The complications don't stop there. Since the theory of the supply curve which we'll encounter in the next two chapters a.s.sumes that an increase in demand will drive up the price, the budget 'line' can't be a line: it must be a curve. In the isolated consumer example, not only did we a.s.sume that changing prices didn't alter the consumer's income, we also a.s.sumed that the consumer's purchases didn't affect the market price. This a.s.sumption is also invalid once we consider more than one consumer, which we must do to construct a market demand curve.

When Friday purchases the first banana, he pays a low price; the second banana costs more to produce (because of 'diminishing marginal productivity,' which we encounter in the next two chapters), so as well as his income changing, the price for bananas rises as his consumption of them rises. Each additional banana that Friday buys will therefore be more expensive than the previous one. The budget curve might start at the same point as the 'line' did (with an isolated consumer) when consumption is zero, but it must slope more steeply than the line as the consumer's consumption rises above zero.

3.12 A valid market demand curve.

The situation is no better when we consider the demand that Crusoe has for the bananas he produces himself: his income rises as price rises, increasing his income, and his demand for bananas still drives the cost up because according to the theory of the supply curve, the cost of production rises owing to falling productivity as output rises. There is no way to know which effect will dominate.

What was a straightforward exercise when each consumer was considered in isolation is therefore an unholy mess when we consider more than one individual, which we must do to derive a market demand curve. You can still derive points of tangency between these moving budget curves and the fixed indifference curves for each individual, and thus derive an individual demand curve, but it will no longer necessarily obey the 'Law' of Demand and you can no longer easily separate the income and subst.i.tution effects either, since you cannot control incomes independently of prices anymore.

Finally, the market demand curve that is produced by summing these now poorly behaved individual demand curves will conflate these wildly varying influences: increasing price will favor the producer (thus increasing his demand) while disadvantaging the consumer (thus decreasing his demand); rising income for the luxury-good producer will increase his income while decreasing that of the necessity producer. As the sum of these tendencies, the market demand curve will thus occasionally show demand rising as price falls, but it will also occasionally show demand falling as price falls. It will truly be a curve, because, as the neocla.s.sical economists who first considered this issue proved (Gorman 1953), it can take any shape at all except one that doubles back on itself.

Crucially, it can disobey the so-called 'Law of Demand': the quant.i.ty demanded can rise as the price rises. This has nothing to do with sn.o.b value, or price signaling quality, or any of the behavioral wrinkles that critics often throw at the a.s.sumptions that neocla.s.sical economists make. The wavy demand curve shown in Figure 3.12 can be generated by ordinary, everyday commodities as soon as you move beyond the isolated individual.

This result known as the 'Sonnenschein-Mantel-Debreu [SMD] conditions' proves that the 'Law' of Demand does not apply to a market demand curve. If the market demand curve can have any shape at all, then there can be two or more possible demand levels for any given price, even if all consumers are rational utility maximizers who individually obey the Law of Demand. If only neocla.s.sical economists had stated the result that honestly and accurately when it was first derived almost sixty years ago, economics today might be very different.

Instead, because the result was found by neocla.s.sical economists who wished to prove the opposite of what they had in fact discovered, the result has been buried by a degree of obfuscation and evasion that makes the average corporate cover-up look tame by comparison.

Cut off at Pythagoras' pa.s.s.

This result was first derived by neocla.s.sical economists who had posed the question 'under what conditions will the market demand curve have the same properties as the individual demand curve?', and they were hardly pleased with their discovery. Though technically the a.n.a.lysis was a 'tour de force' the sort of technical prowess that wins you awed respect from your peers practically they clearly wished that they had proved the opposite result: that, despite the conundrums in moving from an isolated individual to multiple consumers, the Law of Demand still held.

They found themselves in the same situation as the ancient Pythagorean mathematicians, who believed that all numbers could be expressed as the ratio of two integers. The discovery that this was not the case 'destroyed with one stroke the belief that everything could be expressed in integers, on which the whole Pythagorean philosophy up to then had been based' (Von Kurt 1945: 260).

Today, we're all familiar with the fact that if you draw two lines at right angles that are precisely one inch long, and draw a line between them, that line's length will be the square root of two inches long, which is an irrational number a number that can't be expressed as the ratio of two integers. The fact that combining two rational numbers according to the laws of geometry generates an irrational number is now common knowledge. Neither mathematics nor the world has collapsed as a result in fact both mathematics and the world are far richer for this discovery and the many that followed on from it.

However, the initial reaction of Pythagorean mathematicians to this discovery was brutal: they allegedly drowned Hippasus of Metapontum, who was the first to discover that irrational numbers existed. But to their credit, they subsequently embraced the existence of irrational numbers, and mathematics developed dramatically as a result.

