ProMarket published the article “The Antitrust Output Goal Cannot Measure Welfare.” The main claim of the article was that “a shift out in a production possibility frontier does not necessarily increase welfare, as assessed by a social welfare function.” The published version was unclear on whether the theorem contained in the article was a statement about an equilibrium outcome or a mere existence claim, regardless of the possibility that this outcome might occur in equilibrium. When we asked the authors to clarify, they stated that their claim regarded only the existence of such points, not their occurrence in equilibrium. After this clarification, ProMarket decided that the article was uninteresting and withdrew its publication. 

Addendum to Retraction

On July 22nd, ProMarket published an article titled: “The Antitrust Output Goal Cannot Measure Welfare.” As the title suggests, the article argued that output cannot properly measure welfare because an increase in output can reduce welfare. The central claim of the article was a theorem that purports to demonstrate this proposition. We report below the theorem and the proof.

“We will first prove that it is possible for an increase in output to reduce welfare under the assumption that welfare is assessed by a social planner.”

“Suppose in the figure below that the original production possibility frontier is PPF0 and the new production possibility frontier is PPF1. Let USWF be the original level of social welfare, so that the curve in the diagram labeled USWF is the social indifference curve when the technology is represented by PPF0. This implies that when the technology is at PPF0, society chooses the socially optimal point, I, on PPF0. Next, suppose there is an increase in potential output, to PPF1. If society moves to a point on PPF1 which is above and to the left of point A, or is below and to the right of point B, then society will be worse off on PPF1 than it was on PPF0. Even though output increased, depending on the social indifference curve and the composition of the new output, there can be lower social welfare.”

After publication, it was brought to our attention that the theorem, the central claim of the article, may be invalid. In neoclassical economics, the equilibrium point is at the tangency point between the indifference curve and the PPF. Thus, after a rightward shift of the PPF, the new tangency point would be clearly higher in utility terms than the original point, thereby invalidating the theorem.

ProMarket brought this academic concern with the article to the attention of the authors. The authors replied that their claim was only that it is feasible (i.e., technically possible) for agents to be worse off with the expanded PPF, not that they will be worse off in equilibrium. Thus, they raise an out-of-equilibrium possibility. 

Technically, one can also destroy output and be worse off.  For this result to be relevant from an economic point of view—and important for publication in ProMarket— one needs to specify how a point along the PPF is chosen in equilibrium and show that, maintaining this rule constant, the level of utility decreases when the PPF moves to the right. Neoclassical economics assumes agents maximize utility. In working with the authors to revise the article, we were open to considering other behavioral rules as long as the rule was kept the same before and after the rightward shift of the PPF.

The authors stated that their claim had nothing to do with behavior. Rather, it was merely a  technical feasibility. However, since a theorem is commonly understood as “a general proposition not self-evident but proved by a chain of reasoning,” the article as published did not have a theorem. Most importantly, the article only raised a technical possibility, not an economic one, and thus it was self-evident and uninteresting from an economic point of view.

ProMarket takes seriously the academic standards of publication. Had we understood from the beginning the technical, and non-economic, nature of the claim, we would not have published this article. Once ProMarket discovered that it published an article that claims to offer a theorem but does not, we felt we had no choice but to retract the article. ProMarket aims to bring the rigor of academic discussion without the technical jargon and will continue to follow the highest standards for its publications.