The Implications of Non-Linear Pricing

Up is down and down is up

A standard and robust result in industrial organization is that, when firms are restricted to linear pricing, a subsidy equal to the fixed cost of each firm would improve efficiency. Let me explain what I mean.

Suppose that each firm has the cost structure A + Bx. In a competitive market, each firm will sell where marginal cost equals price – that is to say, they will produce at price B. However, if they have to pay a fixed cost A, then they will make negative profits and leave the market. In competition, firms will compete until there are 0 profits left, so firms have to charge a “markup” – a premium over marginal cost – in order to stay in business. Misallocation comes from firms who would have been socially optimal entering (if they could extract all consumer surplus) never entering at all.

Linear pricing is the requirement that firms choose one price to sell their product at, and sell it at that price to all comers. Non-linear pricing might take the form of giving a discount to someone who buys a lot, or changing the quality of goods. Alessandra Peter and Gideon Bornstein’s new paper “Nonlinear Pricing and Misallocation” examines how the welfare implications change with non-linear pricing. Now, the misallocation occurs not between firms, but across consumers. The markups of firms are no longer able to tell you the degree of misallocation. Consumers with a high taste for the good buy too much, and those with low taste too little.

This follows in the lines of “Monopoly and Product Quality” by Michael Mussa and Sherwin Rosen. Suppose that there is a monopolist who offers a product line, a bunch of similar goods differing in their quality. The optimal course of action is to use the product quality to “smoke out” consumer tastes and preferences, and the losses to society come from low-taste consumers being priced out. More varieties of goods are made than would occur under efficient conditions. Bornstein and Peter break with Mussa-Rosen by extending this firm-level behavior to general equilibrium, and showing that if there is an aggregate price index which clears the labor market, then you don’t have “no distortion at the top and quantity rationing at the bottom”, but rather too much at the top and too little at the bottom.

Peter and Bornstein then estimate how meaningful these changes are with data from the Nielsen Homescan consumer panel data. Implementing the optimal policy under linear pricing, which would restore both consumer and labor behavior to the efficient equilibrium, would reduce welfare by 2% instead. For comparison, COVID-19 caused GDP to decline globally by 3 percent.

These results imply important things about the gains from new products. Xavier Jaravel has a 2019 paper, “The Unequal Gains From Product Innovations”, which uses retail scanner data to find how inflation experiences differed across the income spectrum. Richer people had a subjectively lower inflation experience than poor people, with the mechanism for this being that increasing income inequality led to more product innovation. We can’t directly measure the utility from new goods – there are simply too many of them – so we will have to make structural assumptions about how these goods enter into utility. Under any reasonable set of assumptions though, this is a substantial gain.

The problem with this is that, with a Mussa-Rosen monopolist, we don’t know if those new goods are actually a good or bad thing. If there was an increase in market power, it might take the form of monopolists offering more variety, at lower qualities, to the detriment of consumers. There are recent papers arguing that market power has substantially increased, such as (most famously) “The Rise of Market Power and the Macroeconomic Implications” by De Loecker, Eeckhout and Unger – there is considerable debate over how meaningful that paper is, such as from “Some Unpleasant Markup Arithmetic”, which I will not get into now – but it would certainly be interesting if those new goods were actually just monopolistic extraction.

However, some things don’t quite line up. The Mussa-Rosen result predicts that there is no distortion at the top, and considerable distortion below. This is by willingness to pay, which may not line up with income, but my intuition is certainly that richer people are less price sensitive and have a greater willingness to pay. We would predict greater varieties for the bottom of the income distribution and fewer at the top.

I initially came into this thinking that Jaravel would be an overestimate of the inequality of inflation experiences by income, but after reviewing what the models actually imply, it might very well be an underestimate. Rising market power might cause rising but meaningless variety for the lower classes, while secular trends in the income distribution lead to greater innovation for the upper classes.

I am extremely impressed by the Bornstein and Peter paper. It has considerably shook up what I know about the world, and to some degree, given me less confidence that I understand precisely how the world works. It is a rare paper which does this, and I recommend reading it strongly.