Euler’s Theorem

Abstract

Euler’s Theorem on homogeneous functions is one of those useful pieces of multivariable calculus that has tended not to receive the attention in mathematical textbooks that its importance in economic theory warrants. An analogous case is Lagrange multipliers, though there the analysis in most textbooks falls far short of the rigour and depth that are needed for fruitful economic applications, as it often does of Euler’s other discovery of direct importance in economics, the so-called Euler equations in the calculus of variations (for a critical discussion, see Young 1969). With Euler’s Theorem there are no such worries, however, and the discussion in a work like that of Courant (1936, vol. 2, pp. 108–10) is quite adequate.