My 18-month detour through second-degree price discrimination terminology

When I was composing this post about price discrimination last month, I was drawn into a discussion with ChatGPT about second-degree price discrimination. ChatGPT, which I mostly use for checking for inconsistencies and grammatical errors in my draft blog posts, told me that I should refer to menu pricing as a form of second-degree price discrimination. I replied that wasn't correct, because second-degree price discrimination, as defined by Arthur Pigou in the early 1920s, involves offering a declining price for each additional unit that the consumer buys. ChatGPT responded that indeed, Pigou had defined second-degree price discrimination that way, but that in much current industrial organisation usage, second-degree price discrimination includes cases where consumers are offered different options and sort themselves into groups that have different price elasticities of demand (or different willingness to pay) for the good.

That discussion made clear that I had been on an 18-month detour in how I described the degrees of price discrimination. Only last year, I changed the definitions of the degrees of price discrimination in my ECONS101 class to match those that Pigou uses, and therefore moved menu pricing into the definition of third-degree price discrimination (or group pricing). I've held off on posting about my exchange with ChatGPT until now, because I didn't want to confuse my students in this trimester's class about what did, and did not, fall under the different degrees of price discrimination before they were tested on it (and, as it turns out, I didn't test them on that specific aspect of the topic in any case). [*]

This appears to be one of those situations where terminology changes meaning over time, and is a cautionary lesson in making sudden changes to definitions on the basis of reading about the history of economic thought. The issue here is that I had come across Pigou's definitions in one source, and initially dismissed it as it was inconsistent with the way we taught that topic. But then I read The Economics Book by Niall Kishtainy and co-authors (which I reviewed here), which made me more certain about Pigou's definitions. To be clear, I'm not blaming Kishtainy et al. They were perfectly correct in terms of Pigou's definitions. I should have checked some other sources for more current usage. One example is the excellent book Information Rules, by Carl Shapiro and Hal Varian (which I read in 2023 and reviewed here), which made the definitions used in industrial organisation clear (although Shapiro and Varian preferred to use the term 'versioning', rather than second-degree price discrimination).

Now I'm left with the task of combing through my past posts, to ensure that I update my terminology, or revert it to the original text in the few cases where I went back and made changes. I don't want to risk confusing future students, which is a risk given that I refer them to my posts for further detail and examples on topics that we discuss in class.

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[*] I didn't perfectly achieve this goal, because one very alert student picked up the error through her own conversations with Harriet, our ECONS101 AI tutor, an irony that was not lost on me.

A surprising example of block pricing with heterogeneous demand

My wife and I just got back from holiday in Europe, and stopped in the duty-free store at Auckland Airport to pick up some bottles of gin for my mother-in-law. The price was $45 for one bottle, $69 for two bottles, or $95 for three bottles.

Standard block pricing (as described in this post) calls for the seller to sell at a declining marginal price per unit. In this case, the first bottle is $45, and the second bottle is $24 (for a total of $69 for two bottles). However, the third bottle is $26 (for a total of $95 for three bottles). Did the duty-free store get its block pricing wrong?

Certainly, their pricing is inconsistent with the standard block pricing story, because the third bottle should be less expensive (or, at least, not more expensive) than the second bottle. However, as Nobel Prize winner George Stigler noted, the pricing strategies that we see in the real world are likely to be those that work fairly well (otherwise, the strategy wouldn't persist and we wouldn't see them). So, there must be something about this pricing strategy that makes it work.

I think that the duty-free store is doing a bit of a mix of block pricing and menu pricing. Menu pricing is a form of price discrimination, where consumers sort themselves into those who are high-demand consumers and low-demand consumers. Low-demand consumers buy one bottle (or perhaps two), and pay a relatively high price per unit, while high-demand consumers buy three bottles and pay a lower price per unit.

Now, as I noted in this post, block pricing doesn't typically work when there is heterogeneous demand, because low-demand consumers are unaffected by block pricing (they buy the same quantity as if there was no block pricing), while high-demand consumers may buy more of the good, but spend less overall (because of the lower price per unit). The duty-free store avoids this negative outcome because consumers can only buy three bottles of gin duty-free. If they buy any more than that, they have to pay duty on the additional bottles. So, that effectively caps the number of bottles that high-demand consumers can buy to three. So, the high-demand consumers are stopped from buying four, or five, or six, or twenty bottles at the lower price. That means that the high-demand consumers may buy more bottles than if there wasn't block pricing, but they don't end up spending less overall.

