A Refutation Of Austrian Capital Theory And Austrian Business Cycle Theory

1.0 Introduction

I have not posted about a non-fluke switch point in a while. This is an example from Bertram Schefold. I have examined perturbations and variations of this example before.

Here I present an example with tables exhibiting arithmetic. Is this any more transparent than examples presented with graphs?

I have been listening to some lectures on YouTube, especially Richard Wolff. I now have another hypothesis why mainstream economists have been promoting lies, ignorance, and nonsense for half a century: fear. The history of economics includes purge after purge after purge. Maybe many mainstream economists are cowed by their rulers.

2.0 Technology

Three processes are available for use in production. Each process is specified by coefficients of production (Table 1), when operated at an unit level. The person-years of labor employed, the bushels of corn used up in a process, and the number of new and old machines are specified. Outputs consist of bushels corn and new and old machines. Corn is both a consumer good and functions as circulating capital. Machines function as fixed capital. A machine's productivity varies with its age. An older machine requires less labor to operate, but more circulating capital.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)
Labor	1/10	43/40	1
Corn	1/16	1/16	1/4
New Machines	0	1	0
Old Machines	0	0	1
Outputs
Corn	0	1	1
New Machines	1	0	0
Old Machines	0	1	0

Suppose all three processes are run at unit level in parallel. At suppose at the start of the year, the firm has one new machine, one one-year old machine, and 3/8 bushels corn. The output of the first process is one new machine. The previously existing new machine is consumed in the second process, leaving an output of one one-year old machine. The third process uses up the one one-old year machine. So these processes reproduce the stock of new and old machines. But they also use up inputs of 3/8 bushels corn in producing a gross output of two bushels corn. Summing over all three processes, 2 7/40 person years of labor produce, with the capital stock, a net output of 1 5/8 bushels corn. The labor intensity of this technique is 87/65 person-years per bushel.

Assume free disposal for old machines. Another technique would be operated when the use of the machine is truncated after one year. In this case, one should consider the first and second processes being run in parallel at unit level, with a capital stock of one new machine and 1/8 bushels corn reproduced each year. Under this technique, 1 7/40 person years of labor are employed across the two processes. Net output is 7/8 bushels corn. The labor intensity is 47/35 person-years per bushel.

The more labor-intensive technique is the one with the truncated economic life of the machine. How many production cycles firms choose to run machines is an unambiguous physical measure in this example. And choosing to run the machine longer is a choice to adopt a less labor-intensive technique. Just as Eugen Böhm Bawerk says, a longer period of production, in some sense, is a more capital-intensive method. And that increase in the period of production results in greater output per worker. (I am not claiming that the number of production processes is the Austrian average period of production. I am merely noting how transparent the use of time is in this example.)

3.0 Some Accounting

One can easily see how a single firm would operate the last two processes in parallel, or only the process using the new machine, if the use of the machine is truncated. If such a firm was vertically integrated, they would also produce new machines with the first process. The firm can take the wage and the price of corn from the market, under various idealizations. For simplicity, I take a bushel corn as the numeraire. What prices would the accountants use to evaluate new and old machines?

3.1 At an Initial Wage

Consider a starting wage of 35/71 bushels per person-year and prices of machines shown in Table 2. For each process, the cost of capital inputs are the sum of the inputs of corn and machines of specified vintages, evaluated at the given prices. Wages are found from the labor input, evaluated at the given wage. Revenues are the sum of the outputs of corn and machines of specified vintages, evaluated at given prices. I assume wages are paid at the end of the year. So the rate of profits is the ratio of the difference between revenues and wages to the capital costs. With these prices, the owners are happy to operate all three processes. They make the same rate of processes in each, and prices do not signal that they should make any changes.

Table 2: Initial Prices

w = 35/71 ≈ 0.4930, p0 = 99/568 ≈ 0.1743, p1 = 1/284 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.04930	0.1743	100 percent
II	0.2368	0.5299	1.004	100 percent
III	0.2535	0.4930	1	100 percent

3.2 A Higher Wage

Now suppose the wage is 9,055/14,016 bushels per person-year. Table 3 shows accounting when the prices of new and old machines are unchanged. Notice that the rate of profits has fallen, with the rise in the wage, in all processes. But it has fallen to different levels, given that ratio of wages to the cost of capital originally varied among the processes. David Ricardo discusses this effect in the first chapter of his Principles of Political Economy and Taxation. Obviously, the price at which machines are entered into the firm's books must be changed to reflect the change in wages.

Table 3: Initial Prices with Raised Wage

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1743, p1 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.1743	75.5 percent
II	0.2368	0.6945	1.004	30.5 percent
III	0.2535	0.6460	1	39.6 percent

Table 4 shows a set of prices such that the same rate of profits is obtained in all three processes. This is not the end of the story, though, The price of a one-year old machine is slightly negative. (My approach for perturbing reswitching examples can make this price more noticeably negative, but maybe I would end up with even more messy fractions.) Instead of decreasing the revenues for the second process from the output of old machines, the managers of the firm can simply throw the old machine away and enter a price of zero for it on its books.

Table 4: Raised Wage and Updated Prices of New and Old Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1531, p1 ≈ -9.563 x 10-5
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.08852	41.64 percent
II	0.2156	0.6945	0.3054	41.64 percent
III	0.2499	0.6460	0.3539	41.64 percent

Table 5 shows the result of truncating the use of machines. One must, however, set a new accounting price for new machines, as well. Without this adjustment, different rates of profits are obtained in the first two processes. Notice the rate of profits is indeed lower in the third process, which is not used by cost-minimizing firms.

Table 5: Raised Wage and Truncated Use of Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.15313, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.15313	41.64 percent
II	0.21563	0.6945	1	41.68 percent
III	0.25	0.6460	1	41.58 percent

Table 6 shows the final results of correct accounting, with increased wages. The rate of profits, r, is 5/12, halfway between 1/3 and 1/2. Those rates of profits are the switch points in this example. I have told this story as a matter of accounting for vertically integrated firms. But these are the only prices on the market consistent with a long period position with the postulated wage. How and whether market prices would converge to these prices of production, in a gravitational process (as in Adam Smith's metaphor) is not clear to me. I like the idea that Sraffa's book is about little more than accounting. This idea is not too far away from what Ajit Sinha has been arguing for a number of years.

Table 6: Raised Wage, Truncation, Updated Price of New Machines

w = 9,055/14,016 ≈ 0.6460, p0 = 1,431/9,344 ≈ 0.15315, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.0646	0.15315	41.67 percent
II	0.21565	0.6945	1	41.67 percent
III	0.25	0.6460	1	41.58 percent

3.3 Summary

Table 7: Summary

Wage	Labor Intensity	Rate of Profits
35/71 ≈ 0.4930 bushels per person-yr.	87/65 ≈ 1.338 person-yrs. per bushel	100 percent
9,055/14,016 ≈ 0.6460 bushels per person-yr.	47/35 ≈ 1.343 person-yrs. per bushel	5/12 ≈ 41.7 percent

At a higher wage, firms want to run machines for one year, not two years. The economic life of machines is shortened from the physical life. And firms want to hire more workers to produce a net output.

Why might the wage rise and the rate of profits fall? In one theory, known to be nonsense, a shock might lead to labor be less abundant, as compared to capital. Perhaps people become more forward-looking and more willing to save, or the population falls for some reason. Wages rise, and firms take this as a signal to substitute capital for labor. But, in the example, a higher wage is associated with the adoption of a less capital-intensive technique and a rise in labor intensity. Somehow, if equilibrium is to be obtained, an increase in the labor force must be accompanied by a rise in wages.

Perhaps one can find a financial measure of capital, such as Hicks' average period of production, where a higher capital-intensity is always associated with a lower rate of profits around a switch point. But then one would have to grapple with the fact that more 'capital' does not always result in more output. Austrian school economists cannot seem to handle that their theory of 'malinvestment' is just incorrect.

