Friday, July 28, 2006

Can One Respect Henry Hazlitt?

I describe Henry Hazlitt as an author whose work goes well beyond ignorance and as somebody who does not know what he is talking about. Let me give an example. Here's Keynes giving us the theory he wants to attack:
"The classical theory of employment - supposedly simple and obvious - has been based, I think, on two fundamental postulates, though practically without discussion, namely: I. The wage is equal to the marginal product of labour That is to say, the wage of an employed person is equal to the value which would be lost if employment were to be reduced by one unit (after deducting any other costs which this reduction of output would avoid); subject to the qualification that the equality may be disturbed in accordance with certain principles, if competition and markets are imperfect. II. The utility of the wage when a given volume of labour is employed is equal to the marginal disutility of that amount of employment. That is to say, the real wage of an employed person is that which is just sufficient (in the estimation of the employed persons themselves) to induce the volume of labour actually employed to be forthcoming; subject to the qualification that the equality for each individual unit of labour may be disturbed by combination between employable units analogous to the imperfections of competition which qualify the first postulate. Disutility must be here understood to cover every kind of reason which might lead a man, or a body of men, to withhold their labour rather than accecpt a wage which has to them a utility below a certain minimum... ...Subject to these qualifications, the volume of employed resources is duly determined, according to the classical theory, by the two postulates. The first gives us the demand schedule for employment, the second gives us the supply schedule; and the amount of employment is fixed at the point where the utility of the marginal product balances the disutility of the marginal employment." -- J. M. Keynes (1936). The General Theory of Employment Interest and Money
Here's Hazlitt, with my interjections, revealing an ignorance of the theory he wants to defend:
"'The classical theory of employment - supposedly simple and obvious - has been based,' Keynes thinks, 'on two fundamental postulates, though practically without discussion' (p. 5). The first of these is 'I. The wage is equal to the marginal product of labor.' (His italics, p. 5) This postulate is correctly and clearly stated. It is not, of course, part of the classical theory of employment. That adjective should be reserved, in accordance with custom and in the interests of precision, for theory prior to the subjective-value or 'marginalist' revolution of Jevons and Menger.”
Hazlitt is correct (and unoriginal) in asserting that Keynes’ usage of “classical” is confusing.
”But the postulate has become part of 'orthodox' theory since its formulation by the 'Austrian' school and, particularly in America, by John Bates Clark. Having written this simple postulate, Keynes adds eight lines of 'explanation' which are amazingly awkward and involved and do more to obfuscate than to clarify.”
Let me put aside arguments about who originated the theory of marginal productivity. Keynes’ qualitifications are obviously getting at imperfections of competition. For example, if the firm is a monopolist in the product market, the wage, when the firm is in equilibrium, is equal to the marginal value product of labor, not the value of the marginal product of labor. Because Hazlitt is incompetent, he finds Keynes’ qualifications “awkward”.
”He then proceeds to state the second alleged 'fundamental postulate' of the 'classical theory of employment,' to wit: ‘II. The utility of the wage when a given volume of labor is employed is equal to the marginal disutility of that amount of employment.' (His italics, p. 5.) He adds, as part of his explanation: 'Disutility must be here understood to cover every kind of reason which might lead a man, or a body of men, to withhold their labor rather than accept a wage which had to them a utility below a certain minimum' (p. 6). 'Disutility' is here so broadly defined as to be almost meaningless. It may be seriously doubted, in fact, whether this whole second 'fundamental postulate,' as Keynes frames and explains it, is or ever was a necessary part of the 'classical' or traditional theory of employment. Keynes does name and (later) quote A. C. Pigou as one whose theories rested on it. Yet it may be seriously questioned whether this 'second postulate' is representative of any substantial body of thought, particularly in the complicated form that Keynes states it.”
Keynes is here describing the neoclassical theory of the worker trading off leisure with the consumption he can purchase with his wages. Figure 1, which formulates the theory in terms of the utility of leisure, rather than the disutility of labor, may remind you of the textbook theory. Once again, Hazlitt’s ignorance of varieties of this theory reveals nothing more than his incompetence.
Figure 1: Equilibrium Of The Utility-Maximizing Worker
”The 'orthodox' marginal theory of wages and employment is simple. It is that wage-rates are determined by the marginal productivity of workers; that when employment is 'full' wage-rates are equal to the marginal productivity of all those seeking work and able to work; but that there will be unemployment whenever wage-rates exceed this marginal productivity.”
Note that here Hazlitt describes the marginal productivity of labor as being “determined” for a specific volume of labor, the “full” employment level. When the level of employment of labor is less than “full”, the wage can still be equal to the marginal productivity of workers, as calculated for that lower level of employment. Obviously, then, the equality of the wage and the marginal productivity of labor is not enough to determine either wages or employment. Some other relationship must be put forward, in neoclassical theory, to help determine these quantities. That is where the theory of the supply of labor, summarized in the figure, comes in.
“Wage-rates may exceed this marginal productivity either through an increase in union demands or through a drop in this marginal productivity. (The latter may be caused either by less efficient work, or by a drop in the price of, or demand for, the products that workers are helping to produce.) That is all there is to the theory in its broadest outlines. The 'second postulate,' in the form stated by Keynes, is unnecessary and unilluminating.”
I have shown the role the second postulate fills in neoclassical theory. Hazlitt, being incompentent, isn’t able to even count variables and equations.
”Subject to certain qualifications, Keynes contends, 'the volume of employed resources is duly determined, according to the classical theory, by the two postulates [which Keynes has named]. The first gives us the demand schedule for employment; the second gives us the the supply schedule; and the amount of employment is fixed at the point where the utility of the marginal product balances the disutility of the marginal employment' (p. 6). Is this indeed the 'classical' theory of employment? The first postulate - that 'the wage is equal to the marginal product of labor' - does not merely give us the 'demand schedule' for labor; it tells us the point of intersection of both the 'demand schedule' and the 'supply schedule.' The demand schedule for workers is the wage-rate that employers are willing to offer for workers.”
In neoclassical theory, this schedule “is the wage-rate that employers are willing to offer workers” at each level of employment within the possible range of levels. The ‘first postulate’ can, at best, determine the schedule, but not the location at which the labor market is in equilibrium.
”The 'supply schedule' of workers is fixed by the wage-rate that workers are willing to take. This is not determined, for the individual worker, by the 'disutility' of the employment - at least not if 'disutility' is used in its common-sense meaning. Many an individual unemployed worker would be more than willing to take a job at a rate below a given union scale if the union members would let him, or if the union leader would consent to reduce the scale." -- Henry Hazlitt, The Failure of the "New Economics": An Analysis of the Keynesian Fallacies, D. Van Nostrand Company, 1959.
Hazlitt just does not understand the theory he wants to defend. As far as I am concerned, Hazlitt’s entire book attacking Keynes is as incompetent as the above. It might take me some time to further document this claim, if anybody wants me to, since my local library has apparently disposed of the above quoted book. (I copied from an old Usenet post of mine to create this post.)

Tuesday, July 25, 2006

Response To Comments On Steve Keen's Work


In comments on a previous post, Radek comments on some work of Steve Keen's. Since I've let something like a week go by, I thought I ought to raise this response to a post.

I respond more to people I disagree with. But I think I ought to note that, like DSquared, I respect Solow, while disagreeing with him. My favorite polemic from the Cambridge Capital Controversy is this:
“I have long since abandoned the illusion that participants in this debate actually communicate with each other. So I omit the standard polemical introduction, and get down to business at once.” –- Robert M. Solow (1962)

But back to Keen. What I appreciate most in Keen’s book is his attempt to convey to the introductory student and common reader that good reason exists to doubt (mainstream) economics, no matter how much (mainstream) economists attempt to blind one with “science”. Keen claims very little originality for most of what he has to say. As one can see, I have some disagreements with Keen’s attempts at popularization. But the discussion in this post only concerns two out of fourteen chapters in Keen’s book. And Radek does not even concede any virtues in those chapters.

Also, I can do without accusations that Keen is a “hack”, whether “a pretty skillful hack” or not; a “charlatan”; a liar; “dishonest and embarrassing”; “engages in” “dishonest rhetorical trick[s]”. For me, Guiness stout and Monty Python fall in the same category: things I’m still unsure what I think of. But I’m fairly sure abuse is not an argument.

