## Sunday, June 15, 2008

### An Economic Puzzle: Fixed Prices with Variable Unit Sizes

I’ve finally succeeded in inserting the code to make post extensions work (with the help of Hackosphere), so this seems like a good time to pose an economic puzzle I’ve been thinking about.

In the absence of price controls, most goods and services respond to changes in conditions with changes in price, while the size of each unit remains fixed. If grain gets more expensive, for instance, the price of bread rises while the size of loaf stays the same. But can you think of any goods or services for which the price remains fixed while the amount per unit changes, even when the prices are free to fluctuate? I can think of two or three. Can you guess what they are, and can you come up with any others?

The example I had in mind was marijuana. Though I have zero personal experience with buying weed, I’ve seen the transactions take place, and some friends (you know who you are!) have confirmed my observation. Marijuana is typically sold in amounts designated by price, such as the well-known nickel bags (\$5) and dime bags (\$10), as well as larger \$50 or \$100 bags. If there’s a change in supply conditions, like the cost of growing weed, it is apparently reflected in the quantity per bag. Likewise, if you’re buying better quality weed, that will be reflected in a smaller volume in the bag, not a higher price. You don’t see bags of weed with prices like \$19.95.

And there’s a natural economic explanation, courtesy of Ronald Coase: transaction costs. An illicit market puts a premium on fast and discreet transactions, because longer transactions increase the chance of getting busted. Nobody wants to take the time to make change, and that makes it desirable to have prices easily represented by one or two bills.

This explanation suggests a second example, with which I’ve had even less experience: prostitution. I don’t know for sure, but I’d be willing to bet that prostitutes always price their services in denominations of at least \$20, and probably \$100. The reason is the same: minimizing the time involved in making the transaction. I can’t imagine there are any hookers who charge \$349/hour.

And the topic of sex suggests a third example, this one legal, but still characterized by high transaction costs: lap dances in a strip club, which seem to be priced in \$10s and \$20s. In that context, nobody wants to spend time fumbling with change, especially since (a) the dancers don’t usually have pockets and (b) the cash mostly comes straight from the ATM, which dispenses cash in \$20s or higher.

Am I missing any other examples? And do they all have the feature of high transaction costs?

Anonymous said...

Gambling (lottery tickets, plays on a slot machine) They just change your odds (the expected value of your win) but keep the bet size a nice round number.

Some people buy gas (or used to) by going in to the gas station and getting \$10 or \$20 worth from the pump. The pumps could be set to dispense just a fixed dollar amount and then shut off.

Plenty of people buy wine by the price of the bottle, which presumably means the quality of a \$10 bottle will vary.

Everything in a 99c or dollar store.

Brandon Berg said...

I wonder what will happen when inflation renders the "dollar store" business model infeasible. "The Buck-Fifty Store" doesn't quite have the same ring to it, and being the first store in town to make the switch must be really bad for business.

Anonymous said...

It must be more costly, in general, for the seller to change unit size rather than increase the price. So why would the seller do it? perhaps to fool the unsuspecting customer. I think I've seen chocolate bars and other packaged food items shrink in size while the price stays the same.

DonLloyd said...

Following up on the candy bar:

http://mises.org/Community/blogs/donlloyd/archive/2007/10/18/a-candy-bar-inflation-puzzle.aspx

Regards, Don

Alex Tabarrok said...

Actually bread is an example of the opposite. At the fancy supermarket where I buy bread the price has stayed the same but the loaf has gotten smaller.

Glen Whitman said...

Anon of 3:06 -- Lotto tickets and 99c stores are both good examples, and they seem like they're driven by something other than high transaction costs.

I don't buy the gas and wine examples, though. Gas is still priced by the gallon, and customers can choose whether to stop at a number of gallons or a number of dollars. And wine still comes in bottles of about the same size it always did; if customers want to buy lower quality wine to keep the price constant, they most likely have to switch brands to do so.

Anon of 8:24 and Don -- I had thought the candy bar example came from a time when there were government price controls, but perhaps I'm wrong. Candy bars now seem about the same size as they were when I was a kid.

Alex -- What kind of bread are you buying? Seems like Wonder and Roman Meal have had about the same size loaf all my life. (I wish it were otherwise; as a single guy, I can't make it through a whole loaf before it goes stale. When I lived in NYC, they offered a half-loaf size that doesn't seem to be available in L.A.)

Anonymous said...

Quote: I had thought the candy bar example came from a time when there were government price controls, but perhaps I'm wrong.

Chocolate bars are made smaller in steps while remaining at the same price, then they are made bigger in a jump, with a price increase, and then go back to gradually shrinking. On a long view, they are always about the same size. Or at least thats the way 'brand' chocolate bars work in the UK

just_some_guy said...

There's been some talk lately about the amount of beer being poured is smaller (by one to two ounces) at the local bar, though the price remains the same.

DonLloyd said...

"Chocolate bars are made smaller in steps while remaining at the same price, then they are made bigger in a jump, with a price increase, and then go back to gradually shrinking. On a long view, they are always about the same size. Or at least thats the way 'brand' chocolate bars work in the UK"

Assuming that my link was likely broken, this shrinking of size by the manufacturers of single-serving consumer products is to everyones' benefit. Rather than increase prices, the decrement in the unit good size is also the least valuable portion of that size contained in the original product, applying diminishing marginal utility. The tenth bite of a candy bar is far less valuable than the first, whereas an incremental price increase is the most valuable portion of that size contained in the total price.

Regards, Don

Anonymous said...

Ice cream containers are getting smaller while the price remains the same. But I bought smaller bowls and spoons to offset that.

Glen Whitman said...

What ice cream brand is that? Seems like they've been offering pint and 1/2 gallon containers all my life.

Anonymous said...

Funny thing you mentioned ice cream. Five or six years ago, most single-serve yogurt cups were 8oz in size. Now, most of them are 6oz, except the supermarket brands (which mostly remain 8oz). I can't be sure about this either, but I think the price has remained 59c to 79c a cup.

With respect to wine: Trader Joe's "Two-Buck Chuck" (aka Charles Shaw) never has any specific formulation. In any given season, the maker just buys up excess grapes. Season-to-season, quality varies (I have experienced this), presumably according to the grape harvest. But the wine has always cost \$1.99/bottle (in California) since it was introduced a few years ago.