Premium Essay

Leontief Input Model

In: Science

Submitted By elifzorlu7
Words 497
Pages 2
LEONTIEF INPUT OUTPUT MODEL
Leontief input output model is base on the idea that which level of output should produce in an economy in order to satisfy the total demand for that product. By this model we can clearly see how the national economy is affected by the production of output in one industry. Also, in order to produce given amount for final demand , we can easily obtain industries’ total output. By this model one can say that the economy is whether efficient or not. Structure of an input-output model:
We aplly this model to large number of industries and it could be complicated. Thus, to simplify the problem following assumptions must be take into consideration. 1) Each industry produce only one homegeneous commodity. For example, food industry only produce bread. 2) Each industry uses a fixed input ratio for the production of its output. 3) Production in every industry is subject to constant returns to scale.
These assuptions are unrealistic. Also, from these assumption we can assume that in order to obtain each unit of jth commodity ith input needed which can be show by aij.

It is the input-output coefficient matrix. To produce a unit of output ann is required amount of product from industry Sn.
For example, We can see that there are three industries; agriculture, manufacturing, and labor. In order to produce a unit of food the industry need 0.2 units of food 0.5 manufacturing goods and 0.3 labor etc. This matrix shows that whether the economy can satisfy the certain demand for their goods. The Open Leontief Model:
If the economy consitituted by the n industries than these industries purpose will be satisfy the input demand of the same n industries.We include in the model an open sector. In the open model

Similar Documents

Free Essay

Linear

...ted it all. Some of their names are von Neumann, Kantorovich, Leontief, and Koopmans. The first two were famous mathematicians. The last three received the Nobel Prize in economics. In the years from the time when it was first proposed in 1947 by the author (in connection with the planning activities of the military), linear programming and its many extensions have come into wide use. In academic circles decision scientists (operations researchers and management scientists), as well as numerical analysts, mathematicians, and economists have written hundreds of books and an uncountable number of articles on the subject. Curiously, in spite of its wide applicability today to everyday problems, it was unknown prior to 1947. This is not quite correct; there were some isolated exceptions. Fourier (of Fourier series fame) in 1823 and the wellknown Belgian mathematician de la Vallée Poussin in 1911 each wrote a paper about it, but that was about it. Their work had as much influence on Post-1947 developments as would finding in an Egyptian tomb an electronic computer built in 3000 BC. Leonid Kantorovich’s remarkable 1939 monograph on the subject was also neglected for ideological reasons in the USSR. It was resurrected two decades later after the major developments had already taken place in the West. An excellent paper by Hitchcock in 1941 on the transportation problem was also overlooked until after others in the late 1940’s and early 1950’s had independently rediscovered...

Words: 586 - Pages: 3

Premium Essay

Law Paper

...1. Leontief Paradox |[pic] |Wassily Leontief received a Nobel prize in 1973 for his contribution to | | |the input-output analysis. Three of his students, Paul Samuelson, Robert| | |Solow and Vernon Smith are also recipients. | | |The Heckscher-Ohlin theory states that each country exports the | | |commodity which uses its abundant factor intensively. The HO theory was | | |generally accepted on the basis of casual empiricism. Moreover, there | | |wasn't any technique to test the HO theory until the input-output | | |analysis was invented. | | The first Empirical Test of the HO theory |The first serious attempt to test the theory was made by Professor | | |Wassily W. Leontief in 1954. | | |          Result: Leontief reached a paradoxical conclusion that the | | |US—the most capital abundant country in the world by any...

Words: 3401 - Pages: 14

Premium Essay

Linear Algebra Applied to Economics

...Linear Algebra Applied to Economics Input-Output Analysis Introduction: There are several non-mathematical subjects that linear algebra can be applicable too. Economics is a topic that linear algebra can be used to make a formal application, for example in Input-Output Analysis, econometrics, Game theory, and break-even point analysis. As a group we are going to be focusing on the Input-Output analysis, a type of analysis created for the purpose of describing and making predictions of complicated mathematical models using systems of linear equations. It was established by “W. Leontief, who won the 1973 Nobel Prize in Economics” (Hefferon, p.60). In this paper, mathematical and linear algebra formulas, calculations, graphs, diagrams, pictures, etc., will be clearly shown as to further understand the applicability of linear algebra in economics. Calculations and mathematical examples used in economics will be provided in the context of this paper for better understanding. Also, terms and notations used will be explained, derivation and origin of mathematical results will be shown. Definitions: Economics is a branch of knowledge concerned with the production, distributions, and consumption of goods and services. Linear algebra is a branch of mathematics with the properties of finite dimensional vector spaces and linear mapping between the spaces. The equations are represented using matrices and vectors and consist of several unknowns. Econometrics is branch of economics...

