Sobel (1984) on sales
I was thinking about models of sales, since my student, Barick Chung, is working on them. Joel Sobel has a good 1984 model, which I will summarize here.
There are informed consumers, who know all prices as they appear each period, and uninformed consumers, who must pick a seller without knowing the price, and who buy if the price is less than R. All consumers and both the two sellers have a positive discount rate. Sellers pick prices each period.
In equilibrium, sellers usually charge price R and just sell to the uninformed. The informed consumers wait for a sale. For M periods after the last sale, no sale will occur. By then, the number of informed consumers has built up, and the two sellers will start using mixed strategies, either still selling at R, or having an atom of probability at the price B, or selling at a price in the interval [A,B). The price B is low enough that informed consumers are willing to buy at it, because they know it will be at least M periods before the next sale. The interval [A, B) is part of the equilibrium, though, because if Seller 1 always used B as his sale price, Seller 2 would use B-epsilon, and sometimes sales occur by chance in the same period.
That’s a very nice model. It explains why the price is usually high, and why certain sale prices (B) are more common, unlike the one-period Varian model.
The Timing of Sales, Joel Sobel, The Review of Economic Studies, Vol. 51, No. 3. (Jul., 1984), pp. 353-368.
March 6th, 2006 at 7:57 pm
If many a consumer, uninfomred, has a common reservation R, it is no doubt that seller would sell at a price no more than but close to that. The crux of the question is, the supply (goods in stock) and the demand (of consumers including how patient they are).
The trick is also how the “infomred consumer” having been informed that Professor Rasmusen may further explore. Are the “informed” consumers knowing the circumstances, i.e., the sellers, the rules of the game, etc. Or they innately know that the reservation of the uninformed as well as the stock? The former question is more interesting than the latter, but we can swiftly come down to an answer that if supply is adequate, the informed consumer is patient, the selling price to the informed consumer should be about and in-between the two reservation prices.
I am layman. The model is not too funny but adding probability into the decision making process. Thank you for your book.
TOM