That also helps explain why the third bottle can be priced a little higher than the second. A plausible interpretation is that the two-bottle deal is designed to attract moderate-demand consumers, while the three-bottle deal is aimed at the highest-demand consumers who are constrained by the duty-free limit. If that is the case, then the store does not need the third bottle to be cheaper than the second. Instead, it needs the three-bottle bundle to be attractive to a different group of buyers than the two-bottle bundle or a single bottle. Again, this points to menu pricing as part of the explanation.

So, while the duty-free store isn't conducting block pricing exactly as I describe in my ECONS101 class, we can nevertheless puzzle out what they are doing. And it makes sense, even if it is surprising to see a seller that is able to use block pricing when there is heterogeneous demand.

Disney adopts a combination of menu pricing and block pricing for Disney+

My ECONS101 class covered price discrimination this past week. Menu pricing (or second-degree price discrimination) occurs when consumers are offered different options (that the firm knows appeal to consumers with different price elasticities of demand), and consumers select their preferred option. Specifically, the firm will offer a lower price to consumers who are more price-sensitive (those with a higher price elasticity of demand), and a higher price to consumers who are less price-sensitive (those with a lower price elasticity of demand).

So, it was interesting to read this story in the New Zealand Herald last week:

Disney+ has become the latest in a procession of streaming services to hike its rate - though those willing to live with fewer features can stick with the old pricing.

Disney+ currently costs $14.99 per month.

From members’ next billing period, the price will increase by 27 per cent to $18.99 as the service is renamed Disney+ Premium - while the pricing for those who choose to pay annually also increases by 27 per cent from $149.99 to $189.99.

But there will also be a new Disney+ Standard option, which will stay at $14.99 (or $149.99 annually) - but support for two screens at once (compared to the Premium plan’s four) and standard high definition (the Premium plan offers 4K or ultra high definition).

This is an example of Disney using menu pricing. The Disney+ Standard option has a lower price, and will appeal to more price-sensitive consumers, while Disney+ Premium will appeal to consumers who are less price-sensitive.

Interestingly, the annual subscription price also offers an example of block pricing, which I will be covering in class this week. Block pricing occurs when the firm charges a declining price on subsequent blocks of product. In this case, the monthly price for Disney+ Premium is $18.99. However, those who pay for the full year pay just $189.99. In effect, after the first ten months of the year, the last two months are free (for those paying the annual fee). In other words, the first block of ten months cost $18.99, and the second block of two months costs nothing. It is a similar story for Disney+ Standard ($14.99 for the first ten months, and then free for the last two months).

Block pricing tends to work best when demand is homogeneous (as I noted in this post). One way that firms like Disney can get homogeneous demand is to first use price discrimination to separate consumers into relatively homogeneous groups. So, the shift to menu pricing (offering Disney+ Standard and Disney+ Premium) will likely make the block pricing strategy even more effective (and more profitable) for Disney.

The subscription economy as price discrimination

In my last post, I outlined how VinFast selling electric vehicles, with the battery priced separately as a subscription, was an example of two-part pricing. However, not all subscriptions are two-part pricing. Often, first use these subscriptions as a form of price discrimination. Consider the following example from a recent article in The Conversation by Louise Grimmer (University of Tasmania):

From gym memberships to music and movies, to razors, toilet paper, meal kits and clothes, there’s seemingly no place the subscription economy can’t go.

Having conquered the software market – where it gets its own acronym, SaaS (Software as a Service) – the subscription model is now moving into hardware.

Car makers are among the first cabs off the rank, using software to turn on and off optional extras.

German auto maker BMW is offering “in-car microtransactions” to access options for car buyers in Britain, Korea, Germany, New Zealand and South Africa. A heated steering wheel, for example, has a monthly cost of NZ$20 in New Zealand, and £10 in the UK.

Other markets including Australia will soon follow.

In the UK, seven of 13 “digital services” – from heated seats to automatic high beam and driving assistance – are now available in subscription form.

“Welcome to microtransaction hell” is how one headline put it.

But that’s probably overselling the onset of a corporate dystopia where “you will own nothing”. BMW’s motives are pretty straightforward – as is most of what’s driving the subscription economy.

Often, subscription services are taking advantage of customer lock-in - locking customers into buying from the seller, and generating additional profits from the lock-in customers. This was the case with VinFast, and is likely the case with gym memberships, subscription access to movies or music, meal kits, and many others. However, the subscription service that BMW is offering is different. It is different from the more typical subscriptions because it is an add-on to an existing product (the BMW vehicle). It is different from the add-on that VinFast offers, because none of the subscription options from BMW are required in order to operate the vehicle (it will work perfectly fine without a heated steering wheel, I'm sure).

