Privacy Policy

Privacy Policy for http://theoryeconomic.blogspot.com/

If you require any more information or have any questions about our privacy policy, please feel free to contact us by email at ismadoni@gmail.com.

At http://theoryeconomic.blogspot.com/, the privacy of our visitors is of extreme importance to us. This privacy policy document outlines the types of personal information is received and collected by http://theoryeconomic.blogspot.com/ and how it is used.

Log Files
Like many other Web sites, http://theoryeconomic.blogspot.com/ makes use of log files. The information inside the log files includes internet protocol ( IP ) addresses, type of browser, Internet Service Provider ( ISP ), date/time stamp, referring/exit pages, and number of clicks to analyze trends, administer the site, track user’s movement around the site, and gather demographic information. IP addresses, and other such information are not linked to any information that is personally identifiable.

Cookies and Web Beacons
http://theoryeconomic.blogspot.com/ does use cookies to store information about visitors preferences, record user-specific information on which pages the user access or visit, customize Web page content based on visitors browser type or other information that the visitor sends via their browser.

DoubleClick DART Cookie
.:: Google, as a third party vendor, uses cookies to serve ads on http://theoryeconomic.blogspot.com/.
.:: Google's use of the DART cookie enables it to serve ads to users based on their visit to http://theoryeconomic.blogspot.com/ and other sites on the Internet.
.:: Users may opt out of the use of the DART cookie by visiting the Google ad and content network privacy policy at the following URL - http://www.google.com/privacy_ads.html

Some of our advertising partners may use cookies and web beacons on our site. Our advertising partners include ....
Google Adsense


These third-party ad servers or ad networks use technology to the advertisements and links that appear on http://theoryeconomic.blogspot.com/ send directly to your browsers. They automatically receive your IP address when this occurs. Other technologies ( such as cookies, JavaScript, or Web Beacons ) may also be used by the third-party ad networks to measure the effectiveness of their advertisements and / or to personalize the advertising content that you see.

http://theoryeconomic.blogspot.com/ has no access to or control over these cookies that are used by third-party advertisers.

You should consult the respective privacy policies of these third-party ad servers for more detailed information on their practices as well as for instructions about how to opt-out of certain practices. http://theoryeconomic.blogspot.com/'s privacy policy does not apply to, and we cannot control the activities of, such other advertisers or web sites.

If you wish to disable cookies, you may do so through your individual browser options. More detailed information about cookie management with specific web browsers can be found at the browsers' respective websites.

Austrian Insights into Public-Choice Theory

Public choice can be defined as the application of economic theory and methodology to the study of politics and political institutions, broadly defined. Neoclassical price theory has been one of the principal tools of the public-choice theorist, having been applied to address such questions as why people vote, why bureaucrats bungle, the effects of deficit finance on government spending, and myriad other questions regarding the operations and activities of governments.

There has indeed been a public-choice "revolution" in economics. But neoclassical price theory has its limitations, many of which have been investigated by Austrian economists. These limitations have implications for the study of public choice. Namely, if neoclassical price theory is itself flawed, then perhaps its applications to the study of political decision-making have produced uncertain results.

In this article, I shall explore two strands of Austrian economics — theories of competition and of entrepreneurship — and their implications for public-choice theory. I do not claim to provide an exhaustive examination of public-choice theory from an Austrian perspective, but only to offer a few insights.

The first section notes some limitations of applying the neoclassical competitive model to the study of political decision-making. The next discusses the implications of placing more emphasis on the role of political entrepreneurship in the study of public choice. The final section contains a summary and conclusions.

Stephen Williamson, Fool or Knave?

Stephen Williamson quotes Narayana Kocherlakota, apparently a very stupid person:

"Kocherlakota says this...:

'But over the long run, money is, as we economists like to say, neutral. This means that no matter what the inflation rate is and no matter what the FOMC does, the real return on safe short-term investments averages about 1-2 percent over the long run.'

Again, uncontroversial." -- Stephen Willaimson

This, of course, is false. Communities of economists exist who set their theories in historical time and dispute that money is neutral in any run. I prefer to point to Post Keynesians, but Austrian School economists satisfy these criteria also. Furthermore, economists within such schools surpassed mainstream economists in the current historical conjuncture by having pointed out the possibility of the global financial crisis before its occurrence.

I think economists should strive not to tell untruths abouts what economists believe.

Why Income Inequality Leads To Recessionary Conditions

1.0 Introduction
Apparently, some have been discussing whether the gross increased inequality in the USA is connected with the depressionary conditions we are in. So I thought I would climb on my bicycle and do some arithmetic.

I take it as a stylized fact that an increase in inequality is associated with an increase in the average and marginal propensity to save.

There's something called the Harrod-Domar model of growth. I'm not sure I've ever read Domar. I've certainly read more of Harrod than I have of Domar. So in the sequel, I refer exclusively to Harrod.

Harrod defined three rates of growth: the actual rate, the warranted rate, and the natural rate. Increased inequality can result in the warranted rate exceeding the natural rate. Since the warranted rate is unstable and the actual rate cannot long exceed the natural rate, increased inequality is likely to lead to the actual rate of growth falling below and away from the warranted rate, that is, to depressions.

2.0 Harrod's Model
Harrod's model is fairly simple, but it raises deep questions.

2.1 The Actual Rate
Along a steady state growth path, the ratio, v, of the value of capital to the value of net income is constant:

v = K/Y,

where K is the value of the capital stock, and Y is the value of net income. v is known as the capital-output ratio. Thus:

dY/dt = (1/v) dK/dt

Investment, I, is defined to be the change in the value of capital with time. Hence,

(1/Y) dY/dt = (1/v) (I/Y)

The left-hand-side of of the above equation is, by definition, the rate of growth, g, of the economy. The equality of investment and savings is an accounting definition in a model with no foreign trade and no government. Therefore,

g = (1/v) (S/Y)

Define the savings rate, s:

s = S/Y

Then, a steady state growth ratio is the ratio of the savings rate to the capital-output ratio:

g = s/v

That is, the (actual) rate of growth is the quotient of the savings rate and the capital-output ratio.

