Pricing to the demand curve

Many college microeconomics courses include the following exercise. The teacher offers the students an imaginary trip to Hawaii, and asks them to write down on notecards how much they are willing to pay for the trip. The teacher takes the notecards and graphs the bids. Here’s how the graph might look:

The y-axis is the students’ “willingness-to-pay” and the x-axis is the students sorted from highest to lowest bids. The line is known as the demand curve.

Now imagine you’re the company selling these trips. For simplicity, suppose you’ve already bought the trips, so your marginal cost is zero. What’s the optimal price you should charge? If you set the price at, say, $500, then the students who are willing to pay above $500 would buy the trip, and the rest wouldn’t:

Your total revenue and (assuming zero marginal cost) profit will be the area of the green square (revenue times quantity).

Notice the sections under the curve to the right and above the green box. To the right are students who were willing to pay but were priced out. Those are missed sales opportunities. Above the green box are students who were willing to pay more than you charged. That is lost revenue. (Since the underpricing benefits customers, the area above the green box is called the consumer surplus).

After you have chosen the right price, the only way to make the area under the curve greener is to charge different customers different prices. The theoretically optimal way to do this is to look at each notecard and offer to charge each student, say, 10% less than the prices he or she bid. In real life you can’t do this (although Priceline has gotten close by asking customers to enter their willingness to pay). Some companies – most famously Amazon – have attempted outright price discrimination, but this tends to anger customers and can even run afoul of the law.

So the goal of pricing is to capture as much area under the demand curve as possible. In practice, the best way to do this is to find proxies for willingness-to-pay that are easy to observe and that customers will accept.

For example, airlines know that business customers will pay more than vacation travelers. They therefore look for acceptable proxies to segment business and vacation travelers and capture more of the area under the demand curve.

This is why flights are cheaper when you book early, stay over on weekends etc. The airline pricing models assume you are a vacation traveller.

Book publishers would like to price their books according to customer enthusiasm. Hardcore fans will pay more for books when they are first published, and casual readers will wait. If publishers offer the same book at different prices at different times, their price discrimination will be too obvious (interestingly, time windowing for movies doesn’t provoke much outrage). So book publishers offer modestly better goods – hardcovers – to early buyers.

Enterprise software companies price using proxies for the customer’s budget. Oracle databases are priced by the number of processors. Salesforce is priced by the number of end users (“seats”). Many enterprise software companies obfuscate the highest tier of pricing, telling sales prospects at that level to “call us.” What this really means is: “Call us, so our sales people can attempt to estimate your budget and price discriminate accordingly.”

Sometimes, the search for pricing proxies can lead to absurdity. I once heard someone from a prominent hardware company tell a story about how his company had offered two versions of a printer. The cheaper model was identical to the more expensive one, except the cheaper one printed fewer pages per minute. To accomplish this, the cheaper printer had the same hardware as the expensive one, except the cheaper one had an additional chip that forced it to slow down. This made the cheaper printer more expensive to produce. Situations where cost and price have zero or negative correlation are far more common than most people assume.

69 thoughts on “Pricing to the demand curve

  1. Matthew Rayfield says:

    Thanks Chris. A very enjoyable post. Love the printer anecdote.

    Makes me wonder how I’m being priced to without realizing it.

  2. Is this something you guys are working on at Ebay with Hunch’s technology? We are (also) interested in using our personalization technology for ‘desire based pricing’ which is the demand curve in effect. I did not know about the Robinson Portman act though, thanks for that.

    btw, the ‘stars’ widget seems dysfunctional? I wanted to give the post a 5 stars but it ended up -6 stars, sorry.

  3. Dan Wolchonok says:

    Great explanation of demand curves and price discrimination. Companies do a good job of enacting these strategies, especially when consumers benefit (travelers get cheaper tickets than if everyone was charged business traveler fare or the profit maximizing price).

    This is especially true when the profit maximizing price is higher than the price that can be charged through price discrimination. This is the case for HBO: which most people don’t think about.

  4. Great post. Makes me think about Uber’s pricing multiplier that captures a customer’s increasing willingness to pay in the rain or when there is a shortage of cars on the road. I suspect we’ll see more and more services – and pricing models – designed this way.

  5. Luke Chamberlin says:

    Zero marginal cost is such a difficult concept in economics. I still want to say, “But I paid X for the trips, so I have to sell them for Y or I lose money.”

  6. Very interesting post. The corollary (or flip side) to pricing is the perceived value, and I’ve always been fascinated by how companies manage to increase the latter so that they can get away with higher prices – not “just” pricing to demand, but essentially altering the demand curve altogether. The more you get into high end products, the more decisions seem to be based on human emotions as opposed to more rational, price-based reasoning. The classic example is luxury (why would you pay so much for perfume, which is scented water at the end of the day), but as you pointed out this applies to software as well – for example, why is Palantir becoming a multi-billion dollar company so quickly when so many other analytics software companies struggled for many years and were considered just a “nice to have”? Is their software really 10x better, or did somehow manage to create a perceived value that’s much higher?

