“Why some buyers pay more than others.”  Robert Frank begins the so-named chapter of The Economic Naturalist with this statement:

The law of one price applies most forcefully in perfectly competitive markets—roughly speaking, markets like those for salt or gold in which numerous suppliers sell highly standardized products.

Frank goes on to probe the paradoxical-seeming details of discount and “hurdle” pricing.  With airline fares, he shows how the Saturday-stayover discount reduces average fairness and increases convenience for both business and leisure travelers.  Of movie tickets, he writes:

Because the law of one price does not apply in the market for film screenings, economists are not surprised that movie tickets do not all sell for the same price.  Matinees, for example, are generally priced lower than evening showings of the same film because fewer people are free to attend movies in the afternoon than in the evening.

Frank is also an economics columnist for the New York Times, and recently, in the wake of some Hurricane Irma publicity that involved the automobile manufacturer Tesla, Frank called out Tesla’s Model S as a case where the law of one price does not – and should not be expected to – apply.  To facilitate evacuation as Irma approached, Tesla had provided some Model S owners in Florida with a free, range-extending software upgrade – a move that won the company praise (for its proactive whiz-bang technical fix) and renewed criticism (for its policy of restricting, via software, the range of lower-priced lines of the same model).

Frank says that the criticism is off-target.  He notes generally:

Sellers with high fixed costs cannot remain solvent if they charge each buyer only a small markup over the cost of producing additional units. To cover fixed development costs, some buyers must pay substantially more than marginal cost.

And of this case:

If Tesla had charged the same price to every buyer, smaller sales volumes would have required that price to have been even higher than for the premium models. Uniform pricing would have resulted in a worse outcome not only for the company but also for its customers.

In this post I want to take up two issues.

First, given Frank’s long-standing and deserved reputation for bringing the insights behavioral economics to the teaching of microeconomics (Frank also received grateful acknowledgements in both of the “fairness” papers I will cite below), it’s interesting that he takes the seller rather than the buyer view of fairness in his NYT column.  Yes, the Tesla S is an example of hurdle pricing, but it’s also an example of how companies risk backlash when they violate what I will call “the law of one product”.

Second, I was initially puzzled by Frank’s statement that, to cover fixed costs, “some buyers must pay substantially more than marginal cost“.  This statement turns out to be true – or not – depending upon how you set up the problem.  I set up the problem assuming constant marginal cost.  Under these assumptions, Frank’s “must” isn’t a mathematical or economic law, but it is an insight into the severe market and production constraints faced by automotive startups.

[Full disclosure: In my day job, I provide IT services to automotive OEMs, including startups.  However, I’m not involved with these firms’ pricing or marketing strategies in any way.]

The Law of One Product

By the law of one product I refer to the limits of hurdle discounting in a customer-driven market.  Using the Frank examples from above, matinee tickets cost less – but they do not purchase admission to a movie that is truncated after the first 60 minutes.  Leisure travelers may pay less than business travelers for the same flight, but for the same class of ticket they get the same service.  The price is different, the product is not.

My law – and many readers will recognize that I am really talking about the concept of “fairness” as developed by Daniel Kahneman, Jack Knetsch, and Richard Thaler in two 1986 papers – like the law of one price, is of limited but real applicability.  The word “law”, here, should be taken as a marketing term; I’m referring to buyers’ expectations, with the willingness to punish violators, that certain product reference points will not be compromised by sales or discount offers.

My favorite example is how the law came to be applied to stereo receivers in the 1970s.  At the beginning of this period, it was taken for granted that cheaper, lower-output receivers did not perform as well as the expensive high-wattage units.   With lower power came higher total harmonic distortion in the amplifier circuit, lower sensitivity, selectivity, and signal-to-noise ratio in the tuner circuit.  That was the name of the game until the Nippon Gakki Company – which we all know as Yamaha – began to produce receivers with the nearly identical output quality specifications at all price and power levels.  What began as a (highly successful) competitive move quickly became a market expectation for companies seeking credibility with audiophiles; price could vary (substantially) with power, and with additional inputs, outputs, presets, etc., but the core sound quality of the unit, as expressed by certain lab bench measurements, could not.*

Another example is software: a good example, because Frank uses it – apropos of Tesla upgrading the Model S vehicles via a wireless software patch.

