Debunking Economics IV: Aggregate Demand

In a previous post I worked through the ideas contained in the first part of chapter 3 of Steve Keen's book Debunking Economics outlining the so-called Law of Demand. This is not an empirical law such as Newton's Laws of Motion, or the Laws of Thermodynamics. That is to say it's not an attempt to explain the real world based on measurement. The Law of Demand is an attempt to create a mathematical model of theory about how the world works which is based on the 19th century Utilitarian philosophy of Jeremy Bentham. As it happens the Law of Demand works OK for one consumer consuming one product.

However as early as 1953 it became apparent that the Law of Demand as stated does not apply to two or more consumers. The first mathematical proof was by a chap called William Moore "Terence" Gorman (wiki) in this journal article:

Gorman, W. M. (1953) 'Community preference fields,' Econometrica, 21(1):63-80. JSTOR.

The abstract of this paper is visible even though the article itself is behind a paywall or tucked away in a university library. What it says is this:

A series of formal relationships between community indifference maps and the utility possibility maps are stated and it is proved that a given system of personal indifference maps yield a unique community indifference map if, and only if, the personal Engel curves are parallel straight lines for different individuals at the same prices. [emphasis in the original]

What Steve Keen does is decode this - he's not saying anything new here, he's just pointing out what was said in 1953 and drawing out the most obvious implications. Having reviewed his chapter to date I can see the obvious implications of this too - and I have zero background in economics.

I covered Engel curves in part II. These are the curves that are constructed by tracing the points of intersection with various individual indifference curves in the indifference map for one commodity vs all other commodities at different levels of income. Engel curves tell us predict how much of a commodity an individual will purchase at any given income level.

Now SK points out that at zero income the consumer will spend zero dollars on zero of all commodities. So all Engel curves pass through the origin (i.e. through the point where the axes of the graph intersect). He further points out that if two lines which share at least one point (in this case the origin) are parallel lines, then they share all their points, they are in fact the same line. So the upshot of Gorman's mathematical proof is that you can only construct what he calls a community indifference map and we are calling an aggregate indifference map if and only if, all consumers are identical.

And recall that the demand curve is constructed from the indifference map at fixed income and fixed price. So what Gorman is saying is that it is only possible for the Law of Demand to apply to aggregate demand curves if, and only if, all the individual demand curves are identical. As Steve Keen says quite often: "you couldn't make it up!" Just to drive the point home let's say it another way the Law of Demand does not hold for the real world if you have more than one consumer.

Something less obvious from the abstract is that the Engel curves have to be a straight line. The implications of this is that the share of the consumers income spent on commodities remains the same no matter what their income - i.e. that all commodities must be homothetic. This means that a if person earning £10k pounds spends £1k, then a person earning £10 million pounds would spend £1 million, and a person earning £10 billion pounds would spend £1 billion pounds. There is no such commodity in existence. The only condition in which this is true is if there is only one commodity and all consumers spend 100% of their income on it.

But economists have accepted these conditions as valid and proceed to use "aggregate" demand curves. Gorman himself concluded "The necessary and sufficient condition quoted above is intuitively reasonable". (quoted in Debunking Economics p.56) And it seems that those who bothered to read Gorman agree with him that it was "intuitively reasonable" to treat the economy as having a single consumer and a single commodity. And indeed today mainstream economists agree at some point in their careers to pretend that there is only one consumer, and that there is only one product in the economy.

You'd have to be a moron wouldn't you? You start to see why Steve Keen is sardonic, and why economists have screwed things up so badly.

But to be fair quite a bit of the remainder of the chapter deals with how textbooks hide this remarkable proof that the Law of Demand is simply false, and how economists gradually have had the wool pulled over their eyes as they go along.

With an education in science we're presented with simplistic models at first. Then at each stage we go back and examine the weaknesses in those models, and either introduce more sophisticated models or completely new models. From age 13 to age 21 I followed the progress of the history of chemistry from the 19th century up to the present. It seems that in economics one takes all the assumptions economists make as read, and at each stage one incorporates simplifying assumptions as one goes. As I progressed in chemistry I gained an increasing sophisticated knowledge of the subject so that at the end I was able to synthesise complex molecules and understand the process from first principles; and I was able to take an unidentified white powder and determine it's chemical structure. The economist however moves gradually away from the real world and becomes an expert on the model. And almost exactly five years ago we saw the biggest economic crisis in modern times hit virtually every country in the world all at once, and none of the mainstream saw it coming. Indeed they claim no one could have. No one, that is, who was using their economic ideas and models. Other economists did. Quite a few non-economists also saw trouble brewing. The fault lies in the models!

Since Gorman himself failed to grasp the import of his own discovery, and since few economists were numerate enough to understand Gorman's paper the result made little impact. It was rediscovered independently however in the 1970's by three researchers and the conditions of Engel curves being straight and parallel are known as the Sonneschein-Mantel-Debreu (SMD) conditions. However even these economists failed to grasp the implications for the Law of Demand, and since their writing and their mathematics was even more abstruse than Gorman's it seems as though very few economists have even heard of the SMD conditions.

