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Topic: Exercise 3.10
Conf: Chapter 3, Theory of the Firm, Msg: 14976
From: Martin Caley (martin.caley@economics.treasury.gov.im)
Date: 8/20/2004 10:09 AM
Exercise 3.10 Martin Caley MCaley martin.caley@economics.treasury.gov.im
I suggest that you assume constant returns to scale (CRS) so that alpha + beta = 1 if you wish to attempt this exercise. If this is not assumed, all I could get was a nasty expression which I could not simplify.
We have in general that
sigma = f1.f2(f1.x1+f2.x2)/x1.x2.D
where D=2f12.f1.f2-f1.f1.f22-f2.f2.f11.
Under the assumption of CRS this becomes sigma = f1.f2/f.f12.
It is now easy to show sigma = 1-[a.m/(1-a)].[x2/f] for the CRS CMS production function.