I recently noticed that my main ammo type (Trauma Heavy Missiles) almost doubled in price in the past two weeks, from 44ISK to 77ISK. I knew that recently the price of Tritanium had risen to over 4ISK. (Think over $4 gas.) But the rise in material price has been going on for about 2 months and really just now the price of ammo is jumping. In thinking through this problem I stumbled upon a model of downwardly sticky prices that does not rely on adjustment costs and has more of a prisoner's dilemma feel.
In the setup there are many identical firms and consumers. The firms buy raw materials and convert them into finished products which the consumers buy and consume. The wrinkle is firms post sell orders with prices and quantity available. Consumers purchase from these orders and can buy partial quantities. Then if there is a sudden shock to the raw materials, one would expect that prices would immediately rise to be profit maximizing given the now higher replacement costs. The problem is if you are the only producer to adjust your price upward, you lose on sales until the current market orders expire. If there is a cash flow constraint on the producer side then having to wait on sales would harm current production, completely disrupting the firms profit flows. And because the firm doesn't see enough other firms changing their prices, the firm chooses not to adjust due to these disruptions.
It is true that their are implicitly costs of changing the price and production plan, but they are more part of market equilibrium than firm structure. The key components to this model are the structure of market orders and the credit constraints. Relaxing either would cause prices to adjust immediately. There also needs to be some assumptions on speculator, namely they are not big enough to affect the market, and probably a credit constraint on consumers as well. The other problem is I am not sure what market in the real world has this structure. Any ideas or critiques of the model?
Interesting point. I wonder if any of the macro folk have working on models like this, rather than the ad hoc Calvo fairy approach?
ReplyDeleteI don't know. I need to ask some of the Macro people. After posting this I actually figured out how to almost completely justify the ad hoc Calvo Faerie model. The setup is similar to above with the identical firms, but doesn't have the long term orders. The incentive to not change still exists due to the disruption in revenue flow. Further the timing of a change in price is a mixed strategy, like a continuous time contest strategy. The difference between this can the Faerie is the probability of switching is not constant over time. I believe that the solution will have a hazard rate that increases in both time and the number who have switched. The thing to check is that this acceleration as firms change prices doesn't cause it to unravel and have all firms switch immediately.
ReplyDelete