The Wright Brothers #2

In 1896 Orville Wright got typhoid fever, and he was in bed for several weeks. During this time Wilbur began reading about German glider enthusiast Otto Lilienthal, who was recently killed in an accident. Wilbur read aloud to Orville.

A manufacturer of small steam engines and a mining engineer by training, Lilienthal started gliding as early as 1869, along with his younger brother. He took his lessons from the birds. He thought the "art of flight" was to be found in the arched wings of birds by which they could ride the wind. He had no use for balloons, since they had so little in common with birds. To fly one had to be "initimate" with the wind.

Over the years Lilienthal built many gliders. Most were monoplanes with an arched wing consisting of muslin stretched over a willow frame. As pilot he would wear padded knees, position himself below the wings, and begin by running downhill. He would swing his body and legs for balance and control.

He also had himself photographed in action, taking advantage of newly invented cameras. Photos of him gliding appeared the world over, more so in the United States. A long article in McClure's Magazine, with seven photos, reached the largest audience.

In 1894 Lilienthal crashed but survived. In 1896 he crashed and died. News of Lilienthal's death aroused a great interest in Wilbur Wright. He began reading intensely on the the flight of birds, including the book Animal Mechanism from the family bookshelf. He read Animal Locomotion; or Walking, Swimming, and Flying, with a Dissertation on Aeronautics. For most readers it was too daunting. For Wilbur the book was exactly what he needed. Wilbur drew upon and quoted the book for years. It opened his eyes and started him thinking in new ways. Orville recovered from his illness and read the same works.

The automobile appeared and gained popularity. For Wilbur it lacked appeal. His sight was upward.

The Wright Brothers #1

The Wright Brothers is a book by David McCullough. It's widely known that the Wright brothers had a bicycle shop, which they opened in 1893, before venturing into flying.

The following is an amusing historical note about bicycles.

"Bicycles had become the sensation of the time, a craze everywhere. (These were no longer the "high wheelers" of the 1870s and '80s, but the so-called "safety bicycles," with two wheels the same size.) The bicycle was proclaimed a boon to all mankind, a thing of beauty, good for the spirits, good for health and vitality, indeed one's whole outlook on life. Doctors enthusiastically approved. One Philadelphia physician, writing in The American Journal of Obstetrics and Diseases of Women and Children, concluded from his observations that "for physical exercise for both men and women, the bicycle is one of the greatest inventions of the nineteenth century."
     Voices were raised in protest. Bicycles were proclaimed morally hazardous. Until now children and youth were unable to stray very far from home on foot. Now, one magazine warned, fifteen minutes could put them miles away. Because of bicycles, it was said, young people were not spending the time they should with books, and more seriously that suburban and country tours on bicycles were "not infrequently accompanied by seductions."
     Such concerns had little effect. Everybody was riding bicycles, men, women, all ages and from all walks of life. Bicycle clubs sprouted on college campuses and in countless cities and towns, including Dayton" (p. 22).

Approaching Infinity

The title is the title of a book by Michael Huemer, which I read most of, but not all. It’s good in parts. It addresses infinity in several ways. He presents many paradoxes involving infinity and gives his solutions for some of them. He discusses Cantor’s diagonal arguments (see my previous post for one). He doesn’t seem to wholly agree with them, but he doesn’t argue against them either.

He does challenge Cantor concerning Galileo’s paradox. “The puzzle is that there is a compelling argument both that the two sets are equally numerous (the one-to-one correspondence argument), and that one set is larger than the other (for the squares are a proper subset of the natural numbers). Cantor embraces the first of these arguments and rejects the second. His only justification for this is fiat: he proposes to simply define the relations ‘equal to’, ‘greater than’, and ‘less than’ using the one-to-one correspondence criterion.

     Of course, one could not consistently brace both of the arguments Galileo mentions, since they entail contradictory results. But Cantor’s decision to embrace only the one-to-one correspondence argument is not the only alternative. One could embrace the proper-subset argument while rejecting the one-to-one correspondence argument. Or one could, like Galileo, reject both arguments and hold that ‘greater than’, ‘less than’, and ‘equal to’ relations do not apply to pairs of infinite sets. Cantor does not argue for his alternative over the others” (6.9.4).

Huemer did not say one could embrace the proper subset argument for comparing the integers and the rationals.

The weakest parts of the book in my opinion were about the empty set and geometric points.

Huemer misses the strongest reason for having the concept of an empty set. The two major operations on sets are union and intersection. The first forms a new set by combining the members of two or more sets. The second forms a new set by identifying the common members of two or more sets. Say we have set A = {1, 2, 3} and set B = {3, 4, 5}. The intersect of A and B is {3}. But what if B = {4, 5, 6}? Then A and B have no common members. In other words, the intersect of A and B is nothing, i.e. the empty set { }, often symbolized as {∅}. In other words, the empty set is needed to make defined operations complete. It is similar to a need for the number zero, for example 5 – 5 = 0.

Huemer is frustrated with geometric points. He says they are unimaginable, because they have size zero, yet they are supposed to be the building blocks of other geometrical objects (11.2).

I regard the building block perspective as from the wrong direction. Start with 3-dim space, e.g. a cube. Then disregard one dimension to get 2-dim space (a square plane), disregard another dimension to get 1-dim space (a line), and finally to 0-dim space (a point). Alternatively, each intersection of two lines of the square is a point.

Later in the book there is a section (14.6.3) about points as locations. He does not have any arguments against this view, but he doesn’t endorse it either and says he doesn’t understand it. 

In my opinion it is the best view. We often hear people say things like how to get from point A to point B. More concretely it might mean driving a route from one location, such as a town, to another location, another town. In the context of geometry, a point is a location in Cartesian or polar coordinates. For example, the point (2,3) in 2-dim Cartesian coordinates means 2 units to the right of the origin (0, 0) or y-axis and 3 units above the x-axis. Of course, Euclid’s Elements did not have this perspective, since Cartesian coordinates were invented much later. 