The key papers are:

• Debreu, G. (1974) 'Excess demand functions,' Journal of Mathematical Economics. 1(1): 15-21. doi:10.1016/0304-4068(74)90032-9.
• Mantel, R. (1974). "On the characterization of aggregate excess demand". Journal of Economic Theory 7 (3): 348–353. doi:10.1016/0022-0531(74)90100-8
• Sonnenschein, Hugo. (1972) 'Market Excess Demand Functions.' Econometrica 40 (3): 549-563. JSTOR.

A nice result that falls out of their work is the statement that an aggregate demand curve can be any shape that can be described by a polynomial - any curvy line with one y value for every x value. For any given price there is not one level of demand, but arbitrarily many.

SK argues that this result completely invalidates Neo-classical economics with it's assumption of equilibrium (we'll get this to) because it requires a single intersection of supply curve with demand curve, and this can only happen when we assume there is a single consumer and a single product.  The assumption of the standardised individual making rational choices is just wrong, but when we attempt to aggregate the behaviour of such theoretical individuals the model goes awry.


Reflections

Just this result would seem to be a death blow to Neo-classical economics. The theory simply doesn't produce realistic or sensible results, largely because the accumulation of the simplifying (often over-simplifying) assumptions it makes result in unrealistic distortions. But Neo-classical economists have pushed on. S. Abu Turab Rizvi notes:

As the results in SMD theory became well known, for example through Wayne Shafer and Hugo Sonnenschein’s survey (1982), economists began to question the centrality of general equilibrium theory and put forward alternatives to it. Thus in the ten years following the Shafer-Sonnenschein survey, we find a number of new directions in economic theory. It was around this time that rational-choice game theory methods came to be adopted throughout the profession, and they represented a thoroughgoing change in the mode of economic theory. (p.230)

Rizvi. S. Abu Turab . (2006) 'The Sonnenschein-Mantel-Debreu Results after Thirty Years,' History of Political Economy 38 (annual suppl.). doi 10.1215/00182702-2005-024 [pdf]

Now this is interesting because the introduction of game theory, particularly the theories developed by mathematician John Nash feature in Adam Curtis's 2007 documentary The Trap which I discussed in an earlier post. While John Nash is now recovered, at the time he was developing these theories he suffered from paranoid schizophrenia, and it's arguable that the theories reflect this. Indeed Nash in an interview with Curtis admits that the individuals he modelled were not at all like real people. They're like the ideal rational Victorian gentlemen envisaged by the Utilitarians, but utterly selfish and, well, paranoid. These ideas expressed in economic terms began to influence politicians like Margaret Thatcher and Ronald Reagan. A prominent proponent of game theory called Alain Enthoven, who envisaged the "body count" as a way to measure the efficiency of the Vietnam War, was called into the UK in 1984 to restructure the NHS.

I think this illustrates the danger we face. Economic theory is divorced to a large extent from inputs from the real world. The model is all. It takes real world data and interprets it according to this distorted view, and then creates policy by which we order the world. In doing so it appears to strive towards transforming the world to become more like the model, not the other way around.


Another result of the SMD conditions has been the development of Behavioural Economics, but I have not yet looked into this.

There's a lot more material towards the end of the chapter, that I haven't covered here. It's worth reading through but I think most of it is of less general interest - I'm trying to get my head around the basics. Next we'll move on to looking at the other half of the 'iconic supply and demand model' - and since the first section is headed "Why there is no supply curve" I think we can expect a polemical treat.

Debunking Economics II: The Law of Demand.

Key Terms

utils
diminishing marginal utility
indifference curves
budget line
demand curve
income effect
substitution effect
Law of Demand
Hicksian Compensated Demand Curve
Engel curves
homothetic goods 

I studied chemistry at university. I loved the way that things tallied up and the way the implied order in the universe. When you learn chemistry as a subject you typically get the theory first, and then do an experiment in which the observations confirm the theory. I think this confuses a lot of people about the progress of scientific knowledge. At the cutting edge the theory makes predictions and one doesn't know whether they will be right or not. Experiments are designed to allow observations which are then compared to the prediction. These results add to a body of observations against which theory is checked. Theories are models of reality. Their usefulness is in their predictions of reality. If these predictions are inaccurate the theory is not useful.

Economics has never worked this way. At the beginning of economics was a worldview in which the individual was something like the ideal Victorian English Gentleman: rational and alone against the world. This idealisation was combined with assumptions about how the world functions into a model of consumer behaviour that has never really been updated. Steve Keen's explanation of the demand curve shows how this works.

In my first instalment of Debunking Economics notes, I wrote about the Utilitarian view of the individual and the pursuit of happiness through maximising pleasure. In economic Utilitarianism the maximisation of pleasure is assumed to be achieved through consumption of goods. This assumption helped to link happiness to a measurable quantity since consumption is easy to measure. The unit of Happiness or satisfaction is a util, which is assumed to be in a constant ratio to units of consumption. This is assumed to apply to all goods. 

