13 There is only a transient difference between the firm and worker bailouts on this front, while the bailout is being made. Workers' consumption is higher for the duration of the bailout if they receive the money since they spend almost all of what they receive but their incomes are slightly lower than when the firms get the bailout.

14 However, a more complete model is as likely to amplify these basic results as it is to attenuate them. For example, the injection of fiat money puts the banking sector's a.s.sets and liabilities out of balance, when an essential aspect of banking practice is that they are balanced. The firms bailout could thus force the banks to lend more rapidly to bring their a.s.sets back into line with their liabilities, thus amplifying the boost from the fiat money injection.

15 The equation is derived in Keen (2010: 1719). The basic idea is as follows. The monetary value of demand equals wages plus profits, and as explained above this equals the money in the firms' deposit accounts, divided by the turnover period. The monetary value of supply is the price level times output, and output is labor times average labor productivity. The number of workers employed in turn equals the monetary value of wages divided by the wage rate. In this simple model, the monetary value of wages also depends on the balance in the firms' deposit accounts: it's equal to the amount in the firms' deposit accounts, divided by the turnover period, and multiplied by the share of surplus that goes to workers. Some cancelation yields the result that, in equilibrium, the price level will equal the wage level, divided by labor productivity and multiplied by the inverse of workers' share of surplus. A dynamic equation has prices converging to this level over time.

16 Fitting a nonlinear model to data is something mathematicians describe as a 'non-trival' exercise which in lay-speak is something that takes eons to do and requires supercomputer processing power. I will do this for my next book with a far more complex model than the one shown here.

Chapter 15.

1 A subscriber to my blog pointed out another reason: accepting the gamble involves wagering money that has taken you time and effort to earn, against the possibility of a chance gain. Most people sensibly value the effort they've put into earning something more highly than what they might get from a gamble.

2 I say 'almost' because the degree of uncertainty drops as the probability rises. If you were spinning a roulette wheel, and only one of its thirty-eight slots would lose you money, there's far less uncertainty about the outcome of any one spin than there is with a coin toss.

3 These are obviously very similar to those used by Samuelson to derive the concept of revealed preference, but one interesting difference is that von Neumann was aware that at least the first of these was doubtful in practice. However, he argued that, if this were true, then it undermined both his approach and indifference curves: 'We have conceded that one may doubt whether a person can always decide which of two alternatives with the utilities u, v he prefers. But, whatever the merits of this doubt are, this possibility i.e. the completeness of the system of (individual) preferences must be a.s.sumed even for the purposes of the "indifference curve method." But if this property of u>v is a.s.sumed, then our use of the much less questionable [probabilistic method] yields the numerical utilities too!' (von Neumann and Morgenstern 1953: 289).

4 Chaos was first 'discovered' by Henri Poincare in 1899, when he tried to find a solution to the 'many body problem' the problem of gravitational attraction between a star and more than just one planet and instead proved that there was no a.n.a.lytic solution; instead, the bodies would follow complex aperiodic paths (i.e. cycles occur which never exactly repeat themselves, unlike conventional cyclical functions like sine waves, etc.), which were later labelled 'chaotic.'

5 More complex data distributions are predicted by some more elaborate versions of the EMH, but the normal distribution is still the overall yardstick.

6 There are a number of econometric a.n.a.lyses that attempt to account for this. As Peters comments, they capture some of the local statistical features, but fail to capture the overall characteristics (Peters 1994).

7 Haugen is effectively a proponent of 'behavioral finance,' which has been gaining acceptance in applied and academic finance in recent years, though its adherents are still a minority compared to supporters of the Efficient Markets Hypothesis.

8 A remark that Yi-Cheng Zhang made in response to a question from Paul Ormerod as to how Econophysics came about, during a dinner at the first Econophysics conference in Bali in 2002.

