This morning, in a spirit of viewing randomness, I caught "Price Drop TV", a shopping channel. Or it might have been "Bid TV". Or maybe it's just sad.
The format is that the presenter shows and briefly describes some artifact: a collection of ceramic cooking bowls; a set of jewelry-encrusted rings. There is a job-lot of the things, 100 ceramic cooking bowls, 15 rings, and a starter item price appears on the screen.
As you watch, people are phoning in, and whenever the number left stalls for a while, the price reduces ("Price Drop TV"). Eventually, the lot is sold out, and then everybody gets their product at the final price shown.
At first sight, this should be required watching for all economics students. The item price-quantity variable slides down the demand curve until we eventually reach the market-clearing price where supply (the total job-lot number of items for sale) = demand (the total number of telephone orders placed).
But wait. Doing it this way is not at all in the interest of the seller. To show this consider the following example.
Solar-Powered Santa comes in a lot of 100 items with initial price £10. As this price flashes on screen, we see just one taker. The price then reduces in steps, prompting more callers to phone in with their orders. The last santa goes when the price has reached £1 (100 are now sold). Everyone gets the final price so total revenue to the supplier = £100.
We have enough information here to work out the linear demand curve showing the number which would be sold (Q) at any price (P) between £10 and £1. It's
P = 101/11 - (1/11)Q
Suppose the auction had stopped at P = £5. Then 55 solar-powered santas would have been sold at a price of £5 each, for a total revenue of £275. It sure beats £100 even if you have to chuck the remaining 45 santas into the skip.
Welcome to the concept of the monopoly price.
So what do they really do? Compute the demand curve from the early part of the auction process, work out the monopoly price and then stop the auction there, while faking a final 'countdown to the skip' sell-out on-screen?
Feel free to confide if you happen to know.