Profit Not Maximized When Price Equal Marginal Revenue

Chapter 4, “Size Does Matter”, seems to be the most argued about chapter of Debunking Economics. It surprised me too.

Atomistic competition, in which one has a continuum of infinitesimal agents, is a standard assumption in economics. Keen and Standish (2006) point out that the assumption of atomistic competition is that one firm does not change its level of production in reaction to another firm's variation in production levels. Keen (2001) points out that Stigler shows that, under atomistic competition, the demand curve for a consumption good faced by the firm has the same slope as the demand curve for the market. I find Keen is not original in noting that atomistic competition is incompatible with the usual textbook U-shaped average cost curves:
"Of course, global increasing returns to scale (or more modestly, situations in which efficient scale is reached at a level of output which is noninfinitesimal relative to the total size of the market) remains a problem. Also, we do not deny the descriptive reality of the latter situation." -- Duffie and Sonnenschein (1989)

Radek ignores all this motivation for Keen’s simulations, and I find it difficult to argue with Keen’s claims. And they wreck havoc on mainstream introductory textbooks in microeconomics.

I have done work with simulations in quite different contexts. In my experience with certain researchers, they wanted to see their analytical arguments confirmed by both simulations, in which they could control the environment to which their arguments are applied, and practical applications. I think Radek should welcome my simulation. If he looks, he will see that I allow the user to vary the order in which firms make decisions. So I agree with Radek in that I think Keen can be challenged here. I also seem to recall an impression that step size matters to convergence in my simulation. I still think I would need to do further work to substantiate these worries.

The Sonnenschein-Mantel-Debreu Results

Keen brings up the SMD results in Chapter 2 of Debunking Economics. Duffie and Sonnenschein (1999) characterize these results as stating that "the class of excess demand functions generated by economies has no structure beyond Walras' law and homogeneity" (p. 574). They point out the implication that "the equilibrium price set may be an essentially arbitrary subset of the set of relative prices" (p. 574).

Radek states, "SMD is not about aggregating individual utilities in the sense that Keen's talking about." I find Keen to only be echoing the professional literature on this point. Think, for example, of Kirman’s (1992) analysis of representative agent models, which are widespread in New Classical Economics. Keen’s point is that Margaret Thatcher was wrong in asserting that “There is no such thing as society”. Would Radek accept Kirman’s claims, which I think are along the same lines:
"The problem seems to be embodied in what is an essential feature of a centuries-long tradition in economics, that of treating individuals as acting independently of each other...

If we look back briefly to the result that underlies the whole problem expressed here it is clear that in the standard framework we have too much freedom in constructing individuals. The basic artifact employed is to find individuals each of whose demand behavior is completely independent of the others... making individual behavior dependent or similar may open the way to obtaining meaningful restrictions...

If we are to progress further we may well be forced to theorise in terms of groups who have collectively coherent behaviour. Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation. The idea that we should start at the level of the isolated individual is one which we may well have to abandon. There is no more misleading description in modern economics than the so-called microfoundations of macroeconomics which in fact describe the behaviour of the consumption or production sector by the behaviour of one individual or firm. If we aggregate over several individuals, such a model is unjustified...

It is clear that making assumptions on the distribution of agents' characteristics amounts, in some sense, to making assumptions about the organization of society...

In conclusion, then, it is worth repeating that recent theoretical work has shown how little the Walrasian model has to say about aggregate behavior. Economists therefore should not continue to make strong assertions about this behaviour based on so-called general equilibrium models which are, in reality, no more than special examples with no basis in economic theory as it stands."-- Alan Kirman (1989)

Radek comments:
So how 'huge' are SMD results - the fact that one may have multiple equilibria. Well, here I think there's often a good bit of intellectual dishonesty among critics of GE. On one hand they criticise GE for being 'unrealistic' on the other they wave SMD theorem as proof that GE is 'untenable' (again, whatever that means). But seriously, why should you expect the Real World to have a unique equilibrium? Particularly in the presence of wealth effect, which are the driving force behind SMD theorem, and the whole point of doing GE in the first place? Personally I think the possibility of multiple equilibria is a REALISTIC feature of general equilibrium theory and a point in favor of it rather than against it.

