Monday, May 29, 2006

Unregulated International Trade Unjustified By Comparative Advantage (Part 5)

5.0 Conclusions

I don’t think the interesting properties of the above example rely on the following properties:
  • The technology is discrete (generalized Leontief)
  • The circularity in production in ale and corn, in which corn and ale are, directly or indirectly, inputs into the production of ale or corn.
  • The fact that consumption goods and capital goods are the same set of goods, just used for different purposes.

Consider equilibrium prices in an autarky in which both techniques are cost minimizing and the interest rate is positive (see Appendix 4.A). The difference between the equilibrium price for ale and the slope of the Production Possibilities Frontier drives the result that international trade can leave this country worse off. And that difference can arise in models with none of those three properties listed above. The possibility of international trade leaving a country with less commodities to consume is a general possibility in models with capital goods, a positive interest rate, and the assumptions of the (mistaken) textbook argument.

So much for comparative advantage as a justification for neoliberal trade (non) policy.

By the way, the above example is only a start at explaining what Steedman and his colleagues have to say about international trade. Their comments are not all critical. Some are constructuve of alternative theories. But I would like to read the references mentioned here:
When produced inputs are introduced into HOS theory in the form that one of the two 'factors' is taken to be a given total value of capital, that theory simply disintegrates. This is so notwithstanding the apparent denial of this negative conclusion by Either (1979), who states that 'The central message ... is simple. The four basic theorems of the modern theory of international trade ... are insensitive to the nature of capital' (p. 236). In fact Ethier's paper constitutes a striking confirmation of our negative conclusion, because in order to maintain the appearance that capital has no influence on HOS trade theorems, Ethier finds himself compelled to replace the familiar theorems, which predict trade outcomes on the basis of exogeneous data, by entirely different theorems, which merely describe trade outcomes in terms of trade equilibrium prices, etc.

(... on Eithier's conjuring with HOS theorems, see Metcalfe and Steedman, 1981).

  • Ethier, W. J. (1979). "The Theorems of International Trade in Time-Phased Economies", Journal of International Trade, V. 9, N. 2 (May): 225-238.
  • Metcalfe, J. S. and Ian Steedman (1974). "A Note on the Gain From Trade", Economic Record (Reprinted in Fundamental Issues in Trade Theory (edited by Ian Steedman), Macmillan, 1979.)
  • Metcalfe, J. S. and Ian Steedman (1981). "On the Transformation of Theorems", Journal of International Economics, V. 11, N. 2: 267-271.
  • Steedman, Ian (1987). "Foreign Trade", The New Palgrave: A Dictionary of Economics (Edited by John Eatwell, Murray Milgate, and Peter Newman), Macmillan.

Unregulated International Trade Unjustified By Comparative Advantage (Part 4)

4.0 Prices and Profit-Maximizing Choices

The location on the PPF depends on prices. The firms in this economy take prices as given. The fractions in the example I was able to create get fairly messy.

4.1 Autarky Equilibrium

First, consider the interest rate and the prices shown in Table 4-1. Table 4-2 shows the cost of producing one unit (barrel ale or bushel corn) for each known process. I assume that wages and rents are paid at the end the production period, while capital goods are purchased at the start. Hence, Table 4-2 shows interest charges on the capital goods used as inputs into production, but not on labor and land services.

Table 4-1: A Set of Prices for an Autarkic Equilibrium
Wage:5,039/37,650 ~ 0.134 Bushels per Person-Year
Rent:1/10 Bushels per Acre
Ale:563/1,506 ~ 0.374 Bushels Per Barrel
Interest Rate:1/50 = 2%

Table 4-2: Autarky Costs and Revenues
Ale(1/8)(1 + 1/50) + (1)(5,039/37,650) + (9/8)(1/10) = 563/1,506563/1,506
CornA(1)(563/1,506)(1 + 1/50) + 4(5,039/37,650) + (5/6)(1/10) = 11
CornB(1/2)(563/1,506)(1 + 1/50) + 7(5,039/37,650) + (1)(1/10) = 36,973/30,1201

Notice that in Table 4-2, revenue received from producing ale exactly covers the cost. Likewise, the revenue received from producing corn with the first corn-producing process exactly covers cost. There are no pure economic profits. And the cost from producing corn with the second corn-producing process exceeds the revenues. So a cost-minimizing firm would not use the second corn-producing process. These are equilibrium prices in which corn and ale are produced with the Alpha technique. That is, with these prices, profit-maximizing firms would choose to produce such that the economy was at point a = (20 barrels ale, 50 bushels corn) on the PPF shown in Figure 3-2. This is the level of consumption with these prices.

4.2 International Trade

Now introduce the possibility of trading consumption goods on the international market. I postulate a price of ale on this market of 99/200 bushels per barrel. (In a model of a small economy, such as this example, the effects on international prices of variations of output of a small economy are assumed to be negligible.) Assume that factors of production (land, labor, and ale and corn used as capital goods) still cannot be traded internationally. This is the standard introductory assumption of the textbook and Hekscher-Ohlin-Samuelson theory. Since this example constitutes an internal critique of the HOS model, I make the model assumptions.

Table 4-3 shows the accounting for costs and revenues in this case. International trade is like a technological innovation; it introduces more processes into the table. A firm can now produce a barrel ale for consumption by first producing 99/200 bushels of corn for consumption with the cheapest corn-producing process, then trading it for a barrel ale on the international market. This possibility is shown in the second ale-producing process in the table, labeled “Trade”. Likewise, the possibility of international trade introduces a third corn-producing process. Here, 2 2/99 barrels of ale for consumption are produced and traded on the international market.

Table 4-3: International Trade With Autarky Prices
Ale(1/8)(1 + 1/50) + (1)(5,039/37,650) + (9/8)(1/10) = 563/1,506563/1,506
AleTrade[(1)(563/1,506)(1 + 1/50) + (4)(5,039/37,650) + (5/6)(1/10)](99/200) = 99/200563/1,506
CornA(1)(563/1,506)(1 + 1/50) + 4(5,039/37,650) + (5/6)(1/10) = 11
CornB(1/2)(563/1,506)(1 + 1/50) + 7(5,039/37,650) + (1)(1/10) = 36,973/30,1201
CornTrade[(1/8)(1 + 1/50) + (1)(5,039/37,650) + (9/8)(1/10)](200/99) = 56,300/74,5471

What would a profit-maximizing firm produce under these conditions? Notice that the cost of producing ale by first producing corn and trading it exceeds the revenue from selling ale domestically. Clearly, no firm will sell corn on the international market. But there are pure economic profits to be obtained by producing ale and trading it for corn on the international market. So all firms will rush into ale production. Since corn is then nowise produced for use as a capital good under these circumstances, these cannot be equilibrium prices.

But the managers of firms find they have a comparative advantage in producing ale.

4.3 Equilibrium with International Trade

As with invalid introductory mainstream textbooks, I ignore disequilibrium transition paths. Consider the prices in Table 4-4, in which the interest rate remains unchanged. The domestic price of ale is now equal to the (given) international price of ale. The cost accounting shown in Table 4-5 results.

Table 4-4: Equilibrium Prices with International Trade
Wage:75,759/1,100,000 ~ 0.0689 Bushels per Person-Year
Rent:36,499/137,500 ~ 0.265 Bushels per Acre
Ale:99/200 Bushels Per Barrel
Interest Rate:1/50 = 2%

Table 4-5: International Trade Equilibrium
Ale(1/8)(1 + 1/50) + (1)(75,759/1,100,000) + (9/8)(36,499/137,500) = 99/20099/200
AleTrade[(1/2)(99/200)(1 + 1/50) + (7)(75,759/1,100,000) + (1)(36,499/137,500)](99/200) = 99/20099/200
CornA(1)(99/200)(1 + 1/50) + 4(75,759/1,100,000) + (5/6)(36,499/137,500) = 150,239/150,0001
CornB(1/2)(99/200)(1 + 1/50) + 7(75,759/1,100,000) + (1)(36,499/137,500) = 11
CornTrade[(1/8)(1 + 1/50) + (1)(75,759/1,100,000) + (9/8)(36,499/137,500)[(200/99) = 11

No pure economic prices can be earned by operating any process under these prices. Ale and corn for use as capital goods are produced by the domestic ale-producing process and the second corn-producing process. The domestic production of this economy is at point b on the PPF graphed in Figure 3-2. And prices are such that firms would be willing to trade either consumable ale or corn internationally. The revenues just cover costs in both processes labeled “Trade” in Table 4-5.