Infinity contra-Cantor #2

Georg Cantor also famously claimed that the cardinality of the set of rational numbers equals the cardinality of the set of integers because he could devise a 1-1 correspondence or mapping between them as shown here and here.

Relatedly, the continuum hypothesis is: There is no set whose cardinality is strictly between that of the integers and the real numbers (rationals and irrationals).

Accepting certain assumptions Paul Cohen showed that the continuum hypothesis is neither true nor false. I think it’s false, the quantity of rational numbers being greater than the integers, but less than the reals (rationals and irrationals combined). I base this on two  perspectives different from that of Cantor and Cohen. The first is the real number line. There is an unlimited count of rational numbers between 0 and 1, between 1 and 2, and so forth.

The second is part-whole logic. As shown in the above links, a 1-1 mapping can be made. However, note the first column in the array in either link, which is the integers. A different 1-1 mapping or function f(x) = x can also be made. Accordingly, the integers comprise a proper subset of the set of all rational numbers, implying the set of rational numbers is larger than the set of integers.

“Cantor was concerned to combat the Aristotelian view that there cannot be an actual infinity, mainly because Cantor believed that God was infinite.” – Michael Huemer, Approaching Infinity, p. 71.

Infinity contra-Cantor #1

In the late 19th century Georg Cantor chose the method of 1-1 correspondence to decide the different quantities of infinite sets. He called such quantities their “cardinality.” If the members of one set can be paired 1-1 with the members of another set, then they have the same “cardinality” (link). 

As the Wikipedia page shows, some famous mathematicians such as Kronecker and Poincaré objected to some of Cantor’s ideas. But most people who have an opinion about it accept Cantor’s arguments and consider that the cardinality of the positive integers equals that of the even positive integers, as explained on the linked page.

I was astounded when I became aware of that many years ago. Years later I realized Cantor's error. The assumed method of 1-1 correspondence implicitly rules out 2-1 correspondence, N-1 correspondence, and part-whole logic. 

A 2-1 correspondence or mapping can be formed from the natural numbers (integers) to the even numbers as follows: 1, 2 → 2;   3, 4 → 4;   5, 6 → 6;   7, 8 → 8;   9, 10 → 10; and so on. If this mapping did not include “and so on”, then the finite quantity of natural numbers would surely be regarded as being twice that of the even numbers. (See above link, Exercise 3). However, many abandon that idea when “and so on” is included. I do not. From a part-whole logic perspective, imagine having a container with all the integers in it, then removing the odd integers from the container. Wouldn’t the container then have half the quantity of numbers as before? Or partition the container in half vertically, putting the odd integers on one side of the partition and the even integers on the other side. Wouldn’t there be twice as many numbers in the whole container as there are on one side of the partition?

Information and Investment #4

Chapter VIII of Information and Investment is The Need for Adaptability. It includes a very extensive discussion of liquidity.

The author assumes an entrepreneur will adopt the investment plan which offers the highest mathematical expectation of income, irrespective of the degree of dispersion which the possible values of income may show. I know from personal experience in risk management this isn’t wholly true, but I don’t regard it as very wrong.

Ideally, an investment plan is designed to offer positive profits under all possible scenarios likely to develop. In practice, however, such perfectly adaptability is out of reach. So long as the investor holds his resources in the form of money, he remains free to choose to engage in a variety of activities, the range of which is limited by technical, legal, and financial restraints. Whenever he decides to commit his resources in a form other than money, the scope of future activities is to some extent curtailed. However, the committing of resources in that way is the only hope the entrepreneur has for a substantial return. The more capital-intensive is the process, the greater is the fixed cost, and the greater will be the per unit cost of output if the total volume of production has to adapted to a lower level of demand.

Adaptability is enhanced by the power to make net expenditures from a source of readily available purchasing power. This has two dimensions – amount and speed. This is the heart of liquidity. Of course, money is the most liquid asset. Further resources are trade credit granted by suppliers and credit from a bank or other lender. Urgent sales of assets typically mean getting less money in return than patiently waiting.

An actual liquidity position at a particular time may be accounted for not in terms of intentions but as the unplanned result of recent transactions – of unexpected variations in costs or receipts. Cash balances in this sense are ex post, not ex ante in terms of a ‘transactions motive.’

Information and Investment #3

Chapter VI of Information and Investment is The Assortment of Production, or in other words, product differentiation.

Usually economic models assume a fixed set of goods and services, for both consumers and producers. But it is important to deal explicitly with the qualitative composition, for the variety of production is quite great. If we wish to consider, as does an entrepreneur, what kinds and qualities of goods to produce.

Consumers buy goods because of the satisfaction they expect to receive. They also experiment when making purchases as part of an endeavor to find newer and better ways of meeting their desires. Businesses also experiment with product variations to find newer and better ways of meeting customer satisfaction. Most formal economic models, especially the perfect competition model, ignore this.

Imagination, rather than information in an ordinary sense, is what entrepreneurs require in order to discover new ways of combining resources to meet consumers’ desires. Undiscovered ways of production are somewhat like musical tunes awaiting discovery. Often the competitiveness of a market is associated with or defined in terms of the cross elasticity of demand for the products sold in it. A high degree of competitiveness in this sense is much greater in reality than in the so-called pure competition model, which recognizes only price.

Information and Investment #2

Chapter IV of Information and Investment is The Co-ordination of Complementary Investments. It concerns investment by an entrepreneur’s suppliers, actual or potential.

It will be necessary to inquire both about the information which entrepreneurs will wish to have and as to the conditions which will permit access to it. It is probably the qualitative assortment of production that complementary investment is of greatest importance.

An entrepreneur needs to recognize that the profitability of his own investment will depend on the terms on which he can obtain inputs, and therefore indirectly on the volume of investment which has been, or will be, undertaken elsewhere. It is possible for two or more firms to be in a complementary relationship without there being transactions between them. For example, the other party could be a supplier to one’s supplier.

A further complementarity results from the fact that investment of any kind, by generating income, will increase the demand for other goods and services. No very close relationship between particular firms is likely to be created by this form.

