Chapter3_BasicModel_II_012009

Chapter3_BasicModel_II_012009 - The Basic Model II Juan...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
The Basic Model II Duke University and Federal Reserve Bank of Atlanta January 20, 2009 Basic Model January 20, 2009 1 / 15
Background image of page 1

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

View Full DocumentRight Arrow Icon
Firms . Competitive behavior. Hence, we can work with a that stands in for the entire production sector in the economy. Juan Rubio-Ram±rez (DUKE) Basic Model January 20, 2009 2 / 15
Background image of page 2
Technology Neoclassical Cobb-Douglas production function: y t = f ( k t , l t ) = k α t ( A t l t ) 1 α where α 2 ( 0 , 1 ) . A t is the current level of technology. Labor augmenting form. Basic Model January 20, 2009 3 / 15
Background image of page 3

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

View Full DocumentRight Arrow Icon
Characteristics 1 Constant returns to scale ( λ k t ) α ( A t λ l t ) 1 α = λ k α t ( A t l t ) 1 α = λ y t for λ > 0 2 Both inputs are essential. If either the capital k t or labor l t input is zero, output is also equal to zero. 3 Marginal productivities are positive f k = α k α 1 t ( A t l t ) 1 α > 0 f l = ( 1 α ) A t k α t ( A t l t ) α > 0 but decreasing. 4 Inada conditions: lim k t ! 0 f k = lim l t ! 0 f l = lim k t ! f k = lim l t ! f l = 0 Basic Model January 20, 2009 4 / 15
Background image of page 4
Interpretation α is the elasticity of output with respect to the capital input. Take logs of the production function to obtain: log y t = log A t + α log k t + ( 1 α ) log l t and thus d log ( y t ) d log ( k t ) = α . Similarly, the elasticity of output with respect to labor is 1 α because: d log ( y t ) d log ( l t ) = 1 α .
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/13/2010 for the course ECON 110D taught by Professor Schmitt-grohe during the Spring '08 term at Duke.

Page1 / 15

Chapter3_BasicModel_II_012009 - The Basic Model II Juan...

This preview shows document pages 1 - 6. Sign up to view the full document.

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