Anti-Dismal, that outpost of economic rationality down under, points out that Steve Keen's rubbishing of standard microeconomics in "Debunking Economics" doesn't actually pass the test, that quite important test, of being correct. My own view is that even if the critique is correct it doesn't actually matter.
Now I'm about to do a little violence to Keen's point but this is as I understand it. That standard perfectly competitive market, where producers are price takers, depends in the end on the idea that there are an infinite number of producers. For that's the only way that the production of one producer doesn't change market prices: thus, in our absence of an infinite number of anything at all the theory fails its first test. It's actually impossible - thus we cannot have competitive markets and everything is really some mixture of monopolistic and oligopolistic markets. Leave aside whether this is true or not. Our question really is does it matter if it is? At which point I'll offer some anecdata and then an analogy.
I'm intending to do a little mining over the next couple of years. Two men and a dog sort of stuff, not going to shake the world's commodity markets. One product would be one of the rare earths: we'd be producing some 20% of current global supplies. Keen's point about producers is that their own production influences the prices they face, thus they'renotprice takers. And for this project for this metal this is obviously true. We've actually assumed in our calculations that our production will halve the world price of this metal. So far so Keen. Another metal to be produced, we'd be 0.2% of global production. OK, yes, agreed, in the strict model this will indeed change global prices, this additional supply. But it would be pretty silly of us to worry about that in our projections. What happens to the Chinese demand for machine tool steel will be a much more important influence on price than our production. We're assuming that we're price takers. The final metal will produce more like 0.01% of global production of that one. At which point it would be absurd for us to even consider how that is likely to change prices. Which way the war is going in Congo will have more influence than we will.
So even if Keen's actually correct in hismathematics it doesn't actually matter. For we do pretty rapidly get to a number of producers in a market where they are price takers. Where they act as if they're in a perfectly competitive market even if the maths doesn't add up. And as we're trying to describe the real world, not perfect our mathematical models, the critique of standard micro rather falls apart at this point.
As to the analogy, one way of looking at calculus is that curves are really made up of lots of very short straight lines. By making this assumption we're able to do all sorts of useful things. But the assumption is wrong: that doesn't make calculus not useful. We can do things like sending rockets to the Moon by using this known to be wrong assumption. And so it is with standard microeconomics: even if that original mathematical assumption is incorrect it still describes our actual world better than the alternatives. For just as curves are not lots of straight lines, but it's useful to think that way, so, sure, we don't have an infinite number of producers. But we do have a very large number of markets where everyone acts like there are an infinite number so the assumption is a useful one to make when trying to work out what people are going to do.