The problem is to explain how producers may obtain information or assurances about the likely volume of complementary investment sufficiently reliable to persuade them to invest themselves. Complementarity between various lines of production does not imply that investment in them will be simultaneous and coordinated. Although producers may be able, on the basis of implicit collusion, to expect an increase in complementary production, it seems doubtful such expectations could be held with much confidence.

Every business makes plans, with greater or lesser precision, for a set of investment activities. It will be based on an assessment of the various technical and market conditions upon which the prices at which the firm will buy its inputs and sell its outputs. Due to the uncertainty of expectations, an entrepreneur will want to be as flexible or adaptable as possible, to allow for modification. But inflexibility will be to some extent unavoidable, such as due to more or less fixed equipment or personnel. Attempts to secure a more perfect coordination, such as by contracts, may reduce future adaptability.

It is difficult to resist the conclusion that in less developed markets, the coordination of investment, at least in manufacturing, may require more deliberate planning than with advanced markets. Unfortunately, it is in less developed markets that the administrative skill and experience required for such coordination is likely to be absent.

Information and Investment #1

I return to G. B. Richardson's book Information and Investment: A Study in the Working of the Competitive Economy. My previous (November) posts’ titles start with 'The Organization of Industry’ and ‘Perfect Competition.’

Chapter III is The Co-ordination of Competitive Investments. It is about an entrepreneur’s information and consideration of other entrepreneurs who are his competitors. (Like Richardson did, I use he/his for convenience. It could be she/her, or it/its for a firm, as well.)

The profitability of any one investment project is dependent in part on the volume of investment by competitors. Suppose an entrepreneur expects the demand for a particular product to rise, one that he could fulfill. If he believes the situation offers a profit opportunity for him in particular, he needs assurance that that the volume of investment undertaken by his competitors will not be so much that an excess supply will occur. However, the information available for that assurance often doesn’t exist. In a free enterprise system all the competitors don’t meet and plan their levels of production together. The less they cooperate, the more difficult it is to see how the required information could be obtained. Adequate market information seems unobtainable. Nor can one plausibly contend that it is possible to predict the actions of competitors merely by considering what one would do oneself in like circumstances.

In some circumstances certain producers having a temporary monopoly of information about a general profit opportunity may be important to securing its successful exploitation.

The upper limit on the volume of future competitive supply will depend on the number of firms which could increase their capacity in time and to the extent they could do so. Perhaps for some the extra resources aren’t available. The impossibility of borrowing unlimited sums at the same rate of interest is a crucial check, and an ‘imperfection’ of the capital market that is incompatible with the perfect competition model.

When we consider an individual producer, we should couple his supply curve and his demand curve – not the general supply curve and demand curve for his commodity in a wide market.

Perhaps the most obvious way in which a producer may try to secure the loyalty of his customers is by offering a differentiated product which they prefer to any substitutes. Commodities may be differentiated, not only by their particular attributes, but by where they are available due to transport costs.

The market attachment known as ‘goodwill’ has probably received more attention from businessmen than by most economists. Buyers may be unwilling to patronize a different producer, even if momentarily tempted, if they believe loyalty to him affords the best chance of good treatment over a long period.

The availability of information about competitive production depends on various restraints that reduce the freedom of action of individual entrepreneurs. By assuming, overtly or tacitly, that it is zero, and therefore neglecting the whole problem of information, the perfect competition model is unrealistic and inadequate.

China From Above

Monday night I watched an episode of China From Above subtitled Dynamic Coast on the Smithsonian Channel. It was fascinating.

There were aerial views of the big cities with rising populations along the east and south coast.

Part of the episode was about fishermen on icy Chagan Lake. They caught fish from under ice using a huge net, catching several tons of fish in one haul. They have been doing this for many generations.

Part of it was about erecting offshore wind turbines for power generation.

I recommend watching the series. The whole episode of Dynamic Coast is online here, but it seems you have to be a subscriber to a streaming service or have cable TV service including the Smithsonian Channel to get online access. As a Spectrum cable TV subscriber, I am able to see it and two episodes from Season 1. 

Mass shootings

There was an article in yesterday's print edition of the Cleveland Plain-Dealer about mass shootings written by John Lott. When I looked for it on the Plain Dealer website moments ago, it wasn't there. Maybe it will appear later. Anyway, it repeated the article I did find here. It is about left-wing liberals' biased claims about mass shootings.

Of course, mass shootings are tragic. So are the biased claims.

Bohemian Rhapsody

My wife and I saw the movie Bohemian Rhapsody on Nov. 17. We enjoyed it very much. The main character in the movie is Freddie Mercury, the band Queen's lead vocalist. I thought the movie was a little long in the part before Queen's performance at Live Aid. The part showing their Live Aid performance was terrific.

A philosophy professor, and an acquaintance many years ago, wrote a blog-post about the movie, which is here. He enjoyed it as much as I did, maybe more, but his thoughts about the experience of seeing it were very different from mine. I made some comments to his blog-post.

There are some videos on YouTube showing Queen's performance at LiveAid. One of them, this one, has a comical introduction for Queen.

Amazon HQ2 & HQ3 #3

Yesterday at a Thanksgiving celebration I asked a guy who works in information technology about Amazon HQ2 and HQ3, assuming there has been office buzz about it where he works. Part of his reply was that Amazon employees have bought residential real estate near the future new location(s). He didn't say how long ago this started.

So this morning I did a Google search {"Amazon employees" bought "real estate"}. There were lots of hits. Examples:  BoingBoing    Wall Street Journal (pay-walled)

The stories are mostly about Long Island City (HQ3).

Amazon HQ2 & HQ3 #2

This post will be about the reported tax breaks that Virginia and New York will give to Amazon. On Wikipedia there is heavy criticism of the tax breaks. One professor calls the tax breaks overly generous. Another professor says that Amazon's search for other locations was a ruse and a con. It was done to solicit bids from places that they never intended to move to solely to gain tax breaks. However, none of the critics quantify the overly generous tax breaks that they allege.

