Wednesday, July 11, 2018

Neoliberals, Liberals, Progressives, Social Democrats, and Democratic Socialists

I guess this is a post on current events in the United States. Some articles I have recently found interesting are:

I take it socialists want to work towards a society in which, "The free development of each is the condition for the free development of all" (Karl Marx). The idea is that each person should be able to develop their talents to the fullest extent possible, both for their own sake and to contribute as much as possible to society. This is a Christian idea as well, put forth in the parable of the talents (Matthew 25, verses 14-30).

I think traditional conservatives do not agree. They think the vast majority must be consigned to nasty and grubby grunt work. Only those at the top can flourish. Neoliberals put forth a vision of personal development which I find narrow and stilted. In neoliberalism, everybody is an investor developing their human capital for validation by the market. If you have a skill that does not pay - too bad. You wasted your time. For more on this, see Wendy Brown's Undoing the Demos: Neoliberalism's Stealth Revolution.

Somewhere in here I should probably say something about meritocracy. Also, if one wants to look for authoritative Marxist-Leninist accounts of the distinction between socialism and communism, one might look at Marx's private letter, Remarks on the Gotha Program, or Lenin's State and Revolution. But these documents are not what this post is about, since they do not seem relevant to why debates on the post topic are current events.

A crucial question, I think, is whether capitalism could ever be a society in which the free development of all is possible. Social democrats say, "Yes". They think the cruelties of capitalism can be tamed with a generous enough welfare state. One might say, they want a capitalism with a human face. Democratic socialists think not. They want to eventually move beyond capitalism.

I do not see that social democrats and democratic socialists need disagree on immediate, short term programs. Such a tactical coalition can include progressive and liberals. I was curious that none of those three articles linked at the top mentioned Eduard Bernstein. Sure, Otto Von Bismarck created many elements of the first welfare state, as a reactionary response to growing worker power. One might also mention Pope Leo XIII's Rerum Novarum, on the rights and duties of labor. But Bernstein's Marxist reformism - "The movement is everything, the final goal is nothing" - is also important in considering the historical origins of social democracy and democratic socialism.

I was annoyed with Wilentz's suggestion that those further left than him have forgotten John Maynard Keynes. Keynes was historically and globally important in designing the post war Bretton Woods system, a system that brought general prosperity for three decades. For national and international policies, Gunnar Myrdal, Michel Kalecki, Nicholas Kaldor, and Joan Robinson had some influence. Myrdal and Kalecki came to their Keynesianism independently of Keynes.

Where democratic socialists want to go when transcending capitalism is not exactly clear. I do not see that they need to agree. Developing sovereign wealth funds; developing Universal Basic Income (UBI) programs; and supporting labor unions, Employee Stock Ownership Plans (ESOPs), and workers cooperatives are elements of a program fairly radical for these barbaric times.

Update (14 July 2018): A Nicholas Colin article in Medium. There's probably a lot more on-topic current articles.

Friday, June 29, 2018

Lack Of Rigor In Mas-Colell, Whinston, And Green

Whether or not the government should intervene in the economy is a false choice. Government and the economy are not two separate and non-intertwined entities.

The standard introductory graduate microeconomics textbook now current was written by Mas-Colell, Whinston, and Green. This happens to be from Chapter 15, in the part on the Edgeworth box:

"We can now verify a simple but important fact: Any Walrasian equilibrium allocation ... necessarily belongs to the Pareto set... Thus, at any competitive allocation ..., there is no alternative feasible allocation that can benefit one consumer without hurting the other. The conclusion that Walrasian allocations yield Pareto optimal allocations is an expression of the first fundamental theorem of welfare economics, a result that ... holds with great generality...

The first fundamental welfare theorem provides, for competitive market economies, a formal expression of Adam Smith's 'invisible hand.' Under perfectly competitive conditions, any equilibrium for intervention in the economy is the fulfillment of distributional objectives."

  • Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green. Microeconomic Theory, Oxford University Press (1995): p. 524

Adam Smith was little interested in the allocation of given resources, as compared to economic growth. But put aside the dubious historical claim. I want to focus on other reasons why the above passage is nonsense.

What is an "intervention in the economy"? Here are some examples of what could be interventions:

  • Refusing to permit contracts in which people sell themselves into slavery.
  • Banning child labor.
  • Banning the enforcement of clauses in deeds which prohibit owners, in perpetuity, from selling their property to jews, negroes, or members of some other groups.
  • Requiring sellers of food in grocery stores to list the amount of the Recommended Daily Allowance of various vitamins and minerals provided by that food.
  • Inventing a legal structure in which people can form corporations which limit their legal liability.
  • Banning people from copying some books, computer source code, DVDs, and making them freely available or selling them.

Whether to count these as interventions could be viewed as a political question. I would like to think the first four are not current questions. Law provides a background, often taken as given, on which buying and selling can be based. What contracts will be backed up by government varies with time and place.

Some elements of this background that are disputed at the moment, at least by those who can attract the attention of the owners of the means of communication. An alteration or decision on a disputed element could be defined as a matter of government intervention in the economy. But such a definition does not seem to have any place in a mathematical theorem.

What counts as property is a question closely related to what counts as an intervention. It is easy easy to write, "Let ω be a vector of endowments..." But whether or not something is an endowment also varies with time, space, and the legal background. Examples that come to my mind without much thinking include air rights in New York City, a capability of a eight-year old to supply so many hours of labor, and wombs in a society where one can contract for surrogate motherhood.

Notice that conventions on contracts and property law shape the distribution of income. The distribution of income is a subject that mainstream economists have been notoriously poorly-trained to discuss.

Mainstream economists may think they are getting a rigorous introduction to economics, what with the "maze of pretentious and unhelpful symbols" (Keynes) in their books. They are also getting, however, a replication of a confused naturalization and reification of the economy common in popular discourse.

Wednesday, June 20, 2018

The Loss From Trade With Capital Goods: The Sraffian Bonus Can Be Negative

I have written up this result here

Abstract: Paul A. Samuelson extends the Ricardian theory of foreign trade to a model of small open economies in which countries can trade semi-finished capital goods on international markets, as well as trade in produced consumer goods. He argues that this extension provides an additional gain from trade, which he labels the Sraffian bonus. This article demonstrates that trade in consumer and capital goods can result in a loss for an economy, given positive rates of profits in the trading countries, as compared with trade in consumer goods only. In other words, the Sraffian bonus can be negative.

Saturday, June 16, 2018

A Country Worse Off With Trade In Capital Goods

Figure 1: PPFs in Portugal
1.0 Introduction

This post continues these two posts. I change the model here to have wages advanced, not paid out of the surplus at the end of the year.

I here consider an example of a model of stationary states in which two countries can trade in produced commodities to be used for consumption. The countries face given prices on international markets for traded commodities. (They are small open economies, in the jargon.) I take the rate of profits as given in each country. They may differ, since I assume that finance capital cannot be traded internationally. I also assume labor is immobile between countries.

I contrast the model with and without foreign trade being possible in capital goods. Paul Samuelson calls the supposed gains from trade in capital goods the Sraffian bonus. This post demonstrates that the Sraffian bonus can be negative. The inhabitants of a country might be better off, in the sense that the total bundle of consumption goods is larger, if international markets do not exist in capital goods.

