Thursday, August 25, 2005

Supply, Demand, and the Slippery Slope

My mind wandered off a bit today during a lengthy stretch of meetings at work. I pondered a bit about supply and demand curves and pricing. Supply and demand curves themselves are unaffected by price. However, the quantity demanded or supplied is clearly sensitive to it.

Say we have some good selling for $N, and that N is large. Then, tiny changes to the selling price should not affect the quantity demanded. By using the slippery slope argument, all selling prices would yield the same demanded quantity. Even though we know that the slippery slope is a common fallacy, I think it's interesting to discuss a slightly more complex supply and demand model that would accomodate the slippery slope argument, yet not fall into its trap.

If instead of hard and fast supply and demand curves, what if we had blurred curves that represented the probability that quantities would be supplied or demanded at various price levels. Say that you would certainly buy a particular car if it costs $25,000. Now, let's apply the slippery slope to this example. So, we find that at $25,000.01 you're obviously still a buyer. However, for every price movement, the probability that you'd still buy it, at that very instant in time, would change. Even the tiniest changes in price would result in the tiniest change in this probability. For example, at price $0, there would be a 100% chance that a rational person would buy. But, even at $0.01, the probability would no longer be 100%.

Let's not forget that the actual curves would account for all the population and produce an aggregate distribution (the blurred lines). So, now the slippery slope would fail (I think), because at any given point you are merely given a probability that certain quantities would be demanded.

Anyway, I think that adding a simple probability component into the simplest supply and demand model provides a better view of reality. Maybe this is all obvious, maybe it's ridiculous, or maybe it's quite wrong. But, I do know that this topic is what kept me occupied during the string of uneventful meetings I had today.

No comments: