Retail prices are a strange animal. Why does your modest cell phone data plan cost a dollar per gigabyte while another plan with double the data costs only 90 cents a gigabyte? Or why is a single soda more expensive per ounce than a 12-pack?
Economists have a term for those: “nonlinear pricing,” which differs from linear pricing where the price an item stays the same, no matter how much of it you buy. Nonlinear pricing is common in the real world, but most macroeconomic models ignore it and assume firms set just one price.
That gap is what a recent paper, “Nonlinear Pricing and Misallocation,” by Wharton finance professor Gideon Bornstein and NYU economics professor Alessandra Peter, seeks to address. Their model shows that allowing for nonlinear pricing fundamentally changes how economists think about markups and efficiency.
Breaking the Link Between Markups and Misallocation
Setting the context for the paper, Bornstein said “a surge of papers” over the past decade showed that pricing markups by firms have increased steadily since the 1980s. The theoretical consensus in macroeconomics is that “a firm that charges a high markup is inefficiently small because people are not buying enough of the goods of that firm,” he said. That logic implies that big, high-markup firms should actually be subsidized so they can expand.
“But that always sounded odd,” Bornstein said. “Think about a firm like Apple. It charges higher markups than smaller makers of computers and smartphones. It seems strange to argue the economy would be more efficient if we subsidized Apple to make it even bigger. That conclusion is a direct result of assuming firms use linear pricing.”
Bornstein and Peter show that once nonlinear pricing is taken into account, the story changes. Even though large firms may charge higher markups, the allocation of production across firms is efficient. In other words, high-markup firms are not inefficiently small.
The paper puts the point more bluntly: “With nonlinear pricing, there is perfect allocative efficiency across firms, even though larger firms charge higher markups,” the paper stated. “Without the assumption of linear pricing, the tight link between markups and misallocation breaks.”
“[Apple] charges higher markups than smaller makers of computers and smartphones. It seems strange to argue the economy would be more efficient if we subsidized Apple to make it even bigger.”— Gideon Bornstein
Drawing from that, the paper concluded that “there is no rationale” to subsidize large, high-markup firms, which it noted is “contrary to the robust conclusion from models that assume linear pricing.”
Bornstein said the assumptions under classical economic models lead to a policy prescription that if, say, a beer producer charges a very high markup, that means it isn’t selling enough beer and that it therefore needs to be subsidized. He clarified that while policy planners don’t specifically call for those subsidies, the classical economic models they rely on make that tacit by factoring in only linear pricing and overlooking nonlinear pricing.
Where Inefficiency Really Lies
Nonlinear pricing, however, creates a different kind of inefficiency. Because of bulk discounts, high-demand consumers buy too much at low per-unit prices, while low-demand consumers buy too little at high per-unit prices. The misallocation is no longer between firms but within each firm’s customer base.
Using Nielsen scanner data on grocery prices and quantities, the authors showed that this distortion is quantitatively important. Under linear pricing, misallocation across firms implies a welfare loss of about 0.14% of consumption. With nonlinear pricing, misallocation across consumers is about five times larger, 0.7%.
How Nonlinear Pricing Touches Consumers
Nonlinear pricing isn’t always straightforward for companies to implement. “For example, a McDonald’s cannot charge you and me different prices for the exact same Big Mac,” Bornstein said. “The next best thing they can do is design their menu to capture more revenue from different types of customers. They might sell a Big Mac on its own for around $5, or bundle it with fries and a drink for $9. Or they could offer a ‘two for $8’ deal, or give every tenth meal free. The heavy user ends up paying a lower price per item, while the occasional customer who just buys one pays more.”
High-taste consumers would go every day to, say, a Starbucks, whereas a low-taste customer might go there only once a week or once a month, Bornstein said. How that leads to misallocation is when “the high-taste consumer will get that coffee at a lower price and will buy too much of it, but the lower-taste customer buys very little and pays the higher price.”
Bornstein continued to explain the labor implications of pricing strategies. With linear pricing, there is a tight connection between the average markup of a firm and that labor wage. Households may consider working an extra hour to make $30. But if the markups firms charge are high, they may decide they cannot buy much with the additional income and therefore not work that extra hour.
“But in our paper, we find that with nonlinear pricing, labor is decoupled from markups,” Bornstein said. Consumers have an incentive to work more hours and earn $30 an hour because the extra units they buy are cheaper thanks to bulk discounts. “That is why labor distortion is lower with nonlinear prices, and employment will be higher.”
