Except geometry does work, because we do have straight lines. They are not perfect, and the angles aren't perfect, but the model has lines and "lines" means the same thing between model and reality. Geometry is actually very useful because the ideals in the model can be approximated well enough in reality that you get consistent and pred…
Except geometry does work, because we do have straight lines. They are not perfect, and the angles aren't perfect, but the model has lines and "lines" means the same thing between model and reality. Geometry is actually very useful because the ideals in the model can be approximated well enough in reality that you get consistent and predictable results. Machinists can actually make parts that fit together extremely closely, parts designed to do so using geometry.
In other words, we can test how close the model is to reality, and it is damned close even if we can't make reality match the theory exactly.
Perfectly competitive firms are as realistic as spherical cows in a vacuum, functionally speaking. Neither can exist in reality, and the model gives you false insight about how much milk they would produce. Both function in the model completely differently than their real life counter parts do for the purposes we are interested in.
Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
> the model has lines and "lines" means the same thing between model and reality
Not quite. That's why the editors of the text of Euclid (IV BC) which reached us prepended extracts from Theon's explanatory geometry handbook (V AD), including the pseudo-definitions 'a point is that which has no parts' and 'a line is length without width'. We have evidence that Euclid himself wished to disassociate his work from such statements, in that he used a different word for 'point', σημεῖον, which nobody before him used in the context of geometry, than the one Pythagoreans and the Platonic and Aristotelian philosophers had been using in the context of geometry, which was στίγμα. The model 'Euclidean geometry' abstracts some of the properties which real lines (drawn on paper, light rays, taut strings, edges of machined parts and so on) have, idealizes them, and this construct becomes the theoretical entity 'line' about which it is possible to make exact statements and prove theorems. This abstraction-idealization procedure also yields correspondence rules between 'lines' and lines.
> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?
"> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?"
That was my argument, with the examples. I also included the point that internal consistency is not enough.
Please, if you are going to respond to someone's comment, try to respond to their comment and not some half read and quarter understood version of it.
Please to you. That wasn't your argument in the first comment. You wrote
> "a perfectly competitive firm" is something that does not exist, nor can exist, in the real world, and is in fact a construct to make the math easy
> we have a mathematical model about the behavior of firms that can't exist and how they price goods that we can't test
Call me pedantic if you wish, but nothing there says that models differ on how well they help one understand and predict reality despite being abstractions, and that the model of perfectly competitive firms just happens to be particularly bad at it.
We are referring to different posts; I was referring to the post you immediately responded to, not the original in the thread. I didn't make a general attack on mathematical models in the original post, however.
The original post in the thread is about how internal consistency isn't so great, specifically in the example of perfect competition models as a class of mathematical models that achieve it by tautology. Apologies for not making it abundantly obvious, or going out of my way to point out that some mathematical models are not worthless even if that one in particular that I was talking about is. I also didn't feel it necessary to point out that murder is bad, or that one shouldn't steal.
Except geometry does work, because we do have straight lines. They are not perfect, and the angles aren't perfect, but the model has lines and "lines" means the same thing between model and reality. Geometry is actually very useful because the ideals in the model can be approximated well enough in reality that you get consistent and predictable results. Machinists can actually make parts that fit together extremely closely, parts designed to do so using geometry.
In other words, we can test how close the model is to reality, and it is damned close even if we can't make reality match the theory exactly.
Perfectly competitive firms are as realistic as spherical cows in a vacuum, functionally speaking. Neither can exist in reality, and the model gives you false insight about how much milk they would produce. Both function in the model completely differently than their real life counter parts do for the purposes we are interested in.
Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
> the model has lines and "lines" means the same thing between model and reality
Not quite. That's why the editors of the text of Euclid (IV BC) which reached us prepended extracts from Theon's explanatory geometry handbook (V AD), including the pseudo-definitions 'a point is that which has no parts' and 'a line is length without width'. We have evidence that Euclid himself wished to disassociate his work from such statements, in that he used a different word for 'point', σημεῖον, which nobody before him used in the context of geometry, than the one Pythagoreans and the Platonic and Aristotelian philosophers had been using in the context of geometry, which was στίγμα. The model 'Euclidean geometry' abstracts some of the properties which real lines (drawn on paper, light rays, taut strings, edges of machined parts and so on) have, idealizes them, and this construct becomes the theoretical entity 'line' about which it is possible to make exact statements and prove theorems. This abstraction-idealization procedure also yields correspondence rules between 'lines' and lines.
> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?
"> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.
Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?"
That was my argument, with the examples. I also included the point that internal consistency is not enough.
Please, if you are going to respond to someone's comment, try to respond to their comment and not some half read and quarter understood version of it.
Please to you. That wasn't your argument in the first comment. You wrote
> "a perfectly competitive firm" is something that does not exist, nor can exist, in the real world, and is in fact a construct to make the math easy
> we have a mathematical model about the behavior of firms that can't exist and how they price goods that we can't test
Call me pedantic if you wish, but nothing there says that models differ on how well they help one understand and predict reality despite being abstractions, and that the model of perfectly competitive firms just happens to be particularly bad at it.
We are referring to different posts; I was referring to the post you immediately responded to, not the original in the thread. I didn't make a general attack on mathematical models in the original post, however.
The original post in the thread is about how internal consistency isn't so great, specifically in the example of perfect competition models as a class of mathematical models that achieve it by tautology. Apologies for not making it abundantly obvious, or going out of my way to point out that some mathematical models are not worthless even if that one in particular that I was talking about is. I also didn't feel it necessary to point out that murder is bad, or that one shouldn't steal.