The great economic equations

A few days ago, Unlearning Economics twitted a link to an article on "The 17 equations that changed the world." Only one was an economic equation, The Black-Scholes one, and in all fairness it did not change the world, and is not even a central one in economics. First of all, Nassim Taleb has argued convincingly (for example, here) that Black, Scholes and Merton did not invent the formula, and what they really did was to provide a theoretical justification that was compatible with Arrow-Debreu general equilibrium (GE) views. Haug and Taleb say it clearly:

Indeed what Black, Scholes and Merton did was “marketing”, finding a way to make a well-known formula palatable to the economics establishment of the time, little else, and in fact distorting its essence.

So market participants already had formulas to price options, and the idea that their version of the formula "helped create the now multi-trillion dollar derivatives market," as suggested by Andy Kiersz, is clearly incorrect. Unregulated financial markets didn't need the Black-Scholes formula, economists did. And we know how well that ended. Deregulation and the nature of competition in financial markets would have led to the expansion of derivative markets anyway. But GE would not look like it could provide practical answers to real economic problems. Which turns out it couldn't. Besides, as discussed here before, the Arrow-Debreu general equilibrium model is not devoid of problems.

So what are, if any, the great economic equations, you ask. If I had to say one it would be either Keynes' multiplier formula, Y = I/(1 – c), or Sraffa's demonstration of the inverse relation between wages and profits, r = R(1  – w).* The first clearly shows that spending determines the level of activity and provides formal justification for counter-cyclical policies, which have indeed reduced the effects of recessions on the economy, even if, as Kalecki had noted it would happen, austerity is often imposed for political reasons. The second resolved an issue first clearly posed by Ricardo, is part of the clear understanding of what determines long-term prices, and shows the conflictive nature of the capitalist system. Both are central to understanding the way capitalist economies work.

* Where all variables have the standard meaning, Y is output, I investment, c the propensity to consume, r is the rate of profit, R is the maximum rate of profit, and w the wage share.

Lars P. Syll On How to Get Away With Scientific Fraud With Economics Textbooks

By Lars P. Syll

As is well-known, Keynes used to criticize the more traditional economics for making the fallacy of composition, which basically consists of the false belief that the whole is nothing but the sum of its parts. Keynes argued that in the society and in the economy this was not the case, and that a fortiori an adequate analysis of society and economy couldn’t proceed by just adding up the acts and decisions of individuals. The whole is more than a sum of parts. This fact shows up already when orthodox – neoclassical – economics tries to argue for the existence of The Law of Demand – when the price of a commodity falls, the demand for it will increase – on the aggregate. Although it may be said that one succeeds in establishing The Law for single individuals it soon turned out – in the Sonnenschein-Mantel-Debreu theorem firmly established already in 1976 – that it wasn’t possible to extend The Law of Demand to apply on the market level, unless one made ridiculously unrealistic assumptions such as individuals all having homothetic preferences – which actually implies that all individuals have identical preferences.

This could only be conceivable if there was in essence only one actor – the (in)famous representative actor. So, yes, it was possible to generalize The Law of Demand – as long as we assumed that on the aggregate level there was only one commodity and one actor. What generalization! Does this sound reasonable? Of course not. This is pure nonsense!

Read rest here.