2.0 Parameter Values

I assign the numeric values in Table 1 to coefficients of production. For those who do not want to click, a unit of steel can be made in England from a direct and unassisted labor input of l2, C, E person-years. A unit of corn can be made from one unit of steel and l1, C, E. A unit of linen is made from l1, L, E person-years of direct and unassisted labor.

Table 1: Technology for the Example
l1, C, n37
l2, C, n22
l1, L, n12

I take the endowments of labor - LE and LP person-years, respectively - as given. Production Possibility Frontiers (PPFs) are constructed per worker.

I also take rates of profits, rE and rP, as given. I do not strive for realism. But, if you are concerned by the sizes of the rates of profits, pretend that my "year" is actually a decade or so.

3.0 Stationary States with and without Trade in Capital Goods

I now consider what prices could be consistent with stationary states.

First, suppose foreign trade is not possible in capital goods. Only corn and linen can be traded on international markets. Suppose prices are as in Table 2. The cost of producing linen in England:

l1, L, E wE (1 + rE) = 1 (1/6) (1 + 3) = 2/3

If firms in England manufacture linen for both domestic consumption and for foreign trade, they make the going rate of profits. The cost of producing corn in England is:

[l2, L, E (1 + rE) + l1, L, E] wE (1 + rE) = [2 (4) + 3](1/6)(4) = 22/3

Firms in England will not want to produce corn. They would be undercut by foreign competition. You can do the analogous calculations for Portugal. Portuguese firms will produce corn and the needed steel to continue production. They will not produce linen. With these prices and this specialization, consumers in both countries can consume baskets of commodities containing both corn and linen. And firms will be minimizing costs.

Table 2: Example with Foreign Trade in Corn and Linen
Cost of producing corn22/36
Cost of producing linen2/312/7
SpecializationLinenCorn and Steel

Suppose now that international markets exist in corn, linen, and steel. Table 3 shows prices for consideration in this case. One tabulates the cost of producing corn with the steel input evaluated at the international price. For example, the cost of producing corn in England is:

(PS + l1, C, E wE) (1 + rE) = [1 + 3 (1/6)](4) = 6

Going through these tabulations, one will find that the firms in England specialize in producing corn and linen. The cost of producing steel in England exceeds its price. Likewise, firms in Portugal specialize in producing steel. Cost-minimizing firms in Portugal are unwilling to produce either corn or linen.

Table 3: Example with Foreign Trade in Corn, Linen, and Steel
Cost of producing corn617/2
Cost of producing linen2/31
Cost of producing steel4/31
SpecializationCorn and LinenSteel

Notice that the international prices of corn and linen are unchanged between Tables 2 and 3. Steady states are here shown as resulting in an increased wage in Portugal when foreign trade is possible in steel. But rates of profits and the wage in England are shown as constant.

3.0 Production Possibility Frontiers

What about physical quantities of commodities? I restrict myself to stationary states. Figure 2 shows PPFs in England. The PPF under autarky is constructed from technical data on coefficients of production and the endowment of labor in England. When only linen is produced in England, whether foreign trade is possible or not, the same amount of linen is produced as under autarky. Consequently, all three PPFs are shown as rotated around the same intercept in Figure 2.

Figure 2: PPFs in England

Consider England when foreign trade is only possible in corn and linen. Since England specializes in linen, the maximum amount of corn consumed by the English is (LE/l1, L, E)(PL/PC). In this example, that quantity is less than LE/(l1, C, E + l2, C, E), the maximum quantity of corn consumed in England without foreign trade.

When foreign trade is also possible in steel, the maximum quantity of corn manufactured in England is (LE/l1, C, E) units. But not all of this corn can be consumed. Steel must be purchased from Portugal to continue production on the same scale. That is, (LE/l1, C, E)(PC - PS) numéraire units are available for consumption. So the maximum corn consumption in England is (LE/l1, C, E)(PC - PS)/PC units of corn. For England, the Sraffian bonus is positive. The possibility of foreign trade in steel has left the PPF for domestic consumption rotated outwards, even beyond the maximum consumption under autarky.

The situation in Portugal, as illustrated by Figure 1 at the top of this post, is quite different, however. Foreign trade in consumer, but not capital goods, results in a PPF rotated outwards from the autarkic PPF. This conforms to the nonsense long-suffering students in economics taught out of mainstream textbooks must endure. At the prices considered above, Portugal produces only steel when foreign trade is possible in all produced goods. The maximum amount of linen that can be consumed in Portugal is (LP/l2, C, E)(PS/PL) units. Neither intercept with an axis for this PPF is equal to the corresponding intercept for autarky. Furthermore, the PPF with foreign trade in all goods is strictly inside the PPF with foreign trade only in consumer goods. The Sraffian bonus is negative. Suppose one compares the PPF with foreign trade in all goods to the autarkic PPF for Portugal. Whether or not there are gains from trade is ambiguous. It depends on the consumption basket.

4.0 Conclusion

So this post has extended long-ignored proofs that the theory of comparative advantage does not provide a valid a-priori argument for so-called free trade. Opening up markets in capital goods may not provide a country with more goods, setting aside problems of adjustment.

I know of some empirical work purporting to demonstrate gains from trade. I do not know of any that addresses the issues brought forth in this post.

  • Paul A. Samuelson (2001). A Ricardo-Sraffa Paradigm Comparing Gains from Trade in Inputs and Finished Goods. Journal of Economic Literature 39, 4: 1204-1214.
  • Ian Steedman (1980). Trade amongst Growing Economics. Cambridge University Press.

Thursday, June 07, 2018

More On Foreign Trade In Consumer And Capital Goods

Figure 1: Rates Of Profits for Specialization in Consumer Goods
1.0 Introduction

This post is a continuation of this example. How a country specializes in foreign trade depends on distribution. And foreign trade can reduce the consumption basket to be divided among the inhabitants of a country, as compared with autarky.

2.0 Patterns of Specialization

Assume that the consumption basket in both countries contains both corn and linen. In a steady state, international prices and the distribution of income in both countries must be such that at least one country produces each one of the three commodities. Table 1 lists the six possible patterns of specialization in which each commodity is produced in exactly one country. If foreign trade is possible in consumer goods, but not in capital goods, steel must be produced in the same country in which corn is produced. Only cases 2 and 5 are possible. All six cases must be analyzed if foreign trade is possible in both consumer and capital goods.

Table 1: Patterns of Specialization
1CornLinen, Steel
2LinenCorn, Steel
3SteelCorn, Linen
4Linen, SteelCorn
5Corn, SteelLinen
6Corn, LinenSteel

A pattern of specialization is compatible, given the technology, with certain rates of profits between the trading countries. Under the assumption that financial capital does not flow between countries, the rate of profits may vary between countries. Insofar as the determinants of distribution is unspecified, the model is open. A neoclassical closure would specify intertemporal utility-maximizing consumers in each country

Disequilibrium transitions paths are also not considered here. Firms could find their expectations, with which they have produced or bought capital goods, disappointed. Presumably along such paths, trade might be unbalanced, and exchange rates could vary. Keynesian considerations of effective demand come into play. The elasticities of the demands for imports and exports might be of some importance, as reflected in the Marshall-Lerner conditions. The convergence of such transition paths to steady states does not seem assured.

