The obsession with equilibrium
The changes to economic theory beyond the micro level involve a complete recanting of the neoclassical vision. The vital first step here is to abandon the obsession with equilibrium.
The fallacy that dynamic processes must be modelled as if the system is in continuous equilibrium through time is probably the most important reason for the intellectual failure of neoclassical economics. Mathematics, sciences and engineering long ago developed tools to model out of equilibrium processes, and this dynamic approach to thinking about the economy should become second nature to economists.
An essential pedagogic step here is to hand the teaching of mathematical methods in economics over to mathematics departments. Any mathematical training in economics, if it occurs at all, should come after students have done at least basic calculus, algebra and differential equations – the last area being one about which most economists of all persuasions are woefully ignorant. This simultaneously explains why neoclassical economists obsess too much about proofs, and why non-neoclassical economists like those in the Circuit School (Graziani 1989) have had such difficulties in translating excellent verbal ideas about credit creation into coherent dynamic models of a monetary production economy (c.f. Keen 2009).
Neoclassical economics has effectively insulated itself from the great advances made in these genuine sciences and engineering in the last forty years, so that while its concepts appear difficult, they are quaint in comparison to the sophistication evident today in mathematics, engineering, computing, evolutionary biology and physics. This isolation must end, and for a substantial while economics must eat humble pie and learn from these disciplines that it has for so long studiously ignored. Some researchers from those fields have called for the wholesale replacement of standard economics curricula with at least the building blocks of modern thought in these disciplines, and in the light of the catastrophe economists have visited upon the real world, their arguments carry substantial weight.
Steve Keen, Developing an economics for the post-crisis world
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Real-World Economics Review Blog 
Yes, there is no rational way to ignore we are cosmic powered biology surfing big bang at life speed.
The other propaganda mirage economists push is economies of scale, which are really a way to measure capture of government by corporations.
This article is not about the obsession with equilibrium, but is about the importance of the mathematical ways of understanding it. For an unqualified person about to enter into economics, some maths knowledge is essential, but the degree of matters in maths given above is too much.
To understand the significance of equilibrium it is sufficient to claim that it is an ideal condition which is never achieved except for an instant. However the tendency for the economy to go towards this condition is its stability and this is mostly positive except when unnatural or unfair and obsessive hoarding of money, land, capital goods, slaves, etc., will drive it away.
Quote: “To understand the significance of equilibrium it is sufficient to claim that it is an ideal condition which is never achieved except for an instant.”
AFAIK that is not what Keen is saying and not what non-linear dynamic models yield. In non-linear dynamic models there is no single “ideal” point and if there is some sort of center of gravity it may be a point that is actually never reached.
Quote: “However the tendency for the economy to go towards this condition is its stability and this is mostly positive except when…”
Is this your definition of stability or are you arguing that the economy is in fact stable?
The problem is the obstinate obsession with equilibrium as a (present time incorrect) ideology. The solution, now that disequilibrium has been established as the actual and underlying temporal nature of the economy, is the practical policy measures that will create and maintain the classical and quite correct and ethical state of equilibrium. If there is anything worse than an obstinate, obsessive and incorrect ideology it is the folly of a correct assessment which fails to then deal with an unstable condition which is “controlled” and ruled by entrenched powers for their unethical advantage.
There is no reforming domination and enslavement. It requires the ethical sensitivity and good sense that demands solutions rather than palliatives, transformation and evolution rather than triangulating “progress” toward chaos and revolution. Economic theorists cannot avoid also being sages, unless they want to be lumped in with the entrenched powers when TSHTF.
“Any mathematical training in economics, if it occurs at all, should come after students have done at least basic calculus, algebra and differential equations…. to the sophistication evident today in mathematics, engineering, computing, evolutionary biology and physics… Some researchers from those fields have called for the wholesale replacement of standard economics curricula with at least the building blocks of modern thought in these disciplines”
Really ? We are far, far, far away from de “autistic” and “post autistic” project from the beginning … It’s a bit sad
Steve; they never even developed a mathematics for a “precrisis world.” In their 1944 book, Morgenstern and Neumann wrote (Intro) “the concepts of economics are fuzzy but even in those parts of mathematics where the descriptive problem has been handled more satisfactorily, mathematical tools have seldom been used appropriately. Mathematical economics has not achieved very much.” This was said at the time neoclassical economics was establishing itself as the new paradigm. Paradigm for whom, certainly not for mathematicians, and certainly not historians who can read Neumann’s 1944 book.
Steve, while I agree with your opinion, you may wish to take back your “novel” criticism of Marshallian firm theory. It is wrong – while I do not agree with Chris Auld about economics in general, I think Chris Auld got it right here: http://chrisauld.com/2012/12/06/steve-keen-still-butchering-basic-microeconomics/
(relates to http://www.paecon.net/PAEReview/issue53/KeenStandish53.pdf)
dprofit/dQ is different from partial(profit)/partial(q_i). Neoclassical Marshallian theory talks about the latter for maximizing profit, not former. And you can’t assume both partial(q_j)/partial(q_i) = 0 for all j not equalling to i and talk about partial(P)/partial(q_j). That’s just wrong.
Anyway, as Chris Auld says, if you just only think about partial derivative to maximize profit, then everything is fine. What Steve says is calculus is wrong. That merits a mathematics paper, not econ paper.
Since equilibration is a continual correction to out-of-spec conditions, any system based on it is forced to be out-of-spec a certain proportion of the time*. We should instead be looking to have economies that meet spec and stay there.