Economists could have reacted intelligently to their discovery too. They had proved that if you take two consumers whose individual demand curves obey the Law of Demand, and add them together to get a market demand curve, that curve does not necessarily obey the Law of Demand. So adding two or more 'rational' consumers together generates an 'irrational' market. Therefore, market a.n.a.lysis has to transcend the simple rules that seemed to work for isolated consumers, just as mathematicians had to transcend the rules that apply when mathematical operations on rational numbers return only rational numbers.

Such a reaction by economists could have led to a far richer vision of economics than the simplistic one in which the Law of Demand applies, and in which all markets are a.s.sumed to be in equilibrium. Unfortunately, the way that they did react made the irate Pythagoreans who drowned Hippasus look like amateurs. Rather than drowning the discoverer of the result, neocla.s.sical economists drowned the result itself.

Having proved that in general the 'Law of Demand' did not apply at the level of the market, they looked for the conditions under which it would apply, and then a.s.sumed that those conditions applied to all markets. It's as if Pythagoreans, on discovering that the square root of two was an irrational number, forbade for evermore the drawing of equal-sided right-angled triangles.

The Pythagorean a.n.a.logy continues to apply here, because the conditions that were needed to 'ensure' that the Law of Demand applied at the market level are in fact a 'proof by contradiction' that it can't apply. Proof by contradiction is a venerable mathematical technique, and it can be used to establish that the square root of two is an irrational number. Not knowing the answer to a question 'Is the square root of two a rational number?' you a.s.sume that the answer is 'Yes,' and then follow through the logic of your a.s.sumption. If you generate a contradiction, you then know that the correct answer is 'No: the square root of two is not a rational number.'10 The two 'conditions' that economists found were necessary to guarantee that the 'Law of Demand' applied to the market demand curve were: a) that all Engel curves are straight lines; and b) that the Engel curves of all consumers are parallel to each other.

The first condition means that all commodities have to be neither luxuries nor necessities nor inferior goods, but 'neutral' or 'h.o.m.othetic.' Therefore your ratios in which you consume different goods would have to remain fixed regardless of your income: if on an income of $100 a week, you spent $10 on pizza, then on an income of $100,000 a week you would have to spend $10,000 on pizza.

3.13 Straight-line Engel 'curves'

Clearly this is nonsense: as incomes rise, your consumption pattern would alter. There is only one situation in which this wouldn't apply: if there was only one commodity to consume. That is the real meaning of condition (a): there is only one commodity.

Condition (b) is just as absurd. For all consumers to have parallel Engel curves, all consumers have to have identical tastes. Clearly this is also nonsense: different consumers are identifiable by the very fact that they do have different tastes.

Even saying that the Engel curves of different consumers are parallel to each other is an obfuscation it implies that two consumers could have parallel but different Engel curves, just as two lines that are parallel to each other but separated by an inch are clearly different lines. However, as anyone who has studied geometry at school knows, parallel lines that pa.s.s through the same point are the same line. Since a consumer with zero income consumes zero goods in neocla.s.sical theory,11 all Engel curves pa.s.s through the point 'zero bananas, zero biscuits' when income is zero. Therefore condition (b) really is that 'the Engel curves of all consumers are identical.'

There is only one situation in which this could apply: if there was only one consumer.

That is the real meaning of these two conditions: the Law of Demand will apply if, and only if, there is only one commodity and only one consumer. But in such a situation, the very idea of a 'Law of Demand' makes no sense. The whole purpose of the Law of Demand is to explain how relative prices are set, but if there is just one commodity and one consumer, then there can be no relative prices. We have a contradiction: we start from a.s.suming that the Law of Demand applies, and then find that for this to be true, there can be only one commodity and one consumer a situation in which the Law of Demand has no meaning.

These conditions are thus a proof by contradiction that the Law of Demand does not apply to the market demand curve: market demand does not necessarily increase when price falls, even if individual demand does.

This discovery is thus akin to the Pythagorean discovery of irrational numbers: adding together 'rational' consumers can result in an 'irrational' market. This discovery should have had an equally revolutionary and ultimately beneficial impact upon economic theory. The simple parables of intersecting demand and supply curves would have had to give way to a more complicated but necessarily more realistic theory, in which prices would not be in equilibrium and the distribution of income would alter as prices alter.

If only.

Drowning the result.

The economist who first discovered this result the Hippasus of neocla.s.sical economics was William Gorman. As noted earlier, Hippasus was (allegedly) drowned for his trouble. Gorman, on the other hand, drowned his own result. He proved the result in the context of working out whether there was an economy-wide equivalent to an individual's indifference curves: 'we will show that there is just one community indifference locus through each point if, and only if, the Engel curves for different individuals at the same prices are parallel straight lines' (Gorman 1953: 63; emphasis added).