3.0 Trade in Consumer Goods

Consider the model under the assumption that international markets do not exist for steel. Suppose England specializes in the production of linen, and Portugal specializes in the production of corn, as in case 2. Then the international prices of linen and corn must be related:

l1, L, E/(vC, E + l2, C, E rE) < PL/PC
PL/PC < l1, L, P/(vC, P + l2, C, P rP)


l1, L, E/(vC, E + l2, C, E rE) < l1, L, P/(vC, P + l2, C, P rP)


rP < (l1, L, P l2, C, E rE + l1, L, P vC, E - l1, L, E vC, P)/(l1, L, E l2, C, P)

A specific region in the space for the national rates of profits corresponds to each pattern of specialization. Figure 1, above, shows these two regions, as divided by the upward-sloping line. The figure is drawn under the assumption that England has a comparative advantage in producing linen.

4.0 Production Possibility Frontiers (PPFs)

A production possibility frontier (PPF) shows the upper limits on how much linen or corn can be consumed in a given country in a stationary state. Let YC, n represent bushels corn consumed, and let YL, n be the square-yards of linen consumed, where n = E or P for England or Portugal. Let LE and LP be the endowments of labor in England and Portugal, respectively.

I want to consider three PPFs. Here is the PPF for autarky, when a country does not have the possibility to engage in foreign trade:

l1, L, n YL, n + vC, n YC, n = Ln

The PPF for a country specializing in the production of corn is:

vC, n (PL/PC)YL, n + vC, n YC, n = Ln

The PPF for a country specializing in the production of linen is:

l1, L, n YL, n + l1, L, n (PC/PL) YC, n = Ln

Figure 2 graphs these PPFs. The possibility of foreign trade rotates the autarkic PPF, with the pivot on an axis, depending on which product the country specializes in. I have drawn the PPFs such that when the country specializes in the production of linen, it is worse off as a whole. If any corn is consumed at all, foreign trade results in a smaller commodity basket than under autarky.

Figure 2: Production Possibility Frontiers for One Country

4.1 Comparison of PPFs for Autarky and Specialization in Corn

For a country specializing in corn, the ratio of the international price of linen to the international price of corn is bounded above:

PL/PC < l1, L, n/(vC, n + l2, C, n rn)

For a non-negative rate of profits, the right-hand side cannot exceed l1, L, n/vC, n. Hence:

PL/PC < l1, L, n/vC, n


(Ln/l1, L, n) < (Ln/vC, n)(PC/PL)

The left-hand side is the maximum consumption of linen for this country under autarky. The right-hand side is the corresponding maximum consumption when the country specializes in producing corn. Thus, in this simple model, specialization in corn when no foreign markets in steel exist, unambiguously rotates the PPF outwards. In a comparison of stationary states, foreign trade gives the country specializing in producing corn a greater consumption basket to distribute among its inhabitants.

4.2 Comparison of PPFs for Autarky and Specialization in Linen

On the other hand, specialization in linen could make a country worse off. For the PPF to be rotated inward, one must have:

(Ln/l1, L, n)(PL/PC) < (Ln/vC, n)


PL/PC < l1, L, n/vC, n

So a country experiences a loss from trade when it specializes in linen and the following condition holds:

l1, L, n/(vC, n + l2, C, n rn) < PL/PC < l1, L, n/vC, n

Notice a loss from trade is not possible when the rate of profits is zero.

Suppose rates of profits and prices are such that England specializes in the production of linen. Prices can be such that England can gain from trade if and only if:

l1, L, E/vC, E < l1, L, P/(vC, P + l2, C, P rP)


rP < (l1, L, P vC, E - l1, L, E vC, P)/(l1, L, E l2, C, P)

The right-hand side can be positive if and only if England has a comparative advantage in producing linen when rates of profits are zero in both countries.

5.0 Conclusion

So in this simple model, when international markets exist in consumer goods, but not in capital goods:

  • Which country specializes in producing corn and which in producing linen depends on domestic rates of profits.
  • Only one pattern of specialization for a given pair of rates of profits is possible.
  • For each pattern of specialization, a pair of rates of profits exists for that specialization.
  • If a country specializes in producing corn, its PPF is rotated outwards.
  • If a country specializes in producing linen, its PPF may be rotated outwards, but only if:
    • The country has a (technologically-defined) comparative advantage in producing linen.
    • The relative price of linen on international markets is high enough.
  • The PPF may be rotated inwards when a country specializes in producing linen; the terms of trade matter.

I am finding it non-obvious how to complete this analysis when steel can be traded in foreign markets. Also, I should create numerical examples just to confirm my results.

Saturday, June 02, 2018

Ideological Innocence Of The Fox News Viewer

1.0 Introduction

This post deals with a set of ideas that I find appealing, but contradictory. I know I do not fully understand many of them. Perhaps somebody who understands more can either agree with me that there are contradictions here or point to some way of resolving them. This post is also more about current events than is typical of my posts.

2.0 Ideological Thinking, Ideological Identification, And Party Identification

Consider Philip Converse's claim that a mass majority of the public is innocent of ideology, as contrasted with the non-innocence of elites. I know these ideas best as filtered through Kinder and Kalmoe (2017).

Ideological thinking is not a defect, in Kinder and Kalmoe's account. An ideology, such as liberalism or conservatism in contemporary America, structures how you understand and retains facts. Otherwise, the world, in at least its political aspects, will appear as a blooming, buzzing confusion. Ideological thinking can be seen in a couple of ways. First, when surveying people about issues, you can listen to how they justify their stance. Do they refer to liberalism or conservatism? Second, do they exhibit a certain constraint on issues. For example, if they are against abortion generally being illegal, are they also against the death penalty? (Kinder and Kalmoe define issues narrowly. They do not consider a take on whether a larger or smaller government is desirable as a political issue, as opposed to a more philosophical issue.)

Kinder and Kalmoe note that being informed about politics takes quite a bit of work. I think their take goes along with some of Ahler and Broockman's findings on so-called moderates. It is not that moderates necessarily take middle-of-the road positions on issues. Rather, they may take extreme sides on different issues, with no awareness of how they go together, including in prevailing ideologies among those who pay more attention to politics. Apparently, survey questions to test your knowledge of politics are fairly rudimentary. Common practice is to base an assessment on less than twenty multiple-choice questions like: How long is a senator's term? What is Paul Ryan's position? What party was Franklin Delano Roosevelt a member of?

Kinder and Kalmoe distinguish ideological thinking (non-innocence) from both ideological identification and party identification (also known as partisan identification). In the period of their data they find a closer correlation between ideological identification and partisanship, but there are still plenty of people who call themselves conservatives and Democrats. After taking into account of partisanship and stands on issues, ideological identification counts for little.

3.0 Pyschological Traits of Liberals and Conservatives

I think the literature on social psychology about traits among liberals and conservatives is meant to apply to mass publics. John Jost and Jonathan Haidt are the most prominent writers I know of here.

Jost claims liberals are more open to experience; are tolerant of uncertainty; have less need for order, structure, and closure; have more tolerance of ambiguity and less dogmatism; have less fear of death, threat, and loss; and have higher self-esteem. Conservatives are otherwise. Haidt says that liberals' moral intuitions emphasize the avoidance of harm/the provision of care and fairness and reciprocity. Conservatives include these moral concerns. But they also worry more about in-group loyalty, respect for authority, and purity and sanctity.

How does this literature relate to ideological thinking, ideological identity, and partisanship among mass publics in the United States? As I understand Kinder and Kalmoe, they recognize this contrast. They argue that Jost misunderstands their work, and his traits only gets you to ideological identification. I can see how one could be authoritarian, in personality, and be a strong Democrat or even further left. Could an anti-authoritarian be a strong Republican in the current conjecture?

