>> Everyone know Leontieff production functions have pathological properties
>> (check their derivatives)
> 
> An interesting aspect of this approach is that any continuously differentiable
> well-behaved neoclassical production function can be approximated arbitrarily
> closely by linear combinations of processes like those in my examples. I think a
> geometric illustration of two-dimensional isoquants might convince undecided
> readers of this point.

yes but some arbitrarily close approximation is not what you are  using in your
example.  Your example proports to reject standard theory but in fact it just shows
that the particular production functions that you have chosen don't work.  This is
not a genaric result.  Try using Cobb Douglas or CES.   oops the standard theory
doesn't fail anymore does it?

The question is "why are you using a form of production function which
(a) is known to have pathological properties (ie differentiability)
(b) no one uses because we know it doesn't fit the data"

Let me hazard a guess.  Because if you used a more standard production function the
standard model does not fail.

>> and that don't fit data well.
>
> I don't know that. In fact, I am under the impression that their use in Leontief
> input-output analysis is well-established.

like 50 years ago they were used but we know that they are problematic so they are no
longer used.

> Maybe Mr. Simon is under the curious delusion that linear programming is rarely
> used in applied and empirical work too.

Please see any econometrics text.

> As a simple matter of logic, Mr. Simon is mistaken. If the assumptions of a model
> logically entail the conclusions, no set of parameters meeting the assumptions
> can contradict the conclusions.

but thats not whats happening here.  You chose a production function that you knew
would fail when in fact most functional forms - including the ones that seem to fit
the data - do not fail.  I can make any theory fail by rigging the
parameterizations correctly.  If I am so wrong then do the example over using a
Cobb Douglas.

> Certain "models" are simply a logical mistake. For example,

your example is irrelevant to my criticism.  You are rejecting a class of models
because you can find a paramterization that fails.  Big woop we all know it will
fail.  But the parameterizations that the rest of the economics profession uses -
the parameterizations which are monotone and continuously differentiable - do not
fail. If I am wrong then do the example over using Cobb Douglas.

> This is not a question of empiricalism,

only so far as we know the production function that you chose does not fit the data
and the production functions that do seem to fit the data don't fail.  So if you
had to hazard a guess which would you choose

(a) the function that does fit the data (and as a bonus do work)
(b) the function that doesn't fit the data (and unfortunately don't work)

>> Try using Cobb Douglas or CES (like most economists do) and I believe these
>> problems will go away.
>
> I know Mr. Simon's "intuition" of what drives the results is simply mistaken.


then prove it and do the example using Cobb Douglas.   I would be happy to admit
that I am wrong but we both know that I am not.

REFERENCES:

any graduate level economics text book written in the last 20 years