In last Thursday's post [link], I described why I don't like the drunken irrationality argument. Here I give a more complete explanation of what menu costs have to do with the effect of the tax.
Maybe the discussion of menu costs seemed incomplete because I recently took a final exam in my graduate macroeconomics course that covered, of all things, menu cost models. The key to applying menu costs sensibly is to relax the law of one price.
Economists often like to assert that only one price prevails in a market because it makes the math easier, but in a world with menu costs, different producers charge different prices. This is true, in part, because there really is no such thing as perfect competition that equalizes all prices. The competitive model is a useful caricature of the messy economic forces at work, but there still are messy economic forces at work.
Why are there different prices for different places? Some bars adjusted their prices last week, whereas others adjusted their prices ten weeks ago. The out-of-date prices are more likely out of line with current supply and demand. This means, in econo-statistical jargon, the prices have a distribution.
Every firm would love to be at the optimal price, but it is costly to keep the price pegged there. It also doesn't hurt too badly to have a price that misses the target price by a little bit, but as the price drifts downward relative to other firms, profit margins dwindle. If the price increases relative to other firms, customers leave causing profits to fall. With menu costs, bars don't change their prices unless they are very far from the optimal price. But, once the bar decides its price is far enough from its target price, the owner changes prices and by a lot.
Notice that if there is a distribution of prices, the implications change. Not every bar is right near the optimal price. Some have prices that have drifted down relative to everyone else. Some have just changed their menu. When we hit the entire market with a sales tax increase, the effects are different for different bars.
When there are menu costs, a bar really has to benefit from increasing or decreasing its price. With this in mind, here are the predictions:
- If the target price decreases, bars with the highest prices are most likely to decrease their prices (and by a lot), whereas the bars with already low prices get less gain from changing prices, and so they don't.
- If the target price increases, the menu cost model predicts the opposite: low price places really raise their prices, whereas high price bars keep the prices as they were.
So, what happens when the market for cocktails is slapped with a moderately hefty sales tax (say 6 percent)? What do bars want to do with their prices? If the tax is not figured into the price (but lumped on top, like here in Chicago), bars want to decrease their prices to attract customers from home who said "Boooo" to the tax. As the analysis above illustrates, the bars that were relatively overpriced will be the first to cut prices. When they do, they will really adjust prices.
If the price is inclusive of the tax, the high price bars will "eat the tax," while the relatively underpriced bars will redesign their menus. That's what menu cost models say anyway, and I think the story is encouraging for what we learn in Econ101. The Econ101 story tells us qualitatively what happens to the target price. The menu costs tell the rest of the story.