2.2 The Warranted Rate
Suppose the savings rate and the capital-output ratio are as desired by income recipients (consumers) and firms, respectively. This defines Harrod's warranted rate of growth:

g_w = s_d/v_d

where the subscripts on the right hand side stand for "desired". The warranted rate of growth is being achieved when expectations are being realized and current actions are not setting up forces to disturb current expectations.

The warranted rate of growth extends Keynes' analysis to the long period. Consider the stability of a warranted growth path. If the actual rate of growth exceeds the warranted rate, capacity will be utilized at a greater rate than firms expected. They will increase investment faster than the warranted rate, and the rate of growth will deviate from the warranted rate even more. Likewise, if the actual rate falls below the warranted rate, firms will cut back on investment since the plans upon which their investment was made are not being realized. Hence, the warranted rate is unstable.

Harrod suggested that this instability of the warranted rate is more like an inverted flat-bottomed bowl than a knife-edge.

2.3 The Natural Rate
Suppose the labor force is initially fully employed. Let n be the rate of growth of the labor force:

n = (dL/dt)/L

Define the value of output produced per employed worker:

f = Y/L

Harrod-neutral technical change occurs when the value of output per worker grows at a constant rate, m, while the rate of profit stays unchanged:

m = (1/f) df/dt

Harrod-neutral technical progress implies that the productivity of labor is growing at the same rate in all industries.

Anyways, the following equation follows:

dY/dt = f dL/dt + L df/dt

Some algebra yields:

(1/Y) (dY/dt) = ( 1/L) (dL/dt) + (1/f) (df/dt)

The left hand side of the above equation is the rate of growth that keeps the labor force fully employed (or a constant percentage unemployed). Harrod calls this the natural rate of growth. Hence, assuming Harrod-neutral technological progress, the natural rate of growth is the sum of the rate of growth of the labor force and the rate of growth of labor productivity.

g_n = n + m

3.0 Conclusions
Notice that the determinants of the warranted rate of growth - the savings rate and the desired capital-output ratio - are taken as exogeneous constants. The determinants of the natural rate of growth - the growth of the labor force and Harrod-neutral technological progress - are also given. Hence, the warranted and natural rates can only be equal by a fluke.

Solow, following up on some work by Pivlin, suggested that the desired equality between the warranted and natural rates can be brought about by considering the capital-output ratio as a well-behaved function of the rate of interest. Divergences between the two rates can be corrected by variations in the distribution of income. This approach of neoclassical macroeconomics is exemplified in Solow's eponymous growth model, but it has been shown to be not well-founded in the Cambridge Capital Controversy.

If the warranted rate is below the natural rate, a moderate increase in the saving rate is desirable if the economy is exhibiting boom-like conditions. This would bring the warranted rate towards the actual rate of growth while still keeping it below the natural rate of growth.

Notice that when the warranted rate exceeds the natural rate, the economy must sometime fall below the warranted rate. The natural rate sets a limit which the economy cannot long exceed. Because of the instability of the warranted rate, such an economy will experience frequent and perhaps prolonged recessionary conditions. Since increased savings intensify the discrepancies between the warranted and natural growth rates under these conditions, increased savings intensify the frequency and severity of recessions. That is, increased inequality can intensify the frequency and severity of recessions.

References

• A. Asimakopulos (1991) Keynes's General Theory and Accumulation, Cambridge.
  1991
• Roy F. Harrod (1948) Towards a Dynamic Economics, Macmillan.
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.

Barnett's Fried Apples

Ingredients

4 Tablespoons butter
1 #2 can sliced apples or 2 1/2 cups fresh apple
1/8 teaspoon salt
1/4 cup sugar
Cinnamon to taste

1) Peel and core apples.

2) Melt butter in iron skillet. Add apples, salt, sugar, and cinnamon. (I'm generous with the cinnamon.)

3) Fry until soft, between low and medium heat about 1/2 hour. (Do not fry dry.)

Makes approximately 3 servings. (I like them served with pork chops.)

That You Should Listen To Mainstream Economists...

... seems often to me to be the main point of many mainstream economists these days. I deliberately don't write, "Why you should listen..." Somebody as stupid as Kartik Athreya, a PhD. with the research department of the Federal Reserve Bank of Richmond, appears to be doesn't deal in arguments. I also see this sort of babble in recent posts by Frances Woolley, and Mike Moffat. (See also Nick Rowe's comments to those posts.)

(I, of course, have read papers making points along Colander's line.)

Jeffrey Miron And Propertarian Advocacy Taught At Harvard

Jeffrey Miron teaches EC1017 at Harvard. "A Libertarian Perspective on Economic and Social Policy" is the course title, and PDFs for the lectures are available for download.

Based on the notes for the three lectures I looked at, Miron supposedly derives propertarian policy from intermediate principles (e.g., "efficiency"), with little to no data on relative magnitudes. I don't care for this approach myself, never mind the policy conclusions. He seems to mention no names. The reading list (from Spring 2009) does not include his book (which I haven't read). Perhaps Miron's experience is that Harvard students can be counted on to bring up Rawls, Karl Popper's piecemeal social engineering, Alan Haworth, and even Nozick.

"When Adam Delved And Eve Span, Who Was Then The Gentleman?"

I had associated the title of this post with the 17th century and the period of the English Civil War. I think it occurs somewhere in Christoper Hill's The World Turned Upside Down: Radical Ideas During the English Revolution. Hill's book is an account of Anabaptists, Diggers, Levellers, Muggletonians, the New Model Army, Ranters, and Quakers - a very heady and confusing mix.

So I was startled yesterday to read the phrase in Crispin: The Cross of Lead. This is a Newberry-prize winning children's book, by Avi. It is set in England in the 14th century. I think it conveys a good idea of the drudgery and isolation of village life at the time; the seemingly unchangable hierarchy; and the bustle, confusion, and filth of a city before modern plumbing. I also like that Christianity is presented as a form of life, a language that all we see cannot but help using.

