# Debunking Economics - Ch. 3: The Demand Curve

Posted on January 25, 2017 by Tommy M. McGuire
Labels: books, R

# Debunking Economics by Steve Keen

Debunking Economics: The Naked Emperor Dethroned? is a book by Steve Keen, at the time professor of economics and finance at the University of Western Sydney. According to the blurb, it “exposes what a minority of economists have long known and many of the rest of us have long suspected: that economic theory is not only unpalatable, but also plain wrong.” The book contains a “scathing critique of conventional economic theory whilst [whilst?] explaining what mainstream economists cannot: why the [2008] crisis occurred, why it is proving to be intractable [the first edition was published in 2001, this edition was published in 2011], and what needs to be done to end it.”

Keen’s approach to each chapter—with a “kernel” section describing the basic argument, a “roadmap” section spelling out how it will go, and a presentation of the neoclassical idea followed by his counter-arguments—is admirable, he spends a great number of words attacking neoclassical economics and economists. These attacks may be needed by what the book is trying to do, but it does serve to hide the underlying arguments and counter-arguments.

It’s been a rather long time since I was anywhere near an economics classroom (And I cannot find an econ textbook around here!), so these notes are my attempt to understand Keen’s fundamental arguments. In each chapter in the bulk of the book, he presents a traditional “undergraduate” version of a basic economic idea (as taught by what he calls “neoclassical economists”) and then presents an apparently conclusive that the idea has major faults, if not being completely wrong. I am attempting to pick out those basic ideas and avoid the criticism of neoclassical economics and economists.

## The Demand Curve

Chapter 3, the first chapter of part 1, Foundations, addresses the demand curve, one part of introductory economics’ laws of supply and demand.

Note: if you are already familiar with how a demand curve is created, you can skip to the chapter’s punchline at The market demand curve.

### Building the demand curve

Economics begins building a description of demand based on Jeremy Bentham’s (1748-1832) utilitarianism. (I like Jeremy Bentham; he spent time designing prisons and you can visit him at University College London today.) The idea is that, given some commodity such as bananas, having one banana will give you a certain amount of utility, and having more bananas always gives you more utility, although the amount of utility you gain from one more banana is less than the utility you gained from getting the previous banana. Here’s a table, denominated in a utility currency of “utils”:

##   Bananas Utils Change.in.Utils
## 1       1     8               8
## 2       2    15               7
## 3       3    19               4
## 4       4    20               1

(These examples are taken from the book.) Plotted, that looks like:

The problem here is that it uses a currency of “utils”, which doesn’t exist and may or may not be definable. It also does not refer to price. To remove the dependency on utils and introduce a relationship to price requires a few steps, the first of which is to relate the bananas commodity to a new commodity, say biscuits. Biscuits obey the same utility rules as bananas, although with different util values, and biscuits can be traded off against bananas at varying utilities:

##      [,1] [,2] [,3] [,4]
## [1,]    0    9   15   18
## [2,]    8   13   19   25
## [3,]   13   15   24   30
## [4,]   14   18   25   31

Graphed, that looks like:

In this graph, the highest utility is provided by 3 bananas and 3 biscuits, but 2 bananas and 3 biscuits is nearly as high. 1 banana and 3 biscuits has the same utility as 3 bananas and 2 biscuits. This last point is important; Keen writes,

The final abstraction en route to the modern theory was to drop this ‘3D’ perspective—since the actual ‘height’ couldn’t be specified numerically anyway—and to instead link points of equal ‘utility height’ into curves, just as contours on a geographic map indicate locations of equal height, or isobars on a weather chart indicate regions of equal pressure.

Based on this depiction, Keen writes,

Since consumers were presumed to be motivated by the utility they gained from consumption, and points of equal utility height gave them the same satisfaction, then a consumer should be ‘indifferent’ between any two points on any given curve, since they both represent the same height, or degree of utility. These contours were therefore christened ‘indifference curves’.

The properties of these curves are:

• Completeness. Given two different combinations of commodities, a consumer can decide which is preferred or that he is indifferent between the two. (The combinations are ordered.)

• Transitivity. If combination A is preferred to combination B, and B is preferred to combination C, combination A is preferred to C.

• Non-satiation. More is better than less: if A contains the same amount of every commodity as B, except for one, and A has more of that one commodity than B, then A is preferred to B.

• Convexity. “The marginal utility … falls with additional units, so that indifference curves are convex in shape.” (In the graph above, not all of the indifference curves are convex. Weird.)

Price enters the picture at this point.

Assume that bananas and biscuits both cost $1 each, and the consumer has$3 to spend. This allows the consumer to buy 3 bananas and no biscuits, or no bananas and 3 biscuits, or some combination. This assumption allows a “budget line” to be drawn on the graph:

The point on this line that maximizes the utility “height” indicates the combination of commodities that maximizes the utility and therefore satisfaction of the consumer while keeping the price of the combination to the budget; it looks like 1 banana and 2 biscuits is the appropriate combination.

Keen writes:

Economic theory then repeats this process numerous times—each time considering the same income [“budget”] and price for biscuits, but a [different] price for bananas. Each time, there will be a new combination of biscuits and bananas that the consumer will buy, and the combination of the prices and quantities of bananas purchased is the conumer’s demand curve for bananas.