Now we can graph the amount of satisfaction (i.e. the number of utils) received from consuming x amount of good A. Economic theory assumes here that we would always want more of a good, but that the amount satisfaction we get from each new unit of consumption produces less utility. This is knows as diminishing marginal utility. If we imagine a system of two commodities then our maximum satisfaction will be having infinite amounts of both. However there are constraints on how much we can consume, chief of these being our income. At a given level of income, then, various combinations of quantities of each are able to maximise our satisfaction.

2D Indifference Curves

If we lay out the quantities of the goods on the x & y axes of a Cartesian graph with utils on the 3rd z axis then we will see points at which satisfaction are equal. We can join these points into a curve. Since each point on the line presents an equal of utils the individual is indifferent to the different combinations: hence it is called an indifference curve. For any combination of commodities the consumer has a range of indifference curves.
 
But it's more convenient to use two dimensions and what economists use is a series of indifference curves stacked up as per the image right. A term I picked up from another book is to refer to this diagram as an indifference map.

In 1948 Paul Samuelson worked out what properties indifference curves would have if consumers were like the idealised Victorian Gentlemen - i.e. if they really were rational. There are four of these:

• Completeness: choice between any combination of commodities is possible
• Transitivity: so if a combination of products A is preferable to B i.e. A > B & B > C then A > C
• Non-satiation: more always preferred to less
• Convexity: marginal utility is always positive and diminishing but never zero.

Now in this narrative the "rational" consumer tries to maximise their utility by consuming the combination of commodities which provide the highest satisfaction, and this point is where a budget line just touches a single indifference curve. The budget line is a line drawn between two points, one on each axis representing spending all income on one product.

Yet another assumption the theory makes is that all consumers spend all their income. Even savings are just delayed consumption. So for a consumer at fixed income and fixed prices the indifference curves allow us to construct a demand curve. A demand curve is a series of points where the budget line (representing income) intersects the series of indifference curves at constant income and changing prices. It normally slopes down (if the price goes up the demand goes down), and it works OK for one consumer and one commodity. The demand curve shows us how many units of commodity will be consumed at a given price.

A further assumption, and one that simply doesn't hold and must be adjusted for is that price changes do not affect income. But in fact if a commodity that we buy becomes cheaper, then we effectively do have more income. And this is an issue when we consider more than one commodity, because a change in the price of one commodity might change how many we buy of both commodities.

But the demand curve can slop upwards under some circumstances. Imagine we usually buy one jar of instant coffee per week. Then due to a large drop in price of another product we decide we can afford to buy real coffee even though it's more expensive - we therefore spend more on coffee.

Another situation in which demand and price might not be connected in the standard way is if we buy a staple food. Keen uses the example of potatoes in Ireland during the potato famine. We might also use the more recent example of the cost of rice in Asia. In a place like India, for example, consumers might not buy less rice because of the price rise, and may be less of other products instead.

Classic Simple Demand Curve

We now have the classic economic demand curve which is a plain straight line (as unlikely as that seems). This shows that as prices go up that demand goes down. This is called the Law of Demand. This seems reasonable at first glance, but there is one more trick that we need to perform to deal with this problem where it can have a positive slope. And this is the bit I don't understand so well. So I'll quote Steve:

"This increase in overall well-being due to the price of a commodity falling is known as the 'income effect'... The pure impact of a fall in price for a commodity is known as the 'substitution effect'." (p.48)

Now for this demand curve to be useful there can only be one price at which demand equals supply (the next chapter is on supply curves). But the upwards slope stuffs this up because a bendy demand curve might present two or more places at which a supply curve crosses it. (This bit is important later). So economists muck about with the indifference curves to make sure the line is straight.

If prices fall while income is fixed the consumer still enjoys more satisfaction. In this model they go to a higher indifference curve just as though they did have more income. So they artificially hold the consumer on the same indifference curve and "rotate the budget constraint to reflect the new relative price regime" [I think there's some unclarity here in the book]. Anyway the trick is named after the guy who invented it: Hicksian Compensated Demand Curve.

So we now have created a model, without reference to the real world, in which the Law of Demand holds for a single imaginary rational consumer. This is technically micro-economics, but it forms the basis of Neo-Classical macro so we need to get to grips with it. SK admits this stuff is really boring and urges his readers to drink copious amounts of coffee to stay awake.

We have one more subject to cover in this section which is Engel Curves, and these are important later. Engel curves are constructed by changing the amount on income and tracing the intersections with the lines in the indifference map. These curves can have a variety of shapes and broadly there are four categories:

• necessities or inferior goods - take up a diminishing share of budget as income rises
• Giffen goods - consumption declines as income rises
• luxuries or superior goods - take up an increasing share of budget as income rises
• neutral or homothetic goods - share of budget remains constant as income rises

And as SK notes there are no real world examples of homothetic goods - there is no commodity that a consumer will spend a constant share of their income on as income rises.

So now we have all the information we need to look at how macro-economists use individual demand curves to construct aggregate or market demand curves. I plan to create a list of all the various assumptions as a separate post.