9 I will cover these approaches to finance in more detail in my next book, Finance and Economic Breakdown.

10 The fact that unemployment to date has not reached Great Depression heights owing in part to the under-reporting of unemployment in official statistics, as noted earlier should be no comfort until this crisis is over and unemployment has returned to pre-crisis levels. Since the level of private debt is still enormous 260 percent of GDP as of December 2010, 90 percent higher than the pre-Great Depression level it is likely that this crisis has many years to run.

11 I am going somewhat beyond Kornai's logic in this paper, but in the spirit of his concepts of hard and soft budget constraints.

12 Debt that adds to the economy's productive capacity can expand this constraint over time, but Ponzi lending inflates a.s.set prices without increasing the quant.i.ty or productivity of a.s.sets.

Chapter 16.

1 This proof is very easy to understand, even if you don't think you're good at mathematics. If you a.s.sume that the square root of 2 is the ratio of two integers, then you can label these two as yet unknown integers a and b, and know that they have no common factors. Starting from the a.s.sumption that the square root of 2 equals a divided by b, you get rid of the square root by squaring both sides, so that a squared divided by b squared equals 2. This now tells you that a squared equals 2 times b squared, which is only possible if a is an even number since if you square an odd number, you get another odd number. This now means that a has to equal two times some other number call this c. Since a squared equals 2 times b squared, and a equal 2 times c, it also follows that 4 times c squared equals 2 times b squared. Divide both sides by 2 and you now find that b squared equals 2 times c squared. This means that b is also an even number but this means that a and b have the common factor of 2. This contradicts your a.s.sumption that they have no common factors. Therefore the square root of 2 can't be the ratio of two integers, and it is therefore irrational.

2 This is that for changing all incomes and prices by the same factor to have no effect, 'all other nominal magnitudes [including] a.s.sets and liabilities that are expressed in nominal terms)' (Friedman 1969: 1) have to be altered by the same factor as well and even this ignores the fact that debt amortization makes the effect of interest rates nonlinear.

3 One example of this is the paper by Caplan (2000) which attempts to explain findings which show that experimental subjects do not conform to the neocla.s.sical definition of rational. Rather than accepting that the neocla.s.sical definition of rationality may be flawed, Caplan proposes that irrationality may be a 'good,' which people 'consume' like any other, and then represents a rationalityirrationality trade-off using indifference curves. This one article is not the final word on the neocla.s.sical response to such findings. But I expect it to be far more readily adopted by the profession than any acknowledgment that the 'curse of dimensionality' makes rational behavior as economists define it simply impossible in the real world.

4 Though this branch of mathematics provides many tools which enable mathematicians to characterize the behavior of more complex and realistic models of the real world including such things as differential equation models of the economy.

Chapter 17.

1 Though economists from several other schools of thought still pay great attention to Marx's original writings on economics, and see Marx as the father of many important concepts in economic a.n.a.lysis.

2 This story may or may not be apocryphal. Check the website thebeadsite.com/FRO-MANG.html for one perspective, and www.crazyhorse.org/ for another.

3 Sraffa's critique of the concept of an upward-sloping demand curve, and the critiques of the market demand curve covered earlier, also undermine the neocla.s.sical position and support the cla.s.sical view.

4 The subject was a bone of contention from the time of Aristotle on. However, predecessors to the physiocrats were quite unsystematic about the determination of value and price.

5 This means that as output rose, costs of production fell. Smith was thus thinking in terms of a 'downward-sloping supply curve' at least in the medium to long term in contrast to the upward-sloping supply curve that is so central to economics today, which was debunked in Chapter 5.

6 All these examples were hypothetical, of course: Ricardo did not go out and measure the labor involved in producing the means of production in any industry, and then present his findings.

7 'Not only his labouring servants, but his labouring cattle, are productive labourers' (Smith 1838 [1776]).

8 'By the invention of machinery [...] a million of men may produce double, or treble the amount of riches, [...] but they will on no account add anything to value' (Ricardo 1817). Marx commented that 'This is quite wrong. The value of the product of a million men does not depend solely on their labor but also on the value of the capital with which they work' (Marx 1968 [1861]: Part II, p. 538).