To take a "stab" at it I did some rough calculations comparing (a) the extra income taxes that Virginia and New York will collect assuming 25,000 employees at both HQ2 and HQ3 to (b) the reported tax breaks.  My calculations say that it will take nearly 4 years for Virginia and nearly 6 years for New York to recoup the tax breaks via income taxes. Call these "number of years to recoup" (Y). Such simple assumptions likely under-estimate Y.

Complications

The above assumed all the new Amazon employees will come from out-of-state, and they will all be added immediately. Both are obviously false. So let's assume that only half of the employees will come from out-of-state and the average number of employees over the first several years will be about half of the numbers shown above. Adjusting for both of these factors implies that Y will be nearly 16 years for Virginia and nearly 24 years for New York!

Arguably Y could be reduced some for favorable side effects like income to local businesses and rents. On the other hand, there will be unfavorable side effects. The presence of HQ2 and HQ3 will increase other costs to local people for things such as paying more for teachers, food, rent, infrastructure, and so forth. These are, of course, very difficult to quantify. But if the net effects were to reduce Y 1/8th, the result is still nearly 14 years for Virginia and nearly 21 years for New York! I'm inclined to agree with the professors.

I am confident that not many people in the general public do the above kind of analysis. Therefore, politicians can hand out tax breaks to Amazon or whoever, and most people in the affected community will swallow whole whatever the politicians say about it being a great deal for the local economy. Even if some of the people are skeptical about how good a deal it is for the community, there is little or nothing they can do once the tax breaks have been finalized.

Amazon HQ2 & HQ3 #1

According to several news stories Amazon is near announcing its new headquarters. That's two of them, not one as first announced. They are being called HQ2 and HQ3. HQ1, as I'll here call it, will remain in Seattle. HQ2 will be in Crystal City, VA very near Washington, D.C. and Reagan Airport. HQ3 will be in Queens, NY, near LaGuardia Airport but not far from JFK Airport. Some stories say HQ3 will be in Long Island City, which is not on Long Island but adjacent to Queens.

The following story compares real estate prices and more in the two new locations and Seattle.
How Amazon’s HQ2 and HQ3 locations compare with Seattle and the U.S. overall

I don't know how close HQ2 will be to the Crystal City Metro station, but I bet it will allow many to do a brief walk between them. Also, the Crystal City Metro station is only one stop away from the Reagan Airport Metro station (link).

Expected tax breaks for Amazon -- $573 million from Virginia and $1.525 billion from New York (link).

Perfect Competition #3

In this post I will add some points about equilibrium and perfect competition not in Richardson’s book.

A securities market, such as for common stocks, comes closest to meeting the criteria for perfect competition. There are numerous participants. Public information is widely available. What is traded is homogeneous. The trade is impersonal and and momentary. Neither trader has any control over the character of the stock. Neither trader has any control over the aggregate supply of, nor demand for, the stock. However, other markets are much different in every way mentioned. Obviously a model of a securities market does not reduce the workings of a market economy as a whole to its essentials.

Austrian economists  have pointed out the flaws of the perfect competition model. For example: "Contrary to the perfect competition model, what gives rise to a greater competitive environment is not a large number of participants in a particular market but rather a large variety of competitive products" (link). Also see here with its entertaining narrative about shopping for turkey.

Austrian economist Ludwig von Mises’ fictitious evenly rotating economy is like the stationary state economy described in Perfect Competition #1. An equilibrium of unchanging prices and products and repeating volumes of production and consumption each time period are essential features. Mises says the unchanging evenly rotating economy leaves no room for the entrepreneurial function. See more here.

Economists often write as if an equilibrium is expressible as a set of linear equations assumed to have a solution. For example, see here. However:
1. Getting an exact solution for a set of linear equations in mathematics requires that the independent (input) variables be truly independent.
2. Producers in a market economy are very inter-dependent via supply channels and as competitors.

Accordingly, that seems to turn any solution to a set of linear equations alleged to depict a market economy, or even a small part of one, to be little more than wishful thinking. There are trial-and-error methods of finding a best fit solution to a set of linear equations. Genetic algorithms are probably the main kind. However, the degree of a solution’s fit may be very poor.

P.S. I recently saw a Wall Street Journal article that suggested inter-dependency (link with paywall). The price of Apple stock fell 5% one day after one of its suppliers, Lumentum, cut its earnings and revenue outlook. The article doesn’t explain why. I presumed that many investors assumed Lumentum’s act signaled a cut in Apple’s earnings and revenue outlook, and hence the price drop. Related stories found after seeing the WSJ article: Bloomberg, MotleyFool.

Perfect Competition #2

Chapter 2 of Information and Investment is about information available to entrepreneurs. Richardson calls market conditions the projected activity of others – such as customers, competitors or suppliers – by which the profitability of an entrepreneur’s investment is directly or indirectly influenced. All other conditions such as production possibilities created by the existing technology are technical conditions. Corresponding to these are market information and technical information. The extent to which an entrepreneur can obtain market information depends on the nature of economic organization in a way in which access to technical information is not. The profitability of any particular investment project will depend on the investment implementation of other competitors and suppliers. “It follows from the nature of these relationships – which will be considered more fully in later chapters – that any single investment by an entrepreneur will in general be profitable only provided, first, that the volume of competitive investment does not exceed a critical limit set by the demand available, and the volume of complementary investment reaches some minimum level” (31).

[Me: The differences between competitive investment and complementary investment have not been elaborated at this point. They are in chapters 3 and 4. Meanwhile and simply, competitive investments are made by competitors and complementary investments are made by suppliers.]

It is reasonable to expect that information about these would never be quite complete or wholly lacking. Suppose entrepreneurs E1 and E2 accurately predict an increase in aggregate demand for their product, but neither knows about the other’s prediction. Both might increase production enough to satisfy the full amount of increase in demand or a large part of it. If so, there will be an excess supply and the expectations of both are not met. More than two such entrepreneurs make the outcome even less determinate. The perfect competition model even assumes there are numerous competitors. Expectations are sometimes reluctantly considered in the perfect competition model, but there is no recognition that their rational formation requires a basis of information and its availability.