Old Findings For New Times

From John Kenneth Galbraith's The Affluent Society (1958), I know that widespread attitude to waged work among some in the United States is outdated. The conventional wisdom is that work is necessary because it is needed to produce the goods that sustain society. That was largely true before productivity increased so much, for example, in the post war golden age. Some jobs are still essential, by any narrow definition, but much wage work goes to creating goods and services that in any previous society would have been considered useless luxuries. (As I get older though, I disagree with Galbraith about medicines to improve peristalsis.) But waged work, in the current system, is essential for providing the income needed to sustain the demand to keep the system going.

From Paul Davidson and Joan Robinson, I know about the distinction between historical and logical time. It as not as if the economy is in an equilibrium that will be approached again, and quickly, after a downward shock is removed. People will recall, and those who are out of work will try to cut back their spending. States and localities that have had to increase their spending to address such a shock will need to retain the ability to spend, and even to increase spending.

From Michal Kalecki's "Political aspects of full employment" (1943), I know that the ruling bourgeois class cannot be counted on to support what is even in their immediate short term financial interest. Unemployment is convenient for keeping the mass majority of the population, the labor force, cringing and hard to press for more of a share in the commodities that they produce. Even so, the backwardness of politics in the United States these days is hard to explain.

From Hannah Arendt's Eichmann in Jerusalem (1963), I know that one strategy in implementing totalitarianism is to declare a marginal group stateless, outside your laws and international laws. Refugees and immigrants are one such group that one could try to apply this strategy to, if you are for evil. From Carl Schmitt's The Concept of the Political (1932), I know that sovereign is he who can declare the state of exception. I resent that these ideas are relevant today.

A Fluke Switch Point On The Wage Frontier

Figure 1: A Switch Point On The Wage Frontier with Wage Curves Tangent

This post extends the example in my article in Structural Change and Economic Dynamics, suitably emended.

Figure 2 shows an enlargement of part of the parameter space. The parameters of the point where the boundaries of Regions 1, 2, and 3 intersect are shown. In Region 1, the Beta technique is uniquely cost-minimizing for all feasible wages; there are no switch points. Region 2 is a reswitching example, with Beta cost-minimizing at low and high wages. One switch point exists in Region 3, with the Beta technique cost-minimizing at low wages.

Figure 2: Part of Parameter Space

The boundary between Regions 1 and 2 is tangent to the boundary between Regions 1 or 2 and Region 3. In what I am calling a reswitching pattern, the scale factor for the rate of profits is found as a double root for a polynomial equation. I have extended the boundary between Regions 1 and 2, with the dotted line, to show where this double root occurs with a negative scale factor for the rate of profits.

Figure 1, at the top of this post, shows wage curves for the example for the parameter values noted in Figure 2. (I used Octave to help with my arithmetic.) The Beta technique is cost-minimizing for all feasible wages. When the wage is at its maximum, the Alpha technique is also cost minimizing. And, at the switch point, the two wage curves are tangent. This is a fluke switch point twice over.

This sort of fluke switch point cannot be expected to be found in empirical data from, say, National Income and Product Accounts. The fluke cases I have been developing are important in that they illustrate partitions in a parameter space for certain models of the choice of technique. They arise as certain characteristics of markets vary with a perturbation of model parameters.

I am not sure what to make of structures within the parts of the parameter space I have been exploring. If you think about, you can see why that must be a point of tangency in Figure 2. Maybe the most striking structure I have found is parallel lines for partitioning a parameter space associated with an example of Harrod-neutral technical change.

I write this stuff as escapism. A lot of economists I build on are in Italy, which is a worrisome place to be these days. I hope you are doing well.

A Fluke Case With Two Fluke Switch Points

Figure 1: Switch Points On The Axis For The Rate Of Profits And At r = -100 Percent

This is an example of a fluke case in the analysis of the choice of technique. The interest in flukes, for me, is that they show how the characteristics of markets can change. They provide insight into structural economic dynamics, as Luigi Pasinetti calls it.

I have previously shown a fluke case, with a switch point on the axis for the rate of profits with a real Wicksell effect of zero. A perturbation of the example can lead to a reswitching example. The switch point at a wage of zero (when the workers live on air) then becomes one at a positive wage. And around that switch point, a higher wage is associated with cost minimizing firms hiring more workers to produce a given net output.

In the example in this post, the switch point on the axis for the rate of profits exhibits neither a forward nor a reverse substitution of labor. The labor coefficient in the corn industry does not vary with the processes in the technique. The Alpha technique has a ghostly presence. It can only be chosen, and not even uniquely so, when the wage is zero. A perturbation of this example can lead to one of the reverse substitution of labor. The switch point on the axis for the rate of zero would also become one at a positive wage. And that switch point might be the only switch point on the frontier at a non-negative rate of profits. Around that switch point, a higher wage is associated with cost-minimizing firms hiring more workers to produce a given gross output of corn. The labor coefficient in the corn-producing process for the technique preferred at a higher wage is larger.

Table 1: Coefficients of Production for The Technology

Input	Iron	Corn Industry
		Alpha	Beta
Labor	1	0.64097922	0.64097922
Iron	9/20	0.00157618	0.01686787
Corn	2	0.48125981	0.0674715

Table 1 specifies the technology in my usual way. I assume labor is advanced, and wages are paid out of the product at the end of a production cycle. I take a unit of corn as numeraire. Prices of production are here defined with a uniform rate of profits between the industry. I found this example with numerical exploration, so there is some round-off error in the figures.

This post is another demonstration that explaining wages and employment by supply and demand, even under ideal competitive conditions, is incoherent nonsense.

A Market Algorithm

Figure 1: Specification of a Market Algorithm

1.0 Introduction

This article is heavily based on Bidard (2004).

An approach to the analysis of the choice of technique, in keeping with construction of the outer envelope of wage curves, is to consider replacing processes, more or less, one at a time. This post presents this approach as following an algorithm.

Assume that a set of techniques exist where all techniques are at least viable, indecomposable, and produce the same set of commodities. From the set of techniques, one can form a set of processes. In each process, workers produce a single commodity at the end of the year from certain inputs. The inputs, by assumption, are totally consumed in the course of the year. I also assume that the numeraire is specified.

Consider the algorithm specified by the flowchart in Figure 1. For this to be an algorithm, Steps 1 and 3 must be fully specified. One might as well assume that a known pseudo random number generator is used with a specified initial seed. Whether or not a candidate process yields extra profits is found in Step 5 with the prices of production calculated in Step 2. A process yields extra profits if and only if:

p a_.,j (1 + r) + w a_0,j > p_j

where a_0,j is the direct labor coefficient, and a_.,j is a column vector for the new process. I am imagining that a_.,j is the j column of the Leontief input-output matrix for a new technique. This new technique is formed by replacing a process in the technique previously selected in Step 2. Since, by assumption, no joint production exists, the process to be replaced is easily found. It is the process in the current technique that produces the same commodity as the candidate process. I have taken the wage as given in this specification of the algorithm. One could just as well take rates of profits as given.

This algorithm converges to a cost-minimizing technique. Consider the sequence of Steps enumerated as ‘2, 3, 4, (5, 7, 9)*, 5, 6, 2’. This expression denotes a single path around the loop on the bottom left of Figure 1, including zero or more paths around the loop on the right. As long as the loop on the right is repeated less times than the number of techniques, this path can be repeated. The question arises whether or not this algorithm contains an infinite loop. In a simple case, a process would be introduced into a technique because it is cost-minimizing for prices corresponding to the first technique, and that first technique would be cost-minimizing at the prices corresponding to the new technique. It can be shown that the existence of an infinite loop is impossible, under the assumption that no joint production exists. The algorithm always terminates.

(The use of metalinguistic symbols of parentheses and an asterisk to denote a repeated sequence of symbols is a convention in defining regular expressions. A sequence of symbols in a language, where the grammar of that language is specified by a regular expression, is accepted by a finite state machine, a type of automata. This is the lowest level of the Chomsky hierarchy. Chomsky (1965) uses transformational grammars to characterize human languages, which he argues are at the highest level of the hierarchy.)

