An Example With A Cost-Minimizing Technique With Intensive And Extensive Rent

Figure 1: Detail on Variation of Rent per Acre with Rate of Profits

1.0 Introduction

Consider a model of the production of commodities with non-produced means of production that are unchanged by their use in production. In other words, they are types of land. In a simple model of extensive rent, a single agricultural commodity, 'corn', can be produced, on each type of land, with a single production production. This post expands a simple multi-commodity model to postulate the existence of two production processes on one type of land. The model then combines intensive and extensive rent, depending on the choice of technique.

In the example, all three types of land are at least partially cultivated to satisfy requirements for use. Whether or not all three types of land obtain a rent depends on the level of profits. A mixture of intensive and extensive rent is obtained only for a range of the rate of profits.

I repeat a lot from a previous post so that this post somewhat makes sense by itself.

2.0 Technology, Resources, Final Demand, and Feasibility

A model of the production of commodities is specified by the technology, the endowments of unproduced natural resources, and the requirements for use. Technology is specified, in a discrete technology, by coefficients of production for each production process. Each process is assumed to require the same time to complete and to exhibit constant returns to scale, up to the limited imposed by scarce land. The endowments of each type of land are specifed. Requirements for use are specified by final demand.

Table 1 presents coefficients of production for the example. Two commodities are produced, iron and corn. Aside from the use of land, joint production is not possible. Multiple types of land (that is, three types) exist. Only one agricultural commodity, corn, can be produced on the processes in which land is used. For one type of land, more than one process can be operated on land. Only one process is known for producing iron, the industrial commodity. Each column in Table specifies the person-years of labor, acres of a type of land, tons of iron, and bushels of corn needed to produce a unit output of the specified commodity.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Corn
	I	II	III	IV	V
Labor	1	0.517	91/250	0.67	3/10
Type 1 Land	0	0.49	0	0	0
Type 2 Land	0	0	0.59	0	0
Type 3 Land	0	0	0	9/20	3
Iron	9/20	0.03744	0.0009	0.067	0.08
Corn	2	0.048	0.27	0.15	0.15

Various techniques (Table 2) can be defined with this technology. All twenty-four letters in the Greek alphabet are needed to specify the techniques. Not all techniques are feasible, given technology, endowments, and requirements for use. Land is not scarce for the Alpha, Beta, Gamma, and Delta techniques, and ownership of land obtains no rent. The Epsilon through Upsilon techniques are examples of extensive rent. One type of land obtains a rent in the Epsilon through Xi techniques. All three types are farmed in Omnicro through Upsilon, and two types obtain a rent. Phi is an example of intensive rent. Chi, Psi, and Omega are examples of the combination of intensive and extensive rent.

Table 2: Techniques of Production

Technique	Processes	Land
		Type 1	Type 2	Type 3
Alpha	I, II	Partially farmed	Fallow	Fallow
Beta	I, III	Fallow	Partially farmed	Fallow
Gamma	I, IV	Fallow	Fallow	Partially farmed
Delta	I, V	Fallow	Fallow	Partially farmed
Epsilon	I, II, III	Partially farmed	Fully Farmed	Fallow
Zeta	I, II, IV	Partially farmed	Fallow	Fully Farmed
Eta	I, II, V	Partially farmed	Fallow	Fully Farmed
Theta	I, II, III	Fully Farmed	Partially farmed	Fallow
Iota	I, III, IV	Fallow	Partially farmed	Fully Farmed
Kappa	I, III, V	Fallow	Partially farmed	Fully Farmed
Lambda	I, II, IV	Fully Farmed	Fallow	Partially farmed
Mu	I, III, IV	Fallow	Fully Farmed	Partially farmed
Nu	I, II, V	Fully Farmed	Fallow	Partially farmed
Xi	I, III, V	Fallow	Fully Farmed	Partially farmed
Omnicron	I, II, III, IV	Partially farmed	Fully Farmed	Fully Farmed
Pi	I, II, III, V	Partially farmed	Fully Farmed	Fully Farmed
Rho	I, II, III, IV	Fully Farmed	Partially farmed	Fully Farmed
Sigma	I, II, III, V	Fully Farmed	Partially farmed	Fully Farmed
Tau	I, II, III, IV	Fully Farmed	Fully Farmed	Partially farmed
Upsilon	I, II, III, V	Fully Farmed	Fully Farmed	Partially farmed
Phi	I, IV, V	Fallow	Fallow	Fully Farmed
Chi	I, III, IV, V	Fallow	Fully Farmed	Fully Farmed
Psi	I, II, IV, V	Fully Farmed	Fallow	Fully Farmed
Omega	I, II, III, IV, V	Fully Farmed	Fully Farmed	Fully Farmed

