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.