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Consumer theory & individual behaviour

I often get uneasy about some of the basic things I do when teaching microeconomics. One area that does concern is the basic issue of consumer choice. How deep should one dig? This is related to the optimal degree of mathematising microeconomics in this specific area.

In simple terms you can analyse a consumer’s problem as selecting a basket of goods X to maximise a utility U(X) subject to a budget constraint PX = M where P is a conformable vector of prices and M is a consumer’s income.  With some almost obvious maths – you can see the result by inspection – one gets a set of individual demands X=X(P,M).

This is really trite. What one is really interested in here are the restrictions that the hypothesis of a consumer acting to maximise his/her affordable utilities imposes on these demands.  It is known that you don’t get much.

What you learn, with some work, is that substitution effects of a price change here are negative – if you adjust a consumer’s income so that their utility remains constant when you vary a price then the quantity of a good demanded will vary in the opposite direction to a price change.  More generally for a set of demands their ‘substitution matrix’ is negative semi-definite. 

Interestingly, as every graduate student in economics should know, it is easy to show that this is the only consequence of assuming that consumers maximise their affordable utilities since then “integrability” obtains – one can work backwards to recover a consumer’s preferences given the negative semi-definiteness property.

But economists are almost never (perhaps never) interested in individual demands. They are interested in market demands or in the demands of a ‘representative agent’ for whom averaging convexifies preferences leading to non-specialised consumption bundles being selected.  The negative semi-definiteness property does not hold for such aggregates or such representative agents so you lose even this restriction in these cases.

One knows that market demands satisfy homogeneity conditions (changing all absolute prices by the same fraction leaves demands unaltered) and (if preferences are monotonic) Walras’ Law also obtains (the sum of excess demands are zero so that, with N goods, only N-1 market equilibrium conditions can be independently specified).  But homogeneity is a trite consequence of the absence of money illusion and Walras’ Law from the fact that, with assumed monotonicity – so consumers are never satiated in their consumptions – consumers will exhaust their budget.

It might therefore be argued that if you wanted to teach people about consumer theory that you one might well just start with market demands as a primitive. Digging deeper into how a consumer thinks out their choices doeesn’t help explain observables.

Indeed when I think of it the only way I use indifference curve analysis – graphical pictures of how choices are made at an individual level –  is:

1. To illustrate the distinction between the income and substitution effects of a price change so that one can rationalise interest in the empirically irrelevant Giffen Good case – the case where quantities demanded of a good go up when prices rise because, as a consequence of the price rise, a consumer is much poorer and hence buys less normal goods.  This seems to me of little interest other than for curiousity value.

2. To illustrate the effects on worker incentives of a wage rise caused by a tax cut.   The tax cut can increase work effort if the worker has strong substitution effects and pays particular attention to the increased opportunity cost of leisure.  It can reduce work effort if workers react to the increased wage mainly by valuing their leisure more.  This is a more interesting application since it is less a curious quirk – typically workers will demand more leisure when they earn higher income since they can do more things.

3. To show how societies make choices using so-called social indifference curves to show sensible choices given a society’s production possibilities normally drawn as a production possibility frontier.  This is interesting but again one is working at an economy-wide aggregate level not an individual level.

There are general results by Sonnenschein, Mantel and Debreu which showed, decades ago, that market level microeconomics cannot be based on microeconomic principles.  The thoughts above are an instance of this but with particular reference to the way modern microeconomics is taught in the universities – as a series of constrained optimisation exercises.  In fact, I have taught it myself in this way for yonks.  With respect to issues such as demand maybe it is better to follow the practices of business schools and concentrate on market level observables.  Not much is lost.

Provisional thoughts – comments welcome.

4 comments to Consumer theory & individual behaviour

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  • Uncle Milton

    Harry, I don’t agree. What you should do is to teach economics students the standard stuff, then teach the Sonnenschien Mantel Debreu result, then draw out its implication, which is not that “market level microeconomics cannot be based on microeconomic principles”, but that market can have multiple equilibria.

  • conrad

    I’m surprised you guys care so little about behavior at the level of the individual. It’s no wonder that the way you try and control things like drug usage is so different to the way psychologists do.

  • James Boag

    Most of what you teach will have no impact on the real world, anyway. The level of abstraction is too high for much of this theory to be meaningful when applied to standard markets and the individual consumers that populate them.

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