I assume that 100 acres of each of the three types of land are available. Net output consists of 66 tons iron and 88 bushels corn. This completes the specification of the example. The parameters for the example are fairly arbitrary. They are chosen to ensure a reswitching of the order of rentability for the Tau technique and to ensure that the Omega technique is feasible.

Under these assumptions, Omnicron, Rho, Tau, and Omega are feasible. All three types of land are farmed under these three techniques. Type 1 land is only partially farmed under Omnicron, and it is non-scarce and does not obtain a rent. Type 2 land does not obtain a rent under Rho. Type 3 land does not obtain a rent under Tau. All three types are fully farmed under Omega. A linear combination of processesare IV and V are operated side-by-side under Omega. Type 3 land is therefore scarce under Omega. All three types are farmed under Omnicron, with non-scarce Type 3 land only partially farmed.

3.0 Prices of Production

A system of equations specify prices of production for each technique. All operated processes pay the same rate of profits. Rents and wages are paid out of the surplus at the end of the year. A type of land that is only partially farmed is not scarce and pays no rent. I take the net output as the numeraire.

As an example, the system of equations in following five displays specify the prices of production for the Omega technique.

(p₁ a_1,1 + p₂ a_2,1)(1 + r)+ w a_0,1 = p₁

(p₁ a_1,2 + p₂ a_2,2)(1 + r) + rho₁ c_1,2 + w a_0,2 = p₂

(p₁ a_1,3 + p₂ a_2,3)(1 + r) + rho₂ c_2,3 + w a_0,3 = p₂

(p₁ a_1,4 + p₂ a_2,4)(1 + r) + rho₃ c_3,4 + w a_0,4 = p₂

(p₁ a_1,5 + p₂ a_2,5)(1 + r) + rho₃ c_3,5 + w a_0,5 = p₂

Prices of production for the other techniques are specified by a subset of the system of equations for the Omega technique. Each operated process corresponds to an equation in the corresponding system of prices of production. The rent on land that is partially farmed is zero in the corresponding equation, since land in excess supply is not scarce.

The numeraire is specified by a further equation, where the column vector d represents net output.

p₁ d₁ + p₂ d₂ = 1

3.1 On the Solution

A linear combination of the last two equations in the system of prices of production, for the Phi, Chi, Psi, and Omega techniques, eliminates the rent of type 3 land. In the techniques with extensive rent, one of the equations for a corn-producing process does not contain a term for rent either.

This equation for a corn-producing process or the linear combination of the last two equations can be combined with the first equation, for the iron-producing process. This results in a system of two equations in four unknowns, the price of iron, the price of corn, the wage, and the rate of profits. The equation for the numeriare removes one degree of freedom. If the rate of profits is taken as given, this is a linear system which can be solved for prices of produced commodities and the wage.

The rent per acre can be found for each equation remaining in the original system of equations for a technique. The Alpha, Epsilon, Zeta, Eta, Omnicron, and Pi techniques, for example, have the same solution for prices of produced commodities and the wage. Epsilon, Omnicron, Pi have the same rent per acre on type 2 land. Zeta and Omnicron have the same rent per acre on Type 3 land, while Eta and Pi have the same rent per acre on Type 3 land.

