In this episode of the saga I'd like to discuss this comment on the blog Unlearning Economics where the commenter tries to explain the flaws in the logic and math of the Keen/Standish[PDF] paper. In it they admit a few errors but otherwise defend their claims. As I wrote earlier, the logic and math is not what makes Keen's (re)discovery remarkable but the results of his computer simulation. After all, software doesn't have a bias unless it's actively programmed in, whereas "economist" and "bias" appear to be synonymous, at least if Moshe Adler is to be believed. Anyway, I take issue in particular with the following paragraph in the comment:
Then the [Keen/Standish] paper shows some simulations which are meant to support the claim that it is “optimal” for firms to choose collusion. Since the firms are not optimizing, just adjusting their quantities [in] some ad-hoc way in response to changes in their profits, it’s hard to tell what is driving the results. Then we see some attempt to refute Cournot result, but instead of going through standard Nash equilibrium computation (which doesn’t contain any mathematical mistakes – I’ve solved enough homeworks to be confident about this), Keen presents some convoluted model where firms respond to other firms choices in fixed proportion, and derives that optimal level of strategic interaction is zero. Only problem is that he again assumes that optimum = maximizing joint profits.There's a problem in almost every sentence of this paragraph, so I try to address them one by one.
- [It] is“optimal” for firms to choose collusion.
Firms do not "choose collusion". Apart from the fact that that expression has a negative connotation (why would a value-free science call an outcome using a negatively loaded term?), is it not at least thinkable that the outcome called "collusion" is in fact the natural outcome (instead of positive "choice") of perfect competition, and that the one that economists claim (P=MC) is rather a result of their innate bias i.e. wishful thinking?
- Since the
firms are not optimizing, just adjusting their quantities in some ad-hoc
Firms are optimizing (or rather maximizing). I wrote a simple simulator myself, and at the core of the simulation is the following equation evaluated by each firm:
profit = quantity*(unitprice - unitcost(quantity))
As the price is determined by the market, the only value that can be adjusted to maximize profit is the quantity. To increase profit, the quantity must be increased (price is > 0). But of course all other firms do the same thing (increase quantities to maximize profits), so the price may fall as a result, and hence profit. The firms do not know which quantity produces maximum profit (how would they?), and in any case that wouldn't help, because all other firms interfere with any prediction by their own production. So each firm continuously and individually boosts or throttles production depending on whether increasing/reducing production last time round helped to increase/decrease profit. This process is called profit maximization.
- ...it’s hard to tell what is
driving the results.
No, it's not hard to tell what is driving the results: profit maximization is.
- [Instead] of going through standard Nash equilibrium computation [...], Keen presents some convoluted
Of course, if you go through the Nash equilibrium formula you will guarantee the inherent result, because it is constructed that way. Keen's (software) model is not convoluted at all: even a high school kid with some basic programming skills can write a simulator that will yield the same result, because ... I don't know ... perhaps, this is simply the natural outcome of perfect competition, whereas the one that economists claim simply does not materialize, irrespective of how much they want it to be true. After all, a minimum wage does not lead to unemployment, either, despite every economist saying so. Perhaps economists are simply ... well ... wrong about stuff?
...and derives that optimal level of strategic interaction is zero.
If by "strategic interaction" the commenter means "collusion", why is it bad that there is none of it?
problem is that he again assumes...
The software model assumes only (a) a falling demand curve, (b) market participants being price takers, and (c) absence of information sharing, a.k.a. "collusion" (i.e. no firm [taking] the quantity set by its competitors as a given [and evaluating] its residual demand [Wikipedia]).
- ...that optimum = maximizing joint
Firms do not maximize joint profits. How could they? There is no notion of "joint profit" in my simulator (and neither, I presume, in Keen's), and believe me, unless you actively program that notion into your simulator, it does not appear out of nowhere. Instead, they maximize individual profits (see point 2 above). The only information flowing out of the single firm is its production quantity, and the only thing flowing into it is the price that the market determined, based on quantity and falling demand curve. Where would the joint thing come from? Stray electrons in the microprocessor? Perhaps the outcome of the simulator is the natural outcome of perfect competition, and the theory is simply wrong.
Update: As to the maximizing of joint profits (point 6 above): Even if it were true that firms in Keen's software did indeed end up maximizing "joint profits", why would that discredit his findings? Doesn't the so-called "invisible hand" accomplish the same thing without bothering economists at all? After all, they do claim that the pursuit of individual utility maximization will ultimately lead (through the divine magic of the invisible hand) to the maximization of "joint" utility...
Again, it appears that one of the inherent qualities of the "science" of economics is the twisting and turning of any argument as economists see fit. They don't want to know. They want to win.