Are Teslas damaged goods?


In the wake of Hurricane Irma this weekend, Tesla pushed out a software upgrade to owners of Tesla 60kWh versions to give them the range of their 75kWh. Just like when pilots say they will “make up time in the air,” commentators said: “well isn’t that interesting.” It seems like all Tesla’s have the same battery and it is software that can limit the storage capacity in some models.

Alex Tabarrok was quick to point out that taking a perfectly working product and crimping it is a long practiced means of price discrimination. As Ray Deneckere and Preston McAfee showed, by taking a product, expending resources to damage it, firms can sell two versions of the product and earn more revenue through price discrimination (covering the crimping cost). (Here is a less technical version).

As we are in the process of educating, let’s write a little model. Suppose that there is a product of value, v, but at a cost, c, a seller can crimp it so it has a value of ac where a < 1. Imagine that half of all customers have a value v = vH and the other half have a value v = vL (where vH > vL). In this case, the seller has three pricing options:

  1. Sell a non-crimped product to everyone at price = vL and earn average profits of vL
  2. Sell a non-crimped product at a higher price of vH and earn average profits of vH/2
  3. Spend c, and sell the crimped product at a price of avL and a non-crimped product at a price of (1-a)vH + avL (which is the price that makes the high types just indifferent between paying for the non-crimped product and the crimped one at its low price). This gives average profits of (1-a)vH/2 + avL – c

From this, it is optimal to sell the crimped product if (1-a)vH/2 + avL – c > max[vL, vH/2].

There is, however, a subtle difference in the Tesla. Tesla could have shipped a car with a smaller battery which could never have had its range extended. However, it didn’t. It shipped a car that was crimped but in a reversible manner.

Why is this important? It changes the buyer calculus. What the classic model misses here is that cars are an asset as well as a consumption vehicle. So you worry about re-sale. This is apparently why we have a sunroof in our car even though we never open it!

From the standpoint of economics, Tesla had two crimping options. One would work as above where the product is permanently crimped. The second would allow a future buyer of the crimped product to sell the car for more. How much more? Well, that is partly determined by Tesla.

To amend the model, suppose there are two periods — the present and the future. You only buy a car for one period and then you resell it. Imagine (to make our lives easier) that the car does not depreciate and also that Tesla doesn’t care about harming the resale market (that is substantive but I don’t have time here to deal with it). Finally, imagine that the resale market is a seller’s market and so they can price at the full value of their car.

If you buy a non-crimped product, then it is worth vH in the future as well and so the total value is (1 + d)vH where d (< 1) is the discount factor. On the other hand, if you buy a crimped product, then your expected revenue is avL(1/2) plus (vH – Upgrade Price)/2 where the upgrade price comes from Tesla and is (1-a)vH + ‘Crimped Price’. Thus, your expected revenue is a(vL+vH)/2 + ‘Crimped Price’.

What is the ‘Crimped Price’? It is the price that makes someone just indifferent between buying the crimped product or no product. That is,

avL + d(avL/2 + avH/2 + ‘Crimped Price’) = ‘Crimped Price’

which implies ‘Crimped Price’ = (avL + ad(vL/2 + vH/2))/(1-d)

And so,

‘Upgrade Price’ = (1-a)vH + (avL + ad(vL/2 + vH/2))/(1-d)

= (((1-d)(1-a)+a/2)vH + a(1 + d/2)vL)/(1-d)

In this case, Tesla’s average profits are:

(1/2)a(vL + d(vL/2 + vH/2))/(1-d) + (1/2)(((1-d)(1-a)+a/2)vH + a(2 + d/2)vL )/(1-d) – c

compared to ((1-a)vH/2 + avL)/(1-d) – c for the ‘two period’ classic damaged goods case. Notice that the dispersion in prices between the two cases is different. In the classic case, it is high (the low price is lower and the high price is higher) while in the Tesla case, it is lower (the low price is higher and the high price is lower). But we cannot rank the two outcomes (or at least I couldn’t do it right at the moment).