3.2 Wage and Rent Curves

Given the technique, the wage is therefore a function of the rate of profits. Likewise the rent on lands that are always fully-farmed with that technique is also a function of the rate of profits.

The wage is a declining function of the rate of profits in the first four techniques and in the 16 techniques with extensive rent alone. A maximum wage corresponds to a rate of profits, and a maximum rate of profits corresponds to a wage of zero. The wage curve can be upward-sloping in models of extensive rent. The wage curves, in the example, happen to be downward-sloping in the example. Figure 2 shows the wage curves for the feasible techniques in the example. The order of efficiency is the order in which techniques are adopted with increasing net output at a given wage or rate of profits. In models with extensive rent, the order of efficiency can be read off the order of wage curves.

Figure 2: Wage Curves for Feasible Techniques

Figure 3 shows the rent curves for the techniques with non-negative rents in the example. Figure 1, at the top of the post, is an enlargement. Rent curves do not need to have any particular slope. They can slope down or up and vary along their extent. The rent curves for Tau are an example of the reswitching of the order of rentability.

Figure 3: Rent Curves for Feasible Techniques

4.0 The Choice of Technique

Only two techniques, Tau and Omega, are feasible in the example and have non-negative rents for scarce lands. Table 3 lists approximate ranges of the rate of profits and which techniques are cost-minimizing in which ranges. The orders of efficiency and the order of rentability are also shown.

Table 3: Cost-Minimizing Technique

Range	Technique	Order of Efficiency	Order of Rentability
0 ≤ r ≤ 29.05 %	Omega	Type 2, 1, 3	Type 1, 2, 3
29.05 ≤ r ≤ 35.50 %	Tau
35.05 ≤ r ≤ 43.76 %			Type 2, 1, 3

Figure 4 justifies which technique is cost-minimizing in which range of the rate of profits. Capitalists can gain extra profits by adopting process V in the range in which Omega pays positive rents. Type 5 land becomes fully farmed by combining the two processes on Type 3 land, and the Omega technique results. For higher rates of profits, Tau is cost-minimizing, up to the maximum for Tau.

Figure 4: Extra Profits at Tau Prices

Intensive and extensive rents are both obtained by landlords when the Omega technique is cost-minimizing. Whenever the Omega technique is cost-minimizing, and in some range of the rate of profits in which Tau is cost-minimizing, the order of efficiency varies from the order of rentability. Type 2 land is more efficienct or more fertile than Type 1 land. Yet ownership of Type 1 land obtains more rent per acre than Type 2 land. Why would one ever expect competitive capitalist markets to reward efficiency?

5.0 Conclusion

This post presents the first concrete example of a case where a cost-minimizing technique combines intensive and extensive rent. It demonstrates that the concepts of the order of effiency and the order of rentability apply to models with intensive rent. As with models with only extensive rent, the order of effiency cannot be generally defined in terms of physical properties alone. And these orders can differ from one another at some given wage or rate of profits.

The example does not illustrate issues that can arise with intensive rent. Wage curves can slope up. The cost-minimizing technique can be non-unique away from switch points. No cost-minimizing technique may exist, even though feasible techniques exist at a given wage or rate of profits (D'Agata 1983).

The analysis can be extended to more kinds of rent and more complicated production models, while still not treating general joint production. Absolute rent, which may not make sense (Basu 2022) and external intensive rent (Kurz and Salvadori 1995) are examples. Rent might be analyzed in models with systematic, persistent variations in the rate of profits among industries (Vienneau 2024). Likewise, a more general model could have some types of lands that are inputs into processes that each produce a different agricultural commodity. Does it make sense to compare and contrast the order of efficiency and the order of rentability in these models?

