I was wondering if anyone had an idea about the first author to have mathematically computed an isoquant or at least the first occurrence of a drawn isoquant ? My best guess would be F. Edgeworth in Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (1881) but I really doubt it !
A recently published (and perhaps the only one) paper on the matter is
From the Introduction :
"The absence of a history of the isoquant is in marked contrast to the universal recognition that F. Y. Edgeworth (1881) invented the concept of the indifference curve. It turns out that the isoquant does have an interesting history of multiple discoveries or apparent discoveries. Section 1 outlines the first appearances of the isoquant, as far as I have been able to trace them, in chronological order. The contributions of two originators, namely, A. L. Bowley and Charles W. Cobb, seem not to have been noted before. Section 2 discusses the obvious question of why the discovery of the isoquant was not made until more than forty years after the discovery of the indifference curve, when to a modern analyst the isoquant appears isomorphic to the indifference curve and could have been copied straight from utility theory."
In Section 1 we read (p.645)
"The first unquestionable appearance of isoquants is in Bowley 1924"
(Bowely, A. L. 1924. The Mathematical Groundwork of Economics: An Introductory Treatise. Oxford: Clarendon Press)
Lloyd reproduces the figure to be found in Bowley:
As for the term "isoquant" Lloyd writes
"In his second note on the elasticity of substitution in the same journal, Lerner (1934) called the curve the “isoquant.” This is one of the first uses of the term isoquant in the English-language literature."
(Lerner A.P. 1934. “Notes on Elasticity of Substitution II.” Review of Economic Studies 1(2): 147–48.)
As regards the question "why isoquants took so long after the indiferrence curves invention", from the three possible (and not antagonistic) explanations that Lloyd puts forward I find very interesting the third one: in his words (p. 658) (bold my emphasis)
"Following the practice of the English classical writers, all neoclassical writers on production and distribution theory distinguished a trilogy of factors—land, labor, and capital."
So if your mind is fixed to thinking three inputs, (and a very realistic triplet at that), you won't go easily into thinking just two of them -and realize that you can represent them graphically.