It is easy to argue about what is the most important or influential thing that the late Joan Robinson did in economics. More conventional types would probably point to her widely accepted and even textbookified Economics of Imperfect Competition. Some would point to her later more philosophical and methodological writings about historical time versus analytical time. Many Post (or post-) Keynesians revere her closenss to Keynes and Kalecki and see her as the godmother-founder of their movement who could see the unity among their various bickering factions. But others would look to her work on capital theory in the 1950s, her 1954 paper in the RES, "The production function and the theory of capital," along with the appendices to her 1956 The Accumulation of Capital, as well as her influence on Piero Sraffa to publish his famous book in 1960. This was the trigger for the famous Cambridge controversies in the theory of capital that reached a culmination a half century ago when Paul Samuelson agreed that the "parable" he and some of his students had set forth was not true in general, given such paradoxes as reswitching (called the "Ruth Cohen curiosum" by Joan Robinson), with him declaring in 1966 in the QJE that, "the foundations of economic theory are built on sand."
As discussed elsewhere, we know that although the Cambridge, England side won an intellectual victory at that point, it turned out to be pyrhhic as those following the Cambridge, MA side simply ignored these results and proceeded to act as if nothing had happened, merrily estimating aggregate neoclassical production functions with well-behaved capital in them, with never a note or caveat about any potential problems, as well as building growth theory models, as well as general equilibrium macro models on such assumptions. Joan Robinson may have drawn figures showing non-monotonic relations between "real capital" and "output," in the appendices of her 1956 book, as well as non-monotonic relations between interest rates and employment rates elsewhere. But none of that mattered. It was all to be ignored as oddities or whatever, things not to tell the children lest they become upset and lose sleep and cry when fed their porridge.
So it is a curious matter that the question of capital theory has re-arisen recently. It was just two years ago that Thomas Piketty's book, Capital, made the best seller lists. Right now considerable attention is being paid to Anwar Shaikh's voluminous magnum opus, Capitalism. Both of these books take as their central issue that of the underlying forces driving secular trends in income distribution, particularly the division between wage incomes and profit or interest-based incomes.
Curiously, Piketty's theory remains firmly in the neoclassical camp regarding the questions raised by the old Cambridge, England school. He briefly notes those controversies, but more or less dismisses them, perhaps reflecting the influence of being at MIT for a long period of time, even as he mocks excessive mathematical abstraction of much of modern growth theory. Jamie Galbraith and others, including Shaikh, have taken Piketty to task for his dismissal of the issues raised by those old controversies, and many have criticized him for his super-aggregated view of capital that includes not only land but also such things as collectibles, while others have taken him to task for his arguments regarding r >g. Where he has been most praised has been in his presentation of data supporting his broader arguments, as well as his ability to bring in broader historical and cultural support. In any case, he is bringing the issue of capital and the foundations of income distribution front and center, even if he is not doing so along British Cantabridgian lines.
Shaikh is an old fan of Sraffa's and a participant in the original debates. While he also does not present most of his theory as drawing on these old arguments, his approach is much closer to that approach in flavor and discusses it at some length sympathetically, even if he eventually draws more heavily on modern econophysics methods. These fit nicely into his more Marxist approach, even as he downplays Marx. But, of course, it was Marx who more sharply posed these questions regarding the nature of capital and how it affects income distribution, as well as power distribution, within societies.
I note, of course, that the ever increasing emphasis on financial theory in economics is itself an offshoot ultimately of capital theory, even if it has gone off into its own niche with more emphasis on problems related to risk and uncertainty, while ignoring the broader issues of growth and income distribution.
I do not know what Joan Robinson would think about this recent revival, but given what has been going on with income distribution trends in the higher income nations, I suspect she would not be surprised. And unlike many others, she always thought deeply about the problems of capital theory, taking account of historical and philosophical issues well beyond her peculiar graphs showing supposedly paradoxical relationships.
I close this by quoting myself from my 1991 book (p. 125):
"What really is capital and what does it mean for value, growth, and distribution? Is it a pile of produced means of production? Is it dated labor? Is it waiting? Is it roundaboutness? Is it an accumulated pile of finance? Is it a social relation? Is it an independent source of value? The answers to these questions are probably matters of belief."