One would be in trouble if the theorem predicted a continuum of equilibria, or that the First Theorem no longer applied but that's not the case. One can still do local comperative statics and all them multiple equilibria are still Pareto efficient.

I find the above confused. Tony Lawson is the scholar to read when it comes to “realism” and Post Keynesianism. I don’t say every Post Keynesian agrees with him. But one who wants to engage Post Keynesian discussions of realism of assumptions must read at least some of Lawson. I don’t know what it means to say “the Real World” has multiple or unique equilibria. I think equilibria are properties of models, not characteristics of actually existing capitalist economies, independently of how they are described.

I don't care for Radek’s sort of abusive attack on people who say they are echoing the experts in a field, especially when the attackers do not cite any examples of who they are talking about. I think a good appreciation of the SMD results might require a historical perspective on what (some) economists were (and still are?) claiming about General Equilibrium and what the experts in the field now claim:
"It follows from the preceding observation that the Walrasian theory and the existence theorems do not tell us how to relate tastes, technology, and the distribution of wealth to a single set of relative values. Rather, they tell us that there is at least one vector (and possibly many more) of relative values compatible with the data of the model. In the absence of uniqueness, the comparative statics of how prices and allocations will change with a change in the parameter values is not a well-defined exercise. The finiteness result alluded to above may be of some help here, but what is really needed is a completion of the Walrasian theory that describes the particular choices that are made from the equilibrium set. Such a completion will almost surely require a theory that deals explicitly with the adjustment to equilibrium. If forces are not in balance, what changes will take place in order to bring them into balance?" -- Duffie and Sonnenschein (1989)

I suggested to Keen, prior to the publication of his book, that the assumptions that all agents have identical and homothetic utility functions are merely sufficient, not necessary, conditions to get well-behaved utility functions. On this logical point, I agree with Radek. But Keen has convinced me with his book and later work that, in practice, (mainstream) economists do widely adopt these assumptions in applied work, with little justification.

  • Duffie, Darrell and Hugo Sonnenschein (1989). "Arrow and General Equilibrium Theory", Journal of Economic Literature, V. 27, N. 2 (June): 565-598.
  • Keen, Steve (2001). Debunking Economics: The Naked Emperor of the Social Sciences, Zed Books.
  • Keen, Steve and Russell Standish (2006). "Profit Maximization, Industry Structure, and Competition: A Critique of Neoclassical Theory", Physica A
  • Kirman, Alan (1989). "The Intrinsic Limits of Modern Economic Theory: The Emperor has No Clothes", Economic Journal, V. 99, N. 395: 126-139.
  • Kirman, Alan P. (1992). "Whom or What Does the Representative Individual Represent?" Journal of Economic Perspectives, V. 6, N. 2 (Spring): 117-136.
  • Solow, Robert M. (1962). “Substitution and Fixed Proportions in the Theory of Capital”, Review of Economic Studies, V. 29, N. 3 (Jun): 207-218.

Monday, July 17, 2006

Dsquared Howls

In comments on this post, dsquared writes:
I saw the finest minds of my generation wrecked by the Solow model,
starving hysterical naked and calling a residual a theory.

Sunday, July 16, 2006

Income Inequality And Current Events

I recently posted about income inequality and immobility. Apparently, I'm up on what's being discussed among some:

DeLong makes the point that increasing inequality preceded the large-scale introduction of personal computers. The thesis of skills-biased technological change is thus undermined. DeLong does not reference James Galbraith (1998) for this point.

When it comes to explaining personal or functional income distribution, neoclassical economics is intellectually bankrupt. Warren Buffet (CNN, June 2005) understands: "It's class warfare, my class is winning, but they shouldn't be."
  • Galbraith, James K. (1998). Created Unequal: The Crisis in American Pay, New York: The Free Press

Thursday, July 13, 2006

Keen And Ormerod, Econophysics, And The Distribution Of Income

This humble blog is all about documenting fallacies in mainstream economics. Very little of what I have to say is new, and some have tried to popularize some of these criticisms. I think, in particular of Paul Ormerod (1994) and Steve Keen (2001). Ormerod and Keen have some similarities. Both:
  • Have written popular books (Ormerod 1994 and Keen 2001) explaining that neoclassical economics is incorrect
  • Mention Lipsey and Lancaster's theory of the second best
  • Emphasize that mainstream economists studying the theory of General Equilibrium have demonstrated the theoretical untenability of neoclassical economics
  • Recommend an approach to economics based on the mathematics of complexity theory
  • Publish original criticisms of mainstream economics first in their popular books (Ormerod 1999 and Keen 2001) and then later in a physics journal (e.g., Keen and Standish (2006) and Ormerod and Mounfield (2000))

They differ in that they express different opinions on Piero Sraffa in their popular books. Keen (2001) praises Sraffa, while Ormerod (1999) snarks.

