12 Aug 2012

Debunking Economics II: The Law of Demand.

Key Terms

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.

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Keep is seemly & on-topic. Thanks.