He then concluded, believe it or not, that these conditions were 'intuitively reasonable': 'The necessary and sufficient condition quoted above is intuitively reasonable. It says, in effect, that an extra unit of purchasing power should be spent in the same way no matter to whom it is given' (ibid.: 64).

'Intuitively reasonable'? As I frequently say to my own students, I couldn't make this stuff up! Far from being either intuitive or reasonable, Gorman's rationalization is a denial of one of the fundamental issues that most non-economists think economists must understand: the distribution of income. If the distribution of income changes, then surely the consumption pattern of society will change. I regard Gorman's statement here as the economic equivalent of the remark attributed to Marie Antoinette on being told that the peasants had no bread: 'Let them eat cake.'12 Gorman's original result, though published in a leading journal, was not noticed by economists in general possibly because he was a precursor of the extremely mathematical economist who became commonplace after the 1970s but was a rarity in the 1950s. Only a handful of economists would have been capable of reading his paper back then. Consequently the result was later rediscovered by a number of economists hence its convoluted name as the 'Sonnenschein-Mantel-Debreu conditions.'

These economists were far less sanguine than Gorman about the 'conditions' needed for the Law of Demand to apply to a market demand curve. However, they still failed to make the logical leap to realize that they had disproved a core belief of neocla.s.sical economics, and their statements of the result were, if anything, even more obtuse than was Gorman's: 'Can an arbitrary continuous function [...] be an excess demand function for some commodity in a general equilibrium economy? [...] we prove that every polynomial [...] is an excess demand function for a specified commodity in some n commodity economy [...] every continuous real-valued function is approximately an excess demand function' (Sonnenschein 1972: 54950).

Translating this into English, a polynomial is a function consisting of constants and powers of some variable. The most well-known polynomials are the equation for a straight line, which is a polynomial of order one, and a parabola (a polynomial of order two). Any smooth curvy line that doesn't cross over itself can be fitted by a polynomial of sufficiently high order, so what Sonnenschein is saying here is that a demand curve can take any shape at all, except one that intersects with itself.13 Therefore the 'Law of Demand' does not apply to the market demand curve. His joint summary of this result with Shafer for the encyclopedic Handbook of Mathematical Economics (Arrow et al. 198193) was more aware of the absurdity of the conditions, but still didn't connect the dots to comprehend that the conditions were a proof by contradiction that the Law of Demand is false: First, when preferences are h.o.m.othetic and the distribution of income (value of wealth) is independent of prices, then the market demand function (market excess demand function) has all the properties of a consumer demand function [...]

Second, with general (in particular non-h.o.m.othetic) preferences, even if the distribution of income is fixed, market demand functions need not satisfy in any way the cla.s.sical restrictions which characterize consumer demand functions [...]

The importance of the above results is clear: strong restrictions are needed in order to justify the hypothesis that a market demand function has the characteristics of a consumer demand function. Only in special cases can an economy be expected to act as an 'idealized consumer.' The utility hypothesis tells us nothing about market demand unless it is augmented by additional requirements. (Shafer and Sonnenschein 1993) As opaque as those statements might be, if they had been clearly pa.s.sed on to economics students, the realization that the simple parables of supply and demand had to be replaced by something more sophisticated could have developed.

If only.

Don't tell the children.

We now confront what will become a common theme in this book: the mendacious nature of economic textbooks. In the hands of economics textbook writers, the opaque but accurate statements of the SMD conditions above either disappear completely, or are portrayed in such a way that their significance will be perceived only by hypercritical students like yours truly when I suffered through these courses while doing my Master's.

For many years, the leading text for Honors, Master's and PhD programs was Hal Varian's Microeconomic a.n.a.lysis (Varian 1992). Varian 'summarized' this research so opaquely that it's no surprise that most PhD students including those who later went on to write the next generation of undergraduate textbooks didn't grasp how profoundly it challenged the foundations of neocla.s.sical theory.

Varian started with the vaguest possible statement of the result: 'Unfortunately [...] The aggregate demand function will in general possess no interesting properties [...] Hence, the theory of the consumer places no restrictions on aggregate behavior in general.'

The statement 'no interesting properties' could imply to the average student that the market demand curve didn't differ in any substantive way from the individual demand curve the exact opposite of the theoretical result. The next sentence was more honest, but rather than admitting outright that this meant that the 'Law of Demand' didn't apply at the market level, he immediately rea.s.sured students that there was a way to get around this problem, which was to: 'Suppose that all individual consumers' indirect utility functions take the Gorman form [... where] the marginal propensity to consume good j is independent of the level of income of any consumer and also constant across consumers [...] This demand function can in fact be generated by a representative consumer' (ibid.: 1534; emphases added. Curiously the innocuous word 'generated' in this edition replaced the more loaded word 'rationalized' in the 1984 edition.) Finally, when discussing aggregate demand, he made a vague and rea.s.suring reference to more technical work: 'it is sometimes convenient to think of the aggregate demand as the demand of some "representative consumer" [...] The conditions under which this can be done are rather stringent, but a discussion of this issue is beyond the scope of this book [...]' (Varian 1984: 268).