I find that Ormerod and Keen have teamed up with two other authors for a recent paper (Gallegati et al. 2006). This paper contains an approving reference to Sraffa. A major theme of this paper is to question whether the evidence for power laws, in particular in the tails of certain distributions of certain economic variables, is as definite as seems to be claimed sometimes in the econophysics literature.

  • Gallegati, Mauro, Steve Keen, Thomas Lux, and Paul Ormerod (2006). "Worrying Trends in Econophysics", Physica A
  • Keen, Steve (2001). Debunking Economics: The Naked Emperor of the Social Sciences, Zed Books
  • Keen, Steve and Russell Standish (2006). "Profit Maximization, Industry Structure, and Competition: A Critique of Neoclassical Theory", Physica A
  • Ormerod, Paul (1994). The Death of Economics, London: Faber & Faber
  • Ormerod, Paul (1999). Butterfly Economics: A New General Theory of Social and Economic Behavior, Pantheon
  • Ormerod, Paul and Craig Mounfield (2000). "Random Matrix Theory and the Failure of Macro-Economic Forecasts", Physica A

Sunday, July 09, 2006

Reversal Of Great Compression In Income Distribution In U.S.A.

I recently posted about income (im)mobility in the United States. One interested in that subject is probably also interested in the deteriorating (that is, increasingly unequal) distribution of wealth and income in the U.S. On the latter subject, my current favorite reference is a paper by Piketty and Saez, recently presented at the annual conference of the American Economic Association.

Piketty and Saez construct some time series from census data, tax data, and national income accounts. They use census data to find the total number of tax units in a country. A tax unit might be an individual, or it might be a household. Tax data is used to find top incomes and their decomposition by source. National income accounts and their predecessors are used to convert top incomes into shares. Piketty and Saez are sensitive to issues of tax evasion and avoidance.

The figures below are selected results from Piketty and Saez. Rank tax units, each year for, say, the United States, by income obtained. For Figure 1, look at the upper 10% (a decile) of these tax units. The figure shows the trend in the percentage of income obtained by these tax units over almost a century. If income were distributed perfectly equal, the graph would show a straight line at 10% on the vertical axis. Since income is not equally distributed in the United States, the time series is above 10%. The graph starts at 20% to emphasize the observed fluctuations in the proportion of income obtained by the top decile. Notice that Figures 2 and 3 show international comparisons for the top one thousandth, not the top tenth.

Figure 1: Income Share Of Top Decile In United States

Figure 2: Income Share Of Top 0.1% In U.S.A., U.K., And Canada

Figure 3: Income Share Of Top 0.1% In Japan And France

Piketty and Saez show that what Claudia Goldin and Robert Margo name “the great compression” in income distribution has been reversed in the United States. It has not been reversed in Japan and France, though.

Since Piketty and Saez are exploring the upper end of income distribution, they do not document the contrast between the “picket fence” and “staircase” pattern in income distribution. Since this contrast is a basic fact about the United States, I summarize it here. As above, suppose all households or individuals are ranked by annual income for each year. Divide this population into five groups, that is, into quintiles. So the poorest fifth is the first quintile, and the richest fifth is the fifth quintile. Calculate the average (mean) income of each quintile for each year.

You will find that during the post (Second World) War “golden age” (extending roughly until sometime in the 1970s), the average income of all quintiles increased roughly at the same rate. When the increase of the average income by quintile is graphed versus quintile, one obtains a picket fence pattern. On the other hand, one obtains a staircase pattern during the last third of a century or so. The average income of the first quintile seems to have even fallen; middle quintiles increase their income only slightly; and the rich increase their income even more. In the golden age, all groups obtain some of the advantage of increasing productivity, while in current period the rich are able to increasingly monopolize gains in productivity.