So is Avi's use of the phrase an anachronism? Hill may reference it, but, if so, the people of his time were harking back to a previous one. Apparently, the phrase is associated with John Ball, the leader of the 1381 Peasants’ Revolt. I know nothing about the Peasants’ Revolt, although Hill does refer to it in one line. But John Ball does appear in Avi’s book. Crispin, our thirteen-year old hero, overhears him conspiring. John Ball says:

"...that no man, or woman either, shall be enslaved, but stand free and equal to one another. That all fees, obligations, and manorial rights be abolished immediately. That land must be given freely to all with a rent of no more than four pennies per acre per year. Unfair taxes must be abolished. Instead of petty tyrants, all laws shall be made by consent of a general commons of all true and righteous men.

Above all persons, our lawful king shall truly reign, but no privileged or corrupt parliaments or councilors.

The church, as it exists, should be allowed to wither. Corrupt priests and bishops must be expelled from our churches.. In their place will stand true and holy priests who shall have no wealth or rights above the common man..."

Update: I've learned a new vocabulary word: A Jacquerie is a peasants' revolt, named after the French peasants' revolt of 1358.

Infinities Of Infinities

1.0 Introduction

This is mathematics, not economics. It is meant to be an introduction to how abstract mathematicians can be.

2.0 Some Definitions for Set Theory

Two sets are the same size if and only if they can be put into a one-to-one correspondence with each other.

A set S₁ is bigger than the set S₂ if and only if:

• A subset of S₁ can be put into one-to-one correspondence with S₂, and
• S₂ cannot be put into one-to-one correspondence with S₁.

A set is countably infinite if and only if it can be put into one-to-one correspondence with the set of natural numbers N = {0, 1, 2, ...}. (The integers and the rational numbers are both countably infinite.)

The power set P(S) formed from the set S is the set of all subsets of S. For example, the power set for the set {a, b} contains four elements:

P( {a,b} ) = {S | S ⊂ {a, b}.} = { ∅, {a}, {b}, {a, b} }

3.0 A Theorem

Theorem For all sets S, the power set P(S) is bigger than the set S.

Proof: First, show that a subset of P(S) can be put into one-to-one correspondence with S. Consider the set of singletons:

{ {a} | a is an element of S }.

Since each singleton {a} is a subset of S, the set of all singletons is a subset of P(S). And the set of all singletons maps one-to-one to S.

Next, show, by a proof by contradiction, that P(S) cannot be put into one-to-one correspondence with S. Suppose that there exists a one-to-one function f that maps S into P(S).

Notice that, for all a ∈ S, f(a) is a subset of S. For any given a in S, either

a ∈ f(a)

or

a ∉ f(a).

Define the set T to be the set of all elements in S that map under f to a set not containing themselves:

T = { a | a ∈ S and a ∉ f(a)}

Since f is one-to-one and T is a (possibly empty) subset of S, there exists, by hypothesis, an element b in S such that

f(b) = T.

Now consider whether or not

b ∈ T.

Suppose true. But, by the definition of T as the set of elements of S that are not elements of the subset of S that they map to, b cannot be in f(b), that is, T. But, if b is not in f(b), by the definition of T, b must be in T. So either way yields a contradiction. Thus, no such b can exist.

So I have shown that there does not exist an element b in S that maps under f to T. Yet T is in P(S). Thus, f cannot be one-to-one. Which was to be demonstrated.

4.0 Applying the Theorem to the Set of Natural Numbers

An interesting property of the above proof is that it applies to both finite sets and infinite sets. So start with N, the set of natural numbers. N contains an infinite number of elements. But, by the theorem, P(N), the set of all subsets of the natural numbers, is a set containing a bigger infinity. One can go on to form a set of infinite sets, each with a bigger size infinity:

U₀ = { N, P(N), P(P(N)), ..., Pⁿ(N), ...}

(Under the Zermelo Frankel axioms for set theory, the elements of a set do not need to all be of the same "type".) One can repeat the process of forming a sequence of power sets:

U₁ = { U₀, P(U₀), P(P(U₀)), ..., Pⁿ(U₀), ...}.

One can even imagine constructing a power set of all these difference size infinite sets in this sequence of sequences of sets:

P( { U₀, U₁, U₂), ...} )

The definitions of infinite sets need not stop here.

4.0 Conclusion
I don't find the above hard to follow if I think of it as merely a matter of syntactic manipulation of symbols. Do I have a clear idea of these infinities of different size infinities after every point in this sequence of definitions? Does anybody? This is not so clear to me.

Reference

• Paul R. Halmos (1960) Naive Set Theory, Springer Verlag

Onieda-Like Community Near Stroud, In Gloucestershire?

Martin Gardner once received a letter referring to "an Oneida-like community near Stroud, in Gloucestershire". The topic of the letter was something else, on visualizing four-dimensional space. Can anybody provide me with more information on this community?

Full Unemployment

I find amusing the political slogan with which I title this post. We want the engineers to do their job in applying control theory to stepping motors, in creating Artificial Intelligences, in developing techniques of information management, etc. such that nobody need work out of necessity. Maybe in some future day, machinery will produce all we need, including more machinery. When the economic problem is solved:

"Man will be faced with his real, his permanent problem - how to use his freedom from pressing economic cares, how to occupy the leisure, which science and compound interest will have won for him, to live wisely and agreeably and well." -- John Myanard Keynes (1930)

Marx and Engels envision a post-capitalist society:

"Where nobody has one exclusive sphere of activity, but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic. -- Karl Marx (1947, p. 22)

Bruce Sterling (1989) imagines that, in such a world, one will cultivate ones taste for "The Beautiful and the Sublime". At any rate, in this pleasant world of tomorrow, all will be able to devote themselves to great cooking, fostering social relationships, art, or whatever one may choose.

Curiously enough, the classical tradition in economics, as exemplified, for example, in Sraffa or Von Neumann, provides tools for analyzing how prices might be formed in a post-scarcity world. For example, Joan Robinson, in her first essay in (Robinson 1962) has a section titled "A model for the future" with a subsection on "The Robots". This is a model of a (maybe impossible) capitalist economy. In my version, all production is carried out in automated factories, and these factories are owned by firms traded on a stock exchange. Everybody owns shares, and the trading of these shares sets up a tendency torwards a uniform rate of profits.

