His teachers Lauritz Vilhelm Birck and Harald Ludvig Westergaard inspired him to do research in economics.
After working for some years outside of academe, Zeuthen earned in 1928 a doctorate with a dissertation Den Økonomiske Fordeling (The Economic Distribution) on price formation.
Zeuthen's article Das Prinzip der Knappheit, technische Kombination und Ökonomische Qualität (The principle of scarcity, technical combination and economic quality), published in the Austrian Zeitschrift für Nationalökonomie in 1933, was ground-breaking, as the article presented the first formulation using mathematical inequalities for Léon Walras's general theory of economic equilibrium.
The books deals mainly with microeconomics and includes, inter alia, what became an internationally influential mathematical relationship between the prices of production factors and finished goods.
The association has established a scholarship annually awarding the Zeuthen Prize for the best article written on the basis of a master's thesis submitted to the Economics Department at the University of Copenhagen.