4.4 Comparison

In the autarkic equilibrium analyzed in Section 4.2, a consumption bundle of 20 barrels ale and 50 bushels corn is available to the consumers in the economy. After trade is introduced, the firms produce a consumption bundle of 80 barrels ale and 20 bushels corn. Since the price of ale on the international market is 99/200 bushels per barrel, 60 of the 80 barrels available for consumption might be traded internationally to obtain 60 * 99/200 = 29 7/10 bushels corn. That is, after international trade, the consumers in this economy have available a consumption bundle of 20 barrels ale and 49 7/10 bushels of corn. The introduction of trade has resulted in a loss of 3/10 bushels corn in consumption. This contrasts with misleading mainstream economics textbooks in which trade due to comparative advantage moves the PPF unambiguously outward.

The equilibrium prices with trade are different than the initial prices for an equilibrium in autarky. The individuals in this economy might react to this difference in prices by consuming a different proportion of commodities. I leave it to the interested reader, if any, to demonstrate that utility functions can constructed for some economies in which the gain from utils from this exchange effect does not overcome the loss from specialization. Metcalfe and Steedman suggest postulating:
”a homothetic utility function that is the same for all income recipients who, in addition, express their preference between present and future consumption through a universal and positive rate of time preference.”

Appendix 4.A Switch Point Prices

Consider the line segment between points a and b on the Production Possibilities Frontier in Figure 3-2. Along this line segment all three production processes shown in Table 2-1 are cost-minimizing. In other words, this line segment corresponds to switch points on the so-called factor-price frontier. This appendix considers what the price of ale must be at a switch point. For all three processes to be cost-minimizing, the following system of equations must be satisfied:
(1/8)(1 + r) + w + (9/8) W = p

p(1 + r) + 4 w + (5/6) W = 1

(1/2)p(1 + r) + 7 w + W = 1

  • p is the price of ale (in bushels per barrel)
  • w is the wage (in bushels per person-year)
  • W is the rent (in bushels per acre)
  • r is the interest.

Each production process provides an equation in the above system. Note that if the interest rate is specified, this is a system of three linear equations in three unknowns (p, w, and W. The system has a unique solution in terms of the interest rate:
p = (1/2) (15 + r)/(15 + 11r)

w = (1/44)(7r + 5)(r + 9)/(15 + 11r)

W = (3/11)(15 - 14r - 5rr)/(15 + 11r)

Figure 4-1 graphs the price of ale, as a function of the interest rate, at switch points where both techniques are cost-minimizing. The graph ends at an interest rate of r = (-7/5) + 2 sqrt(31)/5, which is approximately 82.7%. Above this rate, the rent is negative, an economically meaningless case.
Figure 4-1: Price Of Ale At Switch Points

Notice that at an interest rate of zero, the switching price is one-half bushels per barrel. And this price is numerically identical to the slope, between points a and b, of the Production Possibilities Frontier shown in Figure 3-2. On the other hand, at positive interest rates, this switching price falls below one-half bushels per barrel. It is this deviation of this switching price from the slope of the Production Possibilities Frontier that creates the possibility that when the firms in a country specialize as according to the theory of comparative advantage, the country becomes worse off.

Sunday, May 28, 2006

Unregulated International Trade Unjustified By Comparative Advantage (Part 3)

3.0 Production Possibilities Frontier

3.1 Alpha Techniqe

Suppose 64 barrels ale are produced with the ale-producing process. And suppose 64 bushels corn are produced with the first corn-producing process. This is a matter of scaling the first two processes defined in Table 2-1. The quantity flows shown in Table 3-1 result. In a stationary state, the 64 barrels ale produced just replace the ale used up in in the corn-producing process. Likewise, eight of the 64 bushels corn produced replace the corn used up as a capital good in the ale-producing process. So the net output of this economy with these quantity flows is 56 bushels corn. These processes at this scale use all of the 320 person-years available from the labor force. They do not use all of the available land, but production cannot be increased in these proportions. The labor force provides a binding constraint.

Table 3-1: Quantity Flows for The Alpha Technique Producing Only Corn (14 2/3 Acres Land Unused)
Labor64 Person-Years256 Person-Years
Land72 Acres53 1/3 Acres
Ale0 Barrels64 Barrels
Corn8 Bushels0 Bushels
OUTPUTS64 Barrels Ale64 Bushels Corn
NET OUTPUTS0 Barrels Ale56 Bushels Corn

Tables 3-2 and 3-3 show the results of other levels of production with the two techniques comprising the Alpha technique. In Table 3-2, the available labor force and the available land are fully used. In Table 3-3 some labor remains unused, but the constraint imposed by the fixed amount of land is binding.

Table 3-2: Quantity Flows for The Alpha Technique Producing Both Ale and Corn
Labor80 Person-Years240 Person-Years
Land90 Acres50 Acres
Ale0 Barrels60 Barrels
Corn10 Bushels0 Bushels
OUTPUTS80 Barrels Ale60 Bushels Corn
NET OUTPUTS20 Barrels Ale50 Bushels Corn

Table 3-3: Quantity Flows for The Alpha Technique Producing Only Ale (149 9/59 Person-Years Labor Unused)
Labor113 53/59 Person-Years56 56/59 Person-Years
Land128 8/59 Acres11 51/59 Acres
Ale0 Barrels14 14/59 Barrels
Corn14 14/59 Bushels0 Bushels
OUTPUTS113 53/59 Barrels Ale14 14/59 Bushels Corn
NET OUTPUTS99 39/59 Barrels Ale0 Bushels Corn

I have shown some quantity flows with the Alpha technique being exclusively used. Figure 3-1 shows all such possible quantity flows in which at least one of the land and labor constraints is binding. The intersection of the graphed locus with the ordinate is defined by Table 3-1. The point with a net output of 20 barrels ale and 50 bushels corn is defined by Table 3-2. And the intersection with the abscissa is defined by Table 3-3. The straight line connecting the intersection with the ordinate and the point (20 barrels, 50 bushels) represents a linear combination of the quantity flows shown in Tables 3-1 and 3-2. The other line segment represents a linear combination of the quantity flows shown in Tables 3-2 and 3-3. Any point on this locus or in its interior can be achieved by this economy operating the Alpha technique, given the endowments of labor and land.

Figure 3-1: Production Possibilities Curve For Alpha Technique

3.2 The Frontier

I relegate to the appendix the specification of stationary state quantity flows for the Beta technique. The analysis of those flows produce a locus like that shown in Figure 3-1, but with different intercepts and a different point (a net ouput of 80 barrels and 20 bushels) corresponding to the full employment of both labor and land.

Figure 3-2 shows the Production Possibilities Frontier. The Alpha technique is exclusively used in the portion of the frontier to the left of point a. Less land is employed here than in the endowment of the economy; hence land services are free for this portion of the PPF. The Beta technique is exclusively used in the portion of the frontier below point b. Labor is not a binding constraint for this portion of the PPF; labor services are free. The line segment connecting points a and b represents a linear combination of the Alpha and Beta techniques. Both land and labor are binding constraints along this segment, including at points a and b.

Figure 3-2: Production Possibilities Frontier

The portion of the frontier between points a and b, inclusive, is the focus of the remainder of this series of posts. The relative combinations of ale and corn, produced net, are different along this segment because of differences in the amount of ale and corn produced by the two techniques. Notice the slope of this segment is one-half bushels per barrels. The slope reflects the rate of transformation possible in comparing two autarkic equilibria. Consider two autarkic economies in stationary states facing this technology and these endowments, and suppose both labor and land are fully employed in these economies. One more bushel of corn is consumed in one economy for every two more barrels of ale consumed in the other.

In the next post, I consider prices for this economy, without and with trade. I don't have ask good leading questions here. Consider equilibria (in which both ale and corn are produced by cost-minimizing firms) without trade:
  • If the interest rate is 2% and rent is 1/10 bushels per acre, how would you figure out what the wage and price of ale must be?
  • For every feasible interest rate, what equations must the wage, the rent, and the price of ale satisfy such that cost-minimizing firms will be willing to adopt a linear combination of both techniques? How does the price of ale for this switch point compare to the slope of the Production Possibilities Frontier between points a and b?

