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.

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 l_{2, C, E} person-years. A unit of corn can be made from one unit of steel and l_{1, C, E}. A unit of linen is made from l_{1, L, E} person-years of direct and unassisted labor.

Table 1: Technology for the Example

Parameter	England	Portugal
l1, C, n	3	7
l2, C, n	2	2
l1, L, n	1	2
Ln	1	1
rn	300%	400%

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

I also take rates of profits, r_E and r_P, 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:

l_{1, L, E} w_E (1 + r_E) = 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:

[l_{2, L, E} (1 + r_E) + l_{1, L, E}] w_E (1 + r_E) = [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

Variable	England	Portugal
PC	6
PL	2/3
Cost of producing corn	22/3	6
Cost of producing linen	2/3	12/7
Specialization	Linen	Corn and Steel
wn	1/6	6/85

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:

(P_S + l_{1, C, E} w_E) (1 + r_E) = [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

Variable	England	Portugal
PC	6
PL	2/3
PS	1
Cost of producing corn	6	17/2
Cost of producing linen	2/3	1
Cost of producing steel	4/3	1
Specialization	Corn and Linen	Steel
wn	1/6	1/10

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 (L_E/l_{1, L, E})(P_L/P_C). In this example, that quantity is less than L_E/(l_{1, C, E} + l_{2, 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 (L_E/l_{1, 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, (L_E/l_{1, C, E})(P_C - P_S) numéraire units are available for consumption. So the maximum corn consumption in England is (L_E/l_{1, C, E})(P_C - P_S)/P_C 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 (L_P/l_{2, C, E})(P_S/P_L) 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.

References

• 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.

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

Case	England	Portugal
1	Corn	Linen, Steel
2	Linen	Corn, Steel
3	Steel	Corn, Linen
4	Linen, Steel	Corn
5	Corn, Steel	Linen
6	Corn, Linen	Steel

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:

l_{1, L, E}/(v_{C, E} + l_{2, C, E} r_E) < P_L/P_C

P_L/P_C < l_{1, L, P}/(v_{C, P} + l_{2, C, P} r_P)

Hence:

l_{1, L, E}/(v_{C, E} + l_{2, C, E} r_E) < l_{1, L, P}/(v_{C, P} + l_{2, C, P} r_P)

Or:

r_P < (l_{1, L, P} l_{2, C, E} r_E + l_{1, L, P} v_{C, E} - l_{1, L, E} v_{C, P})/(l_{1, L, E} l_{2, 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 Y_{C, n} represent bushels corn consumed, and let Y_{L, n} be the square-yards of linen consumed, where n = E or P for England or Portugal. Let L_E and L_P 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:

l_{1, L, n} Y_{L, n} + v_{C, n} Y_{C, n} = L_n

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

v_{C, n} (P_L/P_C)Y_{L, n} + v_{C, n} Y_{C, n} = L_n

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

l_{1, L, n} Y_{L, n} + l_{1, L, n} (P_C/P_L) Y_{C, n} = L_n

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:

P_L/P_C < l_{1, L, n}/(v_{C, n} + l_{2, C, n} r_n)

For a non-negative rate of profits, the right-hand side cannot exceed l_{1, L, n}/v_{C, n}. Hence:

P_L/P_C < l_{1, L, n}/v_{C, n}

Or:

(L_n/l_{1, L, n}) < (L_n/v_{C, n})(P_C/P_L)

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:

(L_n/l_{1, L, n})(P_L/P_C) < (L_n/v_{C, n})

Or:

P_L/P_C < l_{1, L, n}/v_{C, n}

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

l_{1, L, n}/(v_{C, n} + l_{2, C, n} r_n) < P_L/P_C < l_{1, L, n}/v_{C, 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:

l_{1, L, E}/v_{C, E} < l_{1, L, P}/(v_{C, P} + l_{2, C, P} r_P)

Or:

r_P < (l_{1, L, P} v_{C, E} - l_{1, L, E} v_{C, P})/(l_{1, L, E} l_{2, 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.

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?

References

• 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