## Thursday, September 30, 2010

### Keynes - The General Theory - Chapter III

Section I: After two introductory paragraphs in which a fairly clear concept is muddled by ill-defined terms, Keynes offers us a number of equations. Here are the first two: "Let Z be the aggregate supply price of the output from employing N men, the relationship between Z and N being written Z = φ(N), which can be called the Aggregate Supply Function. Similarly, let D be the proceeds which entrepreneurs expect to receive from the employment of N men, the relationship between D and N being written D = f(N), which can be called the Aggregate Demand Function."

There are a number of problems with these equations. First, while there is a general relationship between the number of people employed and the "aggregate supply price", this is not a mathematical function, such that any increase in N would lead to an increase in Z. Hiring a certain individual would cost more than hiring another individual; again, different individuals do different amounts of work. By giving equations, Keynes leads the reader to believe that a certainty exists where there isn't one. It follows that any attempt to combine an equation which is nothing more than a vague relationship will lead to problems.

In addition to the problem with treating N as an aggregate, there is a larger problem with the second equation. D represents "the proceeds which entrepreneurs expect to receive"; but the expectations of entrepreneurs are of less importance than what actually occurs. If the expectations are high, but these expectations are unwarranted--say, if contractors were employing a large number of men to build real estate in 2007--the economy may nonetheless be in very serious trouble. In fact, a large variance between expectation and reality is a reasonable definition for a recession. Unless Keynes has another equation to track reality, I don't see how this second equation will help him.

In what is becoming routine for him, Keynes lays into "the classical theory" in this section: "The classical theory assumes, in other words, that the aggregate demand price (or proceeds) always accommodates itself to the aggregate supply price; so that, whatever the value of N may be, the proceeds D assume a value equal to the aggregate supply price Z which corresponds to N. " Now, you'll have to correct me if I'm wrong on this, but the assumption of the classical theory is full employment in equilibrium. In other words, there is only one value for N. This is not to say that full employment always exists; the economy is a series of moving parts, so equilibrium is always changing. Hence, even the smoothest running economy will have frictional unemployment. Keynes seems to think that none of his predecessors were aware of this.

Another general point: Keynes often speaks in such a way as to confuse the reader about the real relationship between two things. For instance, he writes: "For entrepreneurs will endeavour to fix the amount of employment at the level which they expect to maximise the excess of the proceeds over the factor cost." But no entrepreneur actually thinks this way. Instead, he asks himself if he can afford to hire an individual at a certain cost,; if he expects that the prospective employee will offer him more value than this salary, he hires the man. He doesn't concern himself with the amount of employment in the economy.

Section II: Here we come to the heart of the general theory, though it is presented sketchily as most terms have not yet been defined--which Keynes readily admits. We'll take a look at his list of points one by one:

1) In a given situation of technique, resources and costs, income (both money-income and real income) depends on the volume of employment N.

So long as we remember that N is made up individuals, and therefore, aggregation is of limited utility, I see nothing wrong here.

(2) The relationship between the community’s income and what it can be expected to spend on consumption, designated by D1, will depend on the psychological characteristic of the community, which we shall call its propensity to consume. That is to say, consumption will depend on the level of aggregate income and, therefore, on the level of employment N, except when there is some change in the propensity to consume.

Again, Keynes is aggregating. The propensity to consume--which could just as easily have been called the propensity to save, as the relationship is precisely inverse--is a characteristic of an individual. Hence, despite the fact that Americans are up to their eyeballs in debt, our father is a notorious cheapskate. Also, the propensity to consume varies widely, even among individuals. There is nothing to prevent Scrooge from collecting his horde of gold coins to buy a Christmas goose for Bob Crachit.

(3) The amount of labour N which the entrepreneurs decide to employ depends on the sum (D) of two quantities, namely D1, the amount which the community is expected to spend on consumption, and D2, the amount which it is expected to devote to new investment. D is what we have called above the effective demand.

This one is a bit strange. I guess Keynes is saying that entrepreneurs depend on a certain amount of investment--so as to borrow funds to produce capital goods--and a certain amount of consumption--so as to purchase consumer goods. But the individual entrepreneur is less concerned with this ratio than is with whether or not he can sell his product. Apple isn't worried that Americans are tightening their belts; they're confident that the various iThings will sell.

(4) Since D1 + D2 = D = φ(N), where φ is the aggregate supply function, and since, as we have seen in (2) above, D1 is a function of N, which we may write χ(N), depending on the propensity to consume, it follows that φ(N) - χ(N) = D2.

Substitutions don't work if you're not dealing with actual equalities. Since these are relationships, but not explicit function, they cannot be combined mathematically. The Greek letters he uses, seemingly at random, only adds the confusion.

(5) Hence the volume of employment in equilibrium depends on (i) the aggregate supply function, φ, (ii) the propensity to consume, χ, and (iii) the volume of investment, D2. This is the essence of the General Theory of Employment.

Hopefully he states this more explicitly later, because I can't get myself to remember what the the Greek letters are supposed to represent.

(6) For every value of N there is a corresponding marginal productivity of labour in the wage-goods industries; and it is this which determines the real wage. (5) is, therefore, subject to the condition that N cannot exceed the value which reduces the real wage to equality with the marginal disutility of labour. This means that not all changes in D are compatible with our temporary assumption that money-wages are constant. Thus it will be essential to a full statement of our theory to dispense with this assumption.

Again, each individual decides if a change in D requires him to alter his employment status. We'll see what happens when he gets into the changes in money-wages.