Appendix 3.A Quantity Flows For The Beta Technique

Table 3-4: Quantity Flows for The Beta Technique Producing Only Corn (73 1/3 Acres Land Unused)
Labor21 1/3 Person-Years298 2/3 Person-Years
Land24 Acres42 2/3 Acres
Ale0 Barrels21 1/3 Barrels
Corn2 2/3 Bushels0 Bushels
OUTPUTS21 1/3 Barrels Ale42 2/3 Bushels Corn
NET OUTPUTS0 Barrels Ale40 Bushels Corn

Table 3-5: Quantity Flows for The Beta Technique Producing Both Ale and Corn
Labor96 Person-Years224 Person-Years
Land108 Acres32 Acres
Ale0 Barrels16 Barrels
Corn12 Bushels0 Bushels
OUTPUTS96 Barrels Ale32 Bushels Corn
NET OUTPUTS80 Barrels Ale20 Bushels Corn

Table 3-6: Quantity Flows for The Beta Technique Producing Only Ale (110 Person-Years Labor Unused)
Labor112 Person-Years98 Person-Years
Land126 Acres14 Acres
Ale0 Barrels7 Barrels
Corn14 Bushels0 Bushels
OUTPUTS112 Barrels Ale14 Bushels Corn
NET OUTPUTS105 Barrels Ale0 Bushels Corn

Unregulated International Trade Unjustified By Comparative Advantage (Part 2)

2.0 Technology

Consider a very simple economy in which two goods, ale and corn, are produced from inputs of labor, land, and produced ale and corn. Ale and corn are each both consumption and capital goods. All production processes in this example require a year to complete and exhibit Constant Returns to Scale. One process is known for producing ale, and two processes are known for producing corn. These processes are shown in Table 1.

Table 2-1: Production Processes Known Within The Country
Labor1 Person-Year4 Person-Years7 Person-Years
Land9/8 Acre5/6 Acre1 Acre
Ale0 Barrels1 Barrel1/2 Barrel
Corn1/8 Bushel0 Bushels0 Bushels
OUTPUTS1 Barrel Ale1 Bushel Corn1 Bushel Corn

Assume that endowments of labor and land are given for this economy. In particular, the firms in this economy have access to 320 person-years of labor and 140 acres of (homogeneous) land.

In short, this economy uses two primary factors, labor and land, to produce a net output of two consumption goods, ale and corn. This example differs from misleading introductory textbook models of comparative advantage in that the use of produced capital goods is shown explicitly.

A technique consists of the ale-producing process and exactly one of the corn-producing processes. The technique in which the first corn-producing process is used is called the Alpha technique. The other technique is called the Beta technique. Given the technique and the required consumption goods, one can calculate the levels at which each process in the technique must operate to produce these consumption goods in a stationary state. The amount of labor and land constrains the maximum net output in a stationary state. Economies in a stationary state with this technology and these endowments can consume more ale if they consume less corn. In other words, ale and corn can be traded off in this sense. How would you construct the Production Possibilities Frontier from the above data on technology and endowments to show this trade-off? Does your construction show a linear combination of the two techniques along the frontier?

Unregulated International Trade Unjustified By Comparative Advantage (Part 1)

1.0 Introduction

Why are tariffs, protectionism, etc., bad ideas - at least according to incorrect introductory mainstream economics teaching? Because of the theory of comparative advantage. This series of five posts demonstrates this argument is logically invalid when applied to an economy with produced capital goods and a positive interest rate. I explain a numerical example illustrating the argument in Metcalfe and Steedman (1974).

That is, economists have known for almost a third of a century that the theory of comparative advantage does not justify a lack of tariffs. Most economists have just shamefully ignored this argument.

Consider equilibrium prices in an autarkic economy. These prices convey to agents seemingly possible rates of transformation between, say, corn and ale. Prices on the international market may differ from these autarkic equilibrium prices. If so, the (firms in the) country under consideration will end up specializing somewhat in the production of those commodities in which the country has a comparative advantage. And this comparative advantage is determined by comparing equilibrium autarkic prices with prices on the international market.

On the other hand, consider the Production Possibilities Frontier constructed for the economy in an autarky. The slope of this frontier at any point shows the rate of transformation in the economy between commodities when nobody in the country engages in international trade. This frontier is constructed from data on technology and information on the quantity of resources available; prices do not enter into its construction. Deviations of equilibrium autarkic prices from the slope of this frontier create the possibility that a country specializing according to the theory of comparative advantage may be worse off. The imposition of a tariff can change the incentives of agents and shift the frontier outward in such a case.

Suppose commodities are produced with inputs that are themselves the result of prior production. That is, capital goods are used in production. And suppose the rate of interest is positive. Then deviations between equilibrium autarkic prices and the slope of the Production Possibilities Frontier can arise. A country may be worse off when the firms in that country engage in international trade under such circumstances. A numerical example demonstrates this point.

  • Metcalfe, J. S. and Ian Steedman (1974). "A Note on the Gain From Trade", Economic Record (Reprinted in Fundamental Issues in Trade Theory (edited by Ian Steedman), Macmillan, 1979.)

Is This SF?

I have been reading Thomas More's Utopia. If one classifies it as a novel in the same category as Edward Bellamy's Looking Backward, then it seems it is science fiction. If one thinks of it as like Plato's Republic, then not so much.

More's narrator praises communism:
Now I have described to you, exactly as I could, the structure of that commonwealth which I judge not merely the best but the only one which can rightly claim the name of commonwealth. Outside Utopia, to be sure, men talk freely of the public welfare - but look after their private interests only. In Utopia, where nothing is private, they seriously concern themselves with public affairs. Assuredly in both cases they act reasonably. For outside Utopia, how many are there who do not realize that, unless they make some separate provision for themselves, however flourishing the commonwealth, they will themselves starve? For this reason, mecessity compels them to hold that they must take account of themselves rather than of the people, that is, of others.

On the other hand, in Utopia, where everything belongs to everybody, no one doubts, provided only that the public granaries are well filled, that the individual will lack nothing for his private use. The reason is that the distribution of goods is not niggardly. In Utopia there is no poor man and no beggar. Though no man has anything, yet they are all rich.

For what can be greater riches for a man than to live with a joyful and peaceful mind, free of all worries - not troubled about his food or harassed by the querulous demands of his wife or fearing poverty for his son or worrying about his daughter's dowry, but feeling secure about the livelihood and happiness of himself and his family: wife, sons, grandsons, great-grandsons, great-great-gransons, and the long line of their descendants that gentlefold anticipate? Then take into account the fact that there is no less provision for those who are now helpless but once worked than for those who are still working.

At this point I should like anyone to be so bold as to compare this fairness with the so-called justice prevalent in other nations, among which, upon my soul, I cannot discover the slightest trace of justice and fairness. What brand of justice is it that any nobleman whatsoever or goldsmith-banker or moneylender or, in fact, anyone else from among those who do no work at all or whose work is of a kind not very essential to the commonwealth, should attain a life of luxury and grandeur on the basis of his idleness or his nonessential work? In the meantime, the carter, the carpenter, and the farmer perform work so hard and continuous that beasts of burden could scarcely endure it and work so essential that no commonwealth could last even one year without it. Yet they earn such scanty fare and lead such a miserable life that the condition of beasts of burden might seem far prefereable. The latter do not have to work so incessantly nor is their food much worse (in fact, sweeter to their taste) nor do they entertain any fear for the future. The workmen, on the other hand, not only have to toil and suffer without return or profit in the present but agonize over the thought of an indigent old age. Their daily wage is too scanty to suffice even for the day: much less is there an excess and surplus that daily can be laid by for their needs in an old age...

...What is worse, the rich every day extort a part of their daily allowance from the poor not only by private fraud but by public law. Even before they did so it seemed unjust that persons deserving best of the commonwealth should have the worse return. Now they have further distorted and debased the right and, finally, by making laws, have palmed it off as justice.

This passage reminds me of the surplus approach to the theory of value and distribution:
Since they devote but six hours to work, you might possibly think the consequence to be some scarcity of necessities. But so far is this from being the case that the aforesaid time is not only enough but more than enough for a supply of all that is requisite for either the necessity or the convenience of living. This phenomenon you too will understand if you consider how large a part of the population in other countries exists without working. First, there are almost all the women, who constitute half the whole; or, where the women are busy, there as a rule the men are snoring in their stead. Besides, how great and lazy is the crowd of priests and so-called religious! Add to them all the rich, especially the masters of estates, who are commonly termed gentlemen and noblemen. Reckon with them their retainers - I mean, that whole rabble of good-for-nothing swashbucklers. Finally, join in the lusty and sturdy beggars who make some disease an excuse for idleness. You will certainly find far less numerous than you had supposed those whose labor produces all the articles that mortals require for daily use.