It's little wonder that PhD students didn't realize that these conditions, rather than merely being 'rather stringent,' undermined the very foundations of neocla.s.sical economics. They then went on to build 'representative agent' models of the macroeconomy in which the entire economy is modeled as a single consumer, believing that these models have been shown to be valid. In fact, the exact opposite is the case.

The modern replacement for Varian is Andreu Mas-Colell's hyper-mathematical but utterly non-empirical Microeconomic Theory (Mas-Colell, Whinston et al. 1995). At one level, this text is much more honest about the impact of the SMD conditions than was Varian's. In a section accurately described as 'Anything goes: the Sonnenschein-Mantel-Debreu Theorem,' Mas-Colell concludes that a market demand curve can have any shape at all, even when derived from consumers whose individual demand curves are downward-sloping: Can [... an arbitrary function] coincide with the excess demand function of an economy for every p [price ...] Of course [... the arbitrary function] must be continuous, it must be h.o.m.ogeneous of degree zero, and it must satisfy Walras' law. But for any [arbitrary function] satisfying these three conditions, it turns out that the answer is, again, 'yes.' (Ibid.: 602) But still, the import of this result is buried in what appear to the student to be difficult problems in mathematics, rather than a fundamental reason to abandon supply and demand a.n.a.lysis. Earlier, when considering whether a market demand curve can be derived, Mas-Colell begins with the question: 'When can we compute meaningful measures of aggregate welfare using [...] the welfare measurement techniques [...] for individual consumers? (ibid.: 116).

He then proves that this can be done when there is 'a fictional individual whose utility maximization problem when facing society's budget set would generate the economy's aggregate demand function' (ibid.: 116). However, for this to be possible, there must also exist a 'social welfare function' which: 'accurately expresses society's judgments on how individual utilities have to be compared to produce an ordering of possible social outcomes. We also a.s.sume that social welfare functions are increasing, concave, and whenever convenient, differentiable' (ibid.: 117).

This is already a case of a.s.suming what you wish to prove any form of social conflict is a.s.sumed away but it's still not sufficient to generate the result Mas-Colell wants to arrive at. The problem is that the actual distribution of wealth and income in society will determine 'how individual utilities are compared' in the economy, and there is no guarantee that this will correspond to this 'social welfare function.'

The next step in his 'logic' should make the truly logical and the true believers in economic freedom recoil in horror, but it is in fact typical of the sorts of a.s.sumptions that neocla.s.sical economists routinely make to try to keep their vision of a perfectly functioning market economy together. To ensure that the actual distribution of wealth and income matches the social welfare function, Mas-Colell a.s.sumes the existence of a benevolent dictator who redistributes wealth and income prior to commerce taking place: 'Let us now hypothesize that there is a process, a benevolent central authority perhaps, that, for any given prices p and aggregate wealth function w, redistributes wealth in order to maximize social welfare' (ibid.: 117; emphases added).

So free market capitalism will maximize social welfare if, and only if, there is a benevolent dictator who redistributes wealth prior to trade??? Why don't students in courses on advanced microeconomics simply walk out at this point?

I surmise that there are three main reasons, the first of which is ba.n.a.l. Mas-Colell's book is huge just short of 1,000 pages and lecturers would cherry-pick the sections they teach. I doubt that most students are exposed to this statement by their instructors, and few are likely to read parts that aren't required reading for pleasure alone.

Secondly, the entire text is presented as difficult exercises in applied mathematics. Students are probably so consumed with deriving the required answers that they gloss over English-language statements of these a.s.sumptions which make it blatantly obvious how insane they are.

Thirdly, by the time students get to this level normally in PhD programs they are so locked into the neocla.s.sical 'a.s.sumptions don't matter' mindset that I discuss in Chapter 8 that they don't even worry if an a.s.sumption is insane.