Words: 1271 - Pages: 6

Premium Essay

Heckscher-Ohlin Theory

...Introduction Two Swedish economists Eli Heckscher (1919) and Bertil Ohlin (1933) laid the substantial developments on David Ricardo’s theory of comparative advantage by focusing on the relationships between national factor endowments and commodity trade patterns. Though there have been some attempts to use the Heckscher-Ohlin theory, it seems invalidity in most real-world international trade patterns. In order to evaluate the validity of the Heckscher-Ohlin theory in today’s environment, pros and cons of the statement are illustrated as following. In pro terms, this theory is a simple international trade model with only two nations, two products and two factors of production based on the similar technology. Because of its simplified assumption, the Heckscher-Ohlin theory can be easily applied to analyse theoretical patterns. However, some assumptions proposed in this theory such as the similar technology, constant return to scale, the same demand condition limit its range only to some particular regions, therefore, it seems very hard to apply this theory in many practical terms. In summary, today’s international trading environment is various and complicated, thus this over-simplified theory cannot be sufficient as a good predictor. The purpose of this paper is to examine the Heckscher-Ohlin theory to analyse whether it is a good predictor for international trade in today’s environment. In order to do this, I will describe the content of this theory and then ilustrate...

Words: 2090 - Pages: 9

Premium Essay

Discuss How Trade Leads to the Convergence of Factor Prices in the Heckscher-Ohlin Model. Does Empirical Evidence Validate the Propositions of This Theory?

..._____________________________________________________________ Title of Essay: Discuss how trade leads to the convergence of factor prices in the Heckscher-Ohlin Model. Does empirical evidence validate the propositions of this theory? Word Count: 2,909 words Essay 1 : Discuss how trade leads to the convergence of factor prices in the Heckscher-Ohlin Model. Does empirical evidence validate the propositions of this theory? Abstract The Heckscher-Ohlin model (H-O model) states that a country possesses comparative advantage for those goods whose factors of production are in relatively abundant supply in the country’s endowment. Input combinations depend on the relative factor prices and these in effect, influence the goods prices. Factor prices and the goods prices have a one-to-one relationship. Countries tend to export goods, whose production makes intensive use of the resources. There are four components to the H-O model, and these are: The Heckscher-Ohlin Theorem, The Stopler-Samuelson Theorem, The Rybczynski Theorem and The Factor-Price Equalisation Theorem. The Heckscher-Ohlin model (H-O model) was developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics [Krugman and Obstfeld, 2003]. This model states that a country possesses comparative advantage for those goods whose factors of production are in relatively abundant supply in the country’s endowment. Countries, in this model, are differentiated by the factor intensity of the good they produce. A land-intensive good will have a high land-labour...

Words: 3519 - Pages: 15

Premium Essay

Ebsco

...UNIT 2 INTERNATIONAL BUSINESS THEORIES International Business (Trade) Theories Objectives After reading this unit, you should be able to : • understand the analytical foundations of international business • be familiar with the international trade theories • explain the FDI approaches to international business. Structure 2.1 Foundations of International Business 2.2 International Trade Theories Theory of Mercantilism Theory of Absolute Cost Advantage Theory of Comparative Cost Advantage Heckscher-Ohlin Model Leonief Paradox 2.3 FDI Theories Market Imperfections Approach Product Life Cycle Approach Transaction Cost Approach The Eclectic Paradigm 2.4 Summary 2.5 Key Words 2.6 Self-assessment Questions 2.7 Further Readings 2.1 FOUNDATIONS OF INTERNATIONAL BUSINESS The analytical framework of international business is build around-the activities of MNEs enunciated by the process of internationalisation. The FDI on the part of an MNE attempts to overcome the obstructions to trade in foreign countries. The strategies relating to the functional areas, such as production, marketing, finance and price policies, are adopted by the MNEs in such a manner that an amicable relationship between home and host nations is created. Foreign direct investment can be distinguished from the other forms of international business, such as exporting, licencing, joint ventures and management contracts. Basically...

Words: 8686 - Pages: 35

Free Essay

Werewd

...inear systems of equations arise in many computational tasks in many different disciplines. They arise naturally when a continuous mathematical model is converted to a discrete numerical algorithm. However, there are also a huge number of initially discrete models where they also arise. As Wassily Leontief wrote in Scientific American in 1951 [153]: This article is concerned with a new effort to combine economic facts and theory known as “interindustry” or “input-output” analysis. Essentially it is a method of analysis that takes advantage of the relatively stable pattern of the flow of goods and services among the elements of our economy to bring a much more detailed statistical picture of the system into the range of manipulation by economic theory. As such, the method has had to await the modern high-speed computing machine as well as the present propensity of government and private agencies to accumulate mountains of data. It is now advancing from the phase of academic investigation and experimental trial to a broadining sphere of application in grand-scale problems of national economic policy.1 Gaussian elimination is the oldest and the simplest — but not always the fastest — algorithm for solving matrix equations