Furthermore, except at switch points, the cost-minimizing technique found by the algorithm is unique. Which technique is initially selected at Step 1 or how processes are ordered at Step 3 does not matter, except for performance. The same cost-minimizing technique is ultimately found. The algorithm terminates with the selection of any one of the techniques that are cost minimizing at a switch point, depending on these details.

The algorithm is specified sequentially in Figure 1. Steps 3, 4, 5, 7, and 9 can be distributed. Inasmuch as this algorithm is executed in a capitalist economy, these steps are, in fact, distributed across firms. One might also modify the algorithm to apply when the set of processes and techniques are not known at that start of algorithm. Innovation and technical progress can be accommodated with an appropriate modification of Step 4 and Step 9. Step 7 should be eliminated, and the algorithm would be defined without a termination step, like daemons in operating systems. When the algorithm is modified for distributed processing, more than one process might be introduced into a technique simultaneously, including in the same industry. For which technique, then, are prices calculated in Step 2? This relates to the question of when labor expended in new processes is ‘socially necessary’, as Marx put it.

References

• Bidard, Christian. 2004. Prices, Reproduction, Scarcity. Cambridge: Cambridge University Press.
• Chomsky, Noam. 1965. Aspects of the Theory of Syntax. Cambridge: M.I.T. Press.

Another Example Of The Factor Price Frontier In The Space Of Rental Prices

Figure 1: Real Factor Price Frontier

1.0 Introduction

I am planning on posting at an even slower rate for a while.

This post continues my exploration of a way of visualizing the choice of technique proposed by Carlo Milana. In this post, I show how to correctly apply his visualization to an example from my 2017 ROPE paper.

2.0 Technology

Two techniques are available for producing corn, the consumption good. Each technique consists of a flow-input, point-output technology, with a finite number of dated labor inputs. The technology can also be represented with intermediate produced commodities explicitly shown. Table 1 sets out the example as a Leontief input-output table, in some sense. Each column lists the inputs in a production process needed to produce a unit output of the commodity named in the column heading. The entries for the row for corn are all zero, indicating it is not an input into any production process. All processes require a year to complete and completely use up their commodity inputs in producing their outputs. Each process requires a year to complete, and inputs must be hired at the start of the year, independently of when payments for inputs are contracted to be paid out. The example includes four factors of production: labor, and three capital goods.

Table 1: Coefficients of Production for The Technology

Input	Industry 1	Industry 2	Industry 3	Corn Industry
				Alpha	Beta
Labor	50	0	115	66	0
Commodity 1	0	1	0	0	0
Commodity 2	0	0	0	1	0
Commodity 3	0	0	0	0	1
Corn	0	0	0	0	0

The Alpha process consists of the processes for producing the first two commodities and the corn-producing process labeled Alpha. The Beta process consists of the process for producing the third commodity and the corn-producing process labeled Beta. The net output of a technique, when all processes comprising that technique are operated at the unit level, is a bushel of corn. The non-labor inputs needed to continue production with that technique are reproduced in the same quantities with this activation of processes.

3.0 Price System

I here formulate systems of equations (and inequalities) in terms of spot prices and rental prices for factors of production. A rental price pays for the services of a factor of production, and is paid at the end of the year. I formulate the example with the following variables:

• w_L: The wage, paid at the end of the year. Also known as the rental price for labor.
• p₁: The spot price for the first produced capital good.
• w₁: The rental price for the services of the first capital good.
• p₂: The spot price for the second produced capital good.
• w₂: The rental price for the services of the second capital good.
• p₃: The spot price for the third produced capital good.
• w₃: The rental price for the services of the third capital good.
• p_c: The spot price for corn.
• r: The interest rate.

In a circulating capital model of long period positions, rental prices and spot prices relate like so:

w_j = p_j(1 + r), j = 1, 2, 3

Since this is not a model of a slave economy, no spot price exists for labor. Corn is never used as a factor of production and does not have a rental price.

The price equations are such that no extra profits can be made in any process. Furthermore, costs do not exceed revenues in any operated process. Corn is assumed to be the numeraire. Figure 1, above, graphs the solution. This is actually a two-dimensional representation of a projection of a four-dimensional structure into three dimensions. The fourth dimension is the rental price for the first produced capital good.

3.1 Prices for the Alpha Technique

Suppose managers of firms have adopted the Alpha technique. The condition that the corn-producing process in the Alpha technique is adopted and pays no extra profits is expressed as:

66 (w_L/p_c) + (w₂/p_c) = 1

The above equation gives rise to the blue plane in the figure. The analogous condition for the process to produce the first capital good is expressed as:

50 (w_L/p_c) = (p₁/p_c)

The same sort of condition for the process for producing the second capital good is:

(w₁/p_c) = (p₂/p_c)

When the Alpha technique is adopted, prices may or may not enable managers of firms to activate the process for producing the third capital good. This condition is express as an inequality:

115 (w_L/p_c) ≥ (p₃/p_c)

In the graphed solution, the above inequality is treated as an equality, giving rise to the factor-price curve for the Alpha technique. An inequality arises for the corn-producing process in the Beta technique.

(w₃/p_c) ≥ 1

The above inequality cannot be combined with the other equations in the Alpha price system except between the switch points. That is, the factor price curve for the Alpha technique is the factor price frontier only between the switch points.

3.1 Prices for the Beta Technique

Now suppose that managers of firms have adopted the Beta technique. The condition that the corn-producing process in the Beta technique is adopted and pays no extra profits is expressed as:

(w₃/p_c) = 1

The above equation gives rise to the red plane in the figure. The analogous condition for the process to produce the third capital good is expressed as:

115 (w_L/p_c) = (p₃/p_c)

Inequalities arise for the processes for producing the first and second capital goods:

50 (w_L/p_c) ≥ (p₁/p_c)

(w₁/p_c) ≥ (p₂/p_c)

Likewise, an inequality arises for the corn-producing process in the Beta technique:

66 (w_L/p_c) + (w₂/p_c) ≥ 1

3.3 Solution of Price Equations

Table 2 displays the solution for the two systems of equations and inequalities. The equations impose a relationship between the wage and the interest rate, either of which could be given from outside the period of production. Spot prices for the three capital goods can be found by discounting rental prices to the start of the year.

Table 2: Factor Prices in the Example

Price	Alpha	Beta
(wL/pc)	1/(2 (33 + 25 (1 + r)2))	1/(115 (1 + r))
(w1/pc)	25 (1 + r)/(33 + 25 (1 + r)2)	10/23
(w2/pc)	25 (1 + r)2/(33 + 25 (1 + r)2)	10 (1 + r)/23
(w3/pc)	115 (1 + r)/(2 (33 + 25 (1 + r)2))	1

In both systems of equations, the rental prices of factors of production are expressed as functions of the interest rate. That is, factor price curves in Figure 1 are specified parametrically. Both factor price curves lie in their respective planes. Switch points lie on the intersection of the two planes in Figure 1. Outside the switch points, the factor price curve for the Beta technique is the factor price frontier. Between the switch points, the factor price curve for the Alpha technique is the factor price frontier.

4.0 Conclusion

Milana is correct in asserting that the interest rate is not a factor price, that is, a rental price for the services of a factor of production. The label "factor price frontier" should properly be reserved for a locus in the space of rental prices. This post has illustrated these claims by showing how to draw such a factor price frontier for a reswitching example with a specific structure.

On "Democratic Socialism"

1.0 Introduction

This post is about some usages of the phrase "democratic socialism".

2.0 Democratic Socialists of America (DSA)

In the context of current American politics, I think the most salient usage today of this phrase is associated with Bernie Sanders' campaign and with the Democratic Socialists of America.

DSA was founded in 1982 when the Democratic Socialist Organizing Committee (DSOC) merged with the New American Movement (NAM). The DSOC was established with Michael Harrington leading others out of the Socialist Party (SP) (Gorman 1995: p. 144-145). Apparently, 500 people attended the DSOC founding convention in 1973 (Harrington 1988: 17).