From this bizarre point on, Mas-Colell, like Varian before him, encourages students to build models of the macroeconomy in which all agents have 'the Gorman form' of utility function i.e. models of the macroeconomy in which there is one commodity and one consumer so that students believe that the entire economy can be modeled as a single representative agent. Mas-Colell cautions that this involves a special a.s.sumption, but that caution is probably lost in the mist that envelops the mind of a budding neocla.s.sical economist: If there is a normative representative consumer, the preferences of this consumer have welfare significance and the aggregate demand function can be used to make welfare judgments by means of the techniques [used for individual consumers]. In doing so however, it should never be forgotten that a given wealth distribution rule [imposed by the 'benevolent central authority'] is being adhered to and that the 'level of wealth' should always be understood as the 'optimally distributed level of wealth.' (Ibid.: 118; emphasis added) These high-level texts, though, are at least honest that there is a problem in aggregating from the individual consumer to the market demand curve. Undergraduate students instead are rea.s.sured that there is no problem. Paul Samuelson's iconic undergraduate textbook makes the following didactic statement about how a market demand curve is derived, and whether it obeys the 'Law of Demand,' which flatly contradicts the SMD results: The market demand curve is found by adding together the quant.i.ties demanded by all individuals at each price. Does the market demand curve obey the law of downward-sloping demand? It certainly does.

If prices drop, for example, the lower prices attract new customers through the subst.i.tution effect. In addition, a price reduction will induce extra purchases of goods by existing consumers through both the income and the subst.i.tution effects. Conversely, a rise in the price of a good will cause some of us to buy less. (Samuelson and Nordhaus 2010: 48; emphasis added) The leading undergraduate textbook today, by Gregory Mankiw, is equally misleading. It also implies that all that is needed to derive a market demand curve is to horizontally sum individual demand curves: 'The table in Figure 2 shows the demand schedules for ice cream for the two individuals in this market Catherine and Nicholas [...] The market demand at each price is the sum of the two individual demands [...] Notice that we sum the individual demand curves horizontally to obtain the market demand curve [...]' (Mankiw 2008: 68).

Other undergraduate textbooks either ignore the issue completely, or make similarly false statements. Who, then, can blame undergraduate economics students for believing that all is well with the underlying theory? The blame instead lies with textbook writers, and the question this raises is, do they know they are at fault? Did they knowingly conceal this advanced result from their students, or were they themselves ignorant of it?

Samuelson was certainly aware of Gorman's result, though he may not have followed the subsequent work of Sonnenschein and others because he believed he had proved that the Law of Demand does apply to the market demand curve (Samuelson 1956. And so he had but using an a.s.sumption which shows how utterly unrealistic even the most famous of neocla.s.sical economists can be. He began quite sensibly, by noting that it was absurd to model an entire country as a single utility-maximizing individual: What defense do we make when challenged on the use of community indifference curves for a country or group of individuals? I suppose one of the following: (a) We may claim that our country is inhabited by Robinson Crusoe alone and claim only to show how trade between such single person countries is determined. This is admittedly not very realistic.

(b) In order to give the appearance of being more realistic, we may claim that our country is inhabited by a number of identical individuals with identical tastes; they must also have identical initial endowments of goods if this artifice of examining what happens to the representative individual's indifference curves is to give us a true description of the resulting market equilibrium. This case, too, is not very realistic, though it may seem a slight improvement over Robinson Crusoe [...]. (Ibid.: 3) He then noted that most shopping is done by families, and since these consist of separate individuals, it is impossible even to construct a 'family indifference curve,' so that consumption by a family will also violate the foundations of the Law of Demand (the so-called Axioms of Revealed Preference, which are discussed in the addendum to this chapter).

However, he next surmised that if, within the family, optimal transfers of income are undertaken, then a family indifference curve can be constructed which has all the properties of an individual indifference curve.

Since blood is thicker than water, the preferences of the different members are interrelated by what might be called a 'consensus' or 'social welfare function' which takes into account the deservingness or ethical worths of the consumption levels of each of the members. The family acts as if it were maximizing their joint welfare function [...] Income must always be reallocated among the members of our family society so as to keep the 'marginal social significance of every dollar' equal. (Ibid.: 1011; emphasis added) Finally, he hypothesized that if the entire nation behaves like one big happy family, and optimally reallocates income between its members prior to consumption, then society will also have 'well-behaved' indifference curves that obey the 'Law of Demand': The same argument will apply to all of society if optimal reallocations of income can be a.s.sumed to keep the ethical worth of each person's marginal dollar equal. By means of Hicks's composite commodity theorem and by other considerations, a rigorous proof is given that the newly defined social or community indifference contours have the regularity properties of ordinary individual preference contours (nonintersection, convexity to the origin, etc.). (Ibid.: 21; emphasis added) Words fail me. Samuelson had 'proved' that social indifference curves exist and therefore that market demand curves behave just like individual ones by a.s.suming that in a capitalist society, incomes are continuously adjusted so that an ethical distribution of income is achieved. Did he even live in the United States?14 Yet on this basis, he confidently flourishes to his students that the market demand curve 'certainly does [...] obey the law of downward-sloping demand.'

Samuelson's reason for perpetuating a falsehood is thus similar to Gorman's, who was capable of holding the equally delusional view that the proposition that 'an extra unit of purchasing power should be spent in the same way no matter to whom it is given' is 'intuitively reasonable.' So Samuelson, in a bizarre way, 'knew' what he was doing.

