John Eatwell conludes a 2019 article with the assertion, "There is no neo-classical theory of the rate of profit." As appropriate for a conclusion, this article demonstrates that this proposition is true.
I recently read Robinson (1972). The first crisis in economic theory in her lifetime, she says, is the failure of economic theory to explain the level of production. Keynes addressed that crisis, albeit mainstream economists these days seem mostly ignorant of his ideas. The second crisis concerns what is produced, of the composition rather than the volume of production. This crisis includes concerns about what governments should spend on, while trying to maintain effective demand. More social spending and less spending of technologies for war would be nice.
But here I want to note these passages:
What is the orthodox theory of profits actually received? Many years ago I set out to write a little book on Marxian economics; when I had written a chapter on Marx's theory of profits, I thought I had to write a chapter on the orthodox theory for comparison, and blest if I could fmd one high or low. Ever since I have been inquiring and probing but I still cannot find out what it is. We have Marshall's theory that the rate of interest is the 'reward of waiting' but 'waiting' only means owning wealth. A man 'may have obtained the de facto possession of property by inheritance or by any other means, moral or immoral, legal or illegal. But if, having the power to consume that property in immediate gratifications, he chooses to put it in such a form as to aflford him deferred gratifications, then any superiority there may be in deferred gratifications over those immediate ones is the reward of his waiting'. In short, a man who refrains from blowing his capital in orgies and feasts can continue to get interest on it. This seems to be perfectly correct, but as a theory of distribution it is only a circular argument...
...Each individual goes on saving or dis-saving till the point where his individual subjective rate of discount is equal to the market rate of interest. There has to be a market rate of interest for him to compare his rate of discount to. But of course the whole thing is quite beside the point once we have accepted the Keynesian view that investment governs saving, not saving investment...
...There is also the problem of the relative levels of different types of earned income. Here we have the famous marginal productivity theory. In perfect competition an employer is supposed to take on such a number of men that the money value of the marginal product to him, taking account of the price of his output and the cost of his plant, is equal to the money wage he has to pay. Then the real wage of each type of labour is supposed to measure its marginal product to society. The salary of a professor of economics measures his contribution to society and the wage of a garbage collector measures his contribution. Of course this is very comforting doctrine for professors of economics but I fear that once more the argument is circular. There is not any measure of marginal products except the wages themselves.
In short, we have not got a theory of distribution. We have nothing to say on the subject which above all others occupies the minds of the people whom economics is supposed to enlighten. -- Joan Robinson
This passage reminded me that Eatwell and Robinson collaborated, in the early 1970s, on a textbook. So Eatwell is drawing on Robinson, as well as Sraffa, in his argument about the lack of an orthodox explanation of how capitalists obtain income. And you can see that Robinson's attempt to find such a theory goes back to 1942. The generalization of the General Theory to the long run was a major part of her research program.
I do not think it makes sense to talk about the rate of profits in the Arrow-Debreu model of intertemporal equilibrium, in John Hicks' Value and Capital model of temporary equilibrium, or in models of dynamic equilibrium paths. In these models, relative prices vary over time.
John Eatwell, with others, says that economists changed the question. He is not referring to the marginal revolution. Early marginalists tried to explain the rate of profits, in a model of long run equilibrium with a given quantity of capital. All of their approaches were incoherent. The changed question looked only at prices along short run equilibrium paths, where the agents have perfect foresight. Joan Robinson objected that she could not get these models to stand up long enough to knock them down. They failed to be in historical time.
References- John Eatwell. 2019. 'Cost of Production' and the theory of the rate of profit. Contributions to Political Economy 38(1): 1-11.
- Joan Robinson and John Eatwell. 1973. An introduction to Modern Economics. McGraw-Hill
- Joan Robinson. 1942, 1966. An Essay on Marxian Economics. Palgrave Macmillan.
- Joan Robinson. 1972. The second crisis of economic theory. American Economic Theory 62(1/2): 1-10.

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