Now estimate how few of those who do work are occupied in essential trades. For, in a society where we make money the standard of everything, it is necessary to practice many crafts which are quite vain and superfluous, ministering only to luxury and licentiousness. Suppose the host of those who now toil were distributed over as few crafts as the few needs and conveniences demanded by nature. In the great abundance of commodities which must then arise, the prices set on them would be too low for the craftsmen to earn their livelihood by their work. But suppose all those fellows who are now busied with unprofitable crafts, as well as all the lazy and idle throng, any one of whom now consumes as much of the fruits of other men's labor as any two of the workingmen, were all set to work and indeed to useful work. You can easily see how small an allowance of time would be enugh and to spare for the production of all that is required by necessity or comfort (or even pleasure, provided it is genuine and natural).

Wednesday, May 24, 2006

Corn Models

D-Squared recommends my blog. I showed this to one of my colleagues, and he had trouble reading to the end, what with laughing and all. I suppose he liked this:
"Sraffians also have a frightening habit of creating 'simple examples' to illustrate their system; this is Sraffian for 'something which starts off by calmly claiming that there are two goods called corn and iron, and five minutes later has ballooned into a wretchedly complicated optimisation problem with no differentiable production function, no equilibrium and all sorts of strange terminology, illustrated with a graph that is if anything more incomprehensible than the model'."

D-Squared is talking about examples like in this series of posts. The equilibrium here is my add-on to Garegnani, but I suppose some find Figures 5 or 6, for example, drawn to D-Squared's specs.

When Sraffians talk about the "corn model", however, they usually are referring to something different. They are talking about the interpretation of Ricardo Sraffa puts forward in his (and Dobb's) introduction to the first volume of The Works and Correspondence of David Ricarod (otherwise known as Ricardo's On the Principles of Political Economy and Taxation).

The model on page xxxi of the introduction is easily explained. Consider an economy in which a single agricultural commodity, "corn", is produced. Suppose the capital goods used up in producing corn consist solely of corn (i.e., seed corn). And suppose workers are paid solely corn, which is treated as exogeneously specified, at least as far as the theory of value goes. Profits in agriculture, the excess of the corn produced in the year over the corn advanced for seed and wages, also consist of a physically specified quantity of corn. So you can see that the rate of profits is physically determined in agriculture. In industry, outputs and inputs are heterogeneous, since wages are still in terms of corn and outputs are some other commodity. Thus, if a tendency exists for a common rate of profits to be established among all sectors in an economy, the prices of manufactured commodities must adjust to bring the rate of profits in industry to equality with that in agriculture.

This model helps Sraffa explain Ricardo's interest in the Labor Theory of Value. Workers consume a mixture of commodities, and Malthus insisted that in no industry are the advances and output composed of the same commodity. But if one evaluated commodities in terms of the labor embodied in them, one could form a physical ratio of labor values of the ouput of agriculture (on marginal land) and the labor values of the capital advanced, including the labor value of wage goods. Thus, if the Labor Theory of Value were true, Ricardo would be able to retain the insights of the corn model.

Sraffa explicitly states the corn model "is never stated by Ricardo in any of his extant letters and papers." Sraffa hypothesizes Ricardo put forward the corn model in lost letters and papers in March 1814 or in oral conversations with Malthus. All interpretations of "what Ricardo really meant" have been hottly disputed in the last third of a century or so. Probably Samuel Hollander is the most learned opponent of Sraffa's interpretation to read. It doesn't help matters that Ricardo and Malthus, in their letters, would often formulate their claims in terms of (what they took to be) the other's system. This makes it very confusing to figure out who is claiming what, instead of merely echoing back what they think their opponent is saying. They probably sometimes confused themselves.

Tuesday, May 23, 2006

Should I Be Delighted With More To Read?

I've started to look into just a few of the many articles now on-line from the Socialist Register (announced by Crooked Timber and The Virtual Stoa).

In a 1968 piece by Ralph Miliband, "Professor Galbraith and American Capitalism", Miliband criticizes The New Industrial State. Miliband thinks the owner of firms are still in the driver's seat. According to Miliband, Galbraith's thesis of the rising power of the technostructure is false. And it serves a function as apologetics for capitalism.

In my my earlier appreciation of John Kenneth Galbraith, I tried to mention aspects of Galbraith's thought that have stood the test of time. I took no position on the technostructure.

But consider. Piketty and Saez (2006), "The Evolution of Top Incomes: A Historical and International Perspective", show that composition of income in the top 0.01% in the U. S. is increasingly salaries, and a corresponding lower proportion is returns to capital. Is this not evidence suggesting that ownership of large corporations has become of lesser importance? To conclude that technical knowledge is a more important source of power than merely being a top-level manager would take some further evidence.

Monday, May 22, 2006

Upcoming Posts, Maybe

I'm thinking about posting on:
  • Recent empirical results on the labor theory of value
  • A collection of recent papers from Ian Steedman demonstrating the falsity and incoherence of mainstream textbook partial equilibrium results
  • A numerical example demonstrating that the theory of comparative advantage (given static technology, perfect competition, etc.) does not justify unregulated international trade in consumer goods
  • Some implications of the Cambridge Capital Controversy for General Equilibrium temporary equilibrium models
  • Some errors in Austrian theory and their implications for Austrian Business Cycle Models
For the last two, I might take a while since I'm thinking of improving draft papers.

Update: I want to remind myself to post an explanation of why no such thing as the marginal productivity theory of value exists.

Sunday, May 21, 2006

Against Reification Of Property Rights (Part 3)

This continues some reflections on themes in Dean Baker's The Conservative Nanny State.

In practice, Austrian economics is frequently cited as justification for greed by many people who are just not very bright. But some of those who developed the doctrine were more sophisticated than many of those you encounter on the 'net who imagine they are followers of this school.

For Hayek, capitalism is a system in which many people work together to produce commodities, even though they may be unaware of one another's existence. This extended order did not come about through design, but through the evolution of institutions.

In The Fatal Conceit, Hayek argues that private property (which he calls "several property") is not natural, in that it is not innate or instinctual. Nor is it artificial, in that it is not consciously designed. Hayek rejects this dichotomy, as it does not apply to evolved institutions. Further, in Hayek's view, room exists for further adaptation and experimentation:
"The institutions of property, as they exist at present, are hardly perfect; indeed, we can hardly yet say in what such perfection might consist. Cultural and moral evolution do require further steps if the institution of several property is in fact to be as beneficial as it can be." -- Hayek (1988)

I take from Hayek that the distribution of income that comes out of capitalism can be said to be neither "just" nor "unjust". I think one can propose a change to property rights, in conformity to Hayek's view, with a view to affecting the distribution of income, as long as those changed rules remain impersonal:
" a system of free enterprise chances are not equal, since such a system is necessarily based on private property and (though perhaps not with the same necessity) on inheritance, with the differences in opportunity which these create. There is, indeed, a strong case for reducing this inequality of opportunity as far as congenital differences permit and it is possible to do so without destroying the impersonal character of the process by which everybody has to take his chance and no person's view about what is right and desirable overrules that of others." -- Hayek (1944)

Other Austrians also argue against the naturalization of property rights:
A property system may work well for a society with a specific technology, population density, and so forth, and may have to be modified as these features change. People raised in societies in which private property is highly developed may tend to hold a simplistic view of the nature of 'ownership'. Since 'ownership' (a typical bundle of rights related to some resource) becomes standardized, and incorporates the lessons of centuries of legal cases in tending to bring all the most relevant aspects of a single good under the same owner, 'ownership' comes to be seen as a straightforward, unproblematical relationship between a person and a material thing. Of course, we are all aware that ownership is frequently modified, as for instance, ownership of a piece of land by government zoning regulations, but there is a tendency to think of these regulations as leaving something called 'ownership' essentially unchanged.

Without prior education, someone coming from a technologically-advanced culture in which private property is prominent may be confused by the property rules found in more technologically primitive societies. She may find, for example, that the system of property rights in land is unlike that of private property, and she may be tempted to say that 'they don't have a concept of land ownership' or alternatively that 'their concept of land ownership is different to ours'.