What BMW is doing is price discriminating - charging a higher price for the same product to consumers who have more inelastic demand (and where the price difference doesn't relate to a difference in costs). How does it work? For effective price discrimination, you typically need to meet three conditions:

1. Groups of customers that have different price elasticities of demand (heterogeneous demand);
2. Different groups of customers can be identified; and
3. No transfers across submarkets.

For car buyers, the first condition holds. For buyers with higher income, a BMW takes up a smaller proportion of their income and, as I noted in this post from earlier in the month, that means that car buyers' demand for a BMW will be more inelastic. High income buyers will be less price sensitive than buyers with lower income. So, it makes sense for BMW to charge a higher price to high-income consumers, and a lower price to low-income consumers.

The second condition also holds. Once BMW have created a system where the optional extras like a heated steering wheel cost extra, high-income consumers are more likely to buy the optional extras. The consumers sort themselves into high-income and low-income groups, by the choice they make about optional extras. We refer to this as menu pricing (or second-degree price discrimination). The third condition clearly holds, because you can't transfer your heated steering wheel subscription to someone else (and why would you want to, as you are the one paying for it!).

So, it seems like this is price discrimination. However, as I noted above, price discrimination only occurs where the price is different between consumers, but the cost of providing the good or service is the same for all consumers. Providing a heated steering wheel is costly to BMW, so it seems like that might invalidate it as an example of price discrimination (in the same way that the difference in price between business class airline tickets and economy class airline tickets is not price discrimination). In this case, though, there is no effective difference in cost between the two groups, because the heated steering wheel is already included in every vehicle. It just isn't activated in every vehicle. Activating the heated steering wheel (or other optional extras) simply requires toggling some setting in the car's on-board software to 'on', so there is little cost to BMW at all.

Offering optional extras as a subscription enables BMW to take advantage of price discrimination, selling cars for a lower price to low-income consumers (with the optional extras switched off) and for a higher price to high-income consumers (with the optional extras switched on). Don't get me wrong though - BMW are still taking advantage of locking their customers in as well, because there are no alternative providers of the heated steering wheel for their new BMW.

Shrink-wrapped books and price discrimination

One of the things I tell my ECONS101 class is that, once you know what to look for, you start to see price discrimination everywhere. Price discrimination is where a firm charges different prices to different customers for the same good or service (and where the differences in price do not relate to differences in the cost of providing the good or service).

Last July, Tyler Cowen had an excellent example on the Marginal Revolution blog, of why books are kept shrink-wrapped in Mexican bookstores:

Imagine there are two classes of readers.  The first is poorer, and only buys books when he or she knows the book is truly desired.  Harry Potter might be an example of such a book.   You want to read what everyone else is reading, to talk about it at school, and you don’t need to scrutinize p.78 so closely before deciding to purchase.

The second class of buyer is wealthier and usually will be buying (and reading) more books, indeed for those people book-buying is a significant habit.  That buyer wants to be on top of current trends, wants to have read whichever book is “best” that year amongst the trendy set, and so on.  If book quality is uncertain, such individuals will end up paying a de facto, quality-adjusted higher per unit price per book.  If you can’t sample the books in advance, you will end up buying some lemons, and you can’t just pick out the cherries.

For price discrimination to occur, you typically need to meet three conditions:

1. Groups of customers that have different price elasticities of demand (heterogeneous demand);
2. Different groups of customers can be identified; and
3. No transfers across submarkets.

In the case of shrink-wrapped books, Cowen has given the example of two groups of readers. Do they have different price elasticities of demand? If the first group is poorer, then the price of a book will take up a higher proportion of their income (as noted in yesterday's post, that is one of the determinants of the price elasticity of demand). That would tend to make their demand more price elastic (they are more sensitive to price). If the second group is wealthier, the price of a book takes up a smaller proportion of their income, and their demand is less elastic. So, it seems that this meets the first condition for price discrimination.

What about the second condition? In this case, buyers sort themselves into groups, and that means that the bookseller can tell them apart. The first group (poorer, more elastic demand) only buy the books that are popular and well known. The bookseller knows that those books attract customers with more elastic demand (more price-sensitive), and they set the mark-up (and price) on those books lower. The second group (wealthier, less elastic demand) buy all types of books. The bookseller knows to set the mark-up (and price) higher for all of the books that are not popular and well known. The bookseller is essentially offering different options at different mark-ups (and prices), knowing that some options appeal to more price-sensitive customers, while others appeal to less price-sensitive customers. This is an example of what we call menu pricing (or second-degree price discrimination).

