Wednesday, January 01, 2025
Welcome
The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.
In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.
I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.
Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.
Friday, April 16, 2021
Fluke Switch Points in Pure Fixed Capital Systems
I have a working paper at the Centro Sraffa.
Abstract: This article considers structural economic dynamics, in models with fixed capital and a choice of technique, of the production of commodities. Fluke switch points are described and cataloged. For fluke switch points, parameter perturbations create a qualitative change in how the choice of technique varies with distribution. Techniques are presented for visualizing partitions of parameter spaces such that the analysis of the choice of technique does not vary within each region. Implications are drawn about the choice of the truncation of the operation of (or the economic life of) machines and about the adoption of roundabout techniques.
Wednesday, April 14, 2021
Algebraic Geometry
An Introduction to Algebraic Geometry |
I have been looking for fluke switch points in certain parameter spaces of coefficients for polynomial equations. Bertram Schefold has pointed out to me that I may want to look into algebraic geometry. This may be beyond me. I consider what I have been doing as exploratory mathematics, and I have been relying on numerical algorithms. I started with thinking that there is a parallel to bifurcation theory. But Barkley Rosser convinced me that I should not use that terminology without an explicit dynamic system, presumably of market prices. These two threads on Math Overflow suggest I might want to look at Bertrametti et al. Lectures on Curves, Surfaces and Projective Varieties. I need a physical book for this, I think, not just a PDF.
Saturday, April 03, 2021
Flummery From Robert A. Heinlein
He had been droning along about 'value,' comparing the Marxist theory with the orthodox 'use' theory. Mr. Dubois had said, 'Of course, the Marxian definition of value is ridiculous. All the work one cares to add will not turn a mud pie into an apple tart; it remains a mud pie, value zero. By corollary, unskillful work can easily subtract value; an untalented cook can turn wholesome dough and fresh green apples, valuable already, into an inedible mess, value zero. Conversely, a great chef can fashion of those same materials a confection of greater value than a commonplace apple tart, with no more effort than an ordinary cook uses to prepare an ordinary sweet.'
'These kitchen illustrations demolish the Marxian theory of value — the fallacy from which the entire magnificent fraud of communism derives — and to illustrate the truth of the common-sense definition as measured in terms of use.'
Dubois had waved his stump at us. 'Nevertheless — wake up, back there! — nevertheless the disheveled old mystic of Das Kapital, turgid, tortured, confused, and neurotic, unscientific, illogical, this pompous fraud Karl Marx, nevertheless had a glimmering of a very important truth. If he had possessed an analytical mind, he might have formulated the first adequate definition of value... and this planet might have been saved endless grief.'
-- Robert A. Heinlein, Starship Troopers
I think this sufficient demonstration that Heinlein's ignorant character is attacking a straw person.
Saturday, March 27, 2021
Elsewhere
The Banach-Tarski Paradox |
- The Hahn-Banach theorem is related to how mainstream economics model perfect competition. The video above is mind-bending math.
- The Mountain Goat blog.
- A profile of some economists at Berkeley, some of who I have read when they collaborated with Thomas Piketty or A. Dube. I have read deLong, as well, of course.
- If you cannot name 'capitalism', 'neoliberalism', or 'neoclassical economics', it is difficult to criticize them. Here is a popular account about right-wingers crying about researchers daring to use such terms.
- I conclude with a recent talk, below, by Yanis Varoufakis on the need for pluralism in economics. He argues, at least (I still have more to watch):
- Economic theory can be performative, counter-performative, or reflexive (without using those terms).
- Time, money, debt, and interest rates do not appear in the models in the textbook.
- Markets can exist without a society being capitalist.
- Once you have learned all these models that have nothing to say about capitalism, you might possibly say something intelligent.
Yanis Varoufakis: From an economics without capitalism to markets without capitalism. |
Saturday, March 20, 2021
The Production Function In A Discrete Technology
Figure 1: Isoquants For The Production Function |
I often assume a discrete technology in my demonstrations that what many mainstream economists teach is mostly incoherent balderdash. Some incompetents have told me that such well-established results "just show that the particular production functions that you have chosen don't work. This is not a generic result." So, for my amusement, I will go through a simple example here to explain how any continuously differentiable production function can be approximated arbitrarily closely by the production function for a discrete technology.