Michael Harrington will forever be known for The Other America. In this book, he deliberately did not use the word "socialism". And this book had some influence on the policies of Kennedy and Johnson and the latter's war on poverty. He also was something of a theorist. The Twilight of Capitalist is an attempt to apply a tradition of an "underground" Marxism to the conjuncture of 1970s "late capitalism". Harrington mentions Rosa Luxemburg, George Lukacs, Karl Korsch, the Frankfurt school, and Antonio Gramsci, for example, as well as more current thinkers. Hegel and dialectics are important to how Harrington understood Marx.

Some of the left want to establish a political party for the working class and saw that the Democratic party is not such a party. So they think they should have their own party. DSA is and DSOC was the opposite of that. DSA can be said to be openly pursuing a strategy of entryism. The goal is to influence the Democrats from within.

3.0 An Older Usage

But the term goes back much further than these movements in the United States in the 1970s and 1980s. "Democratic socialism" was used in English, in the United States, in the 1950s and early 1960s, by scholars discussing the "revisionism" of Eduard Bernstein.

I turn to the Second International shortly before 1900. As I understand it, a literal translation of the leading socialist party was something like the "Social Democratic Party of Germany" (SPD). I do not want to read much into the phrase "social democratic" here. At the time, Georgi Plekhanov and Vladimir Lenin were in the Russian Social Democratic Party.

In 1899, Engel's literary heir, Eduard Bernstein published a book. The Preconditions of Socialism and the Task of Social Democracy is a literal translation of its title, I guess. The book built on articles he published earlier in Die Neue Zeit. "The final goal is nothing to me, the movement is everything" is a well-known pithy statement from Berstein. He argued for pursuing reforms, supporting trade unions, and a parliamentary party on the foundation of universal suffrage.

Rosa Luxemburg saw a chance here to raise her profile in the socialist movement. Her response, Reform or Revolution, is another classic.

I have always thought of Karl Kautsky as a politician trying to keep advocates of all these tendencies within a single party. His grandson (Kautsky 1994) argues he was consistent, from the time that Lenin hailed him as the leader of the orthodoxy to the time Lenin called him a renegade. Here is a quote from the later time:

"For us... Socialism without democracy is unthinkable. We understand by modern Socialism not merely social organisation of production, but democratic organisation of society as well. Accordingly, Socialism is for us inseparably connected with democracy. No Socialism without democracy." -- Karl Kautsky, The Dictatorship of the Proletariat (1918), as quoted in Kautsky (1994).

By the way, John Kautsky tells of running into college students who were surprised that his granddad's first name was Karl; they thought somehow or other it was "Renegade"

Around 1900, splits and disagreements between more and less radical factions in socialist parties were an international phenomenon. In France, the syndicalist Georges Sorel was a radical and Jean Jaurès was more reformist. The Russians split in 1903, between the Mensheviks and the Bolsheviks. I gather a large part of the Menshevik faction walked out of the party congress, leaving the Bolsheviks the ability to call themselves the "majority", even though they were a minority of the party.

I skip forward any number of years. Maybe half of Sidney Hook's 1955 book is short selections from others. His reading number 54 is excerpted from a statement "adopted by the Socialist International at Frankfurt-on-Main, Germany, 1951." And it is entitled, "The aims and tasks of democratic socialism".

I think of Sidney Hook as an exemplar of an advocate of social democracy. I guess this section argues that the distinction between social democracy and democratic socialism was, at one time, not clear.

References

• Eduard Bernstein. 1961. Evolutionary Socialism: The Classic Statement of Democratic Socialism (trans. by Edith C. Harvey). Schocken.
• Peter Gay. 1952. The Dilemma of Democratic Socialism. Columbia University Press.
• Robert A. Gorman. 1995. Michael Harrington: Speaking American. Routledge.
• Michael Harrington. 1962. The Other America: Poverty in the United States.
• Michael Harrington. 1976. The Twilight of Capitalism. Simon and Schuster.
• Michael Harrington. 1988. The Long-Distance Runner: An Autobiography. Henry Holt.
• Sidney Hook. 1955. Marx and the Marxists. D. Van Nostrand.
• Maurice Isserman. 2001. The Other American: The Life of Michael Harrington.
• John H. Kautsky. 1994. Karl Kautsky: Marxism, Revolution & Democracy. Transaction Publishers.

Two Propositions: Neoclassical Economics Is Incoherent; A Classical Theory Of Value Exists

Some Mathematics Useful In Understanding Classical Political Economy

I consider the following to have been well established about half a century ago:

1. Marginalism or so-called neoclassical economics is impossible to formulate consistently and with practical applications.
2. A mathematically rigorous approach to the classical theory of value, from William Petty through David Ricardo, including Karl Marx, exists.

Mainstream economists ignore the truth of both propositions. Until they stop spouting lies and nonsense, these propositions should be re-iterated again and again. (On the other hand, I appreciate the work involved in compiling National Income and Products Accounts.)

I find a difficulty in publishing re-iterations of these propositions. I expect editors and reviewers of, say, the American Economic Review, the Journal of Political Economy, or the Quarterly Journal of Economics would simply not publish papers stating either proposition. You can publish articles in, say, the Review of Political Economy which re-state these propositions, but any such article must contain something novel. For my purposes, I seem to stumbled upon a research program that includes:

• Exploring what still holds when prices of production are defined with persisting non-uniform rates of profits.
• Exploring and visualizing the effects of perturbing parameters in models of prices of production.
• Refuting those who claim to have some other analysis of the choice of technique in which, say, reswitching examples are supposedly mistaken.

Others have other focii for their research. For example, historians of political economy might be interested in the publication of critical editions of Marx-Engels Collected Works (MEGA) or of Piero Sraffa's archives. Over the last couple of decades, some have worked on exploring problems in joint production and some limitations of the long period method, such as non-reproducible, exhaustible natural resources (as seen, for example, in the corn-guano model). Many other issues have been explored.

Update To Example In Vienneau (2019)

Maybe this post should be titled "Erratum" or "corrigendum". I have an example in my paper last year in which wage frontiers are supposed to vary with two parameters. One is the markup in the "iron" industry. And the other is σ t. The example should be as in Table 1. All the theory and the visualizations in the paper work out with this example.

Table 1: Technology for Producing Steel and Corn

Input	Industry
	Iron	Corn
		Alpha	Beta
Labor	a0,1 = 1	aα,0,2(t) = (5191/5770) e(1/10) - σ t	aβ,0,2 = 305/494
Iron	a1,1 = 9/20	aα,1,2(t) = (1/40) e(1/10) - σ t	aβ,1,2 = 3/1976
Corn	a2,1 = 2	aα,2,2(t) = (1/10) e(1/10) - σ t	aβ,2,2 = 229/494

• Vienneau, Robert L. 2019. Structural economic dynamics, markups, real Wicksell effects, and the reverse substitution of labor. Structural Change and Economic Dynamics 50: 216-226.

Elsewhere

• John Weeks presents Joan Robinson's contributions to the Cambridge Capital Controversy (CCC).
• A discussion, from 2006, on Daily Kos, about one of my attempts to explain the CCC.
• A post, from 2016, on Naked Capitalism about how the CCC shows microeconomics is all wet.
• J. W. Mason has a handout explaining a definition of capital.
• Doyne Farmer, Fotini Markopoulou, Eric Beinhocker, and Steen Rasmussen, in an essay in Aeon, Collaborators in creation, provide an overview of complexity economics.
• An overview, from 2018, about how women were deliberately kicked out of software development in Great Britain.