Do those who have read these literatures think more could be said here?

4.0 Marshall McLuhan And Media

How is all of the above modified by contemporary events? Once upon a time, those on the left decried the biases of the corporate media. They wanted more explicitly class-based channels that were not afraid to affirm a point of view. It is not what they meant, but we now have Fox News. And they explicitly treat "liberal" as a swear word. How much will a regular viewer get a message, which, if accepted and absorbed, will lead to issue constraint, in Kinder and Kalmoe's sense? (Chemtrails are not an issue.)

But if one worries about the message on Fox News, could one accept Marshall McLuhan's take on media? Supposedly reading encourages analytical, linear thought, while television extends your nervous system to be irritated by going-ons throughout the global village. Would this not be just as true for messages on other television channels? Should one just reject McLuhan's approach?

5.0 Some Caveats

In looking at international data, Kinder and Kalmoe convert "liberal" and "conservative" to "left" and "right". I would not call myself a liberal - I would say I'm more somewhere between a democratic socialist and a social democrat. Those who reject the labels "Liberal" and "Conservative", Kinder and Kalmoe classify as non-ideological. I do not know how I would have answered those survey questions. By the way, I voted on a certain resolution on the New York State ballot last time without knowing much about it, but on the grounds that labor unions were opposed. This group-based approach is not ideological thinking, as I understand Kinder and Kalmoe. A Catholic paying attention to the Church's teaching might endorse both making abortion illegal and getting rid of the death penalty. So they would not exhibit, at least on this issue, the kind of constraint Kinder and Kalmoe take as demonstrating ideological thinking. I doubt that many non-elites fall outside their classification, but how could one know?

  • Douglas J. Ahler and David E. Broockman (2015). Does Polarization Imply Poor Representation? A New Perspective on the "Disconnect" Between Politicians and Voters
  • Pierre Bayard (2007). How to Talk About Books You Haven't Read
  • Philip E. Converse (1964). The Nature of Belief Systems in Mass Publics
  • Jesse Graham, Jonathan Haidt, and Brian A. Nosek (2009). Liberals and conservatives rely on different sets of moral foundations. Journal of Personality and Social Psychology, V. 96, no. 5: pp. 1029-1046.
  • Jonathon Haidt (2013). The Righteous Mind: Why Good People are Divided by Politics and Religion
  • John J. Jost et al. (2003). Political Conservatism as Motivated Social Cognition
  • Donald Kinder and Nathan P. Kalmoe (2017). Neither Liberal nor Conservative: Ideological Innocence in the American Public
  • Marshall McLuhan (1962). The Gutenberg Galaxy
  • Marshall McLuhan (1964). Understanding Media: The Extensions of Man

Saturday, May 26, 2018

Foreign Trade In Capital And Consumer Goods

Figure 1: Specialization In A Single Country
1.0 Introduction

This post considers how the firms in a small open economy will specialize, given prices on international markets and the domestic rate of profits. The example would only be interesting as part of a larger argument, which I have not yet worked out.

2.0 Technology

Consider a small, open economy which has a flow-input, point-output technology for producing two consumption goods, corn and linen. Corn is manufactured from inputs of direct labor and steel. Steel and linen are each manufactured from inputs of direct, unassisted labor. Table 1 shows an input-output table for the technology. The technology is thus specified by three coefficients of production, (l1, C, n, l2, C, n, and l1, L, n).

Table 1: Example Technology
Laborl2, C, n Person-Yrsl1, C, n Person-Yrsl1, L, n Person-Yrs
Steel01 Ton0
Output1 Ton1 Bushel1 Square-Yd

Comparative advantage when the rates of profits is zero in each country is determined by relative ratios of labor embodied in each commodity. The labor value of steel is:

vS, n = l2, C, n

The labor value of corn is the sum of the labor embodied in steel used in producing corn and the direct labor used in producing corn:

vC, n = l1, C, n + l2, C, n

The labor value of linen is:

vL, n = l1, L, n

For a technology in which dated labor inputs extend for a larger number of time periods, finding labor values can require the calculation of sums with a greater number of terms.

3.0 Autarky

In this section, I assume foreign trade is not possible for the country being analyzed.

Let pC, n, pL, n, and pS, n be the domestic prices of corn, linen, and steel when no foreign trade is possible. Let wn be the wage paid for a person-year of labor, and let rn be the rate of profits. Assume labor is advanced and wages are paid out of the surplus at the end of the year.

Under these assumptions, prices, with labor-commanded as the numeraire, are:

pS, n/wn = l2, C, n = vS, n
pC, n/wn = vC, n + l2, C, n rn
pL, n/wn = l1, L, n = vL, n

4.0 Trade in Consumer Goods

Now suppose foreign trade is possible in consumer goods, but not in capital goods. In terms of the example, the firm can trade in corn and linen, but not in steel. Let PC and PL be international prices of corn and linen, respectively.

Two patterns of complete specialization are possible. Suppose the firms in the country want to produce linen (and the required steel), but not corn. Linen is sold on international markets, and corn is purchased. For firms to be unwilling to produce corn, the cost of producing a unit of corn, at the going rate of profits, must exceed the given international price:

[l2, C, n( 1 + rn) + l1, C, n] wn > PC

In a steady state, the cost of producing linen must be equal to its price:

l1, L, n wn = PL

Solving for the wage and substituting, one obtains the following inequality.

PL/PC > l1, L, n/(vC, n + l2, C, n rn)


PL/PC > pL, n/pC, n

For domestic firms to want to specialize in producing corn, the above inequality is reversed. In words, the country specializes in producing those goods whose international prices exceed autarkic prices.

5.0 Trade in Capital and Consumer Goods

In this section, I assume that the country can trade steel on international markets, as well as corn and linen.

Suppose the country specializes in producing linen. The following inequalities and equalities must be satisfied in a steady state:

l2, C, n wn > PS
PS ( 1 + rn) + l1, C, n wn > PC
l1, L, n wn = PL

Following my usual practice of solving for wages and substituting, I obtain two inequalities:

PL > (l1, L, n/l2, C, n) PS
PL > (l1, L, n/l1, C, n)[PC - PS ( 1 + rn)]

When the country specializes in corn, the system of inequalities and equalities is modified in a way that I hope is obvious. As above, two conditions characterize prices on international markets. The same is true for when the country specializes in the production of steel. For the country to specialize in linen, it is necessary but not sufficient that the country would have specialized in linen in trade in steel were impossible. This is not so for specialization in corn. For some combinations of international prices, the country will specialize in corn even when the country would not have so specialized when trade in capital goods was not possible. Likewise, a set of prices exists in which the country specializes in steel when the country would have specialized in corn without the possibility of trade in steel.

6.0 Conclusion

Figure 1, at the head of this post summarizes the analysis. The upward-sloping line extending from the origin divides regions of specialization under the assumption that foreign markets exist for consumer goods, but not for capital goods. When the international prices of corn and linen are in the region above this line, the country specializes in producing linen. When they are in the region below this line, the country specializes in producing corn.

With the possibility of international trade in steel, additional regions appear. If prices of linen and corn are low enough, for a given price of steel, they fall in the rectangle at the lower left in the figure. The country specializes in steel. All of each year's output of steel is sold in foreign trade, and linen and corn are bought with the revenues thereby obtained. A wedge appears in the upper right. If prices are in this region, the country does not specialize in producing linen. It becomes more cost-effective to produce corn, with inputs of steel purchased on international markets.