Few, several, many, and some

I recently had a chat with another guy including about the words few and several. He believes they are interchangeable. I believe that several is more than few. This article says there are no firm rules about their meanings, but agrees with me.

The article says little or nothing about the context. Don't few and several depend on what is being referred to? If I say there have been few National Basketball Association players more than 7 feet, 2 inches tall, few means 27 according to one source. If I say there are few living people on Earth more than 7 feet, 2 inches tall, few means a lot more than 27. In a different context few may mean less than 10.

Several might mean 7 in one context, but 25 in another context, or 100's in yet another context.
Many might mean 15 in one context, but 100's in another context, or 1000's in yet another context.  Suppose 18 people attended a meeting and 15 of the 18 went for lunch together afterwards. Wouldn't 15 qualify as many? Yet in another context 15 could be considered few.

Obviously people in general won't change their usage, but it seems few, several, many and most would have firmer meanings if they were based on percentages. For example, few could mean less than 10%, several at least 10% but less than 20%, many more than 50% but less than 75%, and most 75% or more (but not all). Between 20% and 50%? A bunch? 😊

The article's opinion about the range of some is very narrow -- more than few but less than several. Some has a far wider range in my opinion. That may be due to having studied logic. In logic some means not none (or no) but less than all.

Perfect Competition #1

The economic theory of perfect competition is critiqued in the first two chapters of George B. Richardson’s Information and Investment: A Study in the Working of a Competitive Economy (link).

The theory is a much celebrated attempt to reduce the working of a competitive economy to essentials. Its importance to economists is two-fold. As an instrument of analysis it has held a central position in economic theory for a long time, much due to the ease it lends to mathematical formulation. Second, the prices and outputs associated with perfect competition, in its supposed equilibrium state, have a normative significance, in that they are consistent with the optimum conditions of production and exchange. Perfect competition hence represents an ideal with which actual competitive organization may be compared.

Richardson criticizes the theory in two ways – its concept of equilibrium and what it says about the knowledge of entrepreneurs, and the information available to them (Information and Investment pg.1-2).

The concept of equilibrium is addressed in Chapter 1. The concept is used to say what particular actions are taken in response to the prevailing conditions, such as a change in aggregate demand. The perfect competition model assumes numerous individual economic actors who have equal knowledge about their market, no control over prices, are mere traders of homogeneous goods, and have little or no control over the nature of the goods. In the simplest case, the economic activity in each time period repeats itself, becoming a stationary state. The same amount and kind of product or service is both produced and consumed each time period. How this stationary state came or comes about is largely unexplained.

However, entrepreneurs act not merely on what they know, but also what they expect. Moreover, they may alter the nature of goods and services they offer. Consumers may alter how much they buy and the mix of goods and services they do buy. Both kinds of alterations imply disturbances to the existent equilibrium.

Summarizing, the “theory of the maintenance or the attainment of equilibrium under perfectly competitive conditions fails to account for the process of adjustment in terms of investment decisions by individual entrepreneurs, who have expectations which they could reasonably be presumed to form, on the basis of information which can reasonably be presumed to be available” (28).

My next post will be about Chapter 2, information available to entrepreneurs.

Aristotle's Wheel Paradox #3

The title includes #3 because I posted #1 and #2 in February (link). I am posting #3 because I edited the Wikipedia article about the topic (link).

I improved the first section. It had said the paradox was about two wheels. The section 'Wrong problem entirely ' on the Talk page says the paradox is about one wheel. I wholly agree. So my change to the first section says it is about two circles and one wheel (or a suitable substitute for the wheel).

I added the Analysis & Solution section to include my two solutions to the paradox. To the best of my knowledge the solutions are original. At least I didn't see or hear them anywhere else.

Since others can edit Wikipedia articles at any time, I cross my fingers that somebody won't impair it. I earlier added similar text to the Talk Page. I believe others can alter that too, but maybe they are less likely to do so.

P.S. I later added a third solution, labeled the first solution in the Wikipedia article.

The Organization of Industry #2

A coordinating example Richardson doesn't give is a home-builder, HB for short. HB could contract with an architect to create detailed design and specs for building a new house. After the architect's work is done, HB contracts with an excavator, landscaper, concrete provider, carpenters, plumbers, electricians, painters, roofers, and so forth to build the house. When the home is at least partly built, HB could contract with a realtor to sell the property.

The quantitative mix between direction, co-operation and market transactions can vary due to other particulars such as the size and specialization of the firms. Richardson's paper addresses some of this relying in part on brick-making. "What is important, for our present purposes, is to note that impersonal co-ordination through market forces is relied upon where there is reason to expect aggregate demands to be more stable (and hence predictable) than their component elements. If co-ordination were to be sought through co-operation, then individual brick-makers would seek to match their investment and output plans ex ante with individual builders. Broadly speaking, this does not happen, although traditional links between buyers and sellers, such as are found in most markets, do introduce an element of this kind. Individual brick manufacturers rely, for the most part, on having enough customers to ensure some cancelling out of random fluctuations in their several demands. And where sales to final consumers are concerned, this reliance on the law of large numbers becomes all but universal. Thus we rely on markets when there is no attempt to match complementary activities ex ante by deliberately co-ordinating the corresponding plans; salvation is then sought, not through reciprocal undertakings, but on that stability with which aggregates, by the law of large numbers, are providentially endowed[.] "

Richardson's summary section begins as follows: "This article began by referring to a vision of the economy in which firms featured as islands of planned co-ordination in a sea of market relations. The deficiencies of this representation of things will by now be clear. Firms are not islands but are linked together in patterns of co-operation and affiliation. Planned co-ordination does not stop at the frontiers of the individual firm but can be effected through co-operation between firms. The dichotomy between firm and market, between directed and spontaneous coordination, is misleading; it ignores the institutional fact of inter-firm cooperation and assumes away the distinct method of co-ordination that this can provide."