Piketty and Saez show this staircase pattern extends dramatically into the upper limits. Those last few steps have grown bigger and bigger.

  • Piketty, Thomas and Emmanuel Saez (2006). "The Evolution of Top Incomes: A Historical and International Perspective", Proceedings of the American Economic Association (Jan.)

Tuesday, July 04, 2006

Among Developed Countries, Income Mobility Almost Least In United States

In a previous post, I provided a summary table from a 1997 study on income mobility in the United States. Tom Hertz, with American University, provides a more recent analysis. I select a couple of his results to highlight here.

Hertz looks at how one’s place in the United States income distribution is transmitted to one’s children. He analyzes data on “4,004 children observed in the Panel Study of Income Dynamics (PSID) in their parents’ households in the 1968 survey… The children are then observed again as adult heads of households, or spouses thereof, in” biannual surveys in recent years. The sample was corrected to preserve its original representative demographics. Both parents and grown children are observed near their “prime earning age”.

Table 1 summarizes some of Hertz’s results. Define the “rich” (not shown here) to be those in the top 5% of households, by income. Hertz finds the odds of becoming rich are less than 2% for children of parents in any of the first three quintiles of household income. The odds of becoming rich are approximately 20 times greater if you are born into a rich household than if you are born into a household in the bottom quintile.

Table 1: At Least 65% Of Grown Up Children Are In A Household Within One Quintile Of Their Parents’ Household
Parental 1967-1971
1st Quintile41.5%24%15.5%13.2%5.9%
2nd Quintile22.625.823.118.510.0
3rd Quintile18.725.824.119.616.9
4th Quintile11.119.020.725.124.0
5th Quintile6.

Hertz also provides an international comparison of intergenerational mobility, but I do not understand the source of his data. Hertz looks at the intergenerational elasticity of earnings, that is, the percent increase in expected earnings associated with a one percent increase in parents’ earnings. Table 2 provides his results. Hertz summarizes his findings:
By international standards, the United States has an unusually low level of intergenerational mobility: our parents’ income is highly predictive of our incomes as adults. Intergenerational mobility in the United States is lower than in France, Germany, Sweden, Canada, Finland, Norway and Denmark. Among high-income countries for which comparable estimates are available, only the United Kingdom has a lower rate of mobility than the United States.

Table 2: The U.K. and the U.S. Have Least Mobility
CountryIntergenerational Elasticity Of Earnings
United Kingdom0.5
United States0.47

  • Hertz, Tom (2006). Understanding Mobility in America, Center for American Progress (26 April).

Monday, July 03, 2006

Coase In The Dark On Lighthouses

The "nobel" laureate, Ronald Coase, has some views on public finance and lighthouses. He mentions these views, for example, in a 1997 interview with Reason.

The most recent unrefuted view in the peer-reviewed journal literature, as far as I know, is that Coase is wrong on the facts:
"In 'The Lighthouse in Economics' (Coase, R. H., Journal of Law and Economics, vol. 17, no. 2, 357-76, 1974), Coase reached the conclusion that in England there existed a relatively efficient privately financed lighthouse system, which would refute economists' traditional statements concerning the production of public goods. The purpose of this paper is to challenge his conclusion. We first show that, from a methodological and theoretical perspective, 'The Lighthouse' is consistent with 'The Problem of Social Cost' (Coase, R. H. Journal of Law and Economics, vol. 3, 1-44, 1960). Then, applying Coase's own method (historical case studies), we attempt to re-examine the respective roles and efficiencies of private initiative and government." -- Elodie Bertrand (2006).

This is not a topic that I have a strong opinion on. But I find that some of the more stupid worshippers of Mammon one might meet on the Internet have a tendency to bring Coase up.

  • Bertrand, Elodie (2006). "The Coasean Analysis Of Lighthouse Financing: Myths And Realities", Cambridge Journal of Economics, V. 30: 389-402.