References

• D’Agata, A. 1983. The existence and unicity of cost-minimizing systems in intensive rent theory, Metroeconomica 35: 147-158.
• Basu, Deepankar. 2022. A reformulated version of Marx's theory of ground rent shows that there cannot be any absolute rent. Review of Radical Political Economics 54(4): .
• Kurz, H. D. and Salvadori N. 1995. Theory of Production: A Long-Period Analysis, Cambridge: Cambridge University Press.
• Quadrio-Curzio, A. 1980. Rent, income distribution, and orders of efficiency and rentability, in Pasinetti, L. L. (ed.) Essays on the Theory of Joint Production, New York: Columbia University Press.
• Quadrio-Curzio, A. and F. Pellizzari. 2010. Rent, Resources, Technologies. Berlin: Springer. [I NEED TO READ THIS TO ENSURE THAT I AM ORIGINAL]
• Vienneau, R. L. 2022. Reswitching in a model of extensive rent. Bulletin of Political Economy 16(2): 133-146.
• Vienneau, R. L. 2024. Characteristics of labor markets varying with perturbations of relative markups. Review of Political Economy (36)2: 827-843.

A Non-Reswitching Theorem Inapplicable To Non-Competitive Markets?

Consider a circulating capital model of the production of commodities. A non-reswitching theorem exists:

Theorem: Suppose a commodity exists which is a basic commodity in all techniques. And a smooth, continuously differentiable production function exists for producing that commodity. Then the reswitching of techniques cannot arise.

Marglin (1984: 285-286) states a theorem like this in which continuously differentiable production functions exist for all commodities. He also states:

"Once again, a result I thought to be original turned out not to have been. Reviewing the literature for these notes, I found a proof of the impossibility of reswitching in a continuous-substitution framework in Burmeister and Dobell (1970)." – Marglin (1984: 542).

Marglin's proof is one by contradiction. Capital-reversing is still possible under the assumption of these theorems.

Pasinetti and Scazzieri (2008) find the theorem in Bruno, Burmeister, and Sheshinski (1966), which I do not recall. They, in turn, attribute the theorem to Martin Weitzman and Robert Solow. Pasinetti and Scazzieri doubt the validity of the theorem.

"It is worth noting that Weitzman–Solow's theorem is simply a consequence of the idea that, in the case of a commodity produced by a neoclassical production function, each set of input–output coefficients ought to be associated in equilibrium with a one-to-one correspondence between marginal productivity ratios and input price ratios. No ratio between marginal productivities would be associated with more than one set of input prices, and this is taken to exclude the possibility that the same technique be chosen at alternative rates of interest, and thus at different price systems. The Weitzman–Solow theorem is at the origin of a line of arguments that has been followed up by a number of other authors, such as David Starrett (1969) and Joseph Stiglitz (1973). These authors have pursued the idea that 'enough' substitutability, by ensuring the smoothness of the production function, is sufficient to exclude reswitching of technique. However, non-reswitching theorems of this type involve that, for each technique of production, the capital stock may be measured either in physical terms or at given prices. For in a model with heterogeneous capital goods, if we allow prices to vary when the rate of interest or the unit wage are changed, there is no reason why the same physical set of input–output coefficients might not be associated with different price systems: even in the case of a continuously differentiable production function, the marginal product of 'social' capital cannot be a purely real magnitude independent of prices. Once it is admitted that 'in general marginal products are in terms of net value at constant prices, and hence may well depend upon what those prices happen to be' (Bliss, 1975, p. 195), it is natural to allow for different marginal productivities of the same capital stock at different price systems. It would thus appear that reswitching of technique does not carry with it any logical contradiction even in the case of a smoothly differentiable production function." Pasinetti and Scazzieri (2008)

I do not know about that. But I have never been clear on how substitutability is supposed to justify marginalist theory.

Suppose rates of profits differ among industries. And that the ratios of rates of profits among industries are stable in the long run. I have shown that the arguments of the Cambridge capital controversy extend to such non-competitive markets. In my paper, I had a reswitching example, in a discrete technology, that did not arise in competitive markets.

I conjecture that the non-reswitching theorem for continuous-substitution does not apply to non-competitive markets.