Universal Basic Income: Some Advocates And Analysts

"In fact, the realm of freedom actually begins only where labour which is determined by necessity and mundane considerations ceases; thus in the very nature of things it lies beyond the sphere of actual material production. Just as the savage must wrestle with Nature to satisfy his wants, to maintain and reproduce life, so must civilised man, and he must do so in all social formations and under all possible modes of production. With his development this realm of physical necessity expands as a result of his wants; but, at the same time, the forces of production which satisfy these wants also increase. Freedom in this field can only consist in socialised man, the associated producers, rationally regulating their interchange with Nature, bringing it under their common control, instead of being ruled by it as by the blind forces of Nature; and achieving this with the least expenditure of energy and under conditions most favourable to, and worthy of, their human nature. But it nonetheless still remains a realm of necessity. Beyond it begins that development of human energy which is an end in itself, the true realm of freedom, which, however, can blossom forth only with this realm of necessity as its basis. The shortening of the working-day is its basic prerequisite." -- Karl Marx, Capital, Volume 3, Chapter 48.

This post, I guess, is somewhat about current events. I claim no comprehensiveness for my impressions on the topic. I find my references are aspirational more than usual; some do not even seem to be in print. In this post, I do not compare and contrast UBI with a Job Guarantee, which seems to be argued about a lot on twitter.

Three properties define a UBI, according to Philippe Van Parijs. It is paid to individuals, not households. One obtains a UBI payment independent of need or any other sources of income. And it is not conditional on one's willingness to accept a job or on a requirement to have worked in the past or to work in the future.

I think a UBI is consistent with Keynes' vision in 1931 of "Economic possibilities for our grandchildren". Whether increases in productivity are broadly shared, including in increased leisure or non-work time seems not to be determined by technology. In some sense, the use of such progress for progressive ends is a result of collective choice. By the way, increased non-work time is part of a response to the global climate crisis. I have seen statistics about how less carbon is emitted during recessions. If we labor less voluntarily, and share time somewhat fairly, those trends would continue, I gather. So UBI could be one component of a green policy.

I always like to find those on the right stating their principles support supposed policies of the left. I find Hayek's ideas in The Road to Serfdom as inconsistent with UBI:

"There is no reason why in a society which has reached the general level of wealth which ours has attained the first kind of security should not be guaranteed to all without endangering general freedom. There are difficult questions about the precise standard which should thus be assured; there is particularly the difficult question whether those who thus rely on the community should indefinitely enjoy all the same liberties as the rest. An incautious handling of these questions might well cause serious and perhaps even dangerous political problems; but there can be no doubt that some minimum of food, shelter, and clothing, sufficient to preserve health and the capacity to work, can be assured to everybody." -- Hayek (1944, Chapter IX).

Hayek argues for too much, in that UBI proponents do not claim to be assuring, by this policy alone, that some necessary minimum will be achieved. He argues for too little, in that proponents of UBI do not want to even consider limiting the liberties of those who receive it. Nevertheless, the above quotation, and the chapter in which it is in, might be of interest to advocates of a UBI. From Hayek's perspective, a UBI does not seem to be a threat to the liberty of private property.

I have been reading Steve Wright about a much more radical movement that developed ideas close to a UBI. His book is an intellectual history of operaismo (workerism) and the area of autonomy in Italy in the 1960s and 1970s. Mario Tronti and Antonio Negri are two leaders of these tendencies, albeit they seem like the kind that are, in some sense, leaderless and spontaneous. I find some of the slogans and practices (for example, "the refusal of work" and "self reduction" (autoriduzione)) associated with autonomism intriguing. Workerists developed the concept of the social worker, the idea that the self-reproduction of the economy occurred not only in factories, but outside including by such non-waged individuals as students and housewives. The autonomists wanted to separate pay from productive labor, including a wage for housework. This social "wage" sounds a lot like an UBI to me.

I now turn to an author I know even less about. Philippe Van Parijs seems to be the most prominent academic advocate of UBI. He comes out of the tradition of analytical Marxism. I associate G. A. Cohen, Jon Elster, and John Roemer with this approach, although I knew that the September group had more members. Here Chris Bertram interviews Van Parijs. Van Parijs seems to have a number of books, more than I list below, in which others comment in his idea for UBI and in which he responds. Apparently, in discussing the impact of an UBI on work ethic, this literature also turns to a stereotype of surfers. (I was under the impression that the sunfish sailboat was also the product of a beach bum.)

My favorite approach to economics emphasizes questions of viability and what is needed to sustain human societies. Guglielmo Chiodi connects Sraffa's book with an UBI and normative concerns. No physical surplus is produced in the model in the first chapter of Sraffa's book. The inputs of production processes can be just reproduced from the outputs. Prices of production are determined by the need to redistribute these outputs, in accordance with a division of labor. One can consider these inputs as including commodities to sustain workers, just as they might include feed for horses. I think I take from Bertram Schefold the idea that the inputs might also include investment goods and capitalist consumption. Chiodi goes further. He suggests inputs include consumption by those who are neither capitalists nor working. And he reads Sraffa as emphasizing non-market institutions and non-market values. I am not sure I agree with this reading, but I find it of interest. I agree with Chiodi that Sraffa is more than an internal critique of neoclassical economics, but points to an alternative approach to economics. I do not think I have read anybody other Chiodi as connecting Sraffa to UBI. But I still have more to learn about the autonomist slogan of "the wage as the independent variable."

References

• Rutger Bregman, Utopia for Realists: How we can build the ideal world, 2018.
• Guglielmo Chiodi. Beyond capitalism: Sraffa's economic theory. In Sraffa or an Alternative Economics (ed. by Guglielmo Chiodi and Leonardo Ditta), Palgrave Macmillan, 2008.
• Guglielmo Chiodi. Sraffa and the universal basic income: some notes. In The Evolution of Economic Theory: Essays in honour of Bertram Schefold (ed. by Volker Caspari). Routledge, 2011.
• Guglielmo Chiodi and Leonardo Ditta. Sraffa and Keynes: Two ways of making a 'revolution' in economic theory. In Sraffa and the Reconstruction of Economic Theory: Volume 1 (ed. by Enrico Sergio Levrero, Antonella Palumbo and Antonella Stirati), 2013.
• Mariarosa Dalla Costa and Selma James. The Power of Women and the Subversion of the Community. 1973.
• Phil Edwards. 'More Work! Less Pay!' Rebellion and Repression in Italy, 1972-7. Manchester University Press, 2009.
• David Frayne. The Refusal of Work: Rethinking Post-Work Theory and Practice. 2015.
• F. A. Hayek, The Road to Serfdom, 1944.
• John Maynard Keynes, Economic possibilities for our grandchildren. In Essays in Pursuasion, 1931.
• Philippe Van Parijs (ed.). Arguing for Basic Income: Ethical Foundations for a Radical Reform., Verso.
• Philippe Van Parijs. Real Freedom for All: What (if Anything) Can Justify Capitalism? Oxford University Press, 1997.
• Philippe Van Parijs et al. What's Wrong with a Free Lunch, Beacon Press, 2001.
• Philippe Van Parijs and Yannick Vanderborght. Basic Income: A Radical Proposal for a Free Society and a Sane Economy, 2019.
• Steve Wright. Storming Heaven: Class Composition and Struggle in Italian Autonomist Marxism, 2nd edition. 2017.

Reswitching With Markup Pricing And Fixed Capital

Figure 1: Two Dimensional Pattern Diagram

1.0 Introduction

This post extends an example from Bertram Schefold. It presents markup pricing in an example with a machine that can be operated for two years or junked after one year. This is a case of joint production in which, unlike in some cases, the choice of technique can still be analyzed by the construction of the wage frontier. Also, I do not think the question of requirements for use enter in here, and all matrices are square. As usual, this is a proof that "the marginal productivity theory of distribution" (and the neoclassical theory of supply and demand) "is all bosh" (Robinson 1961).

2.0 Technology

Table 1 shows the coefficients of production for the three processes comprising the available technology. Inputs must be available at the beginning of the year, and outputs become available at the harvest at the end. In the first process, labor uses inputs of corn to produce a new machine. That machine is used by labor in the second process, with inputs of seed corn, to produce more corn and a one-year old machine. In the third process, labor uses inputs of seed corn and the one-year old machine to produce corn. (I did think of calling the machine a "tractor".) The machine varies in physical efficiency over the course of its lifetime.