9 Marx qualified this as 'socially necessary labor-time,' to take account of the possibility of out-of-equilibrium situations in which more labor-time might be lavished on a product than could be recouped by its sale.

10 There is no reason why the rate of surplus value should be constant over time in practice, and Joan Robinson used this as the basis of her critique of Marxian economics. She argued that an increase in c could cause a rise in s/v, the rate of surplus value, so that the rate of profit would not fall over time.

11 There were several counter-tendencies that could attenuate this, but ultimately Marx thought the tendency of the rate of profit to fall would prevail.

12 This is an extremely brief outline of a much more complicated argument. Its purpose is not to provide a detailed exposition of Marx's theory of revolution, but to prepare the ground for critiques of the labor theory of value.

13 This is clearly unrealistic, but the logic is the same even if we incorporate the reality that corn would be needed to produce corn. Steedman's example just made the numerical algebra easier to follow. He then continued his argument using symbolic linear algebra, to establish the generality of his a.n.a.lysis.

14 If I had worked with exact numbers rather than rounded them to two decimal places, the two calculations would have corresponded exactly. The value calculations, on the other hand, differ systematically, and by far more than can be attributed to rounding error.

15 Similar arguments had been made before, as early as at the end of the nineteenth century. Steedman simply provided the most comprehensive and definitive critique.

16 I dispute Bose's reading of Marx on this subject, but find the logic in his 'essence of value' a.n.a.lysis impeccable.

17 He also employed a set of axioms from which his conclusions were derived.

18 At each step in the reduction, one period's capital inputs are reduced to the previous period's direct labor and capital inputs, marked up by the equilibrium rate of profit.

19 Services such as a ma.s.sage, which might appear to be a commodity-free good, involve commodities directly (ma.s.sage bench, oil), and if even these are forgone (an oil-free ma.s.sage while lying on bare ground), they involve it indirectly through the need for the ma.s.seur to eat to stay alive. The commodity 'ma.s.sage' could therefore not be reproduced in the absence of commodity inputs, such as food.

20 Marx's philosophy was derived from Hegel's, with Marx arguing that he replaced Hegel's idealism with realism. Dialectics is popularly known as the trio of thesis-ant.i.thesis-synthesis, and though this concept is popularly a.s.sociated with both Hegel and Marx, it in fact derives from another, lesser-known philosopher, Fichte. For an intelligent discussion of dialectical philosophy in general, and Marx's application of it in particular, see Wilde (1989).

21 In a different type of economy, use-value could well be brought to the foreground: commodities could be produced for the ruling elite at ostentatious expense, without regard to their cost of production. I well remember seeing a backscratcher in the Forbidden Palace in Beijing, made out of jade, gold, diamonds, emeralds and rubies.

22 This 'discovery' of the application of dialectical philosophy to economics occurred after Marx happened to re-read Hegel while he was drafting the Grundrisse (Oakley 1983; Mandel 1971).

23 Marx's discussion of this example still attributed the increased surplus-value to labor; however, the source of this difference was not any difference in the rate of surplus value with respect to labor employed, but to the postulate that the machine's use-value exceeded its exchange-value.

24 'Exchange-value and use-value [are] intrinsically incommensurable magnitudes' (Marx 1867). Notice that Marx describes use-value as a magnitude in this circ.u.mstance. Outside production, when commodities are purchased to be consumed rather than being used to produce other commodities, their use-value will be qualitative, and therefore incommensurable with their exchange-values.

Chapter 18.

1 This is a necessarily brief and personally opinionated survey of five very complex schools of thought. Readers who wish to delve deeper should consult the references given in this chapter. I have also omitted separate discussion of a notable school of economic thought, inst.i.tutional economics, because I expect it to be subsumed under evolutionary economics.

2 Though evolutionary theorists themselves now argue that Darwin's vision of the evolutionary process, in which 'nature did not make jumps,' is flawed, and that therefore Darwinism is an inappropriate label for modern evolutionary theory (Schwartz 2000).

3 And, ironically, some evolutionary theorists are now arguing that biological evolution may in some ways be purposive (McFadden 2001).

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