References

• Bruno, M., Burmeister, E. and Sheshinski, E. 1966. The nature and implications of the reswitching of techniques. Quarterly Journal of Economics 80, 526–53.
• Burmeister, Edwin and A. Rodney Dobell. 1970. Mathematical Theories of Economic Growth. New York: Macmillan.
• Marglin, S. A. 1984. Growth, Distribution, and Prices. Harvard University Press.
• Pasinetti, L. L. and Roberto Scazzieri, R. 2008. Capital theory (paradoxes). The New Palgrave.
• Starrett, D. 1969. Switching and reswitching in a general production model. Quarterly Journal of Economics 83, 673–87.
• Stiglitz, J. 1973. The badly behaved economy with the well-behaved production function. In Models of Economic Growth, ed. J.A. Mirrlees and N.H. Stern. London: Macmillan.

An Example With Intensive And Extensive Rent

Figure 1: Detail on Variation of Rent per Acre with Rate of Profits

1.0 Introduction

This post is the start of an attempt to develop an interesting example with both intensive and extensive rent. A feasible technique exists in the example with both intensive and extensive rent. Yet, it is never cost-minimizing. So this example does not do what I want. I have previously thought about other examples.

The example is an extension of my example of the reswitching of the order of rentability. Such reswitching occurs in this example. But the first switch point of the order of rentability is off the frontier.

I think some perturbation of this example will get me an example where a technique with both intensive and extensive rent is cost-minimizing for some range of the rate of profits. That example will illustrate that the orders of efficiency and of rentability can be analyzed in the context of intensive rent. And these orders need not co-incide in the case of intensive rent too.

2.0 Technology, Resources, Final Demand, and Feasibility

Table 1 presents coefficients of production for the example. Two commodities are produced, iron and corn. Aside from the use of land, joint production is not possible. Multiple types of land (that is, three types) exist. Only one agricultural commodity, corn, can be produced on the processes in which land is used. For one type of land, more than one process can be operated on land. Only one process is known for producing iron, the industrial commodity. Each column in Table specifies the person-years of labor, acres of a type of land, tons of iron, and bushels of corn needed to produce a unit output of the specified commodity.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Corn
	I	II	III	IV	V
Labor	1	0.517	91/250	0.67	3/10
Type I Land	0	0.49	0	0	0
Type II Land	0	0	0.59	0	0
Type II Land	0	0	0	9/20	3
Iron	9/20	0.03744	0.0009	0.067	0.08
Corn	2	0.048	0.27	0.15	0.15

I can define various techniques (Table 2) with this technology. I need all twenty-four letters in the Greek alphabet to specify the techniques. Not all techniques are feasible, given technology, endowments, and requirements for use. Land is not scarce for the Alpha, Beta, Gamma, and Delta techniques, and ownership of land obtains no rent. The Epsilon through Upsilon techniques are examples of extensive rent. One type of land obtains a rent in the Epsilon through Xi techniques. All three types are farmed in Omnicro through Upsilon, and two types obtain a rent. Phi is an example of intensive rent. Chi, Psi, and Omega are examples of the combination of intensive and extensive rent.