Given the varying price of bananas and the corresponding number of bananas purchased in the optimal combination, we can construct something that sort of looks like a demand curve:

The resulting graph is a demand curve: it follows the Law of Demand; that demand increases as price falls. Although Keen does not go into the math, he notes and I believe that the process is well defined mathematically, so that a corresponding demand function can be created to play with analytically. There are some other twists, though. For one, lowering the price of a commodity that is not particularly desirable can result in no more, or even less, of that commodity being purchased.

If, for example, the price of bananas falls while the budget (or “income”, traditionally) and other prices remain the same, then the consumer can buy more bananas and has a higher utility value. On the other hand, if bananas are a major component of the budget yet are relatively undesirable, an increase in income can induce the consumer to buy fewer bananas and more of something more desirable, even if the change in income is the result of changing prices. The canonical example is potatos during the Irish potato famine—consumers bought more potatos even as the prices rose because they could no longer afford more desirable alternatives like pork.

As a result, two effects need to be separated to produce a useful demand curve: the substitution effect is the change in demand purely due to the change in prices, and the income effect is the change in demand due to a change in prices affecting the consumer’s perceived income. The substitution effect is always inversely related to prices: an increase in price produces a reduction in demand. The income effect, however, can have any relation to demand, depending on the commodity.

The income effect produces four classes of commodities:

• Necessities, which take a diminshing share of spending as income grows. Think of, say, toilet paper; you only buy a certain number of rolls per month, no matter what your income is.

• “Giffen” commodities, whose actual consumption falls as income grows. I have not bought many packages of Ramen noodles since I graduated.

• Luxuries, which take an increasing share of spending as income grows. The percentage of income I spend on Picassos is essentially zero, but if I made more, I might find myself buying some.

• Neutral or “homothetic” commodities, which take a constant share of spending as income grows.

Note that the second class is a sub-class of the first, and that the fourth class is unoccupied—what kind of commodity would you spend 10% of your income on, for any income from $10,000 per year to$1,000,000 per year? Pizza?

Anyway, back to the substitution effect and the income effect. The substitution effect is what the demand curve is trying to isolate. Fortunately, it is possible to neutralize the income effect to produce a “Hicksian compensated demand curve” which is well behaved: the demand for a commodity will rise if its price falls. There are certain assumptions that are needed to neutralize the income effect, though, such as that changing the price of bananas does not directly alter an individual’s income—the only change in income is the income effect.

(As an aside, Keen notes that Ted Wheelwright once described this as “tobogganing up and down your indifference curves until you disappear up your own abscissa”. The verb “to toboggan” needs to see more use.)

This is a demand curve for one person and one commodity. The process for creating a market demand curve, though, is very simple: given a market consisting of many consumers, each with their own demand curve, the overall market demand curve is simply the sum of the individual demand curves.

## The market demand curve

Without considering any other effects, that works: the sum of a set of individual demand curves will be a demand curve.

Unfortunately, considering other effects, there is a problem: changing the price of bananas in a market environment will change the income of some of the individuals. Keen uses the example of a market consisting of Robinson Crusoe and Man Friday, and more bananas.

Suppose that Crusoe is a banana consumer, and that Friday is both a consumer and a producer. An increase in the price of bananas will make Friday richer while making Crusoe poorer; Friday will be able to buy more biscuits. (What happens if they’re both producers? The same thing, assuming they are not equally good at producing bananas.)

As a result (Gorman 1953), the market demand function can be any polynomial; the graph is not necessarily negatively sloped. Demand can increase as prices rise. It can then decrease as prices continue to rise. And then increase again. Whee!

Fortunately, the market demand function can be made to obey the Law of Demand under two conditions, also known as the Sonnenschein-Mantel-Debreu (SMD) conditions:

• All of the Engel curves of all consumers are straight lines, and

• All of the Engel curves are parallel.

Keen quotes Gorman:

…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…

An Engel curve is based on an indifference graph, with multiple “budget” or income lines at different distances from the origin, showing the effects of an increasing income.

Joining the points of maximum utility on each budget line in sequence produces the Engel curve. (I have fudged this example; the actual curve for this silly graph should go through the indicated points.)

Engel curves relate back to the classes of commodities described above, with the income effect. Necessities and Giffen commodities produce upward-curving Engel curves, luxuries produce downward-curving Engle curves (such as the line in the bananas vs. biscuits graph above), and neutral commodities produce linear Engel curves.

The problem here is that the two SMD conditions mean that

• All commodities are neutral, and

• Since all Engel curves start from (0,0) and parallel lines through the same point are the same line, all consumers have the same Engel curve.

As a result, the conditions imply that there is a single, “generic” commodity, and a single, “representative” consumer.

The necessary and sufficient condition quoted above is intutively 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.

…which doesn’t seem all that intuitively reasonable.

There is a good deal more to the chapter, such as discussions of further ways of looking at the SMD conditions (including a “benevolent dictator” who redistributes wealth prior to market activity), and demonstrations that the SMD caveats are not discussed in introductory textbooks and not clearly discussed in advanced textbooks.

## Individual demand curves and behavioral economics

As an addendum to the chapter, Keen presents some arguments that the initial idea of a rational consumer maximizing utility to produce an individual demand curve is not necessarily valid, either. His one example is a study of a group of consumers trying to pick the “best” basket of a number of different products. Keen argues that their failure is due to the computational complexity of picking the optimal solution to a largish combinatorial problem.

I believe there are enough other examples from behavioral economics to assert that the “rational” consumer, in practice, does not really exist.