{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture17-2011

Lecture17-2011 - Basic Functions Shepard Duality Shephards...

This preview shows pages 1–5. Sign up to view the full content.

Basic Functions Shepard Duality Shephard’s Duality Proof - Part II: Lecture XVII Charles B. Moss 1 1 University of Florida October 25, 2011 Charles B. Moss Shephard’s Duality Proof - Part II: Lecture XVII

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Basic Functions Shepard Duality 1 Basic Functions 2 Shepard Duality Charles B. Moss Shephard’s Duality Proof - Part II: Lecture XVII
Basic Functions Shepard Duality Basic Functions Following Shephard’s development from the last lecture, we have two basic groups of functions: The distance function, production function, and associated level set. The level set L Φ ( u ) is defined as the set of possible combinations of inputs that can be used to produce the output level u . Given the level set, we can define a distance function as Ψ ( u , x ) = || x | | || λ 0 x | | : λ 0 = min { λ | λ x L Φ ( u ) } (1) The production function can then be defined as Φ ( x ) = max { u | Ψ ( u , x ) 1 } x D (2) In addition, we can define the set of e cient input vectors by the distance function E ( u ) = { x | Ψ ( u , x ) = 1 } (3) Charles B. Moss Shephard’s Duality Proof - Part II: Lecture XVII

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Basic Functions Shepard Duality The function and the cost structure can be defined based on the cost-minimization problem.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}