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# Frederik Zeuthen

## A personal note by Karl Vind

Frederik Ludvig Bang Zeuthen (1888-1959) was a Danish economist, professor at the University of Copenhagen 1930-58. His father was professor of mathematics, famous for his book on the history of mathematics.

Zeuthen is known for contributions to several of the areas of economic theory which became active in the 1930s. In his work on a theory of the labour market he realised that ''supply equal to demand'' could not determine the wage if two monopolies were negotiating. This is what he called economic warfare. lt is what is now called bargaining.

He is known as the first to replace equalities in the Walrasian system with inequalities, so in Zeuthen's formulation general equlibrium theory could explain not just the price of a commodity but also which commodities were free, i.e. having a zero price.

He is known for early contributions (with Hotelling, Chamberlin, Robinson, and von Stackelberg) to the theory of monopolistic competition

l was a student of economics in Copenhagen from 1951, and Zeuthen was one of the few economics professors whose lectures I followed. Technically he was not a good teacher, but the students who were interested could learn a lot. He was modest, open minded, and positive towards new developments. I remember talking with him about Arrow-Debreu (1954) with the first satisfactory existence theorem for a general equilibrium. Zeuthen, of course, appreciated that they referred to a paper of his from 1932, Das Prinzip der Knappheit, but he tried to explain that the idea came from one of his students.

He referred to the paper in his 1955 book, Economic Theory and Method, but he stayed with the popular version of Walras from Cassel.

Zeuthen was not a student of any of the professors in Copenhagen. He found his own problems and he found his own solutions. Zeuthen did not have any students in Copenhagen, but his human qualities and his whole attitude had a very positive influence on the development in Copenhagen. He gave some students the courage to work with economic theory and to solve problems.

Karl Vind, 1996

Karl Vind (1933-2004) was professor in mathematical economics at the Department of Economics, 1966-2004.