I have described before some formulation of a price system consistent with this institutional set up. For now, I want to describe prices when the managers of each firm in an industry have chosen a process for producing the firm's output. As usual, I assume, for simplicity that all processes require the same time to operate, say, a year. Inputs must be purchased at the beginning of the year, and outputs become available at the end of the year. A reference set of prices satisfies the following system of equations:

p A β = p B

where

• A is a square matrix; a_i,j is the quantity of the ith commodity used as input when the jth process is operated at a unit level.
• B is a square matrix; b_i,j is the quantity of the ith commodity produced as output when the jth process is operated at a unit level.
• p is a row vector of prices; p_i is the price of the ith commodity.
• (β - 1) is the rate of profits.

This formulation allows for robots to last for more than one year. The quantity of a dated robot enters as an input, and the output includes a robot one year older, as well as whatever other outputs are produced by that process. The use of such robots is a special case of the more general model of joint production encapsulated in the above system of equations.

Various conditions must be imposed on the coefficients of production A and B to ensure a solution simultaneously exists for prices and the dual problem of the choice of technique. Von Neumann, in fact, assumes that each commodity is either used as an input or produced as an output in a poisitive amount in each process. Joan Robinson assumes the existence of "some standard physical elements (say, nuts and bolts) that enter into the production both of robots and of salable goods." But I do not want to discuss more of the mathematics in this post.

References

• D. G. Champernowne (1945-1946) "A Note on J. v. Neumann's Article on 'A Model of Economic Equilibrium'", Review of Economic Studies, V. 13, N. 1: pp. 10-18.
• John Maynard Keynes (1930) "Economic Possibilities for our Grandchildren", in Essays in Persuasion, W. W. Norton & Company
• Karl Marx and Frederick Engels (1947) The German Ideology: Parts I & III, International Publishers
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.
• Piero Sraffa (1960) , Cambridge University Press.
• J. v. Neumann (1945-1946) "A Model of General Economic Equilibrium", Review of Economic Studies, V. 13, N. 1: pp. 1-9.
• Bruce Sterling (1989) Crystal Express, Ace Books

Nortz's Johnny Cake

Ingredients

1/4 cup sugar
1/3 cup shortening
1 beated egg
1 cup sour milk
1 teaspoon baking soda
1 teaspoon baking powder
1 cup flour
1 1/2 cup cornmeal
1/2 teaspoon salt

1) Mix in above order, stirring thoroughly after adding each ingredient. Bake about 1/2 hour at 400 F.

2) Serve sliced with applesauce or maple syrup.

Makes approximately 10 servings. I usually make a double recipe when making my great-grandmother's Johnny cake.

Phenomenology

"One of the embarrassing dirty little secrets of economics is that there is no such thing as economic theory properly so-called. There is simply no set of foundational bedrock principles on which one can base calculations that illuminate situations in the real world." -- Brad DeLong

My title does not refer to an approach in continental philosophy associated with Husserl and Heidegger. Rather, I refer to a term used in physics and engineering by practitioners who know they are not trying to develop models derived from fundamental laws, but only modeling the phenomena.

I find it of interest that Brad DeLong has recently described economics as phenomenology. A noted "rocket scientist" on Wall Street came to the same conclusion:

"The techniques of physics hardly ever produce more than the most approximate truth in finance because 'true' financial value is itself a suspect notion. In physics, a model is right when it correctly predicts the future trajectories of planets or the existence and properties of new particles, such as Gell-Mann's Omega Minus. In finance, you cannot easily prove a model right by such observation. Data are scarce and, more importantly, markets are arenas of action and reaction, dialectics of thesis, antithesis, and synthesis. People learn from past mistakes and go on to make new ones. What's right in one regime is wrong in the next.

As a result, physicists turned quants don't expect too much from their theories, though many economists naively do. Perhaps this is because physicists, raised on theories capable of superb divination, know the difference between a fundamental theory and a phenomenological toy, useful though the latter may be. Trained economists have never seen a really first-class model. It's not that physics is 'better', but rather that finance is harder. In physics you're playing against God, and He doesn't change his laws very often. When you've checkmated Him, He'll concede. In finance, you're playing against God's creatures, agents who value assets based on their ephemeral opinions. They don't know when they've lost, so they keep trying." -- Emanuel Derman (2004) My Life as a Quant: Reflections on Physics and Finance, John Wiley & Sons.

I think one can read intimations of Soros' reflexitivity or Joan Robinson's historical time in the above quote. Derman is even more direct about a Post Keynesian concept elsewhere:

"Slowly it began to dawn on me that what we faced was not so much risk as uncertainty. Risk is what you bear when you own, for example, 100 shares of Microsoft - you know exactly what those shares are worth because you can sell them in a second at something very close to the last traded price. There is no uncertainty about their current value, only the risk that their value will change in the next instant. But when you own an exotic illiquid option, uncertainty precedes its risk - you don't even know exactly what the option is currently worth because you don't know whether the model you are using is right or wrong. Or, more accurately, you know that the model you are using is both naive and wrong - the only question is how naive and how wrong." -- Emanuel Derman (2004)

Jacob Schwartz (9 January 1930 - 2 March 2009)

Jacob T. Schwartz was a mathematician at the Courant Institute of Mathematical Sciences at New York University. He once gave a series of lectures on mathematical economics, published as Lectures on the Mathematical Method in Analytical Economics, Gordon and Breach (1961). This book, coming out a year after Sraffa's work, seems to very little known. Its findings parallel Sraffa's in many ways:

"Our interest...will...be...in the use of the input-output model as a framework for ...abstract economic analysis." (p. 8)

"If each time labor appears as an input in production we replace this input by the corresponding real wage bill, we come to a hypothetical situation in which the only inputs required for the production of commodities are other (non-labor) commodities. Thus we may, if it is convenient for one or another theoretical purpose, consider our model to refer to a self-enclosed world of material commodities, produced out of each other with no additional input." (p. 10)