But in general I expect that the reason that undergraduate textbooks (written by lesser lights than Samuelson and Gorman) are so misleading is that the authors themselves are unaware of this critical literature.

This may seem bizarre: surely textbook writers must know the economic literature thoroughly in order to write a textbook in the first place? And haven't they done Master's and PhD courses, where they would at least have to read Varian or Mas-Colell on this topic?

Maybe. However, as I've pointed out above, the advanced textbooks present this result in such an obtuse way that it would be possible for a Mankiw to read this material, pa.s.s exams on it, and never even contemplate its true import. He might remember the 'Gorman form' limitation that had to be imposed to make aggregation possible, but he would probably regard this as just too difficult to teach to undergraduates. Undergraduate economic textbooks themselves have been 'dumbed down' so much in the last thirty years that even indifference curves an essential element in this farce are no longer taught in first-year courses. So the basics needed to even explain why there might be a problem are no longer part of the introductory pedagogy. Also, I expect that the Mankiws of the economics profession haven't read the original papers by Sonnenschein, Mantel and so on and as I've noted, in a way they can't be criticized for this. Academics are accustomed to not having to read the original literature in their discipline, because they rely on their textbooks to accurately portray the key results of fundamental research. This belief is justified in physics where even introductory texts point out that quantum mechanics and relativity can't be reconciled but it is a false belief in economics.

Finally, in stark contrast to how a true science develops, this entire literature was developed not to explain an empirically observed phenomenon, but to examine the logical coherence of an utterly abstract, non-empirical model of consumer behavior. Downward-sloping demand curves were therefore not an empirical regularity for which a theory was needed, but a belief that economists had about the nature of demand that the vast majority of them took for granted. Most of them continue to hold this belief, unaware that mathematically erudite economists have shown that it is false. Since the underlying discipline is non-empirical, there is no disconnect between theory and reality that might warn them that something is wrong with the theory.

Worse still, the rationalization of a 'representative consumer' permeates modern economics it has even taken over macroeconomic a.n.a.lysis, so that economists model an entire economy as if there is only one person in it (which they describe by the more general term of 'representative agent'). Many academic economists doubtless believe that the representative agent has been shown to be a valid abstraction. Yet far from being valid, it is in fact a fudge, devised to get around the failure to prove that society can be reduced to the sum of its const.i.tuent individuals.

Following the madding crowd.

There are many other reasons why economists did not recoil from the patent absurdities outlined above, and search for a sounder approach to economic theory than Bentham's individualistic calculus.

One is that economics has been wedded to the vision of society as simply a sum of utility-maximizing individuals since the inception of neocla.s.sical economics in the 1870s. When the proof came, one century later, that this vision was internally inconsistent, the commitment to the vision was too strong to break. Better to search for special conditions which could let the theory survive however ludicrous they might be than to admit failure.

A second reason is that the peculiar language and mathematics used to derive these results makes it difficult to see just how absurd the a.s.sumptions needed to sustain the aggregation process are. It sounds much more highbrow to say that 'preferences are a.s.sumed to be h.o.m.othetic and affine in income' than it does to say 'we a.s.sume all consumers are identical and never change their spending habits as their incomes increase.'

A third reason, perhaps the key one, is the division of mainstream economists into effective 'castes,' with only a tiny but exalted subset of the profession undertaking the detailed mathematical work needed to discover the weaknesses in the theory. The vast majority of economists believe that this high caste, the mathematical economists, did their work properly, and proved that the theory is internally consistent. The caste has indeed done its work properly, but it has proved precisely the opposite: that the theory is consistent only under the most restrictive and specious of a.s.sumptions.

However, rather than taking the next logical step, and acknowledging that the foundations of economics are unsound and must therefore be changed, most mathematical economists are so wedded to this way of thinking, and so ignorant of the real world, that they instead invent some fudge to disguise the gaping hole they have uncovered in the theory.

The majority of economists, blithely unaware of this state of affairs, then accept this fudge by the Brahmins of the profession as faithfully as devout Hindus accept the cleansing properties of the Ganges river. As a result, the fudge then turns up in more mundane areas of economics, such as 'macroeconomics' (discussed in Chapter 10), where economists today a.n.a.lyze the economy as if it consisted solely of a single representative agent.

Consequently, these supposedly more practical theories can provide zip guidance in the serious business of managing a market economy. You would do as well to consult a Ouija board as an economist who rigorously follows economic theory when giving advice.

The Sonnenschein-Mantel-Debreu result is one of many that have effectively split the caste of mathematical economists into two sects. One pretends that business as usual can continue, despite the presence of this (and many other) fallacies in the creed. The other is dabbling in alternative religions such as complexity theory, or evolutionary economics.

