M Kim Section001 Leontief IO Model
1
Math 547
Research Project
Minju Kim
Leontief Input-Output Model
(Application of Linear Algebra to Economics)
Introduction
Professor Wassily Leontief started input-output model with a question, “what level of output should each of the n industries in an economy produce, in order that it will just be sufficient to satisfy the total demand for that product?” Leontief Inputoutput analysis which was developed by Professor Wassily
Leontief in the 1930’s is a method used to analyze the relationships between sectors in an economy. These sectors are interdependent on the other sectors in the economy. In order to produce something, each sector needs to consume of its own output and some of output from the other sectors. He developed the models to model economies using empirical data. He divided U.S. economy into 500 economic sectors and described the interdependence between sectors with input-output matrices. With input-output model, it became possible to determine the total output of industries that must be produced to obtain a given amount for final demand. By using the Leontief Input-output Model, it is possible to find production levels which will meet the demands of all sectors inside and outside of that economy.
On October 18 in 1973, Wassily Leontief won Nobel Prize in economy for this work in this area.
This analysis has been used extensively in economic production planning and in developing countries. Also, by looking at the Leontief Input Output Model, it is possible to tell whether an economy is productive or non-productive.
Assumptions for the Input-Output Model
Since Leontief input-output model normally can have a large number of industries and it will be quite complicated. For a simplification, the following assumptions are adopted
1) Each industry produce only one homogeneous commodity
2) Each industry uses a fixed input ratio for the production of its output
3) Production in every industry is subject to constant return to scale (constant returns to
scale
Math 547
Research Project
Minju Kim
Leontief Input-Output Model
(Application of Linear Algebra to Economics)
Introduction
Professor Wassily Leontief started input-output model with a question, “what level of output should each of the n industries in an economy produce, in order that it will just be sufficient to satisfy the total demand for that product?” Leontief Inputoutput analysis which was developed by Professor Wassily
Leontief in the 1930’s is a method used to analyze the relationships between sectors in an economy. These sectors are interdependent on the other sectors in the economy. In order to produce something, each sector needs to consume of its own output and some of output from the other sectors. He developed the models to model economies using empirical data. He divided U.S. economy into 500 economic sectors and described the interdependence between sectors with input-output matrices. With input-output model, it became possible to determine the total output of industries that must be produced to obtain a given amount for final demand. By using the Leontief Input-output Model, it is possible to find production levels which will meet the demands of all sectors inside and outside of that economy.
On October 18 in 1973, Wassily Leontief won Nobel Prize in economy for this work in this area.
This analysis has been used extensively in economic production planning and in developing countries. Also, by looking at the Leontief Input Output Model, it is possible to tell whether an economy is productive or non-productive.
Assumptions for the Input-Output Model
Since Leontief input-output model normally can have a large number of industries and it will be quite complicated. For a simplification, the following assumptions are adopted
1) Each industry produce only one homogeneous commodity
2) Each industry uses a fixed input ratio for the production of its output
3) Production in every industry is subject to constant return to scale (constant returns to
scale
References: 1) The Leontief Input-Output Model. Web. Retrieved from http://www.personal.psu.edu/kes32/MichiganClasses/math217/Worksheets2/leontief.pdf 2) Kallem, Nicholas. Input-Output Analysis with Leontief Models. Web. Retrieved from http://home2.fvcc.edu/~dhicketh/LinearAlgebra/studentprojects/spring2006/nicholaskalle m/Leontief%20project.htm 3) Chiang, Alpha. Leontief Input-Output Models. Web. Retrieved from http://www.docstoc.com/docs/129503308/From-Chapter-5-Alpha-Chiang-FundamentalMethods-of-Mathematical 4) Duchin, Faye. Rensselaer Polytechnic Institute. Department of Economics. Web. Retrieved from http://www.economics.rpi.edu/workingpapers/rpi0610.pdf