"The proper conclusion at this point is that the rate of profit ρ is not successfully determined by the Walrasian theories from considerations of production coefficients, utility functions, and so forth. What our analysis shows, in fact, is that the determination of the rate of profit is not purely a question of economics at all, but is rather a social-political question involving, among other things, union-management relations, pressures, and counterpressures, etc. Thus an initial skepticism about classical equilibrium analysis is justified. What this analysis aims to give us is a set of prices. But all the price-ratios are already determined by a small part of the theory, to wit by the competitive equality of profit rates. All that remains to be determined on the score of prices, is the rate of profit - but, as we have just seen, the Walrasian determination of this rate is questionable... What are determined more successfully are the amounts of production - but this is more a humble matter of consumption habits at given prices than a highly recondite matter of consumption schedules at a variety of hypothetical prices." (pp. 196-197)

"As our analysis in Lecture 16 shows, as long as we assume a fixed scheme of production the Keynesian conclusion that wage cuts by lowering wage-generated commodity demand must lower demand for labor is inescapable. The neoclassical contention thus depends on the possibility of shifts in the production scheme; a conclusion which the neoclassicist would be the first to emphasize, since the whole apparatus of neoclassical theory, revolving about the notion of marginal product accruing to an increment of each input facor, does in fact center on an analysis of variations in production. This means that the equilibrium analysis of Lecture 16 has come to such distinctly Keynesian conclusions as it has only by assuming away the basis for the neoclassicist's argument. At the present point, therefore, we shall attempt to generalize the analysis of Lecture 16 to include the possibility of shifts in the production scheme, hoping to estimate the extent to which such shifts are likely to affect our earlier conclusions." (p. 239)

"We may at this point remark once more that our analysis of prices shows that even in the framework of the present general model [with a choice of technique] price ratios are determined up to a single parameter from the conditions of production. As we have emphasized in the final paragraph of Section 1, Lecture 3, this conclusion constitutes strong presumptive evidence against theories which attempt to tie prices to consumer demand. More generally, we see that by allowing variation in the scheme of production, we in fact introduce no changes in the fixed-matrix Leontief model other than to make the Leontief matrices dependent on the [rate of profits]." (p. 248)

I prefer Sraffa's book partly on the basis of style.

Quantity Flows For Structural Dynamics

1.0 Introduction
This post presents an example of a model of structural economic dynamics. I consider what quantity flows would arise for an economy in which agents make decisions in which the economy smoothly reproduces. The solution for this exercise turns out to be dynamically unstable in the special case I use for illustration. I think this means that, if I solve this special case in a future post for one way of setting out the price system, the solution for prices will be stable. The model presented in this post illustrates the difficult discovery problems that are solved in successful economies.

2.0 Technology
This economy consists of two sectors. In the first sector, labor produces means of production with existing means of production. In the second sector, labor produces means of consumption with existing means of production. (I use steel as as a synecdoche for means of production and corn for means of consumption.) The technique in use in both sectors exhibits Constant Returns to Scale (CRS). Only circulating capital is modeled; the means of production are entirely consumed in producing the output. Table 1 shows the coefficients of production for the technique in use during the t-th year.

Table 1: The Technology

	Steel Industry	Corn Industry
Labor	a0,1(t) person-years	a0,2(t) person-years
Steel	a1,1(t) tons	a1,2(t) tons
Outputs	1 ton steel	1 bushel corn

The technique improves each year. That is, each coefficient of production decreases at a constant rate of 100 c_i,j percent per year:

[a_i,j(t) - a_i,j(t + 1)]/a_i,j(t) = c_i,j

The above difference equation can be solved in closed form. The coefficients of production evolve as:

a_i,j(t) = a_i,j(0) (1 - c_i,j)^t

A more complex formulation might have non-constant percentage rates of decrease in the coeffients of production. For example, the percentage rate of decrease might be larger if the level of output of an industry was larger. Then one would be modeling "learning by doing" or endogenous growth, following in the tradition of Nicholas Kaldor and Kenneth Arrow. (Mainstream economists would cite Paul Romer's confused balderdash.)

3.0 Conditions for Smooth Reproduction
Let q₁(t) and q₂(t) be the tons of steel and the bushels of corn, respectively, produced as output and available at the end of the t-th year. I want to consider the case in which the labor force is always fully employed, the proportions in which output is produced always turns out to be appropriate, and no excess capacity is ever created.

The gross output of corn each year is divided up between the workers and the capitalists and then consumed. The gross outputs of steel and corn in a given year determine, along with the coefficients of production, how much steel should have been produced in the previous year:

q₁(t - 1) = a_1,1(t) q₁(t) + a_1,2(t) q₂(t)

The amount of labor employed in the t-th year is:

L(t) = a_0,1(t) q₁(t) + a_0,2(t) q₂(t),

where L(t) is the person-years of labor employed. In a general formulation, one might model the number of workers growing each year, but with increased productivity being taken partly in the form of decreased working hours per worker. For simplicity, I here model the labor force as a given constant:

L(t) = L^*

The above equations specify a dynamic system. An initial condition needs to be specified for any solution path to be completely determined. I take the initial ratio of employment in the two sectors as a given parameter:

a_0,1(0) q₁(0)/a_0,2(0) q₂(0) = h

The model can be simplified by expressing one quantity flow in terms of other by use of the condition that labor is fully employed. Some algebraic manipulation yields a single difference equation for the output of steel:

q₁(t) = [a_1,2(t) L^* - a_0,2(t) q₁(t - 1)]/d(t),

where

d(t) = [a_0,1(t)a_1,2(t) - a_0,2(t)a_1,1(t)]

If the coefficients of production were constant, the above would be a linear difference equation. If I recall my mathematics correctly, linear systems either blow up; decay to an equilibrium; or, for coefficients meeting an exact balance, generate a constant wave.