Friday, May 18, 2018

Can A Nazi Be Rational?

Hilary Putnam has long argued that facts and values, or ends and means, cannot be neatly separated. In 1981 he proposed a thought experiment, I assume not to be of contemporary political relevance:

What troubled us earlier was that we did not see how to argue that the hypothetical 'perfectly rational Nazi' had irrational ends. Perhaps the problem is this: that we identified too simply the question of the rationality of the Nazi (as someone who has a world view or views) with the rationality of the Nazi's ends. If there is no end 'in' the Nazi to which we can appeal, then it does seem odd to diagnose the situation by saying 'Karl has irrational goals.' Even if this is part of what we conclude in the end, surely the first thing we to say is that Karl has monstrous goals, not that he has irrational ones.

But the question to look at, if we are going to discuss Karl's rationality at all, is the irrationality of his beliefs and arguments, not his goals.

Suppose, first, that Karl claims Nazi goals are morally right and good (as Nazis, if fact if not in philosophers' examples, generally did). Then, in fact, he will talk rubbish. He will assert all kinds of false 'factual' propositions, e.g., that the democracies are run by a 'Jewish conspiracy'; and he will advance propositions (e.g. that, if one is an 'Aryan', one has a duty to subjugate non-Aryan races to the 'master race') for which he has no good arguments. The notion of a 'good argument' I am appealing to is internal to ordinary moral discourse; but that is the appropriate notion, if the Nazi tries to justify himself within ordinary moral discourse.

Suppose, on the other hand, that the Nazi repudiates ordinary moral notions altogether... I argued that a culture which repudiated ordinary moral notions, or substituted notions derived from a different ideology and moral outlook for them, would lose the ability to describe ordinary interpersonal relations, social events and political events adequately and perspicuously by our present lights. Of course, if the different ideology and moral outlook are superior to our present moral system then this substitution may be good and wise; but if the different ideology and moral outlook are bad, especially if they are warped and monstrous, then the result will be simply an inadequate, unperspicuous, repulsive representation of interpersonal and social facts. Of course, 'inadequate, unperspicuous, repulsive' reflect value judgments; but I have argued that the choice of a conceptual scheme necessarily reflects value judgments, and the choice of a conceptual scheme is what cognitive rationality is all about.

Even if the individual Nazi does not lose the ability to use our present moral descriptive vocabulary, even if he retains the old notions somewhere in head (as some scholars, perhaps, still are familiar with and able to use the medieval notion of 'chivalry'), still these (our present moral descriptive notions such as 'considerate', 'compassionate', 'just', 'fair') will not be notions that he employs in living his life: they will not really figure in his construction of the world.

Again, I wish to emphasize that I am not saying that what is bad about being a Nazi is that it leads one to have warped and irrational beliefs. What is bad about being a Nazi is what it leads you to do. The Nazi is evil and he also has an irrational view of the world. These two facts about the Nazi are connected and interrelated; but that does not mean the Nazi is evil primarily because he has an irrational view of the world in the sense that the irrationality of his world view constitutes the evil. Nevertheless, there is a sense in which we may speak of goals being rational or irrational here, it seems to me: goals which are such that, if one accepts them and pursues them one will be either be led to offer crazy and false arguments for them (if one accepts the task of justifying them within our normal conceptual scheme), or else one will be led to adopt an alternative scheme for representing ordinary moral-descriptive facts (e.g. that someone is compassionate) which is irrational, have a right to be called 'irrational goals'. There is a connection, after all, between employing a rational conceptual scheme in describing and perceiving morally relevant facts and having certain general types of goals as opposed to others.

Hilary Putnam (1981). , Cambridge University Press, pp. 211-214.

But this a thought experiment that takes an obvious consensus for granted. Fascism is bad.

Saturday, May 05, 2018

Neo-Ricardianism: A Marxist Insult

Today is the 200th birthday of Karl Marx.

My favorite school of thought in economics is sometimes called Neo-Ricardianism, instead of Sraffianism. As I understand it, the label "Neo-Ricardianism" was invented in 1974, as an insult, by Bob Rowthorn. Basically, he claimed to more closely follow Marx, and claimed that the Neo-Ricardians were, like neoclassicals, bourgeois economists. Other Marxist economists at the time offered arguments along the same lines. Franklin Roosevelt III, for example, did not use the label "Neo-Ricardian", but rather described Sraffians as in the grip of commodity fetishism.

(This Roosevelt is the grandson of FDR, the United States president. According to Wikipedia, he is a Du Pont on his mother's side, and therefore a descendant of the famous physiocrat. I've also recently read one in the series of Elliot Roosevelt's mystery novels, in which his mother Eleanor is the detective.)

One aspect of the Marxist argument against Sraffians harkens back to J. S. Mill. The claim is that, in Mill, production is taken as a matter of natural law, while distribution is a matter of social laws that can be freely changed, if we collectively decide so, perhaps through government. According to Marxists, production and distribution cannot be separated like that. You can see why this might be described as commodity fetishism, in which social relations are taken as natural relations.

This argument also provides a context for understanding some chapters in Steedman (1977). Sraffa, for some purposes - e.g., internal criticism of neoclassical economics - takes quantity relations as given, while considering what prices would be if some distributive variable were at a different level. But, Steedman argues, that, in principle, one can relax what is taken as given. The length of the working day or the intensity with which laborers work might be varied in the analysis. This is not just a matter of, say, increasing all inputs in a production process by some proportion. You would want to consider how fuel, oil, or other elements of working capital vary with output, how output varies with concrete production processes, and whether or not these variations have an impact of the efficiency on machinery of various ages. I suppose I ought to also mention Steedman's polemics, especially his labeling of some anti-Sraffa Marxists as "obscurantists".

Of course, many arguments have been developed on both sides over the nearly half-century since these charges and counter-charges were first offered. Does Sraffa provide a constructive alternative, as well as an internal criticism of neoclassical economics? Do Sraffian interpretations of classical economics hold up as history? How do issues of money enter? Is Sraffian economics confined to logical - not historical - time? How do market prices relate to prices of production? And what does this all have to do with Marx?

Another famous adoption of "Neo-Ricardism" as an insulting label for Sraffianism comes shortly later from Frank Hahn, who was no Marxist.

  • Frank Hahn (1982). The Neo-Ricardians, Cambridge Journal of Economics, V. 6, iss. 4: 353-374.
  • Frank Roosevelt (1975). Cambridge economics as commodity fetishism. Review of Radical Political Economics, V. 7, no. 4. (Reprinted in Growth, Profits, and Property: Essays in the revival of political economy, (ed. by E. J. Nell) Cambridge University Press, 1980.)
  • Bob Rowthorn (1974). Neo-Classicism, Neo-Ricardianism, and Marxism. New Left Review
  • Ian Steedman (1981, first edition 1977). Marx After Sraffa, Verso.

Tuesday, May 01, 2018

How Has Economics Failed?

The Financial Times is having a debate about whether economics has failed. The first interchange is here, with some followups here. (I happen to have two tabs about neoliberalism open at the moment as well.)

Mainstream economics is a failure in so many dimensions that its failure cannot be characterized shortly in any comprehensive way. For example, I am not going to discuss funding sources and economics role as a system justification. Even so, you might find this post long and wandering.