Table 2: Techniques of Production

Technique	Processes	Land
		Type 1	Type 2	Type 3
Alpha	I, II	Partially farmed	Fallow	Fallow
Beta	I, III	Fallow	Partially farmed	Fallow
Gamma	I, IV	Fallow	Fallow	Partially farmed
Delta	I, V	Fallow	Fallow	Partially farmed
Epsilon	I, II, III	Partially farmed	Fully Farmed	Fallow
Zeta	I, II, IV	Partially farmed	Fallow	Fully Farmed
Eta	I, II, V	Partially farmed	Fallow	Fully Farmed
Theta	I, II, III	Fully Farmed	Partially farmed	Fallow
Iota	I, III, IV	Fallow	Partially farmed	Fully Farmed
Kappa	I, III, V	Fallow	Partially farmed	Fully Farmed
Lambda	I, II, IV	Fully Farmed	Fallow	Partially farmed
Mu	I, III, IV	Fallow	Fully Farmed	Partially farmed
Nu	I, II, V	Fully Farmed	Fallow	Partially farmed
Xi	I, III, V	Fallow	Fully Farmed	Partially farmed
Omnicron	I, II, III, IV	Partially farmed	Fully Farmed	Fully Farmed
Pi	I, II, III, V	Partially farmed	Fully Farmed	Fully Farmed
Rho	I, II, III, IV	Fully Farmed	Partially farmed	Fully Farmed
Sigma	I, II, III, V	Fully Farmed	Partially farmed	Fully Farmed
Tau	I, II, III, IV	Fully Farmed	Fully Farmed	Partially farmed
Upsilon	I, II, III, V	Fully Farmed	Fully Farmed	Partially farmed
Phi	I, IV, V	Fallow	Fallow	Fully Farmed
Chi	I, III, IV, V	Fallow	Fully Farmed	Fully Farmed
Psi	I, II, IV, V	Fully Farmed	Fallow	Fully Farmed
Omega	I, II, III, IV, V	Fully Farmed	Fully Farmed	Fully Farmed

I assume that 100 acres of each of the three types of land are available. Net output consists of 60 tons iron and 80 bushels corn. This completes the specification of the example.

Under these assumptions, Zeta, Lambda, Omnicron, Pi, Sigma, Tau, Upsilon, and Psi are feasible. Types 1 and 3 land are farmed under Zeta, with process IV being operated on Type 3 land. Which of Types 1 and 3 obtain a rent depends on which land is fully farmed. I should say more here.

3.0 Prices of Production

A system of equations specify prices of production for each technique. All operated processes pay the same rate of profits. Rents and wages are paid out of the surplus at the end of the year. A type of land that is only partially farmed is not scarce and pays no rent. I take the net output as the numeraire.

One degree of freedom exists for the system of equations for each technique. Figure 2, below, shows how the wage varies with the rate of profits for each technique. Figure 3 shows the variation in rent per acre with the rate of profits. Figure 1, at the top of this post, is a detail for an interesting part of Figure 3.

Figure 2: Wage Curves for Feasible Techniques

Figure 3: Rent Curves for Feasible Techniques

4.0 Choice of Technique

A technique is not cost-minimizing if it requires a negative rent to be paid. Rent is negative, under Sigma, for both Type 1 and Type 3 lands. Under Zeta, Omnicron, and Pi, rent on Type 3 land is negtive.

This leaves Lambda, Tau, Upsilon, and Psi as feasible techniques that pay positive rents on scarce lands in some range of the rate of profits. Table 1 lists the cost-minimizing techniques, Upsilon and Tau, in order of an increasing rate of profits.

Table 3: Cost-Minimizing Technique

Range	Technique	Order of Efficiency	Order of Rentability
0 ≤ r ≤ 28.49 %	Upsilon	Type 2, 1, 3	Type 2, 1, 3
28.49 ≤ r ≤ 29.05 %			Type 1, 2, 3
29.05 ≤ r ≤ 35.50 %	Tau
35.05 ≤ r ≤ 43.76 %			Type 2, 1, 3

The order of efficiency, at a given rate of profits, is the order in which different types of land would be brought under cultivation as final demand was increased. This order can be read off of Figure 2 by working downward over the wage curves. Since the wage curves for Sigma and for Zeta, Omnicron, and Pi do not intersect, the order of efficiency does not vary, with the rate of profits, in this example. Type 2 land is partially farmed under Sigma. So Type 2 land is first in the order of efficiency. Type 1 land is partially farmed in Zeta, Omnicron, and Pi. Hence, Type 1 land is next in the order of efficiency for techniques in which all three lands are farmed.

The order of rentability is read off of Figures 1 and 3. The order in which rent per acre decreases varies with the rate of profits. For order of rentability differs from the order of efficiency for rates of profits around the switch point between Upsilon and Tau. A change in the order of rentability occurs around the second intersection between the two rent curves for Tau. This effect is a manifestation of the reswitching of the order of rentability. But the order of rentability varies around any intersection of these curves.