4.0 The Solution of a Special Case
I tried a numerical experiment to increase my understanding of this dynamical system. Accordingly, I chose some specific values for the model parameters. Table 2 gives the initial coefficients of production. The difference equation for gross steel outputs is simplified in that the coefficients of production in a sector decrease at the same constant rate. I chose the following rates of decrease:

c_0,1 = c_1,1 = 1/20

c_0,2 = c_1,2 = 1/40

Let the labor force be unity:

L^* = 1

Finally, I carefully specified an initial condition:

a_0,1(0) q₁(0)/a_0,2(0) q₂(0) = 0.22335983

Table 2: The Initial Technology

	Steel Industry	Corn Industry
Labor	a0,1(0) = 1	a0,2(0) = 1
Steel	a1,1(0) = 1/10	a1,2(0) = 1/5
Outputs	1 ton steel	1 bushel corn

One can easily step through the first few years of the solution, thereby obtaining the start of a series for q₁(t) and q₂(t).The solution is dynamically unstable. I carefully chose the initial condition to get six years before the solution blows up. For the first five years, the output of steel grows over 3% and the output of corn grows over 14 1/2%, for a constant labor supply. This set of priorities is the reverse of what was typically achieved in no-longer actually existing socialism. When Imre Nagy, for example, tried to put Hungary on a new course, he was deposed. The distribution of labor, shown in Table 2, is not realistic for a developing capitalistic economy either. In practice, the labor force becomes steadily less concentrated in producing means of consumption and more in producing means of production. Still, I think, this model with a better choice of parameters and perhaps some generalizations can be quite interesting.

Figure 1: Dynamic Distribution of the Labor Force

References

• Karl Marx (1885) Capital, Volume 2
• Luigi L. Pasinetti (1977) Lectures on the Theory of Production, Columbia University Press
• Luigi L. Pasinetti (1983) Structural Change and Economic Growth: A Theoretical Essay on the Dynamics of the Wealth of Nations, Cambridge University Press
• Luigi L. Pasinetti (1993) Structural Economic Dynamics: A Theory of the Consequences of Human Learning, Cambridge University Press

To read:

• Dale W. Jorgenson (1960) "A Dual Stability Theorem", Econometrica, V. 28, N. 4 (October): pp. 892-899

Judt On The Influence Of The Austrian School

I continue to find writers characterizing Austrian school economists as influential.

I think some might quarrel with this description of the influence of the Austrian school on Chicago:

"We are the involuntary heirs to a debate with which most people are altogether unfamiliar. When asked what lies behind the new (old) economic thinking, we can reply that it was the work of Anglo-American economists associated overwhelmingly with the University of Chicago. But if we ask where the 'Chigago boys' got their ideas, we shall find that the greatest influence was exercised by a handful of foreigners, all of them immigrants from central Europe: Ludwig von Mises, Friedrich Hayek, Joseph Schumpeter, Karl Popper, and Peter Drucker." -- Tony Judt (2010) Ill Fares the Land, Penguin Press, pp. 97-98

I don't think differences in details (e.g., aggregation in economic models) adequately refutes Judt's point.

Judt does read, for example, Hayek as more nuanced than some of his followers:

"The intellectual refugees - and especially the economists among them - lived in a condition of endemic resentment toward their uncomprehending hosts. All non-individualist social thought - any argument that rested upon collective categories, common objectives or the notion of social goods, justice, etc. - aroused in them troubling recollections of past upheavals... Men like Hayek or von Mises seemed doomed to professional and cultural marginality. Only when the welfare states whose failure they had so sedulously predicted began to run into difficulties did they once again find an audience for their views: high taxation inhibits growth and efficiency, government regulation stifles initiative and entrepreneuship, the smaller the state the healthier the society and so forth.

Thus when we recapitulate conventional clichés about free markets and western liberties, we are in effect echoing - like light from a fading star - a debate inspired and conducted seventy years ago by men born for the most part in the late 19th century...

It is perhaps worth noting here that even Hayek cannot be held responsible for the ideological simplifications of his acolytes. Like Keynes, he regarded economics as an interpretive science, not amenable to prediction or precision. If planning was wrong for Hayek, this was because it was obliged to base itself on calculations and predictions which were essentially meaningless and thus irrational. Planning was not a moral misstep, much less undesirable on some general principle. It was simply unworkable - and, had he been consistent, Hayek would have acknowledged that much the same applied to 'scientific' theories of the market mechanism...

In the United States, among a younger generation of self-confident econometricians (a sub-discipline of whose bostful scientificity both Hayek and Keynes would have had much to say), the belief that democratic socialism is unachievable and has perverse consequences has become something close to a theology. This creed has attached itself to every effort to increase the role of the state - or the public sector - in the daily lives of American citizens." -- Tony Judt (2010): pp. 102-104

Orthodox Economists As Knavish Lickspittles

Bill Mitchell says:

"The mainstream economists hide behind lies. Most of the time they claim their policy recommendations are derived from economic theory. The reality is that they are not and economists lie and obsfucate.

There are many situations where strident policy suggestions – like the austerity packages – cannot be based on the economic theory that they are associated with – on the theories that economists use to give an air of authority and legitimacy to what are otherwise demands based on their blind ideology.

Unfortunately, the public is not in a position to judge and get swamped by the arrogance of economists..."

The arrogance of orthodox economists plays out in many ways. Philip Mirowski, for example, notes:

"But economists could not begin to discuss the major difference between 1929 and 2008: this time around, professional economists had played a much larger role in producing the conditions leading to systemic breakdown, from theorizing the financial innovations and staffing the financial institutions to justifying the deconstruction of regulatory structures held over from the last Great Depression. The profession did not entirely succeed in distracting public attention from that fact, either." -- Philip Mirowski, "The Great Mortification: Economists’ Responses to the Crisis of 2007–(and counting)", The Hedgehog Review, (Summer 2010)

And there is the matter of funding of inconvenient researchers. So we see Mirowski writing, "My home institution declined to provide any support for this research." And Jacob Hacker and Paul Pierson write something similar:

"The authors received no financial support for the research and/or authorship of this article."

Greg Mankiw seems always willing to demonstrate that he is a varlet. In his post labeled, "The Root Cause of the Crisis", he kowtows to another fool:

"According to Raghu Rajan: Skill-biased technological change, followed by ill-advised policies."

If an economist were honest, he could hardly continue to cite skill-biased technological change as a cause income distribution in the United States.

