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Elluminate08-30-11 - AEB6184SHEPHARD ANDVONLIEBIG...

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ELLUMINATE - 3 AEB 6184 – SHEPHARD  AND VON LIEBIG
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SHEPHARD’S PRODUCTION FUNCTION Let    [0,+ ) denote the output rate. Let  x =  ( x 1 x 2 ,… x n ) denote factors of production. The domain of inputs can then be depicted as Definition : A production input set  L ( u ) of a technology is  the set of all input vectors  x  yielding at least the output  rate  u , for    [0,+ ). { } 0, n D x x x R =
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PRODUCTION INPUT SET ( 29 1 2 , x x ( 29 L u 1 x 2 x
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TECHNOLOGICALLY EFFICIENT SET
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PROPOSITION 3 ( 29 1 2 , x x x λ λ λ = ( 29 L u 2 x ( 29 L u 1 x
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EFFICIENT SETS From the definition of the  efficient subset  E ( u ) of  the production set  L ( u )is  the boundary of the set. Suppose  x   L ( u ), then a  sphere  S δ ( x ), centered on  x  composed entirely of  point in  x  exists. Thus,  y   L ( u ) where  y    x, contradicting the  efficient set.
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