Sunday, July 02, 2006

Proof Of The Falsity Of The Factor Price Equalization "Theorem" (Part 3)

4.0 International Trade
Suppose a number of otherwise identical countries differ in endowments of factors of production. And suppose these countries do not permit trade in factors of production among themselves. For example, workers are not permitted to emigrate from one country and into another. And capitalists cannot invest in foreign countries. But suppose all produced commodities can be traded among these countries on an international market. Then, according to many counfused mainstream economists, the prices of the factors of production will tend towards equality among these countries. For example, the wage will be the same everywhere. In some sense, trade in produced commodities can replace trade in factors of production. If these countries were to allow foreign investment, after trade in produced commodities had already been established, then, according to these confused mainstream economists, the same equilibrium would only be achieved quicker. I expect these confused mainstream economists would qualify this story in practice by relating wages to variations in productivity among countries no longer considered identical, transportation costs, etc.

The above story relies on the factor price theorem, which is most conveniently set out in the case where only two countries exist. This supposed theorem has some conditions, and all these conditions are met by the Mainwaring example being analyzed in this series of posts:
  • Both countries produce the same commodities. In this case, the commodities consist of iron, steel, and corn.
  • Each country has a given endowment of factors, identical in quality but of different relative quantities. For my purposes, I do not need to specify explicitly the quantity of labor available in each country nor to discuss the endowment of the value of capital.
  • Both countries have identical technology.
  • There are no factor reversals. I rely on Mainwaring for the truth of this assumption in this case. I have neither checked it nor fully attempted to understand its statement.
  • All consumers have identical and homothetic utility functions. As with the assumption on endowments, my purposes do not require an explicit specification of utility functions.
  • All commodities that can enter into final output are traded on international markets in which one price rules for each commodity. In this case, the prices of iron, steel, and corn are established on international markets.
  • There are no transportation costs.
  • Perfect competition prevails in all markets.
Keith Acheson has described how to investigate the factor price equalization theorem in the context of a linear model of production:
"From the price equations it is clear that a set of product prices implies a particular wage and rate of interest. For factor price equalization it is critical to investigate the conditions necessary for this to be a one-to-one relationship, so that a common set of product prices in any two countries will necessarily be associated with same wage and interest rate." - Keith Acheson (1970)
In two previous posts, I worked through the analysis of the choice of technique in a three commodity example created by Lynn Mainwaring. Figure 4-1 shows the price of iron at all feasible levels of the rate of profits in this example. Figure 4-2 shows the corresponding price of steel. I have picked out the prices at two rates of profits in the figure. These points are further detailed in Table 4-1. Suppose the prices on the international markets for iron, steel, and corn are 1/4 bushels per ton iron, 1/2 bushels per ton steel, and unity (by definition), respectively. Let the wage in the first country be three bushels corn per person year and the rate of profits be 0%. Let the wage in the second country be one bushel per person year and the rate of profits be 100%. The analysis of the choice of technique shows that this is an equilibrium.

Figure 4-1: The Price Of Iron

Figure 4-2: The Price Of Steel

Table 4-1: Two Equilibria
p1 = 1/4, p2 = 1/2, r = 0%, w = 3, Delta technique adopted
p1 = 1/4, p2 = 1/2, r = 100%, w = 1, Alpha technique adopted

Thus, in Mainwaring's example an equilibrium exists in which:
  • There is one price on the international market of each produced commodity.
  • The wage and the return to financial capital differ between countries.
The above, then, proves that the factor price equalization theorem is false. I suggest, furthermore, that the variation in prices with the rate of profits suggests that the dynamics of international markets can be interesting.

5.0 Conclusion
So that's the theory at a very abstract level. If a country trades produced goods on "free" markets, opening its financial markets to international investors can dramatically change the dynamics of income distribution, or so the theory suggests. As I understand it, mainstream economists, who often get their sums wrong, think the theory implies opening financial markets will only lead to equilibrium with common factor prices, perhaps corrected for differences in productivity, transport costs, and so on, being established quicker.

Why do mainstream economists continue to teach and to try to apply theories show to be false more than a generation ago?

  • Acheson, K. (1970). "The Aggregation of Heterogeneous Capital Goods and Various Trade Theorems", Journal of Political Economy, V. 78, N. 3 (May-June): 565-571.
  • Mainwaring, L. (1976). "Relative Prices and 'Factor Price' Equalisation in a Heterogeneous Capital Goods Model", Australian Economic Papers, Republished in Fundamental Issues in Trade Theory (Ed. by Ian Steedman), Macmillan, 1979.