Elluminate09-05-11

Elluminate09-05-11 - Elluminate - 5 sup cfw_ u x L ( u ) ,...

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Elluminate - 5
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( 29 [ 29 { } 0 sup , 0, u x L u u u +∞ = ( 29 { } ( 29 { } u x L u u x L u
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( 29 { } u x L u ( 29 { } u x L u x x
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If x > 0, or if x ≥ 0 and Φ(λ x ) > 0 for some positive scalar λ, the value of Φ(λ x ) may be made to exceed any output rate u [0,+∞) by choosing a sufficiently large λ. ( 29 as x λ Φ → ∞ → ∞
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The convexity property [P.8] of the input sets L ( u ) implies that the production function Φ( x ) is qausi-concave ( 29 ( 29 ( 29 ( 29 1 min , x y x y θ Φ - + Φ Φ ( 29 ( 29 { } x u x L u Φ ( 29 ( 29 { } y u y L u Φ
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Proposition 3: The production function Φ( x ) = Max { u | x L ( u ), u [0,+∞)}, x D , defined on the input sets L ( u ) of a technology with Properties [P.1], … [P.9] has the following properties: o [A.1] Φ( 0 ) = 0 o [A.2] Φ( x ) is finite for all x D. o
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Elluminate09-05-11 - Elluminate - 5 sup cfw_ u x L ( u ) ,...

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