Plate ii in print

The Markup

the measure of market power: how far the price stands above the cost of the last unit made, the gap that is nothing under competition and yawns under power — and the evidence that, of late, it has been widening.

The posted price reveals the charge; power is measured against a cost it leaves unseen.

— the argument of this plate, after Lerner (1934) and De Loecker, Eeckhout and Unger (2020)

The same price of twelve may sit a hair above a cost of eleven or a chasm above a cost of three, and the buyer, with only the twelve before him, cannot tell the lean margin from the fat. The preceding plate supplied the mechanism: a seller facing a demand of his own can restrain his output and lift the price. This plate asks how much of that room he uses. A price alone cannot answer. The cost relevant to the inquiry is the cost of supplying one more unit, which may bear little resemblance to the amount the firm spent establishing its factory, writing its software, or acquiring its customers. To measure the gap, one must therefore get behind the posted number to an account the customer seldom sees. Power hides in the gap between price and cost, and the gap is the one thing the price will not show.

Abba Lerner gave the gap a precise expression in 1934: subtract marginal cost from price and divide the remainder by price. If one more unit costs eight and sells for twelve, the excess is four, or one-third of the price. This is the Lerner index. Another common measure divides price directly by marginal cost; for the same transaction, that ratio is twelve over eight, or one and a half. A price fifty percent above marginal cost thus yields a Lerner index of one-third. Both measures describe the same example, with different denominators, and much confusion is saved by stating which is being used. Neither supplies the firm's profit margin. The extra four on the unit still has to contribute toward costs that do not vary with that sale. The index fixes a narrower fact: the distance between what the buyer pays and what the last unit adds to the seller's cost.1

1. A. P. Lerner, The Concept of Monopoly and the Measurement of Monopoly Power (1934). Write L = (p − c) / p and μ = p / c, where c is marginal cost. Then L = 1 − 1/μ. In the hypothetical example, p = 12 and c = 8: L = 1/3 and μ = 1.5. Neither expression subtracts fixed costs from total receipts.

For the familiar seller who charges one price, the index has a revealing connection to demand. Selling another unit adds its price to revenue while requiring a reduction in the price received on the units already sold. A seller with many ready substitutes loses customers rapidly when he raises his price; his demand is elastic, and a small reduction can bring a relatively large increase in sales. A seller whose customers find it difficult to leave faces a weaker response. In the smooth, single-product model, equating marginal revenue with marginal cost makes the Lerner index equal to the inverse of the absolute demand elasticity at the chosen quantity. An elasticity of three gives an index of one-third; an elasticity of five gives one-fifth. The elasticity is that of the demand faced by the firm, after accounting for the alternatives its customers can actually use. With positive marginal cost, an interior optimum lies on the elastic part of demand. The seller cannot improve his profit by remaining where a price rise would both increase revenue and reduce production cost.2

2. With absolute price elasticity e, marginal revenue is p(1 − 1/e). The interior first-order condition MR = c gives L = 1/e. Positive c therefore requires e > 1 in this model. The relation presumes a differentiable demand, uniform pricing and an unconstrained interior choice; it is not a general identity for every observed price or every multiproduct firm's strategy.
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The empirical question is whether these gaps have been widening across a substantial part of the economy. Jan De Loecker, Jan Eeckhout, and Gabriel Unger reported a striking result in their 2020 study of publicly traded American firms: their sales-weighted average markup rose from twenty-one percent above marginal cost in 1980 to sixty-one percent above it in 2016. Those figures express price-cost ratios of 1.21 and 1.61. They describe an estimated historical series for the firms in the study, with the rise concentrated toward the upper end of the distribution; they do not say that every shop widened its margin or that sixty-one percent of national income became monopoly profit. The aggregate can rise as high-markup firms gain weight as well as when particular firms increase their own markups. That distinction matters to the account of power. A shifting distribution of business can change the economy's average even while many individual prices remain under close competitive pressure.3

3. Jan De Loecker, Jan Eeckhout and Gabriel Unger, The Rise of Market Power and the Macroeconomic Implications, Quarterly Journal of Economics 135 (2020), 561–644. The abstract states the 1980–2016 estimates; the article distinguishes the markup distribution from its sales-weighted aggregate and examines the role of reallocation. The numbers here retain that study's sample, period and price-over-marginal-cost convention.

The difficulty is that marginal cost is seldom an entry in the accounts. A firm's expenses reveal what it paid for a collection of inputs; they do not directly reveal what one extra unit would have required. The production approach estimates a relation between output and a variable input, then combines the input's estimated output elasticity with its share of revenue to infer a markup. The inference depends on the model of production, the choice of an input that can adjust, and the treatment of the expenditures recorded in the firm's accounts. An expense that changes with production belongs in a different part of the calculation from an overhead that must be paid before any unit is made. Change that classification or the estimated technology, and the inferred marginal cost can change with it. This gives the widening-gap finding a definite intellectual status: an empirical estimate supported by a specified method, open to examination at precisely those joints. The measurement is useful because its assumptions can be inspected; the posted price itself remains silent about them.4

4. De Loecker, Eeckhout and Unger, pp. 570–572 and sections II–III, set out the production approach and its implementation. Under the stated input-cost-minimization conditions, μ equals the output elasticity of a flexible input divided by that input's expenditure share in revenue. Technology estimation, input adjustment and the classification of variable and overhead expenditures affect the interpretation; a revenue-cost ratio taken directly from an income statement is not an observed marginal-cost measure.

A high markup can coexist with an undertaking that earns no surplus after all its costs are met. Suppose a firm sells one hundred units for twelve each, incurs a constant marginal cost of eight, and has four hundred of additional fixed costs for the period. Revenue is twelve hundred; the variable bill is eight hundred; the remaining four hundred exactly pays the fixed bill. The Lerner index is still one-third, but the specified account leaves no residual profit. Software, networks, and other activities in which the first copy or the infrastructure is expensive make the distinction especially visible. A price equal to the cost of the next copy may fail to finance the activity at all. This does not erase the price-cost gap or decide whether a particular price is justified. It makes the next questions unavoidable: how much must be recovered, what alternatives buyers possess, whether an equally capable entrant can appear, and whether the firm is sustaining a productive advantage or defending a protected position.5

5. The fixed-cost example is hypothetical: 100 × 12 − 100 × 8 − 400 = 0. Marginal cost is held at eight throughout the relevant range; all additional costs in this example are assigned to the fixed bill. It separates a positive price-cost markup from residual profit. De Loecker, Eeckhout and Unger examine overhead costs and profit measures separately from markups; the natural-monopoly financing problem receives its own treatment in The Grid.

The markup measures the distance, the demand response helps explain it, and the conditions of entry help determine how long it can last. These are distinct inquiries, joined by the buyer's alternatives. A large firm can face a close rival and little room to move its price; a small local supplier can face customers for whom the nearest substitute is unusable. A high ratio can pay for the invention that made a good possible, reward an advantage about to be overtaken, or capitalize a barrier that will keep returning income long after its original service has ended. Measuring the ratio begins that judgment without completing it. The important advance is to make the number on the shelf answerable to another number, the cost of the last unit, and to ask what keeps the difference in place. If the margin invites a rival, why does the rival fail to arrive? The next plate follows that question to the moat.