15 July 2021

My New Book: Economics Redefined

This may seem like the daydream of a fond old man. But I am confident that my new ebook Economics Redefined deals a death blow to neoclassical economics. I expect few economists to read it and fewer still to understand it. Even so, I expect that eventually it will become the conventional wisdom. Those who have been intimidated by the mathematics of mainstream economics -- the Lagrangians and the bordered Hessians -- will read this book and rejoice because it shows that the math is hogwash.


In September 2014, Jonathan Barzilai, a mathematician at Dalhousie University in Canada, wrote an open letter to William Nordhaus, who was the president of the American Economic Association at the time. Among other things Barzilai pointed out: "In economic preference theory, the claim that ordinal functions can be differentiated is based on elementary errors: Theorems of differential calculus are applied where the assumptions of these theorems are not satisfied and mathematical operations are applied where they are not applicable. The notion that ordinal functions are differentiable is an error. It has no parallel in mathematics and science."

Since a large part of economics rests on the idea of utility maximisation (which is untenable if Barzilai is right) his letter was expectedly not met with enthusiasm. To describe the response as a "deafening silence" might be cliched but quite appropriate and hardly surprising. His claim was after all akin to someone telling physicists that the law of conservation of momentum is incorrect. Nordhaus did not respond. If other economists took note of Barzilai's letter they probably regarded him as crazy.

Unfortunately for mainstream economics Barzilai is right. And it does not take much thought to arrive at that conclusion. If utility is ordinal, then three values of utility a, b and c are of the kind that we can say a > b > c and nothing more. The three numbers 3, 2 and 1 satisfy that ordering but so do 25, 3 and 1. Obviously the operations of differential calculus cannot be applied to them. That is all there is to it. It took me quite some time to realise this because, like most economists, I was thinking of baskets of goods as in indifference curves. Not being a mathematician but an engineer by training, I needed to think in pictures, and it was a couple of years before I convinced myself that Barzilai's argument applies to baskets of goods as well.

In June 2017, Real-World Economics Review, a heterodox economics journal, published a paper of mine where I showed that the demand curve must necessarily take the shape of a rectangular hyperbola, and that when this is the case, macroeconomics can be built from the microeconomics of heterogeneous agents, and that involuntary unemployment must follow as a matter of course. It was a month or so after this, while looking through old issues of Real-World Economics Review, that I first chanced upon two papers by Barzilai as well as a putative refutation of one of his papers, which was actually nothing of the kind.

Four years later, in a moment of transcendental joy, the realisation struck me that Barzilai's idea and mine, though seemingly oceans apart, actually amounted to the same thing. It is because utility is not differentiable that demand curves must be rectangular hyperbolas.

I hope the reader of this book too will be able to savour the joy of that realisation.

A summary of the book is as below:

Chapter 1 shows that the mathematics of profit maximisation is incorrect.

Chapter 2 shows that the mathematics of utility maximisation is incorrect.

Chapter 3 uses the ideas of the previous two chapters to arrive at a non-equilibrium macroeconomics derived from the microeconomics of heterogeneous agents and having involuntary unemployment as a key feature.

Chapter 4 explains how our conception of money is different from that of Keynes and Friedman.

Chapter 5 shows that the idea of the money multiplier is incorrect.

Chapter 6 sets out a way of measuring money.

Chapter 7 shows that the velocity of money has nothing to do with the speed at which money travels from hand to hand and, indeed, has nothing to do with time at all.

Chapter 8 shows why recessions occur.

Category: Economics

Philip George
Understanding Keynes to go beyond him

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