The same person will, however, frequently also have an oversimple view of the meaning of 'ownership' in her own culture. Consider two adjoining pieces of land 'owned' by different individuals. Ownership of one of these pieces of land may or may not give one the right to: burn a fire sending smoke over the adjoining land; pump water from an underground reserve, lowering the water availability in the adjoining land; allow animals (mice, rats, lions) to proliferate on one's own land and thus invade the adjoining land; erect a tall building blocking out sunlight from the adjoining land; shine a light (a candle or a floodlight) that can be seen from the adjoining land; and so forth. According to such variations, the exact meaning of 'owning a piece of land' varies. (Steele 1992: 181-182)

  • Hayek, Friedrich A. (1944). The Road To Serfdom
  • Hayek, F. A. (1988). The Fatal Conceit: The Errors of Socialism (Ed. by W. W. Bartley III)
  • Steele, David Ramsay (1992). From Marx to Mises: Post-Capitalist Society and the Challenge of Economic Calculation, La Salle, IL: Open Court

Saturday, May 20, 2006

Against Reification Of Property Rights (Part 2)

This is another comment on some ideas in Dean Baker's The Conservative Nanny State.

A parallel to some of these ideas can be found in the writings of Robert Lee Hale, who I gather was important in the development of legal realism. Consider:
"But a careful scrutiny ... will demonstrate that the systems advocated by professed upholders of laissez-faire are in reality permeated with coercive restrictions of individual freedom, and with restrictions, moreover, out of conformity with any formula of 'equal opportunity' or of 'preserving the equal rights of others'. Some sort of coercive restriction of individuals, it is believed, is absolutely unavoidable ... Since coercive restrictions are bound to affect the distribution of income and the direction of economic activities, and are bound to affect the economic interests of persons living in foreign parts, statemen cannot avoid interfering with economic matters, both in domestic and in foreign affairs...

...Meanwhile, let it be kept in mind that to call an act coercive is not by any means to condemn it. It is because the word 'coercion' frequently seems to carry with it the stigma of impropriety, that the coercive character of many innocent acts is so frequently denied.

What is the government doing when it 'protects a property right'? Passively, it is abstaining from interference with the owner when he deals with the thing owned; actively, it is forcing the non-owner to desist from handling it, unless the owner consents... The non-owner is forbidden to handle the owner's property even where his handling of it involves no violence or force whatever. Any lawyer could [tell] that the right of property is much more extensive than the mere right to protection against forcible dispossession. In protecting property the government is doing something quite apart from merely keeping the peace. It is exerting coercion wherever that is necessary to protect each owner, not merely from violence, but also from peaceful infringement of his sole right to enjoy the thing owned."(Hale 1923).
Warren Samuels, well-known as an institutionalist economist, has studied Hale's ideas.

  • Hale, Robert L. (1923). "Coercion and Distribution in a Supposedly Non-Coercive State", Political Science Quarterly, V. 38, N. 3 (Sep): 470-494.
  • Samuels, Warren J. (1973). "The Economy as a System of Power and Its Legal Bases: The Legal Economics of Robert Lee Hale", University of Miami Law Review, V. 27 (Spring-Summer): 261-371.
  • Samuels, Warren J. (1984). "On the Nature and Existence of Economic Coercion: The Correspondence of Robert Lee Hale and Thomas Nixon Carver", Journal of Economic Issues, V. 18, N. 4 (Dec): 1027-1048.

Friday, May 19, 2006

Against Reification Of Property Rights (Part 1)

Dean Baker has made his new book available for downloading. I have read the first chapter so far. That chapter is an overview of the remainder of the book. Baker notices that much commentary in the United States, both by conservatives and liberals, pictures liberals as arguing for government interventions into the markets. Conservatives are pictured as arguing against government interventions. This false picture hampers the development of intelligent policy. According to Baker, markets and property rights are not some neutral and natural pre-existing institutions which liberals try to regulate. Rather, markets and property are themselves constituted by government "interventions". (When Greg Mankiw writes, "Baker thinks that American conservatives are not in favor of capitalism with free, competitive markets, as is often claimed, but instead want to use the power of the state to make the rich even richer", his contrast and his naturalization of competitive markets shows that he misses Baker's point.) Both liberals and conservatives advocate active government interventions, and it cannot be otherwise. The difference between them is that conservatives advocate government intervention on the side of the wealthy and powerful to increase their wealth and power.

I appreciate Baker's practical concern and his attempt to encourage commentators to adopt a more intelligent framing of present-day policy concerns. I want to point out, however, that Baker's thesis is not novel. It can be seen as echoing ideas in any of several traditions. I will mention:
  • Marxism
  • Institutionalism and legal realism
  • Austrian economics
In the remainder of this post, I point out ideas in Marxism related to Baker's position. (Not that I think Baker is a Marxist or that the label is of any importance.) In succeeding posts I will point out texts in the other two traditions mentioned above that frame issues like Baker does.

Marx argued that capitalism tended to confuse observers into believing that social relations were natural relations. Marx called this sort of mistaken understanding of social relations commodity fetishism. In addition to Section 4 of Chapter 1 of Volume 1 of Capital, important Marx texts on this point include the distinction between classical political economy and vulgar political economy in the "Afterword to the second German edition" of Capital; Chapter 50 and, in fact, all of Part 7 of Volume 3 of Capital; and the addenda on "Revenue and its sources. Vulgar political economy" in part 3 of Theories of Surplus Value. There is also this text from Marx:
Economists have a singular method of procedure. There are only two kinds of institutions for them, artificial and natural. The institutions of feudalism are artificial institutions, those of the bourgeoisie are natural institutions. In this they resemble the theologians, who likewise establish two kinds of religion. Every religion which is not theirs is an invention of men, while their own is an emanation from God. When the economists say that present-day relations - the relations of bourgeois production - are natural, they imply that these are the relations in which wealth is created and productive forces developed in conformity with the laws of nature. These relations therefore are themselves natural laws independent of the influence of time. They are eternal laws which must always govern society. Thus, there has been history, but there is no longer any. There has been history, since there were the institutions of feudalism, and in these institutions of feudalism we find quite different relations of production from those of bourgeois society, which the economists try to pass off as natural, and as such, eternal. -- K. Marx, The Poverty of Philosophy

Probably, Lukás' essay, in which he develops the concept of reification, is the most important commentary on Marx for my purpose. In effect, Baker is arguing against the reified nature of so much contemporary thought on economics and politics.

  • Baker, Dean (2006). The Conservative Nanny State: How the Wealthy Use the Government to Stay Rich and Get Richer, Washington: Center for Economic and Policy Research.
  • Lukács, Georg (1968). History and Class Consciousness: Studies in Marxist Dialectics, Cambridge: MIT Press.
  • Marx, Karl (1887). Capital, V. 1
  • Marx, Karl (18??) Capital, V. 3
  • Marx, Karl (1971). Theories of Surplus Value, Part III, Moscow: Progress Publishers.

Wednesday, May 17, 2006


Mainstream economists proceed by ignoring that much of what they say has long been shown to be false. A theme of this blog is to point out or to explain some of these demonstrations. This theme raises a question: how is it that "leaders" of economic orthodoxy can just ignore these demonstrations? Perhaps I should be studying up on Friedrich Nietzsche and Michel Foucault.

Part of what prompted me to write this post is the nonsense Greg Mankiw writes. In the (indirectly) linked paper, he writes:
As a result of the three waves of new classical economics, the field of macroeconomics became increasingly rigorous and increasingly tied to the tools of microeconomics. The real business cycle models were specific, dynamic examples of Arrow-Debreu general equilibrium theory. Indeed, this was one of their main selling points.
Why pretend new classical macroeconomists are scientists putting their field on rigorous microfoundations? Doesn't Mankiw know about Alan Kirman's championing of the Sonnenschein-Mantel-Debreu results to point out that representative agent models do not have microfoundations? Or, for that matter, of Hahn's work on the difficulties of introducing money into General Equilibrium theory? Is Mankiw aware that Hahn later teamed up with Solow to write an essay on modern macroeconomics? (Contrary to what one may read in Mankiw, Solow's rebuttal to new classical macroeconomics doesn't consist solely of jokes at Lucas' expense.) These questions don't even get at my favorite literature on the Cambridge Capital Controversy. Does Mankiw, who has written a popular textbook, have the power to have his colleagues just pretend whole literatures do not exist?

Greg Mankiw follows up by illustrating my point with a comment about experimental economics. He cites Vernon Smith's work in experimental economics to assert the scientific nature of economics. Somehow he ignores Smith's fellow "nobel" laureate Daniel Kahneman. And yet experimental economists have shown that Kahneman and Tversky's prospect theory is superior to utility theory in providing a description of how individuals behave.

Not only is the neoclassical theory of the consumer empirically lacking. So is the neoclassical theory of the firm. Steve Keen likes empirical results going back to Hall and Hitch's 1930s work. They show that firms engage in some sort of administrative, full-cost, or markup pricing. Modern industrial corporations do not engage in marginal pricing. So do your microeconomic textbooks teach false theories here too with no indication of alternatives?

