a straw man, that “nobody believes” that wealth creators owe nothing to society. Oh yes they do — it’s usually hidden inside a couple of more socially acceptable excuses, but at their core Ryan and people like him believe that they’re characters in Atlas Shrugged.

    By the way, who built the roads in Galt’s Gulch?

    http://krugman.blogs.nytimes.com/2012/07/21/the-conservative-onion/

    • Bob Murphy says:

      Kevin D. wrote:

      The latest from Krugman bears out my claim that he knows conservatives don’t really base their thinking on orthodox microeconomics…

      Kevin, why do you need to establish “your claim” on this point? Of course that’s what Krugman has been arguing. I never denied it. He is saying conservatives are hypocrites, and that their praise of job-creating entrepreneurs doesn’t mesh with their praise of the market paying people according to their contributions.

      I really think you have missed what my commentary on this was. You keep telling me what Krugman was trying to say, and I keep responding, “Right, I know. That’s what I said upfront. And he was wrong.”

  11. Kevin Donoghue says:

    Bob,
    I wasn’t suggesting that you disputed that, it just struck me as a nice illustration of Krugman’s take on conservatives.

    I’m not missing your commentary. My problem is that if I take it seriously I can’t ever again say “Z = XY hence dZ = XdY + YdX.” Instead I’m going to have to say “Z = XY hence ΔZ = XΔY + YΔX + ΔXΔY.” That’s bad enough, but what’s going to be a lot worse is explaining the Slutsky decomposition. No more splitting price changes into income effects and substitution effects; to satisfy you I have to spell out the substitution effect of the income effect, as well as the income effect of the substitution effect (which won’t be the same).

    I had to go looking for a guide to HTML even to type that. The fact is, when we talk about elasticities for example, we are implicitly using equations which only hold exactly at the limit as dx -> 0. When Krugman writes “textbook economics says that in a competitive economy, the contribution any individual (or for that matter any factor of production) makes to the economy at the margin is what that individual earns” he’s not wrong. You can only argue that he’s wrong by pretending the words “competitive” and “at the margin” are not there.

  12. Vanmind says:

    According to K-brand charlatanomics (pick your preferred “K”), consumer choices are as interchangeable as the automaton workers who produce those evenly-rotating choices. Charlatanomics experts agree that the producer is also the consumer — within the deterministic kind of non-reality that is their Oz. Take out one munchkin, plug another in, if you’re a pretend intellectual it amounts to the same thing in the “we’re all dead” end.

    Calculus, apparently, is the great equalizer. Can K-brand charlatanomics derive us all toward a master race?

    “The Deriver” by K. Forget Garrett, that would be the blockbuster novel of all static-economy timelessness, reaching #1 with a few billion bullets.

  13. William Davis says:

    Maybe I missed something, but it seems to me that Krugman’s mistake is pretty elementary. The idea is that if Wheelerdealer works less, thereby making $10 million less, he thereby reduces the total national output (AKA the “economy”) by $10 million. But since he himself loses $10 million, on net balance everyone else is as “well off” as ever.

    The problem is that what a person receives for his labor is almost always worth (to the rest of society) more than he receives for it. At the margin, of course (in the theoretical case of static equilibrium with perfect competition) there will be some whose output is exactly equal in value to what they receive, but for the vast majority of people their output will be worth a lot more than that to the rest of society. This is just a special case of the fact that, at a market-clearing price, the value of a product is worth a lot more, to most of those who buy it, than the selling price. It’s only for the marginal buyer that the product is worth (to him) exactly what he pays for it. And for any given product, the vast majority of buyers and sellers are NOT the marginal buyer or seller.

    Back to Wheelerdealer. It’s possible, of course, that he’s a marginal producer – i.e., his product is valued (by the rest of society) at exactly what he receives for it. But in the great majority of cases it will be valued at considerably more than that. So when he stops producing however much is lost from his reduction in work hours, the loss to the rest of society (as valued by that society) will be considerably greater than $10 million.

    Note that this analysis holds starting with the first hour of lost production.

    The point here is that the assumption that “in a perfectly competitive economy, factors of production are … paid precisely their marginal product” is just flat out wrong. I find it hard to believe that any economic theory that makes such an assumption can be taken seriously by anyone. The correct statement would be that (under appropriate ideal assumptions) the MARGINAL factors of production are paid precisely their marginal product.

    • Kevin Donoghue says:

      Willliam, it’s not an assumption that “in a perfectly competitive economy, factors of production are … paid precisely their marginal product” it’s a result (a theorem) derived from the standard assumptions of the competitive model. If a factor is being paid less than the value of its marginal product then an entrepreneur can increase profits at least slightly, by employing a little more of that factor. That contradicts the assumption that entrepreneurs maximize profits.

      You can of course find “exceptions” to that rule by invoking special difficulties, like indivisibilities for example. (You can’t increase the number of oil refineries in existence by a fraction of a refinery.) But textbooks qualify the theory in those respects. And Krugman knows what’s in textbooks, since he has read a great many and written a few himself, with his wife and others. Quite simply, he’s right about this.

      • Bob Murphy says:

        KD wrote:

        Quite simply, he’s right about this.

        OK Kevin, so when Krugman accused right-wingers of contradicting themselves on these matters, you think he had in mind that a lot of conservative Republicans have been saying, “Whoa! If Obama gets rid of the Bush tax cuts, there’s one guy in the economy who will reduce his labor input by one man-hour. This would be a disaster and would throw lots of workers out of a job.” ?

        • Kevin Donoghue says:

          K is explicit about the belief he attributes to them: “the 1%, by working harder, are doing the 99% a big favor, creating jobs and raising incomes — and that this gain isn’t fully (or even largely) captured by the money they’re paid.”

          Of course you know the background, but FWIW here’s what I see going on:
          http://anyoldbullshit.blogspot.ie/2012/07/the-krugman-alternative.html

          • Bob Murphy says:

            Right Kevin, and so that quote shows we’re talking about more than one man-hour. I think I’m going to stop this now.

      • Major_Freedom says:

        Quite simply, he’s right about this.

        No, he’s not right about this. Just because total nominal incomes don’t fall, it doesn’t mean non-Wheelerdealers are no worse off. For the total nominal incomes are worth less, as there is less supply.

        Krugman tacitly switched from real incomes to nominal incomes during his post. He first treated income as real, but then by the end he said that incomes don’t fall, hence non-Wheelerdealers are no worse off. But they are worse off, because they have less capital to work with precisely because of Wheelerdealer’s reduction in output.

        Wheelerdealers boost worker’s labor productivity. With fewer individuals boosting labor productivity, even one man hour, that reduces total output.

  14. EJMRTroll says:

    Right, might as well have used meth to do it. Even though it is used so widely by many macro theorists, the Cobb-Douglas production function is not even empirically correct or relevant to the discussion. It assumes (or implies, if you prefer) that factor shares are constant, but in fact the share of capital has been rising, the issue under discussion.

    Murphy embarrassingly pathetic in this particular rant. Just furthers the not-entirely-true meme of Austrian mathematical incompetence. Tries to get mathy and falls flat on his face.

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