Simple Pepper Steak

Ingredients

3 Tbsps olive oil
1 sliced onion
2 sliced (green & red?) peppers
1 lb sandwich steak
1/2 tsp. salt
1/4 tsp. black pepper
3 Tbsps (ginger-flavored?) soy sauce

1) Fry sliced peppers and onions in olive oil over medium high heat about 7 minutes. (Variant: add chopped garlic clove.) Drain oil and lower heat.

2) Meanwhile, cut meat into 1 inch squares. Season with salt and pepper.

3) Add beef to fry pan. (Variant: consider adding additional spices, e.g. 1 tsp. thyme leaves.) Add soy sauce. Cook on low to medium about 10 minutes, stirring frequently.

4) Serve over boiled white rice.

Makes 2 or 3 servings

Congressional Testimony on Building a Science of Economics

The United States House of Representatives has a Committee on Science and Technology, with a Subcommittee on Investigations and Oversight. On Thursday, 20 July, they heard testimony about macroeconomics from Robert Solow, Sidney Winter, Scott Page, David Colander, and V. V. Chari. You can download the hearing charter, prepared statements, etc. I guess V. V. Chari's role is to defend the orthodox.

'Libertarian' Used Correctly

"Less World! More Bank!"

I have been reading Phil Edwards' 'More Work! Less Pay!' Rebellion and Repression in Italy, 1972-7 (Manchester University Press, 2009). He occasionally uses the word 'libertarian', for example:

"the group re-emerged within the 'area' as the Collettivi Politici Operai (CPO; 'Workers' Political Collectives'), opening itself to left-libertarian as well as Leninist influences." -- Phil Edwards (p. 69)

and in translating:

"The first, numerically in the majority, is the 'creative' wing, libertarians with radical leanings ... These are the 'small-a' autonomists, who at one time or another fight for a 'better quality of life' ... The second large strand is that of the professors, the intellectuals, the theorists of the message ... The third strand, finally, is that of the 'capital-A' autonomists, or Autonomia operaia organizzata ['Organised Workers' Autonomy']" -- M. Monicelli, L'ultrasinistra in Italia 1968-1978 (1978, Phil Edwards' translation)

Apparently, the custom of street performances at protests emerged from the area of autonomia. Antonio Negri was a member of the CPO. Perhaps activists in Detroit might consider the establishment of social centers (centri sociali) by squatting in abandoned buildings.

And Every Stinking Bum Should Wear A Crown

Why so much inequality in the United States? I have been reading Hacker and Pierson (2010). (I haven't yet read the commentaries, available for the moment.) I think I have previously made many of their points, as shown below. Hacker and Pierson present some striking graphs taken from work by Piketty and Saez. I reproduce two.

Figure 1: Richest 1 Percent's Share of National Pretax Income (Excluding Capital Gains) (Based on Piketty and Saez)

Figure 2: Average Actual Tax Incidence for Top Incomes (Based on Piketty and Saez (2007))

Anybody who still thinks the mainstream story of skills-biased technical change is a reasonable hypothesis is a feckless fop.

Given contract law and property law, government cannot leave the economy to itself. Policy has been driving increased inequality.

Another driver of increased inequality is a change in ideas and social norms. These include faulty ideas on corporate governance, incorrect theories of factor markets, and performative models of finance.

How did ideas that never had sound empirical and theoretical backing become dominant? Part of the explanation must be a propaganda campaign by vile reactionaries, including the suppression of progress in explaining actually existing capitalist economies.

There is an aspect of cumulative causation here. A smaller government is associated with more inequality. And more inequality is associated with the rich and powerful promoting an exploded and evil ideology.

Increased inequality also leads to failures in aggregate demand. A steadily growing economy needs a certain balance to be maintained. The consequences of the failure to maintain such a balance since the end of the post war golden age are all around us.

Reference

Jacob S. Hacker and Paul Pierson, "Winner-Take-All Politics: Public Policy, Political Organization, and the Precipitous Rise of Top Incomes in the United States", Politics & Society, V. 38 N. 2 (2010): pp. 152-204

Elsewhere

• Cosma Shalizi states a simple ergodic theorem.
• Cosma Shalizi reviews Yves Smith's Econned: How Unenlightened Self-Interest Undermined Democracy and Corrupted Capitalism.
• Victoria Chick and Ann Pettifor argue that the United Kingdom needs more government spending.
• James Galbraith affirms that "There is no economic justification for deficit reduction."
• Updated: David Harvey gives an animated lecture on the causes of the global financial crisis. I like the use of Volume 2 of Marx's Capital.

But Maybe Everything That Dies Someday Comes Back

I think the following three events, at least, were important in the development of the post (second world)-war model of development:

• The 1942 issuing of the Beveridge Report
• The 1944 Bretton Woods conference
• The April 1955 Bandung conference

Shouldn't the documents issued by such conferences and the whole Beveridge Report now be online somewhere? The first 20 pages of the Beveridge Report are here. Extracts from those pages and from Part V are here (mirrored).

Despite the post title, I don't think a Fordist accumulation regime can be recreated. But we need a new mode of regulation with new institutions and transformative events to set up a system that works. The current one doesn't.

Impact of Capital Controversies On Labor Economics

I think some with some exposure to economics might not be impressed by the Cambridge Capital Controversy because of the abstractness of capital. "Capital" can refer to finance, and it can refer to the means of production. And even if one thought that interest rates were determined by supply and demand, what quantity would be supplied or demanded? Loanable funds? Savings? One might expect capital theory to be complicated, even in the view of the defenders of mainstream theory. So why, some might rationalize, should one be surprised by aggregation problems?

I like to emphasize the labor market. This market might seem more concrete to many. (This is one of the illusions created by competition.) Consider cases in which firms have adapted their capital equipment and production techniques to the prices prevailing on both product and factor markets. A logical implication of capital reversing is that, given the level of output, such firms employ more workers at a higher wage. (I have deliberately worded the above to avoid saying, "Increasing wages lead to greater employment" - which is a claim about dynamics.) The sort of example I have in mind doesn't seem to depend on aggregating labor. I often motivate discussion of these matters with the introductory neoclassical textbook story on minimum wages, which is theoretically unfounded and only taught by bad economists. (Nose counting as a refutation of the above statement is a fallacy.)