By the way as far as I know, capital-reversing is consistent with continuously differentiable production functions. Does the late Emmanuel Farhi's work on this theme make progress on Wolfgang Eichert's work? I sometimes worry that a serious exploration by a mainstream economist of the Cambridge capital controversy would lead to psychological depression.
2.0 The ModelI consider a single sector of an economy where, say, Q tons steel are manufactured from inputs of labor and iron. The managers of firm know of S processes for producing steel, where each process is characterized by an ordered pair of coefficients of production. That is, the technology for making steel, T, is defined as:
T = { (a_{0}(s), a(s)) | s = 1, 2, ..., S }
In the sth process, the services of at least a_{0}(s) person-years of labor and a(s) tons iron must be applied for every ton steel produced.
With only two inputs, I can assume that labor coefficients are ordered to be increasing:
0 < a_{0}(1) < a_{0}(2) < ... < a_{0}(S)
And that iron coefficients are decreasing:
a(1) > a(2) > ... > a(S) > 0
With this specification of technology, one can formulate a linear program (LP). Let L be the person-years of labor available to this firm, and let X be the tons of iron available. Define q_{1}, q_{2}, ..., q_{S} to be the tons steel produced with each of the S processes. Consider the following LP:
Given T, L, and X, choose q_{1}, q_{2}, ..., q_{S}
To maximize Q = q_{1} + q_{2} + ... + q_{S} such that
a_{0}(1) q_{1} + a_{0}(2) q_{2} + ... + a_{0}(S) q_{S} ≤ L
a(1) q_{1} + a(2) q_{2} + ... + a(S) q_{S} ≤ X
q_{1} ≥ 0, q_{2} ≥ 0, ..., q_{S} ≥ 0
Let the solution of this LP be:
Q = F(L, X)
Then F is the production function for steel production.
3.0 Selected Properties of a Production FunctionA production function as defined above exhibits constant returns to scale (CRS). Figure 1, at the top of this post, displays isoquants for a particular technology with S equal to four. Any point in the interior of the line seqment between (a_{0}(1) Q, a(1) Q) and (a_{0}(2) Q, a(2) Q), for example, is a switch point. The extremes are non-switching points, where only one process in the technology is operated.
Figure 2 graphs the output of steel as a function of the labor input, given a specified quantity of iron available for input. The physical marginal product is shown below. The marginal product is non-increasing. The horizontal steps are non-switching points, and the vertical jumps occur at switch points.
Figure 2: The Marginal Product Of Labor |
In this example, labor and iron inputs are treated formally the same. So, as Figure 3 shows, the graph of the output of steel as a function of the iron input, and of iron's physical marginal product, look qualitatively the same as the output of steel as a function of the labor input.
Figure 3: The Marginal Product Of Iron |
Linear programming, as I understand it, is not taught as introductory mathematics. On the other hand, one can explain the above graphs without knowledge of calculus. Are there still recent introductory textbooks for microeconomics with graphs like the above?
4.0 ConclusionsOne can generalize the above to consider a production function for more than two inputs. The processes will not be ordered as above, and isoquants would be graphed in a higher dimensional space. Another generalization would consider multiple production funtions, one for each sector, with given prices for the produced outputs. Given endowments for inputs, also known as 'factors of production', the dual problem assigns shadow prices to the inputs. Also, endowments are not given in long-period models.
References- Eichert, Wolfgang. 2014a. Long-period positions in multi-sectoral Cobb-Douglas economies. Metroeconomica 65 (1): 136-153.
- Eichert, Wolfgang. 2014b. Technological Change in Multi-Sectoral Economies: Theoretical Change in Multi-Sectoral Economies. Doctoral thesis, University of Graz.
- Pasinetti, Luigi L. 1977. Lectures on the Theory of Production. New York: Columbia University Press.
Tuesday, March 16, 2021
Private Truths, Public Lies In Mainstream Economics?
I sometimes wonder if most mainstream economists think that most of what they were taught, teach, and research are some combination of false, incoherent, and useless for understanding actually existing capitalism. But they go along out of some sense of professionalism and a belief that their colleagues do not share their views. That is many privately think they are a minority of one, but publically espouse the orthodoxy.
As far as professionalism goes, I suppose some believe that those who go on from their microeconomics class, for example, are expected to have been exposed to certain material. I would hope that some question the ethics of not letting the students know that they are being taught one approach, named marginalism, and other approaches exist.
Maybe one of these days, I will read Timur Kuran's book.