The Organization of Industry #1

The title is that of a seminal 1972 paper by English economist George B. Richardson. The entire text is here. It is also included in Richardson's book Information and Investment: A Study in the Working of the Competitive Economy  (Amazon link).

When Friedrich Hayek wrote about the spontaneous order of a market economy, his main concern was prices. He said that market prices help to guide and coordinate the actions of market participants. Richardson's view of coordination is more extensive.

"[C]o-ordination can be effected in three ways; by direction, by co-operation or through market transactions. Direction is employed when the activities are subject to a single control and fitted into one coherent plan. Thus where activities are to be co-ordinated by direction it is appropriate that they be consolidated in the sense of being undertaken jointly by one organisation. Co-ordination is achieved through co-operation when two or more independent organisations agree to match their related plans in advance. The institutional counterparts to this form of co-ordination are the complex patterns of co-operation and affiliation which theoretical formulations too often tend to ignore. And, finally, co-ordination may come about spontaneously through market transactions, without benefit of either direction or co-operation or indeed any purposeful intent, as an indirect consequence of successive interacting decisions taken in response to changing profit opportunities."

An example of such co-operative coordination is sub-contracting, such as when a manufacturer buys specialized parts from a supplier. The supplier learns in advance what specifications the parts must meet, and the supplier works to assure the specs are met.

Richardson's paper gives the British retailer Marks and Spencer as another example. "Not only do Marks and Spencer tell their suppliers how much they wish to buy from them, and thus promote a quantitative adjustment of supply to demand, they concern themselves equally with the specification and development of both processes and products. They decide, for example, the design of a garment, specify the cloth to be used and control the processes even to laying down the types of needles to be used in knitting and sewing. In the same way they co-operate with Ranks and Spillers in order to work out the best kind of flour for their cakes and do not neglect to specify the number of cherries and walnuts to go into them."

To further distinguish inter-firm co-operation from market transactions: "Where buyer and seller accept no obligation with respect to their future conduct, however loose and implicit the obligation might be, then cooperation does not take place and we can refer to a pure market transaction. Here there is no continuing association, no give and take, but an isolated act of purchase and sale such, for example, as takes place on an organised market for financial securities."

Maximum size of animals

The largest animal is a blue whale, and the largest land animal is an African bush elephant. The average mass of a blue wheel is more than 22 times that of an average African bush elephant. The maximum mass of a blue wheel is more than 15 times that of the largest African bush elephant. Link.

Why can blue whales be so many times larger than an African bush elephant? Galileo Galilei had an answer in Two New Sciences (TNS). TNS is written as a dialogue in which Salviati played the part of Galileo’s own spokesman.

Salviati: "Well, the ability of fish to stay motionless in water is a convincing argument that the composition of their corporeal bulk is equal to water in specific gravity. So if some parts heavier than water are found in them, there must necessarily be an equivalent amount less heavy in order for equilibrium to hold. So if the bones are heavier [than water], it must be that the flesh, or some other material present, is lighter, and that these offset with their lightness the weight of the bones. Thus, what happens in aquatic animals is the opposite of the case with terrestrial animals; namely, that in the latter, it is the task of the skeleton to sustain its own weight and that of the flesh, while in the former, the flesh supports its own weight and that of the bones. And there the marvel ceases that there can be very vast animals in the water, but not on the earth, that is to say, in the air." Link.

A large part of blue whales is blubber. This page cites 50 tons, or about 45.5 tonnes.  If that were from an average sized adult blue whale, it would be about 41% of the body weight. The density of blubber is very near that of seawater (65 pounds per cubic foot).

World Series 2018

The Boston Red Sox won the World Series for the 4th time this century. They were favored to win, given their regular season W-L% (wins/games) was .667 versus the Los Angeles Dodgers' .564.

The Dodgers won only one game, the third. I made an error reporting on that game. My wife and I were visiting Nashville, TN with two other couples. We went to the Grand Old Opry on October 26. Returning to our motel afterwards I looked on my cell phone to see the result of the game. It was well past midnight, and I saw the score as Red Sox 2, Dodgers 1. Assuming the game was over by then, I reported the score to my companions.

The next morning I was mildly chided by my companions, because the Dodgers had won. Looking on my cell phone again, I found that the 2-1 score was after the Red Sox scored a run in the top of the 13th inning, but before the inning ended. (The score was tied 1-1 after 9 innings.) I had unintentionally reported fake news and didn't heed Yogi Berra: "It ain't over 'til it's over." The Dodgers scored a run in the bottom of the 13th inning to tie the game 2-2. The game continued until the bottom of the 18th inning when the Dodgers scored again to win 3-2. It easily broke the record for the longest game in World Series history -- 7 hours, 20 minutes, 18 innings. (link). 

Modern Austrian Economics #5

In Volume 3 Karen Vaughn wrote about Hayek's theory of market order, which he sometimes characterized as a complex, adaptive system and other times as a spontaneous order.

In some of his writing, he described an economy, or market, as a complex phenomena. The complexity of a system depends on a sufficient number of elements showing a pattern of characteristic attributes. The more the number of elements, the more complex it is. Complex systems demonstrate emergent properties, characteristics that cannot be simply reduced to an account of the individual elements.

Hayek took evolutionary biology as a prime example of a complex system to illustrate that the exact outcome of evolution depended on relationships between an overwhelming number of variables, the exact relationships among which could never be fully specified.

Hayek used Walrasian general equilibrium (#1, #2) as an example of a complexity system in social science. General equilibrium describes a pattern of price relationships more or less observed in the real world but the theory itself can never be predictive of actual prices because the initial conditions can never be fully specified. The primary value of general equilibrium theory, he argued, was not to predict the future course of events, but only to provide a general description of a particular kind of order.

Vaughn says that Hayek focused on the number of variables and the complexity of relationships among the elements, but he did not identify the defining features of modern complex adaptive systems: non-linearity of the elements and the path-dependent interactions among them. On the other hand, his emphasis elsewhere on the process of learning in a market suggests non-linearity and path dependency.