  7. nice and clear post. I always enjoyed looking at the price structure for SaaS companies. My favourite ones are those that tie usage with the cost of the software. For instance, Freshbooks charges its customers based on the number of clients they are billing. There are many such examples in SaaS

  8. Good concise overview of this concept. Coupons and senior discounts are other common forms of price discrimination. While many folks reflexively hate price discrimination, it can be an important part of a business model that allows goods to be available at the lower prices that would not be available without price discrimination. The buyers at the higher price can allow production to reach a scale where it can be offered at lower prices (many electronics seem to have this model).

  9. Agreed. It is pretty easy to show that effective price discrimination benefits consumers and producers. Unfortunately it is so taboo that companies need to tiptoe around it.

  10. Yeah, it’s funny how you can almost never charge based on, say, the revenues of the customer (that would seem unfair and annoy them), when in fact that is what sellers are trying to do.

  11. I was thinking of doing some follow up posts on pricing in specific areas (b2b software, consumer internet/software, hardware) but no idea if that is interesting to people. Giffen goods are fascinating but not sure I have much to add beyond what is on Wikipedia.

  12. Thanks. Yeah, pricing affecting perceived value is an interest concept. Flash sales are basically a way for high end brands to offer discounts while obfuscating those discounts so as to not hurt the brand. My understanding is a lot of economists are skeptical of the higher prices can lead to higher perceived value. But I think this is the usual case of economists overestimating people’s rationality.

  13. Chris – My vote = b2b software / SaaS

    We have a very scalable product, where marginal production cost is low. The difficulty is differentiation of market segments and associated pricing strategy. Theory is quite simple but a review of possible strategies would be very interesting.


  14. Thanks Chris. An interesting application of this model is to the virtual goods market. One can argue that gaming companies such as Zynga and Kabam have optimized value extraction from their customers by offering their users to pay anywhere from $0 to $1000 based on their individual demand curves. The comparison is not perfect because each user is getting a different experience depending on how much they pay, but it is a pretty darn good one.

  15. Yeah I don’t know that much about their pricing (I don’t play games like Farmville) but it does seem (as you say) that their ability to segment pricing according to non-payers, small payer, and “whales” is key to their economics.

  16. Yeah, agree that is the beauty of couponing. It is precisely the price sensitive people who will go through the trouble of using couponing. Rebates are another interesting way to do it.

  17. tylernol says:

    this software nerfing /sales segmentation is very common with hardware companies too, for example in the videoconferencing industry. You can buy software licenses to increase the number of calls /ports. It is just easier in most cases to ship a system with the extra hardware and just let it be dark/unused.

  18. There’s also an interesting scenario that used to happen on trains where economy class was significantly worse than first class. Although it was easy and cheap to improve the quality in economy that would lead to some of the high-margin first class people switching over to economy which was not desirable. This is likely to happen when the prices are different enough that even having a few people switch can lead to big drop in revenue.

  19. Wallace says:

    But doesn’t this create a barrier to price competition between vendors(the information needed to match you with a price) , and this increases the price ?

  20. Just read the PMP paper – pretty Interesting but it’s focused on price as the only differentiator. You can argue more luxuries and a higher price are equivalent but different people will have different utilities around it and behaviorally you may see different behaviors. Pretty interesting though. It’s interesting to think about PMP in the internet world where the supply is virtually infinite.

  21. Interesting discussion. I come from the marketing side of things, and
    when we started talking about pricing one thing we always paid attention
    to was the “wince” factor. You want to apply enough pressure with the
    price that buying the product caused a slight hesitation but not so far
    as to cause a wince.

    I now run a company that provides two SaaS products, and I’m not sure
    there’s a theory or two that can explain all of this away. We tinker and
    tinker with price and then measure the hell out of it each time
    (amazing what heatmapping, clicktracking and video captures of visitors
    on your pricing page can tell you), and sometimes it feels like we still
    end up treating pricing like another brand attribute (i.e., is this a
    value-based brand, is it more of a niche premium brand).

    One thing I’ve been wary of is not to become overcomplicated in pricing.
    People prefer a few choices, but when you overburden them with choice,
    they tend to shut down and not make a decision (lots of social
    psychology studies prove this out). And when you start throwing all
    sorts of discounts and rebates and discrimination-based pricing (age,
    budget, etc.), at some point customers may feel like they’re overpaying
    (which is why cable companies almost always relent when you call them
    up and threaten to leave … because you are overpaying relative to
    other customers on recent offers). Which causes lots of customer
    migration back and forth and little brand loyalty.

  22. Another example for you

    Delving into ancient history, IBM used to offer upgrades for their mainframes. You pay maybe $100k, and an engineer comes out and installs your upgrade.
    One of my colleagues watched one of these installations – the engineer arrived with his toolbox, opened up the cabinet and removed a part!

    And now it ran 20% faster

  23. 2joshis says:

    Hyundai did a 10yr/10K Miles warranty promotion.while it could be argued it was to install customer confidence in quality being new entrant. It also picked the price conscious buyers who thought it was too good a deal to pass up

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