Pricing strategy in practice: Cocktail menu edition

One of my favourite topics to teach in ECON100 is pricing strategy. In part, it's because this topic is a bit less about microeconomic theory, and a bit more about practical things that real managers do. That's why I enjoyed reading this article about cocktail pricing, which talks about how real bar managers set prices for drinks.

In the article, there's no pricing where marginal revenue is equal to marginal cost (the theoretical profit-maximising point for the firm with market power). Instead, the managers are making judgement calls about pricing based on their industry experience. For instance, consider this quote:

"I can't say that there's any way to be 100 percent certain that a certain drink will sell better than others," Morgenthaler tells me. "I'm constantly surprised by what is less or more popular on our menus. But with as much experience as I have, I would say I've got a pretty good idea of what's going to sell and what's going to appeal to a more connoisseur crowd."

In other words, the manager is using their market knowledge to set the price. This might involve heuristics (rules-of-thumb, such as the price of a glass of wine being the same as the wholesale price of the bottle - this used to be a common heuristic in the restaurant trade here, but I'm not sure if that still is the case), or it might just involve expert judgment. Cost is an important factor:

A cocktail by nature is a combination, in differing ratios, of a set of ingredients that each have costs, so many cocktail bars spend a lot of time and effort crunching the numbers behind their drinks...

Pour cost is pretty much what it sounds like: the cost a bar incurs by pouring a given cocktail... a bar might decide upon an acceptable range in which its pour costs must fall, given how other aspects of the business factor in, and then calculate the price of drinks based on that range. Between two drinks sold for the same price, the one with the higher pour cost earns the bar a smaller profit...

No matter its size, Cannon points out that "a restaurant will be successful over the long haul if it can pocket"—meaning earn in net profits—"10 cents on the dollar." In other words, for an establishment pulling in $1 million a year in revenue, the owner is fortunate to have $100,000 to show for it after expenses. "That's a tough order," Cannon adds. "Robust liquor sales at solid cost of goods are one of the reasons you can get to that 10 cents on a dollar." Astute cocktail pricing (say, pour costs around 21 percent or less, on average) can be a critical component of a restaurant's overall business strategy and health.

But there can't be any explicit determination of the point where marginal revenue is equal to marginal cost. In order to determine marginal revenue you must know what your demand curve is, which seems unlikely (see the earlier Morgenthaler quote) and if you don't know marginal revenue you certainly can't determine the point where marginal revenue is equal to marginal cost as we do in the textbook examples.

An alternative way of determining the profit maximising price is to use the price elasticity of demand directly (though this only works where the product has elastic demand, i.e. a price elasticity of demand that is greater than one). The formula for the optimal price in terms of the price elasticity of demand (which you can find here, or for a more lengthy explanation see here or the mathematical derivation here) is:

P* = MC[ε/(ε+1)] where ε is the price elasticity of demand (and remember that price elasticity of demand is negative, because as price increases the quantity demanded decreases due to the law of demand - the price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price, and when one of these is negative the other is positive).

For goods which have more elastic demand (i.e. where customers are more responsive to a change in the price), ε is larger (more negative) and [ε/(ε+1)] will be smaller and the price will be a smaller markup over marginal cost. For goods which have more inelastic demand (i.e. where customers are less responsive to a change in the price), ε is smaller (less negative) and [ε/(ε+1)] will be larger and the price will be a larger markup over marginal cost. So, you should charge a lower price (lower markup) if your customers are more price sensitive, and charge a higher price (higher markup) if your customers are less price sensitive.

Of course, this assumes that the price elasticity of demand is constant (which isn't true for a straight line demand curve), but putting that aside it doesn't appear that the bar managers are using an explicit calculation of price elasticity of demand in their pricing decisions either (again, see the Morgenthaler quote above). So, are they getting their pricing decisions wrong?

I would argue (as I do in class on this topic) that the long-term managers we observe in the market are not systematically getting their pricing decisions wrong. The reason is Darwinian. The cocktail bar market is pretty cutthroat - there isn't a lot of margin for error, and a manager who systematically got their pricing decisions wrong is going to lower bar profits either by pricing too high (and having customers go to the competition) or pricing too low (and lowering the per-customer profit making it more difficult to cover rent and staff costs, etc.). A manager who consistently lowers bar profits won't be a manager for very long, so the managers we see (who have been managers for a while) must be the ones who generally price close to the profit maximising point. So, even though these managers are not explicitly using marginal-revenue-equals-marginal-cost or the optimal-price-as-a-function-of-elasticity to determine prices, they must be internalising that through their expert knowledge of the market. And if you talk to bar managers, you can see that they have an understanding of price elasticities (or how their customers respond to changes in price in relative terms), even though they don't use the language of economics.

However, that's not the end of the story, because the pricing of each drink is not undertaken in isolation:

When Cannon and his team revise their cocktail menus, he says they try to price drinks destined for the greatest popularity so that they have the lowest percentage pour costs. For a prospective top-selling drink, "we need to make sure that that one is in a very solid cost of goods range, maybe a point or two below our target, because if a number-one mover that is refreshing and easy to [drink] is priced right, it allows you some wiggle room on some other esoteric things, where the ingredients are more expensive." He adds that, "We'll take a few lumps on this really cool drink that [the bartenders have] created, and it will be great conversation. Meanwhile, the gin sour...this is going to do the heavy lifting for us."

In other words, there are strategic aspects to pricing (as we discuss in ECON100). Sometimes it makes sense to lower the price of a drink, if that drink is going to attract customers who would buy other (higher markup) drinks as well, or who would bring other customers with them who purchase higher markup drinks. The former is the justification for loss-leading (where some products are sold below marginal cost in the hopes of increasing revenue and profits from other products - a common strategy for supermarkets, for instance). The latter is the justification for 'ladies nights' at bars. Again, good managers can be expected to take advantage of opportunities for strategic pricing across the range of product offerings.

And then there's the effect of competition. More bars in the local area will increase competition and lower prices. Customers have more alternatives, so if a bar increases prices (or markups) there will be a greater shift of customers to the competition. This means that customers become more price sensitive when there is more competition, which increases the price elasticity of demand (ε) and lowers the optimal price of drinks. So when there is more local competition, bars should be offering lower priced cocktails.

Finally, bars aren't only offering drinks to customers. They also offer amenity - the atmosphere, music, etc. which customers value. Bars that have attractive more attractive characteristics than their competition will be able to charge a premium for cocktails - again, because their customers are less price sensitive (lower ε, higher optimal price and markup).

So the next time you are drinking a cocktail, spare a thought for the pricing decision-making prowess of the bar manager. They're balancing cost considerations and the price elasticity of demand, as well as strategic pricing and amenity considerations, in determining the price you pay for that Long Island iced tea, whiskey sour, or special creation. And hope they've got the pricing right - otherwise they might not be around the next time you're out on the town.

See also: Fancy a margarita: Why it'll cost you more

[HT: Marginal revolution, back in July]