Non-Linear Pricing

Here is a picture I took the other day at the Deschutes' Portland pub.  It is a little out of focus, the iPhone not quite up to the job of low light detail work, but notice how the beers are priced: $5 for 500ml and $3 for 300ml.  In other words exactly 1 cent per ml.  This seems straightforward, but to me it was astonishing as you almost never see this kind of 'linear' pricing in beer.  Most places are like the Full Sail Tasting Room and Pub in Hood River which prices their imperial pints at $4.25 and half pints at $3.  This is what economists refer to as 'non-linear pricing:' when the price per unit changes as the total units change.  So a pint at Full Sail is about 21 cents an ounce and a half pint is 30 cents an ounce.  This is the norm and it is everywhere in product markets: beer, soda, chips, socks ($4 a pair or 3 pairs for $10), you name it. The question for all you budding economic naturalists (or Beeronomic naturalists) is, why?

One reason for this type of pricing is simple: costs.  It can be cheaper to sell in larger quantities.  I talked recently about the cube-square rule that generally affects packaging costs: the volume from bigger packages increases at a faster rate than the surface area of the packaging - so the costs per unit of the packaging decrease with volume.  There are reduced transactions costs per unit for bulk purchases as well.  In a pub setting, smaller servings may mean more glassware to bus and wash and more visits per table by servers.  So some of what we might be seeing in non-linear pricing is just a reflection of the added costs of smaller quantities.  

But not always.  Bill at the It's Pub Night blog has had an ongoing fascination with non-linear pricing in beer, focusing particular attention on the inflated price of 22 ounce bottles that have gained so much popularity.  Given the cube-square rule and the lower amount of packaging (no paperboard holders) you would assume that the six-pack would be costlier per ounce of beer and therefore if price was just a function of costs, 22 ounce bottles would be less expensive per ounce than six-packs, but Bill finds that the opposite is true.  So, again, what is going on?

The answer, to economists, is well known and goes by the term 'price discrimination,' or more specifically in this case 'second-degree price discrimination.'  Price discrimination in general is the ability to charge different customers different prices for the same good based on their ability to pay.  You charge more to people who value the good more and less to those that don't.  If you can do this two things happen: you do better as a seller, and you sell more than you would otherwise.  You do better because you get to capture most of the surplus from each transaction and you sell more because if you were forced to sell everything at the same price you would keep it reasonably high (if you had any market power) and thus the folks who didn't value it that highly might not get to buy.  If you can charge different prices, however, you are quite willing to sell at a low price to a customer with a low value of the good because you can still sell to the high valuation customer at a high price.

Portland's saturday market is a good laboratory to see how this works.  Go to a booth where an artisan does not post prices and observe how prices are quoted.  You will probably find that price will fluctuate based on some observable characteristics about the customer that might be reasonably related to willingness to pay for the artisan's wares: fancy clothes, watch, age, extra excitement, and so on.  To illustrate this phenomenon I always tell my students tales from when I was a Lewis & Clark College student studying overseas in India and would go to the market.  After a while I got to know the regular prices, but as soon as they saw an obvious westerner, the shopkeepers would immediately double, triple or quadruple the asking price (it helped to know a little Hindi to hear how the prices changed from a local to me).  The shopkeeper made the correct assumption that a westerner in general had a much higher willingness to pay than a local and thus wanted to extract more surplus from that transaction.  He was practicing price discrimination and thus showed himself (it was almost always men) to be a good economist.

This is close to what we refer to as first-degree price discrimination where you can tell something about individual willingness to pay for a good.  The problem with this type is that most market situations are more anonymous - you can't tell by looking at them anything about their willingness to pay or you don't even see them at all.  So what to do, well you might be able to get different types of customers to differentiate themselves by offering different prices.  This is 'second-degree' price discrimination.

Take the pub as an example.  Suppose you know that there are two types of customers: high demand and low demand.  Low demanders are only going to buy one beer and are willing to pay up to $6.  High demanders willingness to pay for one beer is $6, $5 for the second and $4 for a third or a total of $15 for three.  Now let's suppose there are equal numbers of both types and so let's talk about a single table of two people, one of each type.  Lets also assume the marginal cost is constant so that it costs them $2 to provide every beer.  The pub could charge $6 a beer and would sell two, get $12 in revenue, $4 in costs and clear $8 in net revenue.  Or they could charge $5 a beer and sell three, and make $9 net.  Or they could charge $4 a beer sell four (one to the low demander and three to the high), and make $8 net.  But a clever publican would offer a different deal: $6 per beer or three for $15.  The low demander will buy their one beer for $6 and the high demander will go for the three beer deal (if you prefer make it $14.99 so he strictly prefers this deal and gets $0.01 in surplus over one $6 beer).  The pub will make $6 + $15 in revenue, will have $8 in costs and will net $13!  Clearly this is a better plan for the pub and notice it does not require knowing which customers are high and low demanders - they self-select.

This is classic third degree price discrimination and can be applied to Bill's 22 ounce bottles as well.  There are low demanders for these beers who want just a wee bit to taste and high demander who will drink much more.  By pricing the 22 ounce bottle so much higher you charge a premium to the low demanders and you give a discount to the high demanders by offering them a volume discount in six packs (and generally even better deals with 12 packs).

But Bill should not despair (assuming he is a high-demander) because this strategy generally benefits the high demander - they get lower prices than they would in the absence of the price discrimination.  Thus the 22 ounce bottle is a good thing for the six-pack buyer.  Why?  Well, go back to my pub example and notice that the high demander pays only $5 per beer, rather than the $6 they would have paid without price discrimination.

This is a general rule in price discrimination: some groups benefit and some suffer from the practice.  In this case, high demanders see lower prices, but low demanders get the same price.  This is due to the particular simplicity of my example, more often low demanders see higher prices.  

Cheers!