He described a spontaneous order as a social pattern that that emerges as "the result of human action but not of human design," that is, "from the bottom up" through the actions of individuals directed to their own purposes. The order is unplanned in the sense that it was not designed by some higher intelligence or a central planner. The reason that order can emerge from the self-directed actions of individuals is that their actions are not only purposeful but the actors are also rule followers. These rules consist of laws, customs, and habits that emerge as an unintended consequence of individual action -- "emergent properties" in the parlance of complexity theory.

Piecing together Hayek's description of a market economy from his various writing, Vaughn thinks that his understanding of markets is much closer to a complex, adaptive system than it is an example of Walrasian general equilibrium, in terms of a system of simultaneous linear equations. She gives several reasons for this.

Vaughn concludes:

"While many may remain skeptical, I am cautiously optimistic that the science of complexity, by clarifying the characteristics of non-linear, adaptive systems may prove to be an aid in articulating a more Hayekian understanding of market order. For instance, the mature theory of complex adaptive systems can help support Hayek's central argument against central planning.
     Consider the "mathematical solution" which held that all one needed was to set up a system of simultaneous [linear] equations to generate equilibrium prices that could guide planners. At the time of the economic calculation debate, computers were not available to attempt to set up and solve those equations, so even the socialist sympathizers agreed that such a scheme was "practically" impossible, at least for the immediate future. Oskar Lange's "trial and error" solution to the problem of factor pricing was a fall-back to achieve the same goal without computers. However, Lange never gave up on the possibility that one day, computers could be used to direct a centrally planned economy, making his clumsy trial and error solution obsolete. The science of complexity can finally put that fantasy to rest, and at the same time, vindicate Hayek's insight" (p. 344).

Modern Austrian Economics #4

The first chapters of Volume 3 (by different authors) are about "institutional economics." There doesn't seem to be much in common among the institutional economists.  Some focus on the role of institutions and others on change and evolution. They seem most similar as a contrast to neoclassical economists, who strongly assume stable preferences, rationality and equilibrium.

Peter Boettke argues that Austrians are "insitutionalists" due to their focus on change. For example, Hayek wrote about the evolution of institutions -- markets, laws, and rules of conduct -- as they evolve spontaneously as individuals interact. They are the result of human action, not human design.

William Dugger disputes Austrians being in anyway institutionalists. He declares the essence of institutionalist economics is dissent from the mainstream. He says institutionalism is inherently egalitarian. To be an Institutionalist means to be for the "underdog", the poor and workers. The Austrians are inherently elitist, for the rich and entrepreneurs.

Modern Austrian Economics #3

Another chapter in Volume 2 of Modern Austrian Economics is 'Austrian and Neoclassical Economics: Any Gains From Trade?' by Sherwin Rosen. (The article can be read for free on JSTOR with a free account.) Rosen is not an Austrian economist, but the article gives a decent overview of how the two school differ on the importance of some concepts and their meanings. The bold text  following come from some of Rosen's section headings.

Process and Equilibrium

Neoclassical economics is much more concerned about equilibrium under known conditions of resource availability, technology and preferences. Equilibrium is an overall solution in which individual decisions are mutually compatible and can be implemented by all. There is a well-defined solution to resource allocation.

Austrian economics gives far more attention to entrepreneurship, and entrepreneurs disturb the equilibrium. Economic activity is a process. The economy is in a perpetual state of disequilibrium: things are always changing and in a state of flux. It is ever evolving, creating unforeseen profit opportunities that agents are trying to find and exploit.

Me: Ludwig von Mises made an imaginary construct that he called an evenly rotating economy. Production and consumption are unchanging from one time period to the next. It has no room for entrepreneurs. They induce change.

Coordination and the Invisible Hand

In neoclassic economics an 'invisible hand' coordinates the rationality of individual decisions and the fact that commonly known market prices exhaust all gains from trade. Austrians find this misleading. Specialized, individual participants produce and consume only a tiny fraction of the huge set of goods that are actually traded. Many of the goods and services and how they systematically fit can't be identified well by anyone.

Evolutionary Processes

In Austrian economics the fundamental issue is assessing how all the individual pieces fit together and how to make sense of the whole. They don't specify empirical criteria for assessing the performance of the economy as a whole.

The Austrian view is built up from the spontaneous activities of myriad expert specialists single-mindedly pursuing and perfecting their own component businesses, including intermediaries who buy and sell from the most economical suppliers and assemble and market the final product. There is no overall plan.

Markets, Socialism and Central Planning

Before WW II it was popular among economists to claim that a central planner could compensate for various market "imperfections" (monopoly, costs of dislocation, unemployment, and so on). The alleged result would be superior to uncontrolled market forces. Austrians, led by Mises and Hayek, argued that this vision of market socialism was impossible, and it was based on a misguided vision of markets and prices. The central planner doesn't have the information and knowledge to do what markets with decentralized decision-making.

Empirical Content and Justifying Methodology

The building of macro economic models using empirical statistical data goes hand in hand with attempts at political control of the economy. Austrian economists don't want such control.

The Role of the Entrepreneur

Entrepreneurs are important to Austrian economics and rarely mentioned in neoclassical economics.

Me: Entrepreneurs induce change. The longer the time period, the more markets change. Neoclassical economics is far more interested in stability with little change over fairly short time periods.

Modern Austrian Economics #2

In Volume 2 of Modern Austrian Economics Murray Rothbard opines on other economic schools and the other sub-schools of Austrian economics. The chapter's title is 'The Present State of Austrian Economics' (also here). Rothbard was highly polemical and made strawmen of his Austrian school competitors. For example:

"My contentions are: that the correct Austrian paradigm is and can only be the Misesian, that is, the paradigm of Misesian praxeology; that the competing Austrian paradigms, in particular the fundamentally irrational “evolved rules,” “knowledge,” “plans,” and “spontaneous order” paradigm of Hayek and the more extreme “ultra-subjectivist” or nihilist paradigm of Lachmann, have both been fallacious and pernicious" (7).

