Lecture 02-2005 - DefinitionandPropertiesof...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
    Definition and Properties of  the Production Function   Lecture II
Background image of page 1

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

View Full DocumentRight Arrow Icon
    Overview of the Production  Function  “The production function (and indeed all  representations of technology) is a purely  technical relationship that is void of economic  content.  Since economists are usually  interested in studying economic phenomena,  the technical aspects of production are  interesting to economists only insofar as they  impinge upon the behavior of economic  agents.” (Chambers p. 7). 
Background image of page 2
    “Because the economist has no inherent  interest in the production function, if it is  possible to portray and to predict economic  behavior accurately without direct  examination of the production function, so  much the better.  This principle, which sets  the tone for much of the following discussion,  underlies the intense interest that recent  developments in duality have aroused.”  (Chambers p. 7). 
Background image of page 3

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

View Full DocumentRight Arrow Icon
    A Brief Brush with Duality The point of these two statements is that  economists are not engineers and have no  insights into why technologies take on any  particular shape. We are only interested in those properties  that make the production function useful in  economic analysis, or those properties that  make the system solvable. 
Background image of page 4
    One approach would be to estimate a  production function, say a Cobb-Douglas  production function in two relevant inputs:  1 2 y x x α β =
Background image of page 5

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

View Full DocumentRight Arrow Icon
    Given this production function, we could  derive a cost function by minimizing the  cost of the two inputs subject to some level  of production:  1 2 1 1 2 2 , 1 2 min . . x x w x w x s t y x x α β + =
Background image of page 6
    ( 29 1 1 2 2 1 2 1 2 1 1 1 1 2 2 2 2 1 2 0 0 0 L w x w x y x x x x L w x x x x L w x x L y x x α β λ = + + - = - = = - = = - =
Background image of page 7

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

View Full DocumentRight Arrow Icon
    1 1 2 2 1 2 2 1 1 2 L x w x w x x L w x w x = = ( 29 1 * 2 1 2 2 2 1 2 1 2 0 , , w w L y x x x w w y y w w α β λ + + - = ⇒ =
Background image of page 8
    ( 29 1 * 2 1 1 2 1 , , w x w w y y w β α + + = ( 29 1 1 2 1 1 2 1 2 1 2 1 2 1 1 2 , , w w C w w y w y w y w w w w y w w + + + + + + + + + = + = +
Background image of page 9

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

View Full DocumentRight Arrow Icon
    Thus, in the end, we are left with a cost function  that relates input prices and output levels to the  cost of production based on the economic 
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 40

Lecture 02-2005 - DefinitionandPropertiesof...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online