As you can see, I do not take the claim to be that non-mainstream, heterodox economics has failed. In the comment section, for one FT page, Percy Pavilion writes, "So Marshall, Keynes, Kahn, Kaldor and Harcourt failed did they?" I think any opinion on whether Keynes, Kahn, Kaldor, and Harcourt were failures to be irrelevant to the topic. Was it Joan Robinson, commenting on the claim that it is all in Marshall, said something like, "The problem is that the opposite is also in Marshall, too"?

Anyways, I want to focus on the failure of economic theory. I think any well-trained economist in some field knows how to tweak assumptions to get any results that they want. Start with a model of perfect competition. Add an information asymmetry, a transaction cost, a search cost, sticky prices and a Calvo fairy, some monopoly or monopsony, whatever. Then you can argue that some policy will lead back to efficient markets. Or, if so inclined, that government failure prevents any some implementation.

Given this openness to such tweaks in mainstream economics, why is Sraffian economics or some other variety of heterodox economics not more widely accepted? Most of the time, when I or others put forward a model with Sraffa effects, we are not arguing about the implications of an imperfection. Rather, the argument is that the model of perfect competition does not work the way that mainstream economists teach. And this is usually in an open model with no way to resolve class interests in some utopian world. To understand such models, it is helpful to have some understanding of the history of political economy and alternative theories of value and distribution. As Mariana Mazzucato notes at the FT, mainstream economists are trained to be ignorant of such topics.

What to make of empirical research? Some of it, say, on malarial nets, is by researchers striving to be useful. One can raise questions about external validity and whether atheoretical research is possible or desirable. But this is a different direction from my comments above.

But how does the theory relate to the supposed empirical turn? Are textbooks updated to state that some theories (e.g., skills-biased technical change) have been rejected by the evidence? Can you point to an introductory textbook that includes a section on behavioral economics and empirical evidence? (I expect "Yes" to be an answer to this question.) But how many experiments decide between contrasting theories? It is my feeling that the ability to tweak a theory includes an ability to maintain it as consistent with any empirical evidence that shows up. And much empirical work takes a particular approach for granted, without testing it. I like reading Marshall Steinbaum, but will cite him as somebody that does not realize how many effects he takes as a consequence of monopsony might be consistent with Sraffian price theory, before adding in failures of competition.

I am unsure how to take a lot of applied research. I do not think tariffs on steel and aluminum should be imposed on the whim of an ignoramus. I suppose one can use Leontief matrices to trace through the effects of such tariffs on the automotive industry, aluminum cans and the beverage industry, etc. And I suppose that one can apply game theory after the fact to rationalize, say, the Chinese reaction. But can one say beforehand whether soy bean farmers in the mid west or Boeing executives trying to sell Dreamliners should have more to worry about? And is not the question of the long term effects of undermining the World Trade Organization more a qualitative question for historians that data-driven economists? I want to take analysis of the possible effects of the exhaustion of North Sea oil reserves on sustainable social spending in Norway as useful. But I suspect that if I look carefully, I will find theoretical errors embedded in many of the equations in supposedly applied research.

I am amused that Maurice Obstfeld shows up in the FT interchanges, when I have just demonstrated the failure of what Krugman and Obstfeld teach in one edition of their textbook on international trade. I am aware that the boundary between mainstream and non-mainstream economic theory is not necessarily well-defined. Nevertheless, I do not expect most mainstream economists to be able to conduct a reasonable conversation about the topics in this post. At the FT, Diane Coyle, Tony Yates, and Tim Harford exemplify my expectation. And much of what I am saying is old hat. You can see some of what I am saying as echoing Christian Arnsperger and Yanis Varoufakis. Or even Robert Solow.

Wednesday, April 25, 2018

On the Gain and Loss from Trade

I have written up my recent explorations in the theory of international trade.

Abstract: This article considers a model of international trade in which the number of produced commodities does not exceed the number of countries engaged in trade. Technology is modeled such that each commodity can be produced in each country from a finite series of dated labor inputs. The existence of a positive rate of profits may lead a country to specialize differently than how it would with a zero rate of profits. Trade may leave consumers in a country worse off, as compared with autarky, when the rate of profits is positive. The existence of more than two countries provides a possibility that the Production Possibilities Frontier (PPF) with trade is neither unambiguously above or below the PPF under autarky. This article re-iterates, in a setting with more than two produced commodities and more than two countries, demonstrations that the argument for free trade is logically invalid, given positive rates of profits.

Monday, April 23, 2018


  • Howard Reed argues we should rip up textbooks for mainstream economics and start over. (Some of what he says echoes an argument of mine.)
  • I do not think Diane Coyle addresses Reed's points.
  • Cahal Moran argues the problem is economics, not economists.
  • Beatrice Cherrier has some frankly speculative posts on what limitations economists accepted in emphasizing tractability in developing models.
  • Nathan Robinson does not like the word "neoliberalism", but understands there is a point to using it.
  • David Glasner writes about Hayek's introduction of the theory of intertemporal and temporary equilibrium paths into economics. (I have no problem for those who look for Irving Fisher as a precursor of for more-or-less simultaneous discoveries in Sweden.)

Tuesday, April 17, 2018

Class Struggle And Specialization In International Trade

This post continues a previous numeric example. The firms in each of three countries are assumed to know a technology for producing corn, wine, and linen. The technology is such that each commodity can be produced in each country. The technology varies among countries.

Each of these small open economies can specialize and obtain non-produced commodities through foreign trade. I confine myself to patterns of specialization in which:

  • Each country produces exactly one commodity domestically.
  • Each commodity is produced in one country.

Six patterns of specializations meet these criteria. Table 1 lists the commodity produced in each country for each pattern of specialization.

Table 1: Patterns of Specialization

I have found out that, in my example, each specialization is consistent with a long period position. I take the international price of corn as numeraire. That is, p1 = 1. Table 2 lists the prices of the other commodities, p2 and p3, that are traded domestically. It also lists rates of profits, r1, r2, and r3, in each country. This data is sufficient to calculate the wage in each country. The wage is such that supernormal profits are not earned in the commodity produced domestically, but the cost (including profits) does not exceed revenues for produced commodities. With these wages, the costs of producing a commodity in which a country does not specialize will exceed the price. It is cheaper in each country to acquire such commodities on international markets.

Table 2: International Prices and Rates of Profits
of Wine
of Linen
Rate of Profits

The prices shown in Table 2 are not unique. For the given set of rates of profits, international prices must fall within a certain range to obtain a long period position consistent with the pattern of specialization. And rates of profits may vary in certain ranges too. I have not figured out a good way of visualizing how the spaces of prices and rates of profits is divided up by the patterns of specialization. Maybe a region for a given pattern of specialization if, contrary to this example, restitching was possible under autarky.

The numeric example illustrates that:

  • The pattern of specialization in foreign trade can be driven by technology and the distribution of income.
  • Only some distributions are compatible with all countries being able to specialize in a consistent way.
  • The results of such specialization may not provide a country with overall gains from trade, nevermind individual groups defined by the functional distribution of income.

I have assumed constant returns to scale, but which commodity a country specializes in producing may be of importance because of considerations of learning-by-doing. Technological progress may be easier to obtain in some commodities (e.g., manufactured industrial products) than others (e.g., products of agriculture). I suspect these observations generalize to a more comprehensive Neo-Ricardian theory of trade, such as that of Yoshinori Shiozawa.