It remains to demonstrate that the above claims about which is the cost-minimizing technique at each rate of profits. Figure 4 shows that Lambda is never cost minimizing. Extra profits can always be obtained at Lambda prices by farming Type 2 land with process III. At low rates of profits, extra profits can also be obtained by farming Type 3 land with the other corn-producing process available for that type of land.

Figure 4: Extra Profits at Lambda Prices

Figures 5 and 6 show that Upsilon is cost-minimizing below the switch point, and that Tau is cost-minimizing at higher rates of profits. In these ranges, extra profits are not available by operating the process not in the technique.

Figure 5: Extra Profits at Upsilon Prices

Figure 6: Extra Profits at Tau Prices

Both intensive and extensive rent are paid when Psi is adopted. Figure 7 demonstrates that Psi is never cost-minimizing. Extra profits are always available, whatever the rate of profits.

Figure 7: Extra Profits at Psi Prices

5.0 Conclusion

This post has illustrated the analysis of the choice of technique in an example with both intensive and extensive rent. Constructing the wage curve is not necessarily the correct method of analysis in models with general joint production. Looking at whether or not extra profits are available for the prices associated with a technique is always applicable.

Elsewhere

• I find Matt McManus has argued in Damage magazine for liberal socialism.
• The liberal socialism developed by Nello and Carlo Rosselli was sort of endorsed by Mussolini. He had them murdered.
• When it comes to Italian exiles from fascism, I could learn more about Pietro Nenni.
• This Ha-Joon Chan article in the Financial Times is behind a paywall and is generating a buzz. "Economics teaching has become the Aeroflot of ideas". But it is available here.

Revolutionary And Reformist Socialists Splitting Around 1900

The second international was the major organization for socialist parties around 1900. The first international had collapsed with struggles for leadership between Marx and anarchists. The German Social Democratic Party, headed by Karl Kautsky, seemed to be the most successful socialist party in the second international. After Engels, Kautsky became the literary executor for Marx. He edited and put out volume 4 of Capital, that is, Theories of Surplus Value.

Eduard Bernstein was Engels' literary executor and therefore a prominent member of the German Social Democratic Party. He had been the editor of Der Sozialdemokrat, the party's newspaper. Perhaps Bernstein was influenced by his acquaintance with members of the Fabian society when he was in exile in London. He looked at the growing wealth of the German workers; the apparent strength of working-class organizations, such as unions; and the SDP representation in the Reichstag. Economic development was not concentrating wealth in a smaller and smaller capitalist class. These trends did not seem to him consistent with the revolution that Marx foresaw. And he said so.

The Preconditions of Socialism and the Tasks of Social Democracy (Die Voraussetzungen des Sozialismus) is the major statement of Bernstein's views, and was published in 1899. It started as articles in Die Neue Ziet, the SDP paper for more theoretical work. Bernstein was called a revisionist, which has ever after been a pejorative among more radical socialists. His theses were argued about at the SDPss Stuttgart Conference, held in October 1898.

Bernstein argued for legislation and peaceful reform in favor of the workers. Socialists should be a parliamentary party. They should agitate for universal suffrage. They should leave businesses, for the most part, in private hands. Socialists should support the development of civil society.

Rosa Luxemburg saw an opportunity to raise her stature in the German SDP. She had already participated in the Stuttgart conference. Others, including Kautsky, also argued against Bernstein. Luxemburg's Reform or Revolution is a classic statement of the radical, anti-revisionist view. She argued against idealism, against petty bourgeois moralism, and against opportunism. Idealism, in this sense, means basing political views purely on intellectual arguments. Emphasizing universal citizenship loses a working-class standpoint. According to Luxemburg, capitalism will inevitably break down. Socialism is a scientific standpoint, given its historical necessity. I do not know that this is in this pamphlet, but Luxemburg famously said that our choice is socialism or barbarianism.