Sadly, the uninformed majority of the profession believes that the first sect is the bearer of the true religion, and that the members of the second sect have betrayed the faith. A more accurate a.n.a.logy is that the dabblers in alternative religions are experiencing the first flushes of adolescence, while the majority of the profession remains mired in infancy. Clearly, the Benthamite ambition to portray society as simply an aggregate of its individual members is a failure. The whole is more than the sum of the parts.

The neocla.s.sical rejoinder The great irony of this particular critique of economics is that it was constructed by its supporters. There is, as a result, no articulate rejoinder. Instead there are rationalizations, such as the 'representative agent' which, as in Varian (1984), are often openly described as such.

If a defence were to be given of this practice, it would probably be what Samuelson termed 'the F-twist': that the a.s.sumptions of a theory don't matter; instead all that counts is how accurately a theory predicts reality. This popular but clearly invalid methodological defense is debunked in Chapter 8.

So what?

It might seem strange to make such a song and dance about whether market demand curves slope downwards. While economic theory clearly fails to prove that market demand falls smoothly as price rises, there are some sound reasons why demand might generally be a negative function of price. For example, a rise in the price of a commodity can force poorer consumers to subst.i.tute some cheaper alternative or go without. So why does it matter that economists can't prove this?

First, it matters because economists had hoped to prove that a market economy necessarily maximizes social welfare. The SMD conditions establish that there is no measure of social welfare that is independent of the existing distribution of income, and that the distribution of income is not based solely on merit it also reflects consumption patterns as well, since a change in consumption will alter the distribution of income.

Secondly, if we take the SMD conditions seriously, economic theory cannot rule out demand curves with a shape like that of Figure 3.12. Aesthetics aside, one of the many problems which such a curve presents for economic theory is that the resulting marginal revenue curve is even more volatile, and it can intersect the marginal cost curve (which we confront in the next chapter) in more than one place. This possibility undermines one of the key articles of the neocla.s.sical faith, that 'everything happens in equilibrium.' If there are multiple points of intersection between marginal cost and marginal revenue, there will be multiple points where 'everything happens.' How then can you determine which will prevail in practice, let alone decide whether any one equilibrium is better or worse than any other?

These dilemmas flow from what appeared at the time to be a conceptual advance dropping the fiction that utility could be measured in units akin to those we use to gauge weight, etc. While this was indeed more realistic, its interaction with two other aspects of economic theory made it impossible to aggregate the utility of two or more individuals.

3.14 Economic theory cannot rule out the possibility that a market demand curve may have a shape like this, rather than a smooth, downward-sloping curve The culprits are the highly subjective nature of the concept of utility, and the belief that the price system determines income distribution. Since a change in relative prices will change the distribution of income, it therefore changes who consumes what, and hence the 'sum' of the subjective utility of all individuals. Since utility is subjective,15 there is no way to determine whether one distribution of income generates more or less aggregate utility than any other.

Economists originally used this aspect of their theory to argue against social reformers who wished to redistribute income from the rich to the poor. They argued that such a redistribution might actually reduce social welfare by taking a unit of a commodity from a rich person who derived a great deal of utility out of it, and giving it to a poor person who derived very little utility from it.

It is ironic that this ancient defense of inequality ultimately backfires on economics, by making it impossible to construct a market demand curve which is independent of the distribution of income. If the market demand curve depends upon the distribution of income, if a change in prices will alter the distribution of income, and if this does not result in a single equilibrium between marginal revenue and marginal cost, then economics cannot defend any one distribution of income over any other. A redistribution of income that favors the poor over the rich cannot be formally opposed by economic theory in fact, economic theory requires such a redistribution before it can even derive a market demand curve!

Finally, this failure rehabilitates the approach of cla.s.sical economics to a.n.a.lyzing the economy. Cla.s.sical economists such as Smith, Ricardo and Marx divided society into social cla.s.ses, and considered how different policies might favor one social cla.s.s over another. The notion of cla.s.s has been expunged from economics by the concept of the indifference curve and its 'one size fits all' treatment of everyone from the poorest Somali to the richest American. Yet because the preferences of different individuals cannot be meaningfully aggregated, this concept is invalid for the a.n.a.lysis of anything more than an isolated individual.

But the conditions under which aggregation is valid when tastes are identical and unaffected by changes in income are at least reasonable as first approximations when the a.n.a.lysis splits society into different social cla.s.ses. It is not too unreasonable to lump all workers, all landlords, and all capitalists together, as Smith, Ricardo and Marx used to do. Incomes within a cla.s.s vary substantially less than incomes between cla.s.ses, and tastes are far more likely to be common within cla.s.ses than between them. A model with both Robinson Crusoe and Friday is at least slightly more reasonable than a model with Robinson Crusoe alone.