Table 1: Coefficients of Production for The Technology

Input	Machine Industry	Corn Industry
		One Process	Another Process
Labor	a0, 1 = 1/10	a0, 2 = 43/40	a0, 3 = 1
Corn	a1, 1 = 1/16	a1, 2 = 1/16	a1, 3 = 1/4
New Machines	a2, 1 = 0	a2, 2 = 1	a2, 3 = 0
Old Machines	a3, 1 = 0	a3, 2 = 0	a3, 3 = 1
Output
Corn	b1, 1 = 0	b1, 2 = 1	b1, 3 = 1
New Machines	b2, 1 = 1	b2, 2 = 0	b2, 3 = 0
Old Machines	b3, 1 = 0	b3, 2 = 1	b3, 3 = 0

The technology is summarized by a row vector a₀, the input vector A, and the output vector B. The example satisfies various assumptions that show the economy hangs together, in some sense, and that it is more than viable.

The technology also presents a choice of technique. Managers of firms in corn-production may want to truncate the use of the machine to one year, given certain configurations of prices. In the Alpha technique, the machine is used for two years. I call the technique in which the machine is only used for one year the Beta technique.

3.0 Prices of Production

The price equations for the Alpha technique are:

p A (I + r S) + w a₀ = p B

where p is a row vector of three prices (the price of corn, the price of a new machine, and the price of a one-year old machine), w is the wage, and r is the scale factor for the rate of profits. In a common notation, I is the identity matrix. The square matrix S is a diagonal matrix. Its diagonal elements express persistent differences in the rate of profits among processes or industries. The rate of profits in the jth process is r s_j.

I take corn as the numeraire. This can be expressed as:

p e₁ = 1

where e₁ is the first column of the identity matrix.

4.0 Some Visualizations of the Solution

Assume, without loss of generality, that the markup coefficient, s₁, in the process producing new machines is unity. Figure 2 shows how the choice of technique varies with the wage in the case where the markup coefficients in corn-producing processes do not vary with the age of the machine. When barriers to entry in producing new machines ensure that the markups in corn production fall appreciably below the overall rate of profits, managers of corn-producing firms will operate the machine for its full physical life, whatever the wage. On the other hand, roughly, if the corn-producing industry maintains barrier to entries, the machine will be operated for its full life only at low and high wages. At intermediate wages, the use of the machine will be truncated after one year. As still higher markups in corn-production, the machine will only be operated for the full two years for high wages.

Figure 2: A Pattern Diagram

Figure 2 can be constructed in two ways. One is by constructing the wage frontier out of the wage curves for the two techniques. Figure 3 shows an example. This case is for what I call a reswitching pattern. The two wage curves are tangent at the single switch point. In finding the wage curve for the Alpha technique, one can also solve for the price of a one-year old machine. In the analysis of truncation with fixed capital, the machine is operated for only one year when this price turns negative. Switch points between the two techniques arise for wages in which the price of a one-year old machine is zero. I believe this analysis applies with the formulation of markup pricing in this post.

Figure 3: Wage Curves for a Reswitching Pattern

Figure 1, at the top of this post, generalizes the analysis to all values of the markups in the corn-producing processes. Regions are indicated in which the machine is operated for two years, whatever the wage; in which this is an example of reswitching; and in which the machine is operated for two years only for high wages. The dashed (45-degree) line shows the case in which the markup is the same in both corn-producing processes.

I wonder if it makes any economic sense to consider cases off the 45-degree line in Figure 1. In this simple example, the two corn-producing processes are in the same industry, in some sense. If one agrees with this limitation for economic sense, a question arises. How, in some formulation of markup pricing, should such constraints be formulated, in general, for prices of production in models of joint production? Could markups, for instance, vary between the production of mainly wool and mainly mutton? Since definitions of even basic commodities vary among analyses of joint production, I do not see how to identify such processes in general where you might want to raise the question. Maybe these questions could be partly addressed by considering the process of vertical integration.

5.0 Conclusions

This post has illustrated that the analysis of the choice of technique must be performed in models with fixed capital. Managers of firms always have the choice of truncation, of adopting a technique in which the economic life of a machine is shorter than its physical life. This presents a challenge to attempts to justify Marx's theory of value with Sraffa's standard commodity. I have not even gone into some of the complications raised by pure joint production and models in which multiple types of machines are used.

References

• Luigi L. Pasinetti (ed.) 1980. Essays on the Theory of Joint Production. New York: Columbia University Press.
• Joan Robinson. 1961. Prelude to a critique of economic theory. Prelude to a critique of economic theory 13: 53-58.
• Bertram Schefold. 1980. Fixed capital as a joint product and the analysis of accumulation with different forms of technical progress. In Pasinetti 1980.

Precursors of Piero Sraffa

I want to consider contributions to economics after 1870 that reconsidered classical or Marxist economics, used input-output models and linear algebra, or bear a family resemblance to at least some points in Sraffa's 1960 book.

• Vladimir K. Dmitriev. Used input-output analysis in an interpretation of Ricardo's theory of value.
• Ladislaus Bortkiewicz. Had a simple three-good model, with one basic good, input-output model of prices of production. Sraffa and others argued against aspects of his interpretation of Marx's theory of value.
• Georg von Charasoff. Apparently, around 1909 and 1910, he came up with the concept of "original capital". In a infinite series, much like Sraffa's reduction to dated labor, the capital goods needed more and more indirectly in producing some given net output converge to Sraffa's standard commodity.
• Father Maurice Potron. A fairly conservative Jesuit priest and mathematician, writing in French. I know of him from this collection.
• Wassily Leontief. His empirical work extends from the 1920s. I do not know that those building on his work often cite Sraffa.
• Walter Isard. Applied Leontief input-output analysis to regional or spatial economics in 1951.
• John von Neumann. I am thinking of the 1945-1946 translation of his A Model of General Economic Equilibrium. Kurz and Salvadori read this as a response to Robert Remak.
• Jacob T. Schwartz. A mathematician whose 1961 Lectures on the Mathematical Method in Analytical Economics criticizes neoclassical and Austrian economics. Personally, I found his work not as rigorous as Sraffa's.

I do not know much about many of these authors, but other economists in the post Sraffian tradition have written about them.

Why Does The Labor Theory Of Value Work Empirically As A Theory Of Prices?

Anwar Shaikh On The Transformation Problem

Lots of empirical work shows that prices tend to be proportion to the labor embodied in commodities. My references in this article document this claim. Furthermore, empirical wage-rate of profits curves tend to be close to straight lines. This is not what, say, Sraffa' mathematical economics would lead me to expect. What explains these surprising empirical findings?

Almost 34 minutes in, in the above video, Shaikh makes the above point about the contrast between theory and empirical findings. He concludes with speculation, including with comments on Bertram Schefold's work with input-output matrices formed out of random matrices.

I offer some speculations myself in this post. I do not have much theory to back these suggestions up.

The Leontief matrices obtained from National Income and Product Accounts (NIPAs) are still highly aggregated. The empirical results on the LTV are obtained with matrices that have on the order of, say, 100 industries. One of these industries, if disaggregated, might contain commodities that are produced with a high Organic Composition of Capital (OCC) and a low OCC. Their prices of production would deviate more from labor values than an average combining them both. The extremes would be cancelled out in forming an average.

In my examples of pattern analysis, I also suggest that Sraffa effects could be difficult to see, in that they arise in a transition from one very long run position to another. But I concoct those examples to make a point about possibilities. I do not want to insist on any empirical point here.

Technical progress, despite how I usually model it, is endogenous. If in process of production adopted in some industry, some input is noticeably more expensive than others, managers of firms will seek out and research processes in which that input is reduced or some other cheaper input is substituted for it. Perhaps after a couple of centuries of rapid technical change under these incentives, empirical Leontief input-output matrices will have the properties Schefold highlights for random matrices. I suppose one could confirm this by showing wage-rate of profits curves are closer to affine functions for more highly developed economies. I have done some empirical work along these lines.

