Here's a hypothetical question Russ asked one of the podcasts. How would taxing each cup of coffee 20 cents affect the size of the cup? I'll put my answer in the comments. The blog is also supposed to have an answer,and if I find it, I'll paste the URL in the comments, too.
5 comments:
The size of the coffee cup should increase. This is because with a fixed .20 cent tax, you can decrease the tax per coffee by selling a larger amount of coffee in each cup.
Here's a discussion of the problem, but I didn't see an answer by the Professor; Just some hints. Still, I'm pretty confident in my answer.
http://www.econtalk.org/archives/2009/10/willingham_on_e.html#comments
I don't know if the fault is yours or Russ's, but the setup of the question should've been more clear. When I first read it I thought you meant an additional 20 cents on top of existing taxes. Your first comment clarified that, but I think that choosing 20 cents was a bad number. I'm guessing that a cup of coffee is often >$3, so with a 7% sales tax, 20 cents would be a tax decrease (in which case the conclusion is obvious).
I'm guessing that the question was intended to give a situation where there is an initial increase in tax, yet a potential decrease in tax per unit volume as you point out. In that case I agree with you under one assumption: people want as much coffee as they can possibly afford. This might very well be true, I haven't observed the coffee culture all that much though.
On the other hand, I've noticed that beverages in general are cheaper per unit volume the larger the quantity you buy (like getting a 32 oz slurpee for something like $1.29 and a 64 oz slurpee for $1.89), yet people don't always buy the largest option. Maybe this is a manifestation of the same principle though. The initial cost of the slurpee machine is relatively substantial whereas the cost of the frozen sugar water is minimal, so it reduces 7/11's cost/unit to offer mammoth slurpees.
I think the question is clear enough and your first reading is correct: The question assumes that the tax is a new tax, not a replacement tax. Whether there is already some sort of sales tax or there is no tax at all is irrelevant to the effect of a new 20 cents per cup tax on top.
I agree with your analysis of a replacement tax, and the analysis of the actual problem is similar. The key is that the tax is per cup, not per ounce. Suppose you drink 12 oz. of coffee a day. You usually buy two 6 oz cups at $1.00 each. Now with the tax you are paying $2.40 for 12 oz. (assuming the seller can pass the tax on to you. If not, the analysis is the same, but from the seller's perspective.) The other option, however, is to buy one 12 oz. cup, which, even if it costs the same per oz. at the coffee shop, will reduce your tax 20 cents, because you only buy one cup. Sure, your coffee might get cold, etc. But all other things being equal, the incentive is going to be to sell a larger cup of coffee.
Your slurpy example is demonstrating something else, I believe: the marginal utility a consumer derives from a product. That's because people get full or tire of a particular product. The pricing is designed to respond to decrease in marginal utility with a price decrease.
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