Tuesday, May 16, 2006

Empirical Evidence Exists On Sraffa Effects

As I have pointed out in the past, economists have discovered that, given standard neoclassical assumptions, competitive firms are sometimes willing to adopt a more labor-intensive technique at a higher wage. For some reason, you will have difficulty finding this possibility described in any textbook written by an author who is not self-consciously heterodox. Sometimes economists respond to this circumstance by asserting that no empirical evidence exists that technology can have the consequences highlighted by the sort of example I presented. This response has always seemed to me to be a non sequitur, as well as just mistaken.

I haven't read all the references I am about to mention. Not only do I not see how empirical evidence is relevant to a logical contradiction, I don't have the needed language skills:
"I have gathered that the most active discussion, both theoretical and empirical, on the how probable the occurence of reswitching is, has recently been taking place in the Italian language journals - one estimate puts the number of such papers in recent years to around seventy! I did not have access to any of them." -- Ahmad, Syed (1991). Capital in Economic Theory: Neoclassical, Cambridge, and Chaos, Aldershot: Edward Elgar: 250.
Empirical results that economists have explicitly connected to my favorite controversy in economics can be thought of as falling into three categories:
  • Case studies of particular industries
    • Albin, Peter (1975). "Reswitching: An Empirical Observation, A Theoretical Note, and an Environmental Conjecture", Kyklos, V. 28: 149-153.
    • Asheim, Geir B. (1980). "The Occurrence of Paradoxical Behavior in a Model where Economic Activity has Environmental Effects", Norweigan School of Economics and Business Administration Discussion Papers.
    • Barnes, Trevor and Eric Sheppard (1984). "Technical Choice and Reswitching in Space Economies", Regional Science and Urban Economics, V. 14: 345-352.
    • Hartwick, John (1976). "Intermediate Goods and the Spatial Integration of Land Use", Regional Science and Urban Economics, V. 6: 127-145.
    • Ozanne, Adam (1996). "Do Supply Curves Slope Up? The Empirical Relevance of The Sraffian Critique of Neoclassical Production Economies", Cambridge Journal of Economics, V. 20: 749-762.
    • Prince, Raymond and J. Barkley Rosser, Jr. (1984). "Environmental Costs and Reswitching Between Food and Energy Production in the Western United States", James Madison University mimeo
    • Prince, Raymond and J. Barkley Rosser, Jr. (1985). "Some Implications of Delayed Environmental Costs for Benefit Cost Analysis: A Study of Reswitching in the Western Coal Lands", Growth and Change, V. 16: 18-25.
    • Schweizer, U. and P. Varaiya (1977). "The Spatial Structure of Production with a Leontief Technology-II: Substitute Techniques", Regional Science and Urban Economics, V. 7: 293-320.
    • Scott, A. J. (1979). "Commodity Production and the Dynamics of Land-Use Differentiation", Urban Studies, V. 16: 95-104.
  • Analysis of input-output data from national income accounts
    • Han, Zonghie and Bertram Schefold (2003). "An Empirical Investigation of Paradoxes (Reswitching and Reverse Capital Deepening) in Capital Theory" (draft) (Sep).
  • Simulation and analytical results on the likelihood of reswitching and capital reversing.
    • Bidard, Christian and Lucette Carter (2000). "Comment", in Critical Essays on Piero Sraffa's Legacy in Economics (ed. by Heinz D. Kurz), Cambridge: Cambridge University Press.
    • Mainwaring, Lynn and Ian Steedman (2000). "On the Probability of Re-switching and Capital Reversing in a Two-Sector Sraffian Model", in Critical Essays on Piero Sraffa's Legacy in Economics (ed. by Heinz D. Kurz), Cambridge: Cambridge University Press.
    • Petri, Fabio (2000). "On the Likelihood and Relevance of Reverse Capital Deepening", University of Sienna working paper N. 279 (Feb).
    • Salvadori, Neri (2000). "Comment", in Critical Essays on Piero Sraffa's Legacy in Economics (ed. by Heinz D. Kurz), Cambridge: Cambridge University Press.
    • Zambelli, Stefano (2004). "The 40% Neoclassical Aggregate Theory of Production", Cambridge Journal of Economics, V. 28, N. 1: 99-120.

Sunday, May 14, 2006

Income Immobility In The U.S.A.

Compared to other advanced industrial economies, wealth and income in the United States is distributed very unevenly. Mobility is low as well. In countering illusions and right-wing lies on the latter point, I have usually cited Gottschalk and Danziger (1997). They use data from the Panel Study of Income Dynamics (PSID). I need to update my understanding to reflect Hertz (2006), who also uses the PSID. I could also look at some other articles listed in the references to this post.

Both Gottschalk and Danziger (1997) and Hertz (2006) report a variety of analyses, investigating how robust their results are and the impact of various variables (e.g., race, education) on their results. I think Table 1 provides a useful summary of a central result from Gottschalk and Danziger. They have data on the income quintiles of the families of 1,909 persons in 1968 and 1991. They find that over approximately a quarter century, about two thirds or more of these people end up in families within one quintile of the families within which they start.

Table 1: Two-Thirds End Up In Families Within One Quintile Of Starting Family
1st Quintile46.9%25.1%17.7%9.0%1.3%
2nd Quintile24.224.822.319.19.7
3rd Quintile10.820.520.527.021.2
4th Quintile10.416.427.020.425.9
5th Quintile7.513.013.724.241.6

  • Bowles, Samuel and Herbert Gintis (2002). "The Inheritance of Inequality", Journal of Economic Perspectives, V. 16, N. 3: 3-30.
  • Gottschalk, Peter and Sheldon Danziger (1997). "Family Income Mobility - How Much Is There and Has It Changed?", (Draft?) (Dec)
  • Hertz, Tom (2006). "Understanding Mobility in America", American University for the Center for American Progress (26 Apr)
  • Mazumder, Bhashkar (2005). "Fortunate Sons: New Estimates of Intergenerational Mobility in the United States Using Social Security Earnings Data", Review of Economics and Statistics, V. 87, N. 2: 235-255

Thursday, May 04, 2006

An Example of Capital Reversing (Part 3)

In the first part, I describe the technology a firm faces. This technology consists of two production processes for producing iron and one process for producing corn. A technique of production is defined in this example to consist of exactly one iron-producing process and the corn-producing process. In the second part, I describe the levels of operations of the processes comprising each technique such that net output consists of one Bushel corn.

Consider the managers of a competitive firm. They know this technology and decide on the level of operation of each production process. In this model, the prices the firm faces are taken as parametric by the firm. The firm is assumed to begin the year owning an inventory of iron and corn. This inventory, if it is not in the correct proportion to serve as inputs in the production processes that managers decide upon, can be traded on the market. The value of the inventory, however, imposes a constraint. The value of the inputs to the production processes cannot exceed the value of the inventory. (Since labor is assumed to be paid out of the product at the end of the year, labor does not enter into this constraint.) The firm decides on the level of operation of each process to maximize the increment of value.

I take a Bushel corn as the numeraire. So the price of iron is expressed in units of Bushels per Ton, and the wage is expressed in units of Bushels per Person-Year. Some notation is useful to set out the firm’s decision problem. Let:
  • X1 be the gross amount of iron produced with the first iron-producing process.
  • X2 be the gross amount of iron produced with the second iron-producing process.
  • X3 be the gross amount of corn produced (with the corn-producing process).
  • p be the price of iron (in units of Bushels per Ton).
  • w be the wage (in units of Bushels per Person-Year). The wage is paid at the end of the year to workers employed during the year.
  • r be the rate of (accounting) profits.
  • ω1 be the Tons iron in the firm's inventory at the start of the year.
  • ω2 be the Bushels corn in the firm's inventory at the start of the year (after having sold net output to consumers at the end of the last year).

