William Baumol and David Bradford’s 1970 article “Optimal Departures from Marginal Cost Pricing” is a cornerstone in the economics of public utility regulation. While it appeared in the American Economic Review as a work of formal economic theory—complete with equations and proofs—it also has clear significance for law & economics. Baumol and Bradford demonstrate how regulators should think about pricing in industries where marginal cost pricing—the economists’ ideal—is not feasible. That problem arises in settings like electricity, telecommunications, and transportation, where costs are often decreasing, and prices set equal to marginal cost would not recover total expenditures.
The paper begins with what Baumol and Bradford call a paradox: marginal cost pricing, which maximizes allocative efficiency in theory, cannot always work in practice. A regulator who insists on pricing at marginal cost will create deficits that must be filled through taxation. But raising taxes distorts other prices in the economy. As a result, there is no way to implement marginal cost pricing without creating inefficiencies somewhere else. This is the essence of a “second-best” problem: when the first-best solution is unattainable, the best achievable solution will involve systematic departures from it.
The article’s contribution is to show that second-best pricing is not unique. While there is one first-best solution (price equals marginal cost), there is a continuum of equally second-best solutions once cost-recovery constraints are imposed. The authors demonstrate that quasi-optimal pricing rules can be expressed in different but equivalent forms. One version is the “inverse elasticity” rule: goods with more elastic demand should be priced closer to marginal cost, while goods with inelastic demand can bear larger markups. Another is the “proportional reduction” rule: outputs should be reduced proportionately from the levels that would occur under marginal cost pricing. Both approaches reflect the same principle: regulators should spread the distortions required for cost recovery in a way that minimizes welfare losses.
To make this case, Baumol and Bradford use the tools of constrained welfare maximization, a framework that goes back to Frank Ramsey’s 1927 paper “A Contribution to the Theory of Taxation.” Ramsey showed that, when governments must raise revenue through distortionary taxes, the least-costly approach is to spread the distortions inversely to demand elasticities. A.C. Pigou and Ursula Hicks elaborated on this logic in the mid-20th century, and Marcel Boiteux’s 1956 work applied it directly to regulated monopolies. Baumol and Bradford synthesize these earlier strands of literature, offer new proofs, and make the theory more accessible. They also bridge welfare economics, taxation theory, and public-utility regulation, showing that all three rest on the same analytical foundations.
From a law & economics perspective, the paper speaks directly to questions of institutional design. Regulation of natural monopolies—industries where competition cannot be relied upon to set prices efficiently—has long been a central concern. Harold Hotelling’s 1938 work argued that marginal cost pricing could guide rate design for utilities, but he acknowledged that cost recovery would pose difficulties. Coase’s 1946 “The Marginal Cost Controversy” rejects Hotelling’s argument, arguing that marginal cost pricing for utilities is impractical—even if it is, in principle, the first-best pricing solution. Coase instead argued that we should focus on designing institutions to allow average-cost pricing for public utilities. Baumol and Bradford formalize and extend that insight: regulators face a constrained-optimization problem, and the solution involves pricing rules that diverge from marginal cost in systematic ways.
This matters, because it explains why regulatory commissions adopt rate structures that do not resemble textbook marginal cost pricing. Two-part tariffs in telephone service (a fixed monthly fee, plus per-call charges); peak-load pricing in electricity; and cross-subsidization across different customer classes all reflect attempts to reconcile efficiency with cost recovery. Baumol and Bradford provide the economic justification for these practices, and their framework continues to influence regulatory design today.
One of the most important insights is the recognition that, once the first best is unattainable, there is no single second-best solution. Baumol and Bradford are not the first to recognize this insight (see, e.g., R.G. Lipsey and Kelvin Lancaster’s “The General Theory of Second Best”). But this insight resonated strongly for me with this paper. If regulators cannot achieve the first-best outcome, achieving a second-best means that they must face a continuum of equally efficient options. This helps explain why pricing debates in utility regulation are so persistent: there is no uniquely correct answer. Choosing among second bests inevitably involves normative judgments about distribution, political feasibility, and administrative simplicity. Baumol and Bradford’s analysis clarifies the tradeoffs, but cannot eliminate them.
The paper is not easy reading for those without an economics background. It is filled with formal derivations and multiple formulations of the same theorem. But the payoff is substantial. For legal scholars, the article provides a rigorous foundation for understanding the economic logic behind regulatory-pricing debates. It also illustrates a broader law & econ lesson: institutional design must account for tradeoffs when first-best solutions are unavailable. In this respect, the article connects to Richard Posner’s early work on economic regulation, which emphasized that regulatory choices must be assessed in terms of their incentive and efficiency effects, rather than in terms of unattainable ideals.
The significance of Baumol and Bradford’s article can also be seen by situating it in the broader canon. Alongside Ramsey, Pigou, Hicks, Boiteux, and Hotelling, it forms part of the foundational literature on second-best pricing. Later law & economics work on rate-of-return regulation, price caps, and incentive-based mechanisms builds on these insights. Jean Tirole’s influential “The Theory of Industrial Organization” (1988) and his later work on regulation are direct intellectual descendants of this line of thinking. And contemporary debates about broadband pricing, electricity-market design, and carbon pricing all rest on the principles articulated here.
At the same time, the paper has limits. It abstracts from political and institutional constraints that shape real-world regulation. Regulators face pressure from interest groups, constraints from statutory mandates, and information asymmetries that make precise application of Ramsey-style rules difficult. These complications help explain the shift in the 1980s and 1990s toward incentive regulation, such as price-cap systems that encourage cost reduction while limiting monopoly power. Baumol and Bradford provide the theoretical benchmark, but implementation requires institutional adaptation.
The enduring value of “Optimal Departures from Marginal Cost Pricing” lies in its clarity about the nature of regulatory tradeoffs. By showing that cost recovery necessarily requires departures from marginal cost pricing, and that there are multiple ways to structure those departures, the article reframes utility regulation as a problem of choosing among second-best options. That insight remains as relevant today as it was in 1970.
For law & economics, the lesson is twofold. First, even highly technical economic analyses can illuminate core legal and regulatory problems. Second, the field must grapple with the reality that institutions operate in second-best worlds. Baumol and Bradford help us see why the search for uniquely correct pricing rules is misguided. Instead, the challenge is to design institutions that navigate among equally second-best choices, balancing efficiency, equity, and feasibility. That recognition makes the article not only a technical contribution to welfare economics, but also a lasting resource for understanding the legal and institutional dimensions of regulation.