For the third condition, there is no point in someone paying the low price on-selling to someone paying the high price, since the wealthier consumers can already buy the popular and well-known books at the same low price.

As Cowen noted, this is likely to be an example of price discrimination. Once you know what to look for, you see it all around you.

Why two-part pricing doesn't work for heterogeneous demand

A firm uses two-part pricing when it splits the price into two parts (the clue is in the name!): (1) an up-front fee for the right to purchase; and (2) a price per unit. If the consumer wants to buy any of the product, they must first pay the up-front fee. We can think about two-part pricing first by contrasting it with a monopoly firm pricing at a single price-per-unit, as in the diagram below (for simplicity, I'll use a constant-cost firm).

The monopoly firm using a single price-per-unit selects the price that maximises profits. This occurs where marginal revenue is equal to marginal cost, i.e. at the quantity QM with price PM. The producer surplus (profit) the firm earns is the rectangular area CBDF.

However, if the firm switches to two-part pricing, then we first recognise that the firm can charge an up-front fee equal to the consumer surplus, and the consumer would still be willing to purchase the same quantity (Q0). So, the up-front fee could be as large as the area ABC, in which case profits would be the combined area ABDF.

The firm can do even better than that. Profitability is all about creating and capturing value. So, if the firm can create more value (by increasing the consumer surplus), they can capture more profit (by increasing the size of the up-front fee). So, by lowering the price to PS, the consumers would be willing to buy the quantity QS, and would receive consumer surplus equal to the area AEF. By setting the up-front fee equal to AEF and the per-unit price at PS, the firm then increases their profit to be all of the area AEF.

We can also show the effect of two-part pricing using the consumer choice model. This is illustrated in the diagram below. The black budget constraint represents the most the consumer can afford to buy with their income, when there is a single price-per-unit for Good X (with 'All Other Goods' [AOG] on the y-axis). The consumer purchases the bundle of goods E, which includes X0 of Good X, and A0 of All Other Goods.

With two-part pricing, the firm charges an up-front fee (so the budget constraint starts at a lower point on the y-axis, since paying the fee is like giving up income for the consumer), and a lower per-unit price. So the budget constraint for two-part pricing (the red budget constraint) is flatter. Let's assume it passes through the point E (so the consumer could still purchase that bundle of goods if they wanted to. There is one other point that we need to recognise - if the consumer buys none of Good X, then they do not need to pay the fee. So Bundle C is also an option for the consumer.

With two-part pricing, this consumer can now reach a higher indifference curve, by buying the bundle of goods D (their new best affordable choice). This bundle includes more of Good X (X1), and less of All Other Goods (A1). Because they are buying less of All Other Goods, they must be spending more on Good X.

Two-part pricing works well when the firm faces homogeneous demand for its product (i.e. when all consumers have similar demand for the product). We can also use the consumer choice model to demonstrate why two-part pricing doesn't work so well when there is heterogeneous demand.

Consider two consumers - one with low demand (shown on the diagram below with the blue indifference curves), and one with high demand (red indifference curves). With a single price-per-unit, the low demand consumer buys Bundle G, which includes X1 of Good X, and A1 of All Other Goods, and the high demand consumer buys Bundle J, which includes X3 of Good X, and A3 of All Other Goods.

When the firm moves to two-part pricing instead, the low demand consumer can no longer afford bundle G (it is outside the new budget constraint). The highest indifference curve they can get to is I0, where they buy Bundle C. This bundle includes none of Good X. These low demand consumers find themselves better off by not buying any of Good X at all, because then they don't have to pay the up-front fee.

The high demand consumer would be better off moving to buying Bundle K, which is on the highest indifference curve they can now reach. Bundle K contains more of Good X (X4), so two-part pricing does induce these consumer to buy more. However, Bundle K includes more of Good A (A4), which means that even though these high demand consumers are buying more of Good X with two-part pricing, they are actually spending less on Good X.

So, two-part pricing doesn't work so well for heterogeneous demand, because the lowest demand consumers will stop buying the good entirely, while the highest demand consumers will buy more of the good, but spend less on it. The combination of these two effects is likely to reduce the firm's profit.

This is why you don't often see two-part pricing alone 'in the wild'. Most often, firms will price discriminate first (often through menu pricing - offering different options to different consumers, knowing that each option will appeal to a different 'type' of consumer), then within each subgroup use two-part pricing.

Read more:

• Is the marginal cost of electricity falling? Some evidence from recent two-part pricing changes