But the law of one product applies to software.  Oracle’s database customers accept that their license fees vary with the number and power of the servers that hosts the software, and with the addition certain features like clustering, advanced replication, rapid fail-over, etc.  What they would be less likely accept are price-based constraints on the functioning of structured query language itself , say, limitations on the rows that could be returned by a query.  That would be the equivalent of turning on the lights after 60 minutes of Casablanca.

Was Tesla violating the law of one product?  You certainly could not say so from the conversations the NYT’s Tiffany Hsu recorded last September with satisfied and grateful Florida Tesla owners.  But it’s not just current owners’ perceptions of fairness that Tesla needs to be concerned with.  The company’s new Model 3, with its far lower sticker, must reach buyers whose fairness-sensitivity may be high.  I suspect it was with an eye to the hurdle it faces in achieving mass-market penetration that Tesla, over the summer, dropped the software-regulated battery capacity pricing differential.  The new batteries really do have distinct physical capacities, and the law of one product will not apply.

Must Some Buyers Pay More?

Other than raise the flag on my made-up law, I don’t know that Robert Frank would strongly disagree with the previous section.  Customers’ perception of fairness is obviously an issue for sellers – or Frank would have had no motivating issue for his Tesla column.

But in that column, Frank’s concern is less to elucidate fairness and more to illustrate that hurdle pricing can benefit all parties – and that it is sometimes necessary: “To cover fixed development costs, some buyers must pay substantially more than marginal cost.”

There are very common conditions under which Frank’s statement is correct, but, taken alone, it is at odds with the basic math of fixed and average cost.  That math states that any company that can price above (constant) marginal cost will eventually be profitable – at precisely the point the unit price it charges exceeds its average unit cost – assuming that it can both produce and sell the required quantities of its product.

To illustrate, let’s consider an imaginary manufacturer, Bestla Automotive.  Bestla has one vehicle model, the “T’, for which it incurs fixed costs of $60, and marginal production costs of $2.50.  Bestla can imagine selling its new vehicle for as much as $12 or little as $5.  Figure 1 shows that both pricing strategies will “work”, assuming no production or demand constraints.

So far, we have no “must” around differential pricing.  But let’s add constraints like those frequently encountered by real manufacturers.  First, let’s say that, at its current level of investment in plant and equipment, Bestla can only produce 20 vehicles per year.  Crucially, let’s add that the $60 “fixed cost” is not true one-time development cost, as might be the case with a software firm, but the annual “rent” paid by Bestla for the capitalized cost of R&D, plant, and equipment.  The $60 fixed cost must be met every year until the associated debt is retired.

These restrictions change the interpretation of Figure 1: if Bestla can only make and sell 20 vehicles per year, $5 is too low a price to recoup its fixed costs.  Bestla must charge more.  Now, the $12 strategy looks better, but it brings by itself no “must” for differential pricing.

We still have to consider demand.  At the $12 price, Bestla can make money if it can sell 7 vehicles, but can it?  A demand curve must be added to the diagram to answer this question.  In Figure 3, we add a (pretend) downward sloping demand curve.

Figure 3, as I have drawn it, is trouble for Bestla.  There is only enough demand at $5 to sell 11 Model T’s – not nearly enough to make an annual profit.  But neither is there enough demand at $12 for Bestla to take the high road.**

What Bestla needs, clearly, is to make the Model T into a “platform” from which it can multiple offerings, at different price points, to customers.  This is only another way of saying that it must get beyond a single-product demand curve.  What if Bestla could produce a “luxury” or an “extended range” Model T?  Then Bestla might be able to leverage two demand curves.  It could sell both low and high.

