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.

Domino's' block pricing fail

This week in ECONS101, we covered pricing strategy. I love this topic, not least because it covers material that you typically wouldn't see in an introductory economics textbook. One of the strategies we talk about is block pricing. A firm uses block pricing when it charges a relatively high price until the consumer reaches some threshold, then a lower price for every unit the consumer buys after the threshold. Buy-one-get-one-half-price is an example of block pricing. The idea is to price high for those consumers who don't buy much from you, and lower the average price for consumers who buy a lot (you can see how block pricing works in more detail in this post).

Also this week, we had the first ECONS101 test of the semester, and the tutors and I met up for pizza beforehand. Ordering the pizzas online, the banner ads caught my attention. First, this one:

Value pizzas for $5 each. Seems like a good deal. Then this:

Upgrade to extra large for $3 more. Sounds like an even better deal, right? The extra large gives you 50% more pizza for just $3 more (if you zoom in, you'll see that it's 50% more in the fine print). But wait! If you upgrade a value pizza to extra large, you're paying $3 more, which is an increase in price of $3/$5 = 60%! So, you pay 60% more in order to get 50% more pizza. [*]

It's not quite a two-for-the-price-of-three fail, but it clearly isn't block pricing done right. Unless Domino's is relying on it's customers being somewhat innumerate?

*****

[*] Once you factor in the delivery charge, then maybe this deal pays off for the consumer, because the extra $3 would be less than 50% of the cost including the delivery charge. Similarly, for more expensive pizzas, the extra $3 is less than 50% of the cost. However, for pick up customers collecting value pizzas, it clearly doesn't pay off.

Why block pricing doesn't work for heterogeneous demand

On Sunday I covered two-part pricing. Today it's the turn of block pricing. A firm uses block pricing when it charges a relatively high price until the consumer reaches some threshold, then a lower price for units after the threshold. In reality, there could be multiple thresholds. Buy-one-get-one-half-price is an example of block pricing. As with two-part pricing, we can think about block 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 again 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 Q1 with price P1. The producer surplus (profit) the firm earns is the rectangular area CBDF.

However, if the firm switches to block pricing, then the firm can choose an initially higher price (P0), at which point the consumers purchase Q0 of the good. If the firm lowers the price to P1 for every unit the consumer buys after Q0, then the consumer will buy Q1 of the good (and pay P0 for the first Q0 units, then P1 for the rest). The firm's profits would increase by the area HGJC.

The firm could block again, offering a lower price than P1 for units purchased beyond Q1, and capture more profits (I haven't shown this on the diagram though). Again, this demonstrates that firm profitability is all about creating and capturing value.

We can also show the effect of block 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 block pricing, the firm charges the standard price Px up to the quantity X0, then pays a lower price beyond that quantity. This causes the budget constraint to pivot outwards (and become flatter) from the point E. So 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.

As with two-part pricing, block pricing also 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 block 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 curve), 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 block pricing instead, the low demand consumer is not affected. The highest indifference curve they can get to is still I0, so they continue to buy Bundle G. 

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 block 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 block pricing, they are actually spending less on Good X.

So, block pricing doesn't work so well for heterogeneous demand, because the lowest demand consumers will not be affected, 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, but notice that it isn't as bad as for two-part pricing that I described on Sunday.

Again, this is why you don't often see block pricing (or two-part pricing) alone 'in the wild'. Firms must first ensure they have relatively homogeneous demand, and they achieve this through price discrimination (e.g. through menu pricing - offering different options to different consumers, knowing that each option will appeal to a different 'type' of consumer). Then within each homogeneous group they can use block pricing or two-part pricing.

Read more:

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