Aside: Here is another YouTube video with Anwar Shaikh. He sounds a lot like he accepts Milgate and Eatwell's critique of "imperfectionism". Actually existing capitalism is to be analyzed by a theory that accepts empirical reality, not by deviations from a neoclassical utopia that could never exist in any conceivable world.

Only The Super-Rich Can Save Us!

Neoliberals are hostile to labor unions and every other institution that would allow the vast majority of the population to have some effect on how we are ruled. And they have been so successful that only the super-rich can save us, as the title of a Ralph Nader novel a few years back had it. A couple of recent examples of journalism are about movements of the super-rich:

• Sheelah Kolhatkar writes, in the New Yorker, about Patriotic Millionaires.
• Theodore Schleifer writes, in Vox, about Resource Generation.

I suspect most of the super-rich, however, are vicious, reactionary fools. Apparently, Benjamin Page, Jason Seawright, and Matthew Lacombe provide evidence in their recent book, Billionaires and Stealth Politics. I've read and commented on their previous working paper.

In the United States and elsewhere, we had a progressive movement reacting to the terrible effects and excesses of the "roaring twenties" of a century ago. Of course, there was a fascist movement, too, that resulted in global war.

In the United States, prominent celebrities such as Henry Ford and Charles Lindbergh supported fascism. The super-rich did not step back. The business plot was an attempt by millionaires to stage a coup against Franklin Delano Roosevelt. They tried to get Major General Smedly Butler to act as a figurehead. I know of him for saying, war is a racket. I do not know if this falls in the politics of the super-rich, but I only recently learned about the Christian Front, a fascist organization inspired by the radio demagogue Father Coughlin. In 1940, their office in New York City was raided by the FBI for trying to overthrow the government. Seventeen members was arrested, but their prosecution was unsuccessful. (Caveat: I have not read the books and literature linked to in this paragraph.)

I think we need a better material basis than the well wishes and work of the super-rich to bring about hopeful change.

Towards the Derivation of the Cambridge Equation with Expanded Reproduction and Markup Pricing

I have a new working paper.

Abstract: Does the Cambridge equation, in which the rate of profits in a steady state is equal to the quotient of the rate of growth and the savings rate out of profits, hold in an economy with widespread non-competitive markets? This article presents a multiple-good model of markup pricing in an attempt to answer this question. A balance equation is derived. Given competitive conditions, this model can be used to derive the Cambridge equation. The Cambridge equation also holds in a special case of markup pricing, with one capital good and many consumption goods being produced. No definite conclusions are reached in the general case.

The Factor Price Frontier In The Space Of Factor Rental Prices

Figure 1: Real Factor Price Frontier

1.0 Introduction

Carlo Milana has proposed a new way of visualizing the choice of technique, including in the case of reswitching. This way of describing what he has done is not neccessarily how he thinks of it. In this post, I describe his approach with a reswitching example, in a model of the production of commodities by means of commodities.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs. (This example is taken from one of my papers.)

Table 1: Coefficients of Production for The Technology

Input	Steel Industry		Corn Industry
	Alpha	Beta
Labor	1	275/464	1 Person-Yr
Steel	1/10	113/232	2 Tons
Corn	1/40	0	(2/5) Bushels

Two techniques of production arise in this example. The Alpha technique consists of the Alpha process for producing steel and the corn-producing process. Both steel and corn are basic commodities, in the sense of Sraffa, for the Alpha technique. The Beta technique consists of the Beta process for producing steel and the corn-producing process. Only steel is a Sraffa-basic commodity for the Beta process. Suppose, however, corn is the only consumption good in this example. Then in the Beta technique, as with the Alpha technique, both steel and corn will be (re)produced for both techniques.

3.0 Prices of Production

If the Alpha technique is in use in a long-period position, prices satisfy the following two equations:

((1/10) p_α,1 + (1/40) p_α,2)(1 + r) + w_α = p_α,1

(2 p_α,1 + (2/5) p_α,2)(1 + r) + w_α = p_α,2

Prices are spot prices. The services of produced inputs are paid for at the start of the year, while wages are paid out of the surplus at the end of the year.

The corresponding equations for prices for the Beta technique are:

((113/232) p_β,1)(1 + r) + (275/464) w_β = p_β,1

(2 p_β,1 + (2/5) p_β,2)(1 + r) + w_β = p_β,2

At this point, I take a bushel corn as the numeraire. One can solve the Alpha system of equations, for example, to find (w_α/p_α,1) as a function of the interest rate. This is the wage curve for the Alpha technique and is shown below. The wage curve for the Beta technique is also graphed. The outer envelope of these curves, called the wage frontier, shows which technique is cost-minimizing at any given interest rate. Both techniques are cost-minimizing at the switch points, which arise for interest rates of 20 percent and 80 percent. Between the switch points, the Alpha technique is cost-minimizing. Outside the switch points, the Beta technique is cost minimizing.

Figure 2: Wage Curves and the Wage Frontier

4.0 Rental Prices for Factor Inputs

In marginalism, the choice of technique is often analyzed in terms of rental prices for factors of production. One can think of the example in terms of three factors: labor, steel, and corn. Steel and corn are capital goods.

Since a choice of production processes arises in the steel industry, I here take steel as numeraire. The rental price, also known as the factor price, for labor is the real wage:

w_α,L = w_α/p_α,1

The rental or factor price for steel is the cost of a the services of a ton of steel when paid at the end of the year:

w_α,Steel = p_α,1(1 + r)/p_α,1

Likewise, the rental or factor price of corn is:

w_α,Corn = p_α,2(1 + r)/p_α,1

Using these definitions, the condition that, when in use, no extra profits are made and no extra costs are in incurred in producing steel with the Alpha process yields the following equation:

(1/10) w_α,Steel + (1/40) w_α,Corn + w_α,L = 1

Notice that this is a linear equation in three variables. It is illustrated by the blue plane in Figure 1. The factor prices for the Beta process yield another linear equation:

((113/232) w_β,Steel + (275/464) w_α,L = 1

The plane for Beta is shown in red in Figure 1.

At a switch point, both the Alpha and the Beta processes are eligible for adoption by cost-minimizing managers of firms. Accordingly, switch points must lie on the intersection of the two planes described above. The intersection, although difficult to see, is shown in black in the figure.

In discussing rental or factor prices, I have yet to take into account that corn must also be produced. If one substitutes, on the right-hand side in the three equations defining rental prices, the solution of the Alpha system of equations in Section 3, one obtains factor prices as a parametric function of the interest rate. This is the real factor price curve for the Alpha technique and is shown in blue above. The real factor price curve for the Beta technique, in red, is easier to see. (Each real factor price curve lies within the plane of the same color.) For each curve, when it lies on the real factor price frontier is indicated. And the switch points do indeed lie on the intersections of the real factor price curves.

5.0 Conclusion

Does the real factor price frontier in Figure 1 provide a mechanism for analyzing the choice of technique? Is the factor price curve for the cost-minimizing technique always furtherest from the origin?

The wage frontier, where applicable, can be drawn in a two-dimensional diagram for examples with any number produced of produced commodities. If n commodities are produced, Milana's diagram illustrates, roughly, the intersections of hyperplanes of dimension (n - 1). And those intersections will be themselves hyperplanes of dimension (n - 2). Switch points, if any, lie in those intersections. The factor price curves will still be one-dimensional curves, as I understand it, in the appropriate hyperplanes.

Obviously, this cannot be visualized in higher dimensions. Nevertheless, the mathematics still works out. Different valid approaches to finding the cost-minimizing technique in a long-period position, given an exogenous specification of the distribution of income, in some sense, will all yield the same answer. That is the case for the reswitching example presented here.

