Pot-Sticky Information

There is a Chinese restaurant on the outskirts of town. The restaurant posts its prices on its window and waits for customers to arrive.

Everyone in the town has a price that they are willing to pay for Chinese dinners. Everyone in town has information about how much the restaurant charges for food from two sources: active and passive. They can visit the restaurant and look at the window to see what it is charging now, or they can rely on word of mouth to inform them of any price change that occurred in the past. There is some cost to visiting the restaurant and obtaining up-to-date information, but out-of-date word of mouth information is free.

The speed of word-of-mouth knowledge propagation is proportional to the price change. Very few people will call up their friends and tell them that the last time they ate Spicy Chicken, the meal cost a nickel less. But they will call their friends if the price was cut in half.

Suppose first that the restaurant is charging a price that everyone knows. Those who are willing to pay this price visit the restaurant and buy a meal, and those who do not pay the price do not visit. We are at maximum sales.

Next, suppose the restaurant is allowed to change prices, and people know this. They form some probability distribution of various states of the world — prices are unchanged from their last known price, prices will be higher by a certain amount, or prices will be lower by a certain amount.

There is now uncertainty as to what the price of a meal will be when households visit the restaurant, and so those close to the indifference point will not visit. Quantity traded decreases. But there is also a second order effect — from the point of view of the restaurant, if the restaurant lowers prices, then those who visit the restaurant will pay less than they are willing to pay. But they will tell their friends of the price change. As it takes time for this knowledge to spread, there will be a loss to the restaurant until the knowledge spreads and diners update their probability distributions.  Because a small change in prices will spread slowly, it may not be worth it to the restaurant to lower prices by a small amount.

Suppose the restaurant is thinking about raising prices by a small amount. As everyone who thinks about visiting the restaurant has received a price signal that is the current price or a lower price, the restaurant will not lose any additional business even if the information propagates slowly. It makes more sense for the restaurant to raise prices than to lower them.

This (non-mathematical) description leads to the following:

  • It is not going to change prices very often. There is an optimum trade-off between maximizing sales in response to demand shifts or cost shifts via price flexibility and minimizing the reduction in sales due to the uncertainty that price flexibility brings.
  • When it does change prices, the restaurant is more likely to raise rather than lower prices.
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Pot-Sticky Information

2 thoughts on “Pot-Sticky Information

  1. There’s also the effect that small regular upward changes in prices don’t generally affect trade volume. It’s like there is a range that relative prices can move to before the price change registers.

    Probably to do with the same social effect that causes people to throw away small change. It is seen somehow as ‘insignificant’. The trick with a business is to push your prices in that ‘insignificant change’ window.

  2. Yes, I think ‘word-of-mouth’ here is a proxy for people solving their optimization problem. It is too hard to find the ideal solution, and there is no available mechanism to coordinate among each other. So we rely on rough heuristics, and part of that involves throwing away or de-emphasizing insignificant information and prioritizing important information. I’m thinking of a mental priority queue.

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