I realize lots of literature backs up my position; I am not being original. I like to cite Graham White (2001) and Tony Aspromourgos (2001). I recently stumbled upon another economist who forcefully states a similar position.

John Weeks has been updating his 1989 book, A Critique of Neoclassical Macroeconomics. Two parts of the update-in-progress are currently available online: part I, part II. I extract some random quotes from the relevant chapter in part II:

"Reswitching implies an unexpected conclusion: theory tells us that in general capitalists will not necessarily select more labour-intensive techniques when wages fall.

This result is a potential disaster for the neoclassical macro model and its parable about real wages and employment."

"In the introduction to this book a quotation from The Times was cited, which ventured the assertion that '...few economists would argue with the general proposition that lower real wages will mean higher employment...' If it refers to theoretically competent neo-classical economists, this statement is false."

"One can conclude that when referring to actual economic outcomes, there is no theoretical basis for the generalization that lower real wages will stimulate more employment. The opposite conclusion has equal theoretical merit. The neoclassical parable, upon which so many policy prescriptions are based, is a false guide to real economies."

References

• Tony Aspromourgos (2001) "Is Labour Cheapening a Means to Reducing Involuntary (Labour) Unemployment?", History of Economics Review, V. 34: (Summer) pp. 7-18
• John Weeks (1989) A Critique of Neoclassical Macroeconomics
• Graham White (2001) "The Poverty of Conventional Economic Wisdom and the Search for Alternative Economic and Social Policies", The Drawing Board: An Australian Review of Public Affairs, V. 2, N. 2 (November): pp. 67-68.

Neoclassical Economics Overthrown A Half-Century Ago

Today the 50-year anniversary of the publication of Piero Sraffa's The Production of Commodities by Means of Commodities is being celebrated at Queen's College, Cambridge.

Manifestations of Sraffa Effects in General Equilibrium Models?

A Strange Attractor Arises From The Lorenz Equations

I think reswitching, capital reversing, and Sraffa effects may be the source of both dynamic and structural instabilities in General Equilibrium models. I am not so much interested in dynamics of a tâtonnement process in some sort of no-time before the beginning of time in the Arrow-Debreu model of intertemporal equilibrium. Rather, I find more of interest the dynamics of spot prices in models of temporary equilibrium.

My claim that the Cambridge Capital Controversy can be drawn on for examining the dynamics of certain economic models is not original. Barkley Rosser (1983) related reswitching to a cusp catastrophe. A cusp catastrophe, as I understand it, is a kind of structural instability. Overlapping Generation Models (OLGs) provide my favorite neoclassical closure of Sraffian production models. Saverio Fratini (2007) has investigated cases in which reswitching gives rise to multiple stationary state equilibria in OLGs. I've convinced myself that whether multiple equilibria are associated with a "normal" or "perverse" switch point can depend on the form of the utility functions in OLGs.

An issue arises in showing that Sraffa effects are associated with the appearance of complex and chaotic dynamics in models of General Equilibrium. Researchers have already established that complex dynamics can arise in such models anyways, including OLGs, for other reasons. For example, John Geanakoplus states:

"Grandmont ..., following related work of Benhabib and Day ... and Benhabib and Nishimura ..., gave a robust example of a one-commodity, stationary economy ... giving rise to a three-cycle... Of course a cycle ... is also a cyclical equilibrium for the economy, hence there are robust examples of economies with cycles of all orders." -- John Geanakoplos (2008)

Geanakoplos is relying on Theorem 1 in Li and Yorke (1975). In the references, I give sources for identifying literature exploring the dynamics of General Equilibrium models, including OLGs, independently of considerations raised in the CCC.

The consequences of modeling the economy as potentially exhibiting complex non-linear dynamics are far reaching. Rajiv Sethi, in a series of blog posts, has pointed out some implications of a serious concern with non-linear dynamics for mainstream macroeconomics:

• An Outsider's View of Modern Macroeconomics
• On the Consequences of Nominal Wage Flexibility
• On Buiter, Goodwin, and Nonlinear Dynamics
• On Rational Expectations and Equilibrium Paths

I think one can show that Sraffa effects can give rise to complex dynamics in OLGs, even with the knowledge that OLGs can produce chaotic dynamics otherwise. I need to find an OLG model with perhaps a single good being produced in each period and in which complex dynamics do not arise for the specified form of the utility function. Then one should alter the production model to be a two or three-good reswitching example. Finally, one should establish complex dynamics arise in the resulting models. Even if this strategy is not successful, one pursuing it will have to explore and understand already existing models with complex dynamics.

References

• Jess Benhabib (2008) "Chaotic Dynamics in Economics", in The New Palgrave Dictionary of Economics (Ed. by S. N. Durlauf and L. E. Blume), 2nd edition, Palgrave Macmillan
• Jess Benhabib (editor) (1992) Cycles and Chaos in Economic Equilibrium, Princeton University Press
• Saverio M. Fratini (2007) "Reswitching of Techniques in an Intertemporal Equilibrium Model with Overlapping Generations", Contributions to Political Economy, V. 26: pp. 43-59.
• John Geanakoplos (2008) "Overlapping Generations Model of General Equilibrium", in The New Palgrave Dictionary of Economics (Ed. by S. N. Durlauf and L. E. Blume), 2nd edition, Palgrave Macmillan
• John Guckenheimer and Philip Holmes (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag
• Yijun He and Willam A. Barnett (2006) "Existence of Bifurcation in Macroeconomic Dynamics: Grandmont was Right"
• Tien-Yien Li and James A. Yorke (1975) "Period Three Implies Chaos", American Mathematical Monthly, V. 82, N. 10 (Dec.): pp. 985-992
• J. Barkley Rosser, Jr. (1983) "Reswitching as a Cusp Catastrophe", Journal of Economic Theory, V. 31: pp. 182-193
• Paul A. Samuelson (1958) "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money", Journal of Political Economy, V. 66, N. 6 (December): pp. 467-482
• Robert Shiller (1978) “Rational Expectations and the Dynamic Structure of Macroeconomic Models: A Critical Review”, Journal of Monetary Economics, V. 4: pp. 1-44.