1 / 14

AEB 6184 – Shephard and Von Liebig

AEB 6184 – Shephard and Von Liebig. Elluminate - 3. Shephard’s Production FUnction. Let u  [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

virginia-hutchinson
Download Presentation

AEB 6184 – Shephard and Von Liebig

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. AEB 6184 – Shephard and Von Liebig Elluminate - 3

  2. Shephard’s Production FUnction • Let u  [0,+) denote the output rate. • Let x = (x1, x2,…xn) 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 u  [0,+).

  3. Production Input Set

  4. Technologically Efficient Set

  5. Proposition 3

  6. 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(x), centered on x composed entirely of point in x exists. • Thus, yL(u) where y  x, contradicting the efficient set.

  7. The first point is to define a closed ball. • Given this definition of the closed ball, there exists some distance measure R where the ball is tangent to the level set.

  8. The intersection of L(u)  Dyis a bounded, closed subset of L(u). (a) (b)

  9. In the second case (b) • Let x denote the minimum. • Then x  E(u) and y = x + y with y ≥ x, so y  (E(u) + D). • Definition: The production isoquant corresponds to an output rate u > 0 is a subset of the boundary of the input set L(u) defined by

  10. Different Isoquants

  11. Definition of Production Functions • The production function is a mathematical form defined on the production input sets of a technology, with properties following from those of the family of sets L(u), u  [0,+∞) which can be best understood this way instead of making assumptions ab initio on a mathematical function. • For any input vector x  D, consider a function Φ(x) defined on the sets L(u) by • Giving to the production function Φ(x) the traditional meaning as the largest output rate for x.

  12. A Comparison of Alternative Crops Response Models • This paper compares a response function based on a quadratic functional form and specifications of the von Liebig including the Mitscherlich-Baule. • Quadratic Functional Form • Von Liebig Functional Form • Mitscherlich-Baule

More Related