Lecture 16-2005 - Shephards Duality Proof: Part I Lecture...

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Unformatted text preview: Shephards Duality Proof: Part I Lecture XVI Definition of the Distance Function As a starting point of the discussion of the distance function, Shephard defines the space of possible inputs over the nonnegative domain D . Then the space of all possible input bundles is segmented into a sequence of regions: The origin: {0} Interior points of D : The boundary points of D excluding the origin: { } 1 D x x = 2 1 0, n i i D x x x = = = D 2 is further subdivided into two regions The last segregation segregates D 2 into those points that are on a level set ( L ( u ) ) and those points not on a level set ( 29 ( 29 { } 2 2 , for some 0, D x x D x L u u = ( 29 ( 29 { } 2 2 for some 0, D x x D x L u u = Looking at the definition if at least one x i is equal to zero, but production is still possible (i.e., the input is not strongly necessary). Thus, 2 1 0, n i i x D x x = == ( 29 : x L u u 220d The second possibility is that inputs are strictly...
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This note was uploaded on 07/15/2011 for the course AEB 6184 taught by Professor Staff during the Fall '09 term at University of Florida.

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Lecture 16-2005 - Shephards Duality Proof: Part I Lecture...

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