These theoretical observations, I guess, are enough to blow up much mainstream teaching on trade. I might have even made some progress on the work of Mainwaring, Metcalfe, and Steedman. Nevertheless, this model puts much aside. I am thinking of, especially, Keynesian issues of exports, imports, and effective demand; foreign exchange rates and monetary policy; and international finance.

Monday, April 09, 2018

The Gain And Loss From Trade: More On A Numeric Example

Figure 1: The Production Possibility Frontier, With And Without Trade, In "Germany"
1.0 Introduction

I continue to blunder around in parameter space in exploring my numeric example in the previous post. In this post, I continue to adopt the same assumptions for a model of three countries engaged in international trade with three produced commodities. In particular, workers are assumed to be unable to immigrate, capitalists only invest in their own country, and produced means of production are not traded. Thus, wage rates and rates of profits may vary among countries, with no tendency to change or approach equality.

2.0 Outline of the Model

For this intellectual exercise, I make the same assumptions about technology, available in each country, but differing among them. Corn, wine, and linen can each be produced from a dated series of labor inputs. Under the restrictive assumptions illustrated by the numeric example, one can rank commodities by how labor-intensive they are. Corn is most labor-intensive, and linen is least. Wine is of an intermediate labor-intensive. The endowment of labor is also taken as given.

The rate of profits is taken as given in each country. One then wants to find a set of international prices for corn, wine, and linen such that a pattern of specialization can arise for the given data. Under a model of small, open economies, the firms in each country take prices as given. In such specialization, each country will specialize in producing at least one commodity, and each commodity will be produced in one or another country. The wage in each country will be such that no pure economic profits (also known as supernormal profits) will be earned in the production of any commodities. And costs, including charges for the prevailing rate of profits, will exceed the price of all commodities that firms in each country are unwilling to produce.

3.0 Countries Specializing in Producing One Commodity

Table 1 exhibits a set of prices, for the given rates of profits, that meets these conditions. Each country specializes in the production of one commodity. England produces linen, Portugal produces corn, and Germany produces wine. The wages in each country are as shown.

Table 1: Prices with Trade
Cornp1 = 3240/11
Winep2 = 324
Linenp3 = 4050/11
Rate of Profitsr1 = 2/5r2 = 3/2r3 = 7/10
Wagew1 = 4050/1199w2 = 162/121w3 = 1

For this particular set of prices, each country specializes differently than they would if the rates of profits were zero in each country. And they specialize differently than they would at the prices and positive rates of profits in my previous exploration of this example.

4.0 Production Possibility Frontiers (PPFs)

In the textbook theory of comparative advantage, an unambiguous gain from trade is shown by comparing the Production Possibilities Frontier (PPF) with trade and under autarky. The claim is that the with-trade PPF is moved outward from what it would be under autarky. If the consumption basket contains any commodities that must be bought on international markets, the with-trade equilibrium is supposedly unambiguously better for the country. No commodity must be consumed in a smaller amount than under autarky, and some commodities can be produced in larger quantities. Some may be hurt by trade, perhaps because they receive profits from industries whose domestic production has been replaced by imports. But they could be compensated out of the increased consumption basket, while still leaving everybody else better off in the country under consideration.

To check the textbook argument, one would look at the PPFs in each of England, Portugal, and Germany. And the textbook story is validated for England in this numeric example, with these prices and pattern of specialization. The PPF for England is rotated outwards, as compared with autarky. They coincide at the intersection with the linen axis. For every other consumption basket with non-negative quantities, the English with-trade PPF lies outside the autarkic PPF. England gains from trade.

The with-trade and autarkic PPFs for Portugal (Figure 2) replicate my previous finding that specialization can result in a loss from trade. The argument from comparative advantage is logically invalid, given positive rates of profits among countries engaged in international trade. The with-trade PPF in Portugal is rotated inwards. Portugal is unambiguously worse off with trade.

Figure 2: The Production Possibility Frontier, With And Without Trade, In "Portugal"

The story from Germany illustrates a possibility that cannot arise in the two-country, two-commodity model. The with-trade PPF (Figure 1) is neither rotated outwards nor inwards, as compared with the autarkic PPF. Along one dimension (linen), the with-trade PPF lies outside the autarkic PPF. Along another dimension (corn), it lies inside the autarkic PPF. Whether Germany is worse or better off with-trade depends on the composition of the commodity basket.

5.0 Remarks on Krugman and Obstfeld

I am unsure what I think of Krugman and Obstfeld, so far. Chapter 2 presents the argument from comparative advantage. They hammer home that, in the Ricardian model, countries are better off with-trade, no question about it. In this chapter, inputs consist only of labor, and no profits are earned. I do not know that they are clear that labor inputs are only direct. (In my example, I have labor inputs distributed over time, thereby providing a role for a rate of profits.)

In Chapter 3, they have manufacturing goods produced from labor and capital, as specified by a production function. I am not sure they ever take the marginal product of capital. They show output as a function of labor, with a diminishing marginal product. Although they do have some remarks on the supply of labor, they seem to be considering a medium term model where manufacturing output is produced with given technical conditions and a given set of production facilities. The point is to show that trade has impacts on the distribution of income in a country and can hurt some, if they are not compensated out of the supposed gains.

Chapter 4 sets out the Heckscher-Ohlin-Samuelson model in the two-factor, two-country, two-commodity case. The factors are labeled labor and land. This is as far as I've gotten in my reading.

One reading of the above is that Krugman and Obstfeld are carefully working around the Cambridge Capital Controversy. I do not know that they entirely succeed in Chapter 3. Their chapters have points, and I, of course, question their Chapter 2 claim that the gains of trade are unambiguously positive. Presumably, they would point to later chapters that put forth qualifications about imperfect competition and increasing returns to scale - a textbook presentation of the work that won Krugman a Nobel prize. Or they might point to a need in pedagogy to drum home simple points. Furthermore, their textbook, they could argues, teaches what (mainstream) economists have settled on as a consensus of what international economics is.

But what happens when the consensus has been shown to be simply wrong almost half a century ago? I know I have previously thought Krugman's offhand remarks on his blog about the CCC did not seem particularly informed. Has he ever referenced, say, Ian Steedman, in his academic work?

  • Paul R. Krugman and Maurice Obstfeld (2003). International Economics: Theory and Policy, sixth edition.

Thursday, April 05, 2018

The Loss From Trade: A Numeric Example With Three Countries And Three Produced Commodities

Figure 1: The Production Possibility Frontier, With And Without Trade, In "Germany"
1.0 Introduction

This post presents a numeric example of a Ricardian model of small, open economies engaged in trade. Each of three countries specializes in producing one of three commodities. Technology is modeled following an Austrian approach. Each commodity can be produced in each country from inputs of labor and "capital". Endowments of labor are taken as given parameters. It makes no sense to take the endowment of capital as a given parameter.

The with-trade Production Possibilities Frontier (PPF) can be compared to the autarkic PPF in each of the three countries. And it is unambiguously rotated inwards in one country for the set of international prices and rates of profits I consider. One cannot correctly conclude, in the traditional textbook approach, that free trade makes the inhabitants of a country better off in the aggregate.

I have previously written up an analogous argument in the two-commodity, two-country case. I should have cited Steedman and Metcalfe (1973). If I had, I would have known that my originality was less than I suggested. Shiozawa argues convincingly that the sort of model illustrated in this post can only be offered as an intellectual exercise. A more empirically applicable model would have trade in intermediate products, and the number of traded commodities would exceed the number of countries. On the other hand, I do not know of any comparable write-up of an example with three or more commodities and countries, as here.