(7) On the classical theory, according to which D = φ(N) for all values of N, the volume of employment is in neutral equilibrium for all values of N less than its maximum value; so that the forces of competition between entrepreneurs may be expected to push it to this maximum value. Only at this point, on the classical theory, can there be stable equilibrium.

I'm not sure what Keynes means by "neutral equilibrium". If N does not square with full employment--setting aside those voluntarily unemployed, for n less than N--we are not in a state of equilibrium at all.

(8) When employment increases, D1 will increase, but not by so much as D; since when our income increases our consumption increases also, but not by so much. The key to our practical problem is to be found in this psychological law. For it follows from this that the greater the volume of employment the greater will be the gap between the aggregate supply price (Z) of the corresponding output and the sum (D1) which the entrepreneurs can expect to get back out of the expenditure of consumers. Hence, if there is no change in the propensity to consume, employment cannot increase, unless at the same time D2 is increasing so as to fill the increasing gap between Z and D1. Thus — except on the special assumptions of the classical theory according to which there is some force in operation which, when employment increases, always causes D2 to increase sufficiently to fill the widening gap between Z and D1 — the economic system may find itself in stable equilibrium with N at a level below full employment, namely at the level given by the intersection of the aggregate demand function with the aggregate supply function.

The psychological law which Keynes observes sounds right, but it is not binding, and it is therefore not a law. It might seem reasonable that if I get a raise, I won't go out and spend all of it, but there is nothing to prevent me from doing so. I can, in fact, take the raise and spend that amount plus some of my savings--though if I was a good Keynesian, I'm not sure how much savings I would have. Hence anything which depends on this "law" holding true at all times will go awry should individuals not conform their behavior with the so-called law.

Regarding Keynes conclusion, it would be useful to attack the problem from a different direction. I'm not certain this could be done praxeologically, but at least theoretically, one could demonstrate that, despite a variance of savings rate--i.e. the propensity to consume--different rates of employment are possible. This seems to be the big take away here: if the propensity to consume isn't high enough--or low enough?--unemployment will result. I can't seem to find what that rate should be, so if you could point that out, I'd be grateful.

Section III: The rhetoric in this section is scurrilous. I've commented before on how poorly written the General Theory has been, but here, Keynes shines. He doesn't so much offer an argument, however, so I'll end my summary here.

This is arguably the most important chapter in the book, so please point out anything you think I may have missed or glossed over.

Jeff said...

There is a larger problem with the second equation. D represents "the proceeds which entrepreneurs expect to receive"; but the expectations of entrepreneurs are of less importance than what actually occurs.

The expectations are important to the individual entrepreneurs, because that is what they are basing their decisions on. As you mention later, entrepreneurs do not think in the aggregate so the combination of expectations within an aggregate demand function has no value to economic analysis.

For instance, he writes: "For entrepreneurs will endeavour to fix the amount of employment at the level which they expect to maximise the excess of the proceeds over the factor cost." But no entrepreneur actually thinks this way.

Correct, one of the many problems with looking at economic analysis in the aggregate is that it is not applicable to the real world, which should be the purpose of economics. Business owners do not try to fix employment at a certain level anymore than individuals try to fix their consumption at a certain level.

I guess Keynes is saying that entrepreneurs depend on a certain amount of investment--so as to borrow funds to produce capital goods--and a certain amount of consumption--so as to purchase consumer goods. But the individual entrepreneur is less concerned with this ratio than is with whether or not he can sell his product.

From my experience with Keynesian academia, D1 is essentially the expectations discussed earlier. If the community is expected to consume a large amount of goods, then the entrepreneurs will employ more laborers to satisfy this demand. Essentially, D1 is an unclear and roundabout way of saying that Apple is expecting the community to buy iThings.

Hopefully he states this more explicitly later, because I can't get myself to remember what the Greek letters are supposed to represent.

The Greek letters represent nothing more than an arbitrary mathematical function. φ, supposedly means that the output Z is based on employment N by some relationship. Instead of admitting that there is no absolute relationship between the two, Keynes uses a Greek symbol to denote a relationship which does not need to be specified. x, represents the propensity to consume, but as you stated the propensity to consume is an individual characteristic. Therefore, using it to relate employment to expected consumption is a loose connection at best. Claiming that this is integral to the General Theory of Employment does not inspire much hope in his theory.

Regarding his eighth proposition, that When employment increases, D1 will increase, but not by so much as D, I think Keynes is making much ado about nothing. The idea that D2 (investment) must grow in order to increase productivity is consistent with economic theory. In order to lengthen the structure of production, individuals must lower their time preference and save more of their income. Thus Keynes has it backward, an increase in employment does not automatically increase new investment; new investment spurs economic growth and new employment opportunities.
This seems to be the big take away here: if the propensity to consume isn't high enough--or low enough?--unemployment will result. I can't seem to find what that rate should be, so if you could point that out, I'd be grateful.

I don’t think even Keynes knows what the rate should be; just that he thinks a low propensity to consume – high savings rate – is bad for employment. I don’t think I need to go into why this is an incorrect assertion, but if you want to talk about it further I would be happy to.

Jeff said...

Sorry if the format is unclear. I attempted to use your style of italics for the portion of text I am commenting on, but could not get it to work. What's the secret?

A Wiser Man Than I said...

What's the secret?

Become a computer programmer. Either that or just know one.

You should at least know a few html tags.

For italics, it goes: less than sign, i, greater than sign, text you want in italics, less than sign, backslash, greater than sign.

If you replace the i with b, you get bold. The Wiki has a pretty thorough list; I've come across many of them while coding, but you only need to use a few for commenting on the Internet.