Figure 4 shows the demand curve for two Bestla offerings based on Model T platform.  Clearly, in the real world, these differences can be as minor as “trim lines” (cloth vs. leather seats) or different brand names sold be different channels: Ford, at one time, visibly based both the Ford Fusion and the Lincoln Mk Z on the same, well-recognized Mazda 6 platform.  What matters is that the differences between the offerings be perceived as real and accepted by consumers at the price differentials demanded by manufacturers.  How much it matters is shown by Figure 5.  Bestla can sell 4 high-end Model T’s and as few as 11 low-end Model T’s and achieve annual profitability – even though we raised marginal costs (to illustrate a “real” product difference) for the high-end model.

Conclusion

Nothing written above is definitive.  I’ve pictured – very simply – a possible production/demand/pricing situation that shows that the “musts” of tiered pricing come from market constraints and also illustrates the fairness scenario I call “the law of one product”.  Obviously, I’ve used crude linear curves.  And a different demand curve could have been used to support a different claim.

However, I believe a couple of general points would survive any tinkering with the numbers.

The first is that no-seller-cost hurdle pricing does not always work.  Robert Frank suggested that Tesla’s software-applied range change was “fair” in that – like airlines’ Saturday night stay-over hurdle – it benefited both high-end and low-end buyers.  I’m suggesting that Tesla’ situation reflects less the difference between leisure and business travelers and more the difference between economy and first class.  I’m supported by the fact that Tesla has changed its product line to pursue the second difference – but whether I’m right about Tesla is less important than being right about the overall importance of product differences being credible.  It’s get complicated, of course, since these pricing strategies can readily coexist – the airline industry uses both no-seller-cost hurdles and “real” service differences to fill planes and run them profitably.

The second point is that, absent monopoly, fairness is in the eye of the buyer.  It’s consumers who decide, ultimately, whether a pricing strategy such as Tesla pursued with the Model S is acceptable.  The fact Tesla has abandoned a no-seller-cost strategy of differentiating its products suggests that, at some level, the market was already applying the law of one product to Tesla’s offerings.

Notes

*I hope I remember this nearly fifty year-old example correctly.  No doubt the quality standardization in stereo receivers was made possible by technical innovation, say, by the switch from tube to solid state technology.  Fairness expectations always have a context, or they wouldn’t be “fair”.  I do remember market expectations – as expressed by the opinions of friends and reviewers in stereo magazines – changing in response to Yamaha’s move.

**Do companies actually know the demand curves for their products?  Two famous papers have modeled the assumption that in the few seller/many buyer situation – such as exists for durable goods – companies do know at least the market demand curves for the types of products they sell.  See Novshek and Sonnenschein (1978) and Mas-Colell (1982).  A non-technical summary (from which I found out about these papers) is in Athreya (2105), p. 85.

References

Athreya, Kartik B. Big Ideas in Macroeconomics: A Nontechnical View. MIT Press, paperback ed., 2015.

Frank, Robert H.  “Tesla’s Tiered Pricing Is a Hurdle, but a Fair One.”  New York Times, October 27, 2017.  Accessed online on December 3, 2017 at https://www.nytimes.com/2017/10/27/business/teslas-pricing-hurdle-not-hindrance.html.

Frank, Robert H. The economic naturalist: in search of explanations for everyday enigmas. Basic Books, 2007.

Hsu, Tiffany.  “Tesla Boosts Car Battery Power During Irma, Raising Questions of Control.”  New York Times, September 11, 2017.  Accessed online on December 3, 2017 at https://www.nytimes.com/2017/09/11/business/tesla-battery-irma-upgrade.html.

Kahneman, Daniel, Jack L. Knetsch, and Richard Thaler. “Fairness as a constraint on profit seeking: Entitlements in the market.” The American Economic Review (1986): 728-741.

Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler. “Fairness and the assumptions of economics.” Journal of Business (1986): S285-S300.

Mas-Colell, Andreu. “The Cournotian foundations of Walrasian equilibrium theory: an exposition of recent theory.” In Hildenbrand, W. (Ed.), Advances in Economic Theory: Invited Papers for the Fourth World Congress of the Econometric Society. 1982.

Novshek, William, and Hugo Sonnenschein. “Cournot and Walras equilibrium.” Journal of Economic Theory 19.2 (1978): 223-266.