"Hayek’s entire work, on the contrary, is devoted to a denigration of human reason. As David Gordon has pointed out, Hayek virtually assumes that human beings act unconsciously—of course, a contradiction in terms—and therefore that they neither know nor think nor choose. Therefore, their actions do not require understanding; hence Hayek’s emphasis that the best that can be done is rely on a blind and unconscious adherence to evolved rules" (23).

"Hayek presents three crucial concepts as ways of highlighting his reliance on human blindness and irrationality: “spontaneous order”; the “unintended consequences of human action”; and the product of “human action, but not human design.” We need not tarry on the phrase “spontaneous order,” except to note that the word “spontaneous,” once again, connotes lack of thought, activity that is not consciously chosen, but rather purely reflexive and tropistic. It would have been far more accurate to use a term such as “voluntary,” which would at least focus on voluntarily chosen, rather than coerced, actions" (25-6).

Hayek did denigrate "constructivist rationalism", but not human reason in the absurd, sweeping manner Rothbard claims. Hayek's main criticism was for advocates of central planning and their hubris and ignorance, not typical private sector producers and consumers. Hayek's "spontaneous order" was a contrast to the "command order" advocated by fans of central planning. Hayek's "unintended consequences" was mainly to identify consequences of implementing central planning that the central planners or their supporters did not intend or anticipate.

A clear case of Rothbard making a strawman is others' alleged misuse of "evolution."  Rothbard says evolution requires the existence of genes and mutations. That misses the point. When analogies have been made between economics and evolutionary biology, the noted similarity has been adaptation, competition, and comparing the trial-and-error method of entrepreneurs to mutations.

Rothbard was also very critical of the ideas of Israel Kirzner and Ludwig Lachmann. I skip more details.

The next chapter of Modern Austrian Economics 'Praxeology and Understanding: An Analysis of the Controversy in Austrian Economics' (also here) by G. A. Selgin gives a much more balanced and objective view. For example, in Hayek's view:

"Praxeology, in seeking "apodictically certain" conclusions, had so drained itself of content as to become useless as an independent means for deriving useful truths about reality. Far from relying exclusively upon the fact of purposefulness, applications of praxeology to catallactic phenomena involve unacknowledged auxiliary assumptions about the dissemination and use of knowledge by market participants; assumptions "about causation in the real world"."

"The thrust of Hayek's essay is, however, unaffected by the specific type of empirical evidence it recommends. It claims that even pure economics, insofar as it concerns market phenomena and not merely isolated actions of individuals, must be partly an empirical or psychological science rather than a logical-deductive one. It must investigate the meanings attached by individual actors to their situation, and it must examine the particular motivations and stimuli that give rise to their choices. It must become a science, not just of action, but of people's reactions, and how these reactions may reflect the use and dissemination of knowledge."

Modern Austrian Economics #1

Modern Austrian Economics is a 3-volume set (link for volume 1) about the Austrian School  of  economics since about 1970. Ludwig von Mises was the prominent member of the school from about 1920-50. Then the school split into two main camps, one exemplified by Mises and the other exemplified by Friedrich Hayek. Mises died in 1973 and Hayek's attention turned mostly to law and political science. Subsequently leadership of the Austrian School more or less divided into camps led by three men -- Murray Rothbard, Israel Kirzner, and Ludwig Lachmann.

Rothbard is very loyal to Mises and anti-Hayek. Kirzner and Lachmann agree with Hayek in some respects, but not the same ones.  Kirzner and Lachmann have their own disagreements, especially about entrepreneurship.

The editor of Modern Austrian Economics writes: "Rothbardians have remained at the margins of this new development in Austrian thought, since the concepts of institutions and of societal evolution are hardly compatible with the Misesian emphasis on rationalism. In this respect, the criticisms directed at the Hayekian idea of cultural evolution is evocative. It focuses essentially on the Hayekian idea of the efficiency of institutions that have been selected throughout history. That an institution is the outcome of an Evolutionary process must not hide the fact that all human action is, by definition, based on reason and is, by no means, conditioned by habit or custom. 'Hayek's entire work, on the contrary, is devoted to a denigration of human reason' (Rothbard, 1992, p. 142). The core concepts of the theory of cultural evolution -- 'spontaneous order', 'unintended consequences of human action', 'product of human action but not of human design' -- are subject to vigorous objections. The notion of spontaneity makes choice appear an act of unawareness. According to Misesians, individuals take recourse to institutions to ensure a satisfactory outcome of their economic decisions, but not because they are conditioned, that is, because they would understand that their past choices have turned out to have been efficient. Rather, the individuals' choice is based on their own free will and is conscious, it is the outcome of a means--end calculus. Human action is always, by definition, intentional. ... The Hayekian critique of constructivism appears, in this respect, to collide head on with rationalism that is unable to grasp the reasons for its emphasis on the unintended consequences of human actions" (Volume 1, xxviii-xxix).

What did Mises mean by "rationalism"?

"Human action is necessarily always rational. The term "rational action" is therefore pleonastic and must be rejected as such. When applied to the ultimate ends of action, the terms rational and irrational are inappropriate and meaningless. The ultimate end of action is always the satisfaction of some desires of the acting man" (Human Action, 18)

"When applied to the means chosen for the attainment of ends, the terms rational and irrational imply a judgment about the expediency and adequacy of the procedure employed" (20).

"Praxeology deals with the ways and means chosen for the attainment of such ultimate ends. Its object is means, not ends" (21)

Despite his avowed loyalty and contrary to Mises, Rothbard asserts that rationalism is about ends or goals as well as means. "At the core of the constellation of crucial differences between the Misesian and Hayekian paradigms is their respective attitudes toward human reason. Man, affirms Mises after Aristotle, is the uniquely rational animal; reason is man’s unique and essential instrument to find out what his needs and preferences are, and to discover and employ the means to achieve them. Mises’s stress on action, on acting man, therefore necessarily stresses the vital importance of human reason. Misesian Man acts, and therefore consciously selects goals, and decides how to pursue them.
      Hayek's entire work, on the contrary, is devoted to a denigration of human reason." (Modern Austrian Economics, Volume 2, p. 28; also here, p. 23).

To be continued.