Friday, February 10, 2006

Marshall and Walras

There are two easy, classic models for how supply and demand equilibrate over iterated periods in the face of imperfect information. In the Walras model, the price is given by an equation of the form
p' = ED * (p-P)
where p is the present (non-eqm) price, ED is the excess demand, and P is the equilibrium price. The prime is change in time--the new price at the next iteration. The Marshall model says something similar about the quantity,
q' = q_D - q_S
and here q is the quantity, q_D is the price that demanders will pay at a given quantity of production, and q_S is the price suppliers want--their marginal cost.

As Nicholson's Micro book says, the Walras model is more appropriate when quantity is fixed (like at an auction, in the very short run), and Marshall's model is better where prices are fixed (say, by long-term contracts), and quantity can be shifted easily, say from long-term inventory.

Unemployment is clearly an example of Marshallian shifting. Wages stay roughly constant, but people are thrown out of work. Why is that? I can understand this for minimum wage workers, but Marshall seems to describe almost everyone. Why shouldn't people's wages be reduced if the labor supply outpaces production in a recession? You can't answer this by saying that workers are risk-averse, and so they want constant wages. By hypothesis workers' wages are varying--down to zero, when they get laid off.

In fact, if workers are risk averse, then they have a diminishing marginal utility of cash, and they'd certainly prefer--in an actuarially fair game--a certainty of a moderately lower wage than a gamble between their old salary and being laid off.

So, why are wages slow to respond but unemployment goes up or down? Why does quantity do all the work in mitigating the business cycle while (wage)-price is slow to react? Most people don't have employment contracts for either time or wage. Maybe those who are likely to be laid off have less power to affect the system: either they're less competent, or less senior.

This post was originally titled "I am the Walras" but I am reading IP law now and I'm afraid of being sued.


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