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Cost and Revenue Constrained Production by Prof. Rolf Färe, Prof. Shawna Grosskopf (auth.) PDF

Xo with P is a closed correspondence and R( xik , r) is convergent, thus u(XO, r) E P(XO) and lim sUPk_+oo R(X ik , r) = ruo ~ R(xO, r). 7. In our discussion of the cost function, we provided a condition on the technology that is sufficient for differentiability of C( u, p) in (positive) prices. A similar condition can be developed for the revenue function.

The corresponding efficient input set consists of [be]. One may prove that if L(u) is nonempty, so too is EffL(u). 26 The proof hinges on the closedness of L( u). 4) E f f L( u) is bounded for all u E R~. 5) 1 1 The Cobb-Douglas technology L(u) = {(Xl,X2): u ~ xlxi}, on the other hand, has unbounded efficient input sets. 6) L(u) £;; EffL(u) + R~. 6) is left to the reader. 7) C(u,p) i~f{px ~ : x E L(u)} inf{px: x E EffL(u)+ R~} x mln{px : x E EffL(u)}. E f f L( u) is nonempty and compact, thus px attains its minimum on E f f L( u).

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