Some People Who Have Shaped Economics

"The University [of Chicago] is the best investment I ever made in my life." -- John D. Rockefeller

Consider the following people and selected activities:

• Lewis Brown founded the American Enterprise Institute, in 1938.
• Jasper Crane cofounded the Foundation for Economic Education, in 1946.
• Leonard Read cofounded the Foundation for Economic Education, in 1946.
• Harold Luhnow, even before 1947, directed spending for the Volker Fund.
• Sir Antony Fisher funded the Institute for Economic Affairs, around 1956.
• Lord Ralph Harris, first general director of the Institute for Economic Affairs.
• Arthur Seldon, first editorial director of the Institute for Economic Affairs.
• F. A. Harper founded the Institute for Humane Studies, in 1961.
• Charles Koch funded the development of the Virginia school, notably including James Buchanan's work.
• Edwin Feuler, founded the Heritage Foundation, in 1973.
• Edward H. Crane founded the Cato Institute, in 1977.
• Eamonn Butler cofounded the Adam Smith Institute, in 1978.
• Madsen Pirie cofounded the Adam Smith Institute, in 1978.

I've written on the influence of fundings sources on the development of economics before. A developing body of scholarly literature explores the impact of the above list of people. The above list is not complete. For example, John Blundell seems to be an important fellow in the world hinted at above.

I think funding sources have been concentrated on the right. I suppose you can try to make a list not so concentrated on the right. George Soros and the Institute for New Economic Thinking, John Reed of Citicorp and Santa Fe Institute, John Podesta and theCenter for American Progress (CAP) would all be in the list. I do not know where funding for the Economic Policy Institute comes from. It seems to me a distinction exists between investigating ideas and trying to publicize conclusions you already believe.

2019 Nobel Prize Celebrating The Triumph Of Institutionalism?

Elizabeth Warren Echoing A View Institutionalists Understand

This year, the "Nobel prize" in economics went to Abhijit Banerjee, Esther Duflo, and Michael Kremer. They champion empirical economics over theory. Previously, institutionalist economics was described as 'measurement without theory' (Koopmans 1947). Does institutionalist economics parallel the supposed mainstream empirical turn?

Although institutionalists, as far as I know, did not have the resources to create randomized control trials (RCTs), they did collect and analyze statistical data. I think especially of Wesley Clair Mitchell and the National Bureau of Economic Research (NBER).

Institutionalists was not atheoretical, I think. They developed qualitative analytical concepts. I think of C. E. Ayres extension, for example, of the Veblenian dichotomy. Sometime, I intend to read John R. Commons' 1924 book to see how he breaks up a transaction. John Kenneth Galbraith's concept of the technostructure and Alfred Eichner's idea of the megacorp are other examples here. Institutionalists contributed to the development of Industrial Organization. John Maurice Clark had, at least, a verbal description of the business cycle that combined the multiplier and the accelerator.

Institutionalist economics is not a strictly American school of thought. I include Geoffrey M. Hodgson and Gunnar Myrdal as institutionalists. I suppose I should read the Journal of Economic Issues or the Journal of Institutional Economics more frequently. The Association for Evolutionary Economics (AFEE) puts out the JEI.

References

• John R. Commons. 1924. Legal Foundations of Capitalism Macmillan.
• John S. Gambs. 1946. Beyond Supply and Demand: A Reappraisal of Institutional Economics. Columbia University Press.
• Tjalling C. Koopmans. 1947. Measurement without theory. Review of Economics and Statistics 29(3): 161-172.

A Fake Switch Point in an Example With Circulating Capital

Figure 1: A Switch Point and a Fake Switch Point on Wage Curves

1.0 Introduction

In the analysis of the choice of technique, I typically consider examples of technology with a finite number of techniques. For each technique, I find the wage as a function of the rate of profits. The outer envelope of these curves shows the cost-minimizing technique at each rate of profits (or each level of the wage). Points on more than one wage curve are switch points.

This approach is valid when, for example, all techniques produce the same set of commodities, and each commodity is basic, in the sense of Sraffa. That is, all commodities enter directly or indirectly into the production of all commodities.

But another requirement is that prices of all commodities in common between two techniques be identical at a switch point. Points of intersection on wage curves without this property of identical prices are known as fake switch points. I have previously considered fake switch points in (an extension of) an example from Christian Bidard. In this post, I present an example of a fake switch point in an example with single production (or circulating capital) only. It is critical to this example that a non-basic commodity is the numeraire and that the techniques vary in the process used to produce a non-basic commodity.

The necessity to consider prices in the analysis of the choice of technique is, as I understand it, a critical point from Milana. I think he extends this point, though, to examples in which it cannot be used to criticize Sraffians.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs.

Table 1: Coefficients of Production for The Technology

Input	Corn Industry	Silk Industry
		Alpha	Beta
Labor	1	1	2 Person-Yrs
Corn	1/5	3	(38/15) Bushels
Silk	0	0	0 Square-Yds

The first produced commodity, corn, enters directly into the production of both commodities. It is a basic commodity, in the sense of Sraffa. Silk is a non-basic commodity. It does not enter, either directly or indirectly, into the production of corn.

3.0 Price Equations

I take a square yard of silk as the numeraire. The same rate of profits is assumed to be made in both industries when prices of production prevail. Labor is advanced, and wages are paid out of the net product at the end of the year.

3.1 The Alpha Technique

The following two equations specify prices of production for the Alpha technique:

(1/5) p_{1, α} (1 + r) + w_α = p_{1, α}

3 p_{1, α} (1 + r) + w_α = 1

The variables are:

• r: The rate of profits.
• w_α: The wage, for the Alpha technique.
• p_{1, α}: The price of corn, for the Alpha technique.

The solution, in terms of the rate of profits, is:

w_α(r) = (4 - r)/(19 + 14 r)

p_{1, α}(r) = 5/(19 + 14 r)

3.2 The Beta Technique

The price equations for the Beta technique are:

(1/5) p_{1, β} (1 + r) + w_β = p_{1, β}

(38/15) p_{1, β} (1 + r) + 2 w_β = 1

The solution is:

w_β(r) = 3(4 - r)/[2( 31 + 16 r)]

p_{1, β}(r) = 15/[2( 31 + 16 r)]

4.0 Switch Points

Suppose, at the given rate of profits, the Alpha technique is in use and prices of production for the Alpha technique prevail. Figure 2 shows the cost of producing silk, for each process, at these prices. The advances, at the beginning of the year, for produced inputs are costed up at the going rate of profits. The cost of producing silk with the process in the Alpha technique, under these assumptions, is unity for any feasible rate of profits. Extra costs are not incurred in the Alpha technique. Neither are supernormal profits available.

Figure 2: Cost of Producing Silk at Alpha Prices

But supernormal profits are available for the silk-producing process in the Beta technique if the rate of profits is feasible and exceeds the rate of profits at the switch point. The Beta technique is cost-minimizing here, while the Alpha technique is only cost-minimizing at lower rates of profits. The same conclusion about when each technique is cost-minimizing would be drawn if one started with prices of production for the Beta technique.

The switch point occurs at a rate of profits of 50 percent. The wage is (7/52) square yards per person-years, and the price of corn is (5/26) square yards per bushel at the switch point. Prices of production are the same, at the switch point, whichever technique is used.

5.0 A Fake Switch Point

Figure 1, at the top of this post, graphs the wage curves for the two techniques. Consider rates of profits that equate wages:

w_α(r*) = w_β(r*)

The wage curves have two intersections. One is at the switch points, at a rate of profits of 50%. At the maximum rate of profits of 400 percent, the wage is zero. In the Alpha system, the price of corn is (1/15) square yards per bushel, while it is (3/38) square yards per bushel in the Beta system. Since, prices of production vary among techniques at the maximum rate of profits, it is not a switch point. Rather, it is a fake switch point.

6.0 Conclusions

I would like to find another example of a fake switch point in a circulating capital example with a choice of processes for producing a non-basic commodity. I want a fake switch point not at an extreme, with a wage of zero. The example in Stamatis (2001) seems not to work; maybe there is a misprint in the coefficients of production. Both techniques, however, have the structure of Sraffa's "beans".

References

• Carlo Milana. 27 Nov. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital
• Georg Stamatis. 2001. Why the comparison and ordering of techniques is impossible. Political Economy 9: 5-44.