This controversy was echoed in other countries. In France, Jean Jaurès led the reformists. I think of Georges Sorel as an intellectual leader of the revolutionaries. His 1908 book, Reflections On Violence does not strike me as particularly Marxist. You maybe should read 'violence' in the title as what is today called direct action. Sorel, at the time, was an advocate of syndicalism. He was kind of mystical in his emphasis on non-rational motives for mass movements. Hence, his myth of the general strike.

In Italy, Filippo Turati, a founder of the Italian socialist party (PSI), was a reformist. The radicals were called maximalists. They seem to me more positivist than Marx would ever be. They saw the revolution as inevitable, not something to be brought about by political action in the here-and-now. Socialists should organize and educate, holding themselves back until the revolution comes.

In Russia, the split was between the Mensheviks and the Bolsheviks. Apparently, these names mean 'the minority' and 'the majority'. Bolsheviks were only the majority because some supporters of the Mensheviks had walked out of the Second Congress of the RSDLP (Russian Social Democratic Labor Party), at which the split occurred. Julius Martov was an important leader of the moderates, while Lenin headed the Bolsheviks. Lenin's pamphlets, What is to be done? (1902) and Two steps forward, one step back (1904) are essential primary sources here.

Lenin argued for agitation on all fronts, not just for economic improvements for the workers. He wanted an organization of professional revolutionaries, and developed the idea of democratic centralism. The Bolsheviks should have the freest discussion in deciding on policy and tactics. But once a vote has decided the issue, the comrades follow the party line. The establishment of an all-Russian newspaper, Iskra, is the immediate implementation called for in What is to be done?

I ought to say something about Austria.

I have said nothing about Sweden, Denmark, Norway, or Finland. Bernstein provided the intellectual structure for what became democratic socialism and social democracy. I do not know historical details about Scandinavia. He said, "The final goal, no matter what it is, is nothing; the movement is everything."

Some Results From My Research

I have written about my research program before. Here I write about results.

1. A numerical example of a new capital-theoretic paradox, the reswitching of the order of rentabily.
2. A numeric example of, perhaps, another new capital-theoretic paradox, the recurrence of truncation without reswitching or capital-reversing. (I have not yet had this published.)
3. A demonstration that the critique developed in the Cambridge capital controversy extends to non-competitive markets.
4. A diagram illustrating how the analysis of the choice of technique varies with the perturbation of a parameter in models of the production of commodities.
5. A claim that certain capital-theoretic paradoxes are (usually?) only transient in the very long-run, secular time.
6. The discovery and presentation of certain generic structures in parameter spaces, associated with qualitative change in the analysis of the choice of technique. This is the broadest claim in my series of papers.

I do not imagine that Christian Bidard, Heinz Kurz, Neri Salvadori, Bertram Schefold, or Ian Steedman, for example, would be surprised by the first two or three bullet points. I concentrate on producing concrete numerical illustrations. I do not expect ever to state the fifth and sixth point with full mathematical rigor. I know the fifth point cannot be completely general.

Richest Man In The World Kills Hundreds Of Thousands, Will Kill Millions

This post is current events.

I refer to the illegal and unconstitutional elimination of United States Agency for International Development (USAID). This agency was eliminated by the unelected, nazi-saluting Elon Musk, working for the traitor Donald Trump.

Some documentation:

• Cavalcanti et al., 30 June 2025. Evaluating the impact of two decades of USAID interventions and projecting the effects of defunding on mortality up to 2030. The Lancelet.
• Malone. 31 May 2025. Bono criticizes USAid cuts in lengthy interview with podcaster Joe Rogan. Irish Times.
• Ensor. 30 May 2025. DOGE cuts to USAID blamed for 300,000 deaths ' most of them children. The Times.
• Donati et al. 16 May 2025. US aid cuts leave food for millions mouldering in storage. Reuters.
• Belz. 8 May 2025. Aid cuts could disrupt historic drops in child and maternal mortality. Christianity Today.
• Colarossi. 30 March 2025. "It's unacceptable": BU mathematician tracks how many deaths may result from USAID, Medicaid cuts. The Brink.