Herbert Scarf (1930-2015)

Herbert Scarf died this 15th of November. I think of Scarf as the economist who first demonstrated that general equilibria need not be stable. Something more, some special case assumption or another approach entirely, is needed.

From his Wikipedia page, I learned that have been exposed to more of Scarf's work than I knew. Long ago I took a course in Operations Research, in which we were taught queuing theory and how to find policies for optimal inventory management. Apparently, that approach to the study of inventory policies comes from Scarf.

I did not find the New York Times obituary enlightening. I wish they had mentioned that his algorithm was for finding so-called Computable General Equilibrium (CGE). I have never quite got CGE models. The ones I have seen do not have the dated commodities of the Arrow-Debreu model of intertemporal equilibrium. I have never been sure that they really belong with that tradition, or, like Leontief's model, really fit with a revival of classical economics. Perhaps they are an example of temporary equilibria, as put forth by J. R. Hicks in Value and Capital.

Quite some time ago, Rajiv Sethi discussed Duncan Foley's appreciation of Scarf as a teacher.

Update: Barkley Rosser provides some comments on Scarf (hat tip to Blissex). Here is an obituary from the blog, Leisure of the Theory Class.

(Unrelated to the above, Cameron Murray recently comments on economists confusion about what is meant by "capital".)

"Those to whom evil is done/Do evil in return"

"...I spent the evening walking round the streets, especially in the neighbourhood of Trafalgar Square, noticing cheering crowds, and making myself sensitive to the emotions of passers-by. During this and the following days I discovered to my amazement that average men and women were delighted at the prospect of war. I had fondly imagined what most pacifists contended, that wars were forced upon a reluctant population by despotic and Machiavellian governments. I had noticed during previous years how carefully Sir Edward Grey lied in order to prevent the public from knowing the methods by which he was committing us to support France in the event of war. I naïvely imagined that when the public discovered how he had lied to them, they would be annoyed; instead of which, they were grateful to him for having spared them the moral responsibility..."

Meanwhile, I was living at the highest emotional tension. Although I did not foresee anything like the full disaster of the war, I foresaw a great deal more than most people did. The prospect filled me with horror, but what filled me with even more horror was the fact that the anticipation of carnage was delightful to something like ninety percent of the population. I had to review my views on human nature. At that time I was wholly ignorant of psychoanalysis, but I arrived for myself at a view of human passions not unlike that of the psychoanalysts. I arrived at this view in an endeavour to understand popular feeling about the War. I had supposed until that time that it was quite common for parents to love their children, but the War persuaded me that it is a rare exception. I had supposed that most people liked money better than almost anything else, but I discovered that they liked destruction even better. I had supposed that intellectuals loved truth, but I found here again that not ten per cent of them prefer truth to popularity. Gilbert Murray, who had been a close friend of mine since 1902, was a pro-Boer when I was not. I therefore naturally expected that he would again be on the side of peace; yet he went out of his way to write about the wickedness of the Germans, and the superhuman virtue of Sir Edward Grey. I became filled with despairing tenderness towards the young men who were to be slaughtered, and with rage against all the statesmen of Europe. For several weeks I felt that if I happen to meet Asquith or Grey I should be unable to refrain from murder. Gradually, however, these personal feelings disappeared. They were swallowed up by the magnitude of the tragedy, and by the realization of the popular forces which the statesmen merely let loose.

-- Bertrand Russell (1951). The Autobiography of Bertrand Russell: The Middle Years: 1914-1944

Update to my Paper on Pension Capitalism

I have updated my paper, "A Neoclassical Model of Pension Capitalism in Which r > g". Changes include:

• Deletion of the claim that, in general, inequality increases in a steady state when the real rate of return on finance exceeds the rate of growth.
• Deletion of states of portfolio indifference, in which the real rates of return on money and on bonds are equal, from the model.
• Addition of illustrations of the solution to the (nonlinear) model with some graphs of some state variables along dynamic equilibrium paths.
• Inclusion of a description of one method for finding such solutions numerically.
• Many minor corrections and rewording.

In general, I try to write papers so anybody, including me several months hence, can follow all the details all they want. I realize in submissions to publication, my appendices would have to be drastically shortened or deleted altogether. My typesetting of the mathematics in this paper needs modification, but it is kind to those with old eyes.