I suspect that if we modelled the resale market more carefully (something I have done before here), I think the Tesla model will produce a higher marginal revenue and then by Theorem 3 of McAfee (2007), it will earn Tesla more for the same crimping cost, c. The intuition is that when there is a damaged good, it harms the liquidity in the re-sale market by giving those who have undamaged goods more power and segmenting the re-sale market rather than pooling it. When damage is reversible, there is more pooling and a consistent price differential ex post. This is just a conjecture but I am sure some enterprising graduate student might work out the reversible model.

More critically, there are more options to explore. For instance, Tesla could have chosen a subscription model to the upgraded service (much as we do when we get a cable box and choose to subscribe to HBO). This may allow users who do not need range except for the occasional long trip to pay for it then. Again, this would enhance efficient use of the asset and perhaps would be better than the blunt instrument of a ‘once off’ upgrade option. As we move to software based versioning in cars (where c is for all intents and purposes, 0), I think we are likely to see more service than purchase options available.

Regardless, I do not agree with Tabarrok “that Tesla may have made a marketing faux-pas.” Instead, given that they had a crimped product, un-crimping it for an emergency got them ahead of a potential marketing disaster (a la Uber and airline surge pricing). Moreover, when they actually sell the car, the can use the fact that the asset can be upgraded as a plus rather than a negative as would be the case for buying other cars.


4 Replies to “Are Teslas damaged goods?”

  1. While the above is an economic view, my first thought was an engineering view, that high voltage batteries like in the Tesla degrade least when maintained and operated in a “safe zone,” (operating at 30-70% charged is a range that automotive engineers have said would allow the batteries to last indefinitely). Software enforces a bit of safety headroom on both ends of the range. Adding miles of range by taking away some of the safety headroom could be marketing and sales overriding engineering.

    What’s viewed as crimping is not solely that. It’s at least partially a trade-off, where the previous 60 kWh owner, while gaining mileage range, will reduce battery longevity with the software update to make 75 kWh available (taking away some of that safety zone headroom that engineering almost surely designed in).

  2. Why isn’t the question whether it’s cheaper for Tesla to crimp the product rather than make a separate, lower-quality product? I imagine it could be a bit cheaper to make one battery and limit its use via firmware than to manufacture two batteries, even if it must then be a relatively high-end battery. Tesla Model S sedans can double in price from the base to top trim. I’m sure there is considerable value to them in having a lower-price option, and if they are absorbing some loss on the hardware itself at the lowest price point but sparing themselves the expense of making separate hardware and gaining a larger user base, isn’t that reasonable? I just wonder if it isn’t cheaper for them to offer a loss leader through firmware than through a separate manufacturing process.

    When you refer to the resale market, are you assuming that Tesla is repurchasing and offering CPO on these cars? In general, cars, and especially high-end luxury cars, do not make sound investments and lose value very quickly. A quick glance online tells me that Model S sedans lose 30% of their sticker price value within two years, which is less than some unfortunate Gernan models see in depreciation, but not what I would normally associate with a seller’s market. Only collectible cars get that distinction, but those are subject to outright mania. Maybe I’m missing the forest for the trees here but I wasn’t able to follow the implications of what sounded like unrealistic assumptions about expectations of the car’s value in your discussion.

    P.S. Open your sunroof!

  3. There’s another possibility (a variation on Joe T’s comment).

    Manufacturing is not an exact science. For instance, Intel sells the same microprocessor at several speed ratings. This is because after manufacturing the processors are tested and some run faster than others. Rather than getting a low yield of high speed processors, they get a high yield of processors at varying speed ratings.

    So Tesla may be producing one battery pack. Suppose the resulting battery packs have capacities up to about 80-90kWh under all rated conditions (the car’s full rated temperature range). They take the ones with at least 75kWh and put those in the higher capacity car, the ones with at least 60kWh in the lower capacity car.

    However, the rated power is under all conditions. If a battery can supply 60kWh at cold, Minnesota winter temperatures (I think battery power is lower at lower temperatures), it may reliably supply 75kWh at warmer temperatures. So allowing the larger range in an emergency situation might make sense, but that larger range doesn’t make sense under all conditions.

    The business question becomes why Tesla enforces a uniform usable battery capacity on its cars. This could be to avoid people shopping for which car has the higher actual capacity, or getting used to driving a longer distance in fair weather only to run out of power doing extreme conditions. It isn’t necessarily Tesla intentionally down-rating the batteries on some products.

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