2.0 Assumptions

Consider a model of three countries - England, Portugal, and Germany - in which three commodities are potentially traded on international markets by each country.

  • Each country can produce any of the three commodities.
  • The managers of firms in each country know a given flow input-point output technology with the structure described in Section 3. The technology differs among countries.
  • Each country has a given endowment of labor, the only non-produced factor of production in each country. The endowment of labor may vary between countries.
  • Only commodities produced for consumption can be traded internationally. Workers can neither immigrate nor emigrate. Intermediate goods, also known as capital goods, cannot be traded internationally.
  • Financial capital is only invested domestically. Consequently, the rate of profits may vary across countries.
  • Free competition obtains in all domestic markets; transport costs are negligible; and free trade exists in all commodities produced for consumption.

3.0 Technology

In each country, each commodity can be produced by a uniform application of labor for a specified number of years (Table 1). In each country, less total labor is required to produce a unit wine than is required to produce a unit of corn, with the labor uniformly distributed over a longer period of time in producing wine. Wine is a less labor-intensive and more capital-intensive commodity than corn, in some sense. In the same sense, linen is a less labor-intensive and more capital-intensive commodity, as compared with wine. England has an absolute advantage over Portugal, and Portugal has an absolute advantage over Germany, in producing each commodity. Nevertheless, a set of prices on international markets can exist, for corn, wine, and linen, such that firms in each country will want to specialize in producing a single commodity.

Table 1: Example Technology
Years of
Labor Input per Year (Person-Yrs)
Linen32545200/3 ≈ 66.6

The data on technology, along with the endowment of labor in each country, is enough to draw the Production Possibility Frontier (PPF) for each country in an autarky (without trade). Let X1, n, X2, n, and X3, n be the quantity of corn, wine, and linen consumed in the nth country (n = 1, 2, 3). The plane outlined by the heavy lines in Figure 1, above, is the autarkic PPF for Germany. L3 is the endowment of labor in Germany. l1, 3, l2, 3, and l3, 3 is the labor embodied in each commodity, when produced in Germany. These quantities are 320, 240, and 200 labor-years for this technology.

4.0 Prices and Specialization With Trade at a Rate of Profits of Zero

Next, consider an equilibrium with trade. Suppose the prices of a unit of corn, wine, and linen are as in Table 2. The question arises of whether there is a pattern of specialization among countries and a distribution of income in each country consistent with the given international prices. At this point, I take the rate of profits as zero. And I have calculated the wages shown for each country.

Table 2: Prices with Trade with Zero Rate of Profits
Cornp1 = $300
Winep2 = $225
Linenp3 = $200
Rate of Profitsr1 = 0r2 = 0r3 = 0
Wagew1 = $3w2 = $3/2w3 = $1

Table 3 shows relative prices in each country, where the numeraire varies among countries. That is, a person-year of domestic labor is taken as the numeraire. (In Table 2, I have implicitly taken German labor - the lowest paid, as numeraire.) Notice that, in Table 3, the prices of corn in England, wine in Portugal, and linen in Germany are all equal to the labor values in the respective countries. And the prices of all other commodities falls below their labor values. Thus, since the rate of profits is zero, English firms will specialize in producing corn, Portuguese firms will produce only wine, and German firms will produce only linen. To obtain a domestic consumption basket, in any country, that contains all three commodities, each country must engage in international trade. It turns out that the PPF is unambiguously rotated outward for each country, for a pattern of specialization with a rate of profits of zero.

Table 3: Renormalized Prices with Zero Rate of Profits
Cornp1/w1 = 100p1/w2 = 200p1/w3 = 300
Winep2/w1 = 75p2/w2 = 150p2/w3 = 225
Linenp3/w1 = 200/3p3/w2 = 400/3p3/w3 = 200
5.0 Prices and Specialization With Trade at Positive Rates of Profits

It is well-known that, in general, prices deviate from labor values when the rate of profits is positive. Suppose the prices of corn, wine, and linen are as shown in Table 4. I also take the rates of profits as given in each country. These data yield the wages shown in the Table.

Table 4: Prices with Trade
Cornp1 = 4275/26
Winep2 = 9063/52
Linenp3 = 855/4
Rate of Profitsr1 = 3/5r2 = 1/2r3 = 9/10
Wagew1 = 9063/5408w2 = 1w3 = 855/1664

I suppose the fractions are somewhat less awkward when normalized, as in Table 3. Unlike the case with a zero rate of profits, one should not compare these prices with labor values, in order to figure out the pattern of specialization. Rather, one should compare these prices with dated labor inputs costed up at the going rate of profits. For example, consider England. Since corn is produced with only one year of labor, its labor cost is still 100 person-years. (I am assuming wages are paid at the end of the year, not advanced.) Since p1/w1 is less than 100, England will import corn and not produce any. The cost of wine is 40(1 + 3/5) + 40 = 104. England will produce wine, and no super-normal profits are earned in its production. Linen is costed up as 25(1 + 3/5)2 +25(1 + 3/5) + 25 = 129. p3/w1 is, approximately, 127.55. It is more costly to produce linen domestically, and, so, England will not do that. As a result of similar calculations, one can see that Portugal will specialize in producing linen and Germany in corn. The prices permit a consistent pattern of specialization, with all commodities being produced in some country and no firm earning more than the going rate of profits. And every country specializes in producing a different commodity shown above for the pattern with a zero rate of profits.

Table 3: Renormalized Prices
Cornp1/w1 = 5200/53p1/w2 = 4275/26p1/w3 = 320
Winep2/w1 = 104p2/w2 = 9063/52p2/w3 = 1696/5
Linenp3/w1 = 128440/1007p3/w2 = 855/4p3/w3 = 416

One can draw the PPFs, for each country, with this pattern of specialization and prices on international markets. The PPFs for England and Portugal are rotated out. For any consumption basket that contains some commodity not produced domestically, more is available to the country as a whole in England and Portugal. But the PPF is rotated inwards in Germany, as illustrated in Figure 1. The possibility of trade has diminished the commodities available for consumption in Germany.

6.0 Conclusion

I like that, in the above example, the pattern of specialization has each country producing a different commodity in the case with a positive rates of profits, as compared to the case with a rate of profits of zero. I'd like to convince myself that no other pattern of specialization is possible when the rate of profits is zero. I'd also like to find an example where the with-trade PPF is rotated outwards on one dimension and inwards on another. So whether every commodity in a nation's consumption basket is improved or decreased by trade would depend on its composition. I can show in the above model how a country's endowment of capital varies in value with the domestic rate of profits. And the model can be set out, in general, with any number of produced commodities and countries, with the number of commodities not exceeding the number of countries. In such a general setting, I think I will retain the severe restrictions of an Austrian model so as to exhibit that my point does not depend on, for example, capital-reversing.

It has been known for decades that the argument from comparative advantage is not a valid justification for a lack of tariffs (also known as free trade). Even setting aside such matters as, for example, increasing returns to scale or Keynesian failures of aggregate demand preventing a country from being on its PPF, the argument fails on its own terrain. This post is one more demonstration. Of course, this does not imply that any random, ill-natured, and ill-considered imposition of tariffs is likely to be a good idea in any specific case.

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  • Shiozawa, Yoshinori. 2018. An Origin of the Neoclassical Revolution: Mill’s ‘Reversion’ and its Consequences.
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