Leading mathematical economists have made very similar musings to this. Alan Kirman made one of the strongest such statements in his provocatively t.i.tled paper 'The intrinsic limits of modern economic theory: the emperor has no clothes.'16 After discussing these and other theoretical failures of neocla.s.sical economics, Kirman concluded that If we are to progress further we may well be forced to theories in terms of groups who have collectively coherent behavior. Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation. The idea that we should start at the level of the isolated individual is one which we may well have to abandon. (Kirman 1989: 138) In the end, then, the one benefit of neocla.s.sical economics may be to have established why cla.s.sical economists were correct to reason in terms of social cla.s.s in the first place.

Addendum: an anti-empirical theory.

There is one striking empirical fact about this whole literature, and that is that there is not one single empirical fact in it. The entire neocla.s.sical theory of consumer behavior has been derived in 'armchair philosopher' mode, with an economist constructing a model of a hypothetical rational consumer in his head, and then deriving rules about how that hypothetical consumer must behave.

The aim of this armchair theorizing was to derive a watertight proof of market rationality from an underlying set of principles of rational individual behavior. The fact that this endeavor failed that rational individual behavior can lead to an 'irrational' market therefore means that the entire endeavor has been a waste of time. But many economists cling to this 'utility-maximizing' vision of how consumers behave because it seems so intuitively reasonable to them as a description of individual behavior.

Fittingly, this armchair theory has been proved to be empirically false by an experimental study. The experiment, by the German economist Reinhard Sippel, attempted to test the 'Axioms of Revealed Preference' that were developed by Paul Samuelson (Samuelson 1938a, 1938b) one of the truly dominant figures in the development of neocla.s.sical economics as a way to derive a theory of consumer behavior in which utility did not need to be explicitly considered. Though this was not Samuelson's main intention, it also incidentally allowed the theory of utility maximizing behavior to be tested.

Samuelson defined a 'rational consumer' on the basis of how that consumer would behave when confronted with choices between bundles of goods, and he devised four rules to distinguish rational behavior from irrational: Completeness, Transitivity, Non-satiation and Convexity.

Completeness meant that a rational consumer was able to compare different bundles of commodities shopping trolleys containing different selections of goods from a supermarket and decide which bundle he preferred. There were three possible outcomes: given a choice between the selection of goods in shopping trolley A and shopping trolley B, a rational consumer should be able to say that (a) he preferred trolley A to trolley B; (b) that he preferred B to A; or (c) that he was indifferent between the two.

Transitivity meant that if the consumer said he preferred trolley A to trolley B, and he also preferred trolley B to trolley C, then he necessarily had to prefer trolley A to trolley C.

Non-satiation means that more is preferred to less. So if trolley B has the same contents as trolley A plus one additional chocolate bar, trolley B must be preferred to trolley A.

Finally, the most complex property was Convexity, which is a mathematical expression of the concept of diminishing marginal utility. It argues that if you have two very different shopping trolleys, A and B, then any linear combination of the contents of these two trolleys should be preferred to the trolleys themselves. For example, imagine that trolley A contains ten chocolate bars and nothing else, while trolley B contains ten packs of chips and nothing else. Ten other shopping trolleys could be constructed by swapping one chocolate bar for one pack of chips, each of which would be more desirable than trolleys A and B.

These rules sound reasonable to most people when first explained to them like many concepts in neocla.s.sical economics, they are superficially appealing but Sippel's experiment concluded that, if obeying these rules makes one rational, then the vast majority of us are irrational.

Sippel tested the theory in a very systematic way. He gave his student subjects a set of eight commodities from which to choose (see Table 3.3), a budget line, and a set of relative prices. This was repeated ten times, with each of the ten different price and budget line combinations being designed to test various aspects of Revealed Preference. Subjects were given as much time as they liked to make their choices, and after the ten tests, they got to consume one of the bundles they had selected.

I expect that Sippel conducted the experiment in order to confirm the theory. I would not be surprised to find that his intention was to use the results to derive 'indifference curves' for each of his subjects, and thus confirm that economic theory accurately described their behavior. But the results were a surprise: eleven of his twelve subjects failed the test of rationality! He repeated it with a larger group of thirty to find that twenty-two of these were also 'irrational' according to Samuelson's definition of rational behavior.

Sippel then tried to rescue the theory in a number of ways, none of which worked. One of the most ingenious methods was to hypothesize that real-world consumers can't as easily distinguish the utility they get from different bundles of goods, by a.s.suming that indifference curves were 'thicker' than the thin lines drawn in neocla.s.sical textbooks. This did indeed reduce the number of violations of the 'Axioms of Revealed Preference'; but it also had the undesirable impact that it made random choice simply choosing what to consume by rolling dice appear more rational than the consumption decisions of his students!