You seem to have taken Keen at his word that there is a “traditional approach” which assumes “firms do nothing” in response to the actions of other firms and that approach is to be contrasted with a new approach invented by Steve Keen which is more realistic. That is simply not true, as you can easily verify for yourself.

Keen’s solution is a very confused exposition of a special case of a very traditional, in fact, archaic, approach (again, look up “conjectural variations”). And much like in other cases in which he claims to have invented something that is actually well-known, Keen proceeds to try to solve his new invention himself and doesn’t get the right answer.

With regard to your math: Of course I do not think and in no place did I imply that “a derivative implies a relationship where the variable in the denominator is independent and the variable in the numerator is dependent.” Taking derivatives with respect to Q is an ill-defined operation because “what happens to the profits at firm_i if it and/or any other firm changes its output” depends on the distribution if that change in output, not just its magnitude (it’s not a “sufficiently well-behaved variable”). Suppose profits_1 = [ q_1^2 – ln(q_2) ] and Q=(q_1 + q_2). What is d(profits_1)/dQ?

Differentiating with respect to Q does not “describe what happens to the profits at firm_i if it and/or any other firm changes its output.” If firm i changes its own output (and that’s what we should be modeling, as own-output is the firm’s choice variable) we want to evaluate d(profits_i)/dq_i. If we seek a Nash equilibrium, we set dq_j/dq_i = 0 forall j ~i when evaluating that expression, and then solve the resulting system of equations for an equilibrium. That is not the same as assuming that firms believe their competitors won’t make strategic responses (look up the concept of a “reaction function”). If we wanted to “describe what happens to the profits of firm_i if it and/or any other firm changes its output” we would write an expression for d(profits_i) letting the entire vector of outputs change. That is not the same as the derivative of firm i’s profits with respect to Q. The standard Cournot (1838, yes, that’s the year of publication) model, which is what this is despite Keen’s claims to have invented it, generates a position of the *system* which is an equilibrium in a formally-defined sense.

Finally, as I said above, none of this is new. You can find countless expositions of the conjectural variations model Keen claims to have invented in textbooks written 50 to 70 years ago, and many mathematically rigorous expositions of standard game theoretic representations of the modern model in any modern IO textbook (along with much more sophisticated dynamic and stochastic models, and with extensive empirical evidence). For example, consider this textbook’s exposition of these basic models, along with some pointers to some modern extensions and empirics:

http://www.econ.yale.edu/~steveb/Econ600/chapter2.pdf

Generally, I encourage you to go look this stuff up in credible sources rather than trying to learn economics from Steve Keen.

]]>So what about biologists who believe in a creator? You do realize that the term “creationist” doesn’t just apply to the young earth creationist, “people lived with dinosaurs” crowd, right? You are aware that science and philosophy are different fields of inquiry and that science is limited to the physical world, right? You do realize that making metaphysical claims with a field of inquiry that doesn’t examine the metaphysical is absurd, right?

I sure hope so. Otherwise, the post is pretty good.

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