An ex-student of his writes-
the first sentence he uttered in the first year undergraduate course on production theory at Presidency College was that the production function is concave because of super additivity. Since we had not even heard of additivity let alone super additivity, we couldn’t understand a word of what he said. He, on his part, couldn’t understand what we couldn’t understand.Short run production functions are concave because of 'decreasing returns'- adding inputs does not lead to a proportionate rise in output because of some bottleneck or resource crunch. Superaddivity means a sequence such that - i.e. it has increasing, not decreasing returns. Now if a function starts from zero, is convex and increasing then its sequence is superadditive. But a superadditivity does not imply convexity. Thus, the cause of concavity can't be superadditivity. On the contrary, a convexity, under certain conditions, implies superadditivity but the reverse is not the case. Furthermore, there is no mathematical reason to tell a bunch of beginners in Econ that superaddittivity causes anything or, indeed, has anything to do with the assumption of diminishing returns.
Perhaps Chakravarty simply wasn't very good at maths. The first paragraph of the booklet concludes with this anecdote-
In the Netherlands in 1981 he was visited by professors from many different disciplines and they would engage in engrossing conversations as between equals. The only exception was when a mathematician visited him. Sukhamoy da asked him what he was working on. He replied don’t ask Sukhamoy. You won’t understand.A little later on the booklet appears to contradict this view. But does it really? It seems to me that something is being left unstated after each sentence. I will take the liberty of uttering what I think the authors are skating over discreetly. My remarks are in bold.
He was renowned for his mathematical prowess. But not among genuine mathematicians who knew he couldn't understand what they were working on. Yet mathematical economics was not an end in itself. D'uh! Mathematical Economics aims at the same thing Economics does- viz. economizing on scarce resources. A good mathematician can save a company, or a consumer, or a country money by coming up with a better algorithm or formula.
Analysis of economic development and economic policy choices did not flow immediately from these abstract mathematical models. Unless they weren't wholly worthless. A mathematical model devised after analysing economic development and policy choices might help save money or improve efficiency. Putting the cart before the horse could never do so. According to him, they emerged from the combination of such constructs and analysis of historical experience. “Economics as a discipline appears to me to be located at the edge of ‘history’ and ‘theory’.” History comes in not only as time is irreversible, but provides important insights into the emergence of institutions over time, an open ended process. Insights are not necessarily provided “by looking at institutions as solutions of suitably defined repeated games”.This is sheer nonsense. Economics is about looking at a time series and saying- this is where things started to go wrong. We've got to restore the system to how it was before we screwed up. Time is not reversible, but Policy is. History provides time series data. It does not provide 'insights'. There is no such thing as 'Theory' or 'Economics as a discipline'. What Chakravarty is talking about is academic availability cascades with zero alethic value or social utility.
Institutions may be 'focal points' for coordination games. They are not solutions to repeated games because, by the folk theorem, there would be no need for them. Thus they would have neither any coercive power nor any budget allocation.
Chakravarty was keenly aware of the limitations of such models. Their limitation was that they were utter shite. However, they were not useless (1989) as they provide a basis for discussions with political decision makers. Hilarious! Political decision makers are people like Ron Reagan or Rajiv Gandhi or, nowadays, Donald Trump. They don't know any math and have zero capacity to evaluate mathematical models of the economy. When, in the history of the world, has a mathematical economist been able to use his model as a 'basis of discussion' with anybody with real power? All he can do is pretend to be wiser than he is. But that is the modus operandi of the mystagogue and charlatan through the ages. Optimal growth paths provide scenarios for a dialogue between planners and the policy makers (Chakravarty, 1988). No they don't- for the same reason that Astrological Charts don't provide scenarios for dialogue between the scoundrel and the person he is duping. His proficiency in mathematical modeling and reasoning as in the well known Chakravrty, Eckaus, Lefeber Parikh model and his awareness of their limitations was one of his dualities, different to that pointed out by Prof. Samuelson of his being at home in both the sciences and humanities in his preface to his Capital and Development planning.This CELF model was incredibly stupid. It assumed no technological or structural change between 1960 and 1972! Man had landed on the Moon, but this model assumed technology did not change! Indira Gandhi appointed this idiot head of the Planning Commission (because more honest, less sycophantic people had turned down the job) where he turned a blind eye to Sanju's corrupt and criminal dealings. No wonder India stagnated under Indira! Chakravarty's entire approach was worthless. He'd have been better off practicing Voodoo!
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