Using this notation, the firm’s problem is easily expressed:
Choose X1, X2, and X3
To Maximize [p - (1/10) p - (1/40) - w] X1
+ [p - (229/494) p - (3/1,976) - (305/494) w] X2
+ [1 - 2 p - (2/5) - w] X3
Such That
[(1/10) p + (1/40)] X1
+ [(229/494) p + (3/1,976)] X2
+ [2 p + (2/5)] X3
does not exceed (p ω1 + ω2)
And X1, X2, and X3 are all nonnegative

The above Linear Program has a dual:
Choose r

To Minimize (p ω1 + ω2) r

Such That

[(1/10) p + (1/40)](1 + r) + w is not less than p

[(229/494) p + (3/1,976)](1 + r) + (305/494) w is not less than p

[2 p + (2/5)](1 + r) + w is not less than 1

And r is nonnegative

Dual Linear Programs have some elegant mathematical properties. If a decision variable is positive in the optimal solution to the primal Linear Program, the corresponding constraint is met with equality in the dual. For example, suppose profit-maximizing firms would like to operate the first iron-producing process (X1 > 0). Then the cost of operating this process, including the imputed profits earned on the financial capital advanced to pay for the inputs, just covers the revenue obtained from producing the iron. In other words, the first constraint in the dual Linear Program is met with equality.

The above analysis shows which processes, if any, firms will be willing to operate at any given wage and price of iron. But firms will be willing to operate both the corn-producing process and at least one iron-producing process only at specific configurations of these prices. Yet this industry is sustainable only if firms are willing to operate such a combination of processes. Accordingly, I analyze only combinations of prices in which firms in this vertically-integrated industry can continue to operate.

For example, suppose firms are willing to operate the first technique (X1 > 0 and X3 > 0). Then the costs, including imputed profits, of producing a Ton of iron (with the first process) and a Bushel of corn must be equal to the price of iron (p) and the price of corn (unity), respectively. These conditions determine a system of two equations with three unknowns (w, r, and p). Suppose the wage is externally specified, perhaps on a competitive labor "market". Then, if firms are to be willing to adopt this technique, the price of iron and rate of profits must be as specified by this system of equations. A corresponding system of equations arises for the second technique from the dual Linear Program.

Table 3-1 shows some solutions of the price equations that arise from this logic. The selected solutions are shown for increasing wages or decreasing rates of profits. (When I write about "increasing" or "decreasing", I am now only making claims abouts the shapes of certain mathematical functions. See Samuelson (1975)). The rate of profits is lower for higher wages. At a certain upper limit on wages, the rate of profits is zero. At wages higher than this, no price of iron exists at which firms will be willing to produce both iron and corn, and the data would be inconsistent with an economy continuing to be reproduced. But consider the wages shown in the table. At a wage of 459/64,100 Bushels per Person-Year, the second technique is cost-minimizing. The cost of producing iron with the first iron-producing process exceeds the price of iron by 245/48,716 Bushels per Ton. On the other hand, the first technique is cost minimizing at wage of 13/220 Bushels per Person-Year. At this wage, the cost of producing iron by the second iron-producing process exceeds the price of iron by 45/10,868 Bushels per Ton. At the wage of 13/850 Bushels per Person-Year, both techniques are cost-minimizing. A wage, or rate of profits, like this, at which more than one technique is cost-minimizing is defined to be a switch point. It is left as an exercise for the reader to find rates of profits and prices of iron in general. (Hint: the other switch point in the example is at r = 20%.)

Table 3-1: Some Price Data
459/64,10090%2,985/48,716X2, X3
13/850805/68X1, X2, X3
13/220505/44X1, X3

Since both techniques are cost-minimizing at the switch point at w = 13/850 Bushels per Person-Year, the value of capital per worker can be at different levels with unchanged prices. At these prices, capital per worker can take on any level between the two values shown in the last column of Table 3-2. This variation of capital intensity at a switch point, in which the physical composition of capital goods varies but prices are unchanged, is known as a real Wicksell effect. Neoclassical economists used to think of prices as scarcity indices (e.g., Hayek 1945). Suppose the rate of profits were a scarcity index for capital. Then a willingness of consumers to supply more capital (i.e., increase savings) would result in a lower rate of profits. One would expect that the technique preferred at a rate of profits slightly lower than the switch point rate of profits would be more capital-intensive than the technique preferred at a slightly higher rate of profits. This expected negative association between the rate of profits and the change in the value of capital due to changes in the physical composition of capital goods is known as a negative real Wicksell effect.
"...a negative real Wicksell effect is the appropriate concept of 'capital deepening' in a model with many heterogeneous capital goods." (Burmeister 1987)

Table 3-2: Capital-Theoretic Properties Of Switch Point At r = 80%
X1, X3200/49 Tons,
41/49 Bushels
947/833 Bushels947/4,930 Bushels
X2, X31,976/315 Tons,
43/63 Bushels
175/153 Bushels35/170 Bushels

The example shows that the concept of capital deepening as a supposedly logical implication of profit maximizing is no such thing. The technique in the last row in Table 3-2 is more capital-intensive. Yet, as illustrated in Table 3-1, this technique is also preferred at rates of profit somewhat higher than the switch point being examined here, while the technique in the first row is preferred at interest rates slightly lower. This phenomena of a positive association between capital intensity and the rate of profits, where the variation in capital intensity is due to a variation in the composition of capital goods at a given switch-point rate of profits, is known as a positive real Wicksell effect, reverse capital deepening, or capital reversing. Its possibility, as proven by this example, shows that the vision underlying the Neoclassical theory of value and distribution is logically invalid.

These capital theory findings have implications for labor economics. Here’s one opinion:
“ is now clear that there is no general way to classify technological processes as simply more or less labor-intensive, at least not if one means by that form of words that more labor-intensive technologies always correspond (in a given state of technological knowledge) to a lower real wage and therefore a higher interest rate along the factor-price frontier in steady-state equilibrium. More generally, and more important, it is not true, even with all the standard assumptions, that steady states with lower interest rates have higher consumption per worker. That is interesting.”
(Solow 1975)

I would put it somewhat differently. Table 3-3 gives some more information about the switch point at which capital reversing occurs. The stationary state consumption per worker is shown in the second column. The technique in the lower row has higher consumption per worker. Since around this switch point, the technique in the upper row is cost-minimizing at lower rates of profits, this example illustrates the point that Solow says is “more important”. The last column in Table 3-3 gives a measure of the labor intensity of these two techniques. The technique in the first row is more labor intensive. Around this switch point, the more labor-intensive technique is adopted at higher wages, while the less labor-intensive technique is adopted at lower wages. Since the rate of profits is not a scarcity index for capital, wages are not a scarcity index for labor. Firms wanting to hire more labor at a higher wage, given technological knowledge and the level of net output, is consistent with the theory of competitive profit-maximizing.

Table 3-3: Labor-Theoretic Properties Of Switch Point At w = 13/850
X1, X349/290 Bushels290/49 Person-Years
X2, X39/50 Bushels50/9 Person-Years

  • Burmeister, Edwin (1987). "Wicksell Effects", New Palgrave: A Dictionary of Economics (Edited by John Eatwell, Murray Milgate, and Peter Newman), Macmillan.
  • Hayek, F. A. (1945). "The Use of Knowledge in Society", American Economic Review, V. 35, N. 4 (Sep.): 519-530.
  • Samuelson, Paul A. (1975). "Steady-State and Transient Relations: A Reply on Reswitching", Quarterly Journal of Economics, V. 89, N. 1 (Feb.): 40-47.
  • Solow, Robert M. (1975). “Reswitching: Brief Comments”, Quarterly Journal of Economics, V. 89, N. 1 (Feb.): 48-52.

Wednesday, May 03, 2006

An Example of Capital Reversing (Part 2)

This post continues an examination of the technology described in Part 1 Let
  • X1 be the gross amount of iron produced with the first iron-producing process.
  • X2 be the gross amount of iron produced with the second iron-producing process.
  • X3 be the gross amount of corn produced (with the corn-producing process).
In a technique, as defined in this series of posts, either X1 or X2 is zero. The other variable is positive, and corn is also produced at a positive level. Consider, for example, the technique in which X2 is zero. Suppose that the iron output of this technique just replaces the iron used up in production, and the net output of corn is one Bushel. These conditions yield the following system of equations:
0 = X1 - (1/10) X1 - 2 X3

1 = X3 - (1/40) X1 - (2/5) X3

The conditions on output provide the left-hand side of this system of equations. The coefficients of production for the processes comprising the technique provide the constants on the right hand side. This is a system of two linear equations in two unknowns, and it is easily solved. Economists talk about the Leontief inverse in describing the solution in a more general problem. The remainder of this part considers the solution to the above system and to the system comprising the other technique.

Consider a firm that produces X1 = 200/49 Tons of iron with the first iron-producing process and X3 = 90/49 Bushels of corn. This firm requires inputs of (1/10) X1 + 2 X3 = 200/49 Tons of iron and of (1/40) X1 + (2/5) X3 = 41/49 Bushels of corn. Notice that the iron produced by this firm just replaces the iron inputs used-up in making the firm's output. On the other hand, the firm has a net output of one Bushel corn, after replacing the corn used up in production. Thus, this firm is a vertically-integrated corn-producing firm using a technique consisting of the first iron-producing process and the corn producing process. The firm employs (1) X1 + (1) X3 = 290/49 Person-Years of labor per bushel corn produced net.

Consider a second firm. This second firm produces X2 = 1,976/315 Tons of iron with the second iron-producing process and X3 = 106/63 Bushels of corn. Similar calculations show that this firm has a net output of no iron and one bushel corn. In other words, this is a vertically-integrated corn-producing firm using a technique containing the second iron-producing process. This firm employs 50/9 Person-Years of labor per bushel corn produced net. Notice that this firm employs 160/441 Person-Years per bushel corn less than the first firm.

This part has described the amount of labor used per net bushel of corn produced by each of the techniques. But for what combinations of prices would the firm want to adopt any particular combination of production processes, if any? The next part answers this question.

An Example of Capital Reversing (Part 1)

I thought I would, for my own amusement, create an example of capital-reversing. I go through the example, emphasizing the implications for the labor "market". Any detailed example is lengthy, even for me. So I break the exposition up into three, maybe four, parts. (I haven't yet finished the last part.)

This part discusses the data on technology, which is presented in Figure 1-1. This table presents coefficients of production for three processes which exhibit Constant Returns to Scale. The inputs must be available starting at the beginning of the year. The inputs provide their services over the course of the year, and the iron and corn inputs are totally used up in production. The outputs become available at the end of the year.

Figure 1-1: Production Processes Known By Firm Managers
Labor1 Person-Year305/494 Person-Year1 Person-Year
Iron1/10 Ton229/494 Ton2 Ton
Corn1/40 Bushel3/1,976 Bushel2/5 Bushel
OUTPUTS1 Ton Iron1 Ton Iron1 Bushel Corn

This type of data on Constant-Returns-to-Scale production processes is enough to construct production functions. Consider the production function for iron, for example. Let:
  • X be the gross amount of iron produced.
  • X1 be the gross amount of iron produced with the first iron-producing process.
  • X2 be the gross amount of iron produced with the second iron-producing process.
  • Q0 be the Person-Years of labor available for iron production.
  • Q1 be the Tons of iron available as input into iron production.
  • Q2 be the Bushels of corn available as input into iron production.

For purposes of constructing the production function, the quantities of labor, iron and corn available as input to iron production are taken as given. The amount of each input needed to produce iron by any specified combination of levels of the iron-producing production processes can be found from the coefficients of production. These combinations of levels are constrained by the necessity of not having input requirements that exceed the available inputs. The following Linear Program expresses the problem of maximizing the amount of iron produced while meeting these constraints:
Choose X1 and X2
To Maximize X = X1 + X2
Such that
1 X1 + (305/494) X2 does not exceed Q0
(1/10) X1 + (229/494) X2 does not exceed Q1
(1/40) X1 + (3/1,976) X2 does not exceed Q2
X1 and X2 are both nonnegative.

One can express the value of the objective function in the solution to this Linear Program as a funtion of the parameters specified by the available inputs. Let f( Q0, Q1, Q2 ) be this function. This is the production function for iron. It exhibits Constant Returns to Scale and non-increasing marginal products for each input. Any “smooth” well-behaved microeconomic production expressed in terms of physical inputs can be approximated by enough production processes, as above. “Capital”, as measured in monetary or numeraire units, is not a physical input.

(In the third part, I present dual Linear Programs characterizing the firm’s choice of level of operations of the production processes. Neither of these later Linear Programs repeat the above Linear Program. For example, the firm does not have predefined resources devoted to iron-production, as in the constraints in the above Linear Program. How much labor, for example, the firm managers want to hire for iron production and for corn production are decision variables.)

This discrete model of iron production is not characterized by a Leontief or fixed-coefficient production function. The production function for corn, though, is Leontief. Neither the discrete nature of this model of iron production nor the Leontief production function for corn, however, drive capital-reversing. Capital-reversing can arise in models with "smooth" production functions (Steedman 2002). Since I am interested in behavior around a switch point (defined in Part 3), the assumption of fixed coefficients for corn production involves no loss of generality. Typically, techiques on two sides of a switch point differ in only one process (see, for example, the theorem on page 542 of Bruno et. al 1966). In the case of the above technology, those processes are iron-producing processes.

I think that in a model with more sectors, the costs of the various processes available for producing one or another commodity can vary more dramatically than in this example. Perhaps some day I will blog about the empirical evidence that technology is not unlikely to be such that “Sraffa effects” can arise.

Now to pose questions that are answered in the next part. Define a technique to consist of a positive level of operation of exactly one iron-producing process and the corn-producing process. For each of the two techniques so defined, at what levels can the two processes in the technique be operated so that the net ouput consists solely of corn? (The net output is what remains after replacing the iron and corn used up in production. If the net output is consumed, production can continue on the same scale for the adopted technique.) How much labor is employed per Bushel corn in net output for each of the two techniques?

  • Bruno, Michael; Edwin Burmeister; and Eytan Sheshinski (1966). "The Nature and Implications of the Reswitching of Techniques", Quarterly Journal of Economics, V. 80, N. 4 (Nov.): 526-553.
  • Steedman, Ian (2002). "Non-Monotonic c(r) Relations in the Abscence of Complementarity", Metroeconomica, V. 53, N. 1: 25-36

Tuesday, May 02, 2006

On David Card and Minimum Wages

Introductory economics classes often teach students an application of an incorrect model of labor markets governed by supply and demand. In this application, minimum wages cause unemployment. Those who accept this model were surprised a decade ago by Card and Krueger's results. They found little evidence for decreased employment from increases in minimum wages.

Their results had two major components: a meta-analysis (Card and Krueger 1995) and statistical analysis of data gathered in a natural experiment (Card and Krueger 1994). In their meta-analysis, they quantitatively examine over 30 time series studies of the minimum wage. They find that as more data becomes available, the statistical significance of the employment effect of minimum wages declines. That is, additional data results in finding that it is less and less likely that increased minimum wages decrease employment.

The most famous natural experiment Card and Krueger analyzed arose when New Jersey raised its minimum wage at a time when Pennsylvania kept its minimum wage unchanged. Card and Krueger "surveyed 410 fast-food restaurants in New Jersey and eastern Pennsylvania before and after the rise". They found no evidence that rises in minimum wages reduce employment.

Card is well-regarded by economists, as evidenced by his receipt of the John Bates Clark medal (Freeman 1997). Card and Krueger's book, Myth and Measurement, which repeats these results received a lengthly review in the Journal of Economic Literature. Kennan (1995) concludes: "Myth and Measurement is a serious, well-written book, well worth reading..." Kennan also calls for more resources to be devoted to data collection.

Naturally, this work generated controversy. Neumark and Wascher (2000) is probably the most well-known rexamination of the New Jersey case (Card and Krueger 2000 is a response). As far as I know, their meta-analysis has received no extended criticism. Given this work, I don't see how one can conclude that politically-feasible increases in the minimum wage will have large employment-decreasing effects.

Recently, Card (2005) has done some empirical work on immigration. You may sometimes encounter the claim that these recent results are inconsistent with his earlier work on minimum wages. This claim of inconsistency makes sense if you interpret Card's results to be about the elasticity of demand and supply in labor markets. These empirical results, however, are consistent if you think labor markets are not described by a model of supply and demand.

  • Card, David (2005). "Is the New Immigration Really So Bad?", working paper(?)

  • Card, David and Alan B. Krueger (1994). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania", American Economic Review, V. 84, N. 4 (Sep.): 772-793.

  • Card, David and Alan B. Krueger (1995). "Time-Series Minimum-Wage Studies: A Meta-Analysis", American Economic Review, V. 85, N. 2 (May): 238-243.

  • Card, David and Alan B. Krueger (2000). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry and Pennsylvania: Reply", American Economic Review, V. 90, N. 5 (Dec.): 1397-1420.

  • Freeman, Richard B. (1997). "In Honor of David Card: Winner of the John Bates Clark Medal", Journal of Economic Perspectives, V. 11, N. 2 (Spr.): 161-178.

  • Kennan, John (1995). "The Elusive Effects of Minimum Wages, Journal of Economic Literature, V. 33, N. 4 (Dec.): 1950-1965.

  • Neumark, David and William Wascher (2000). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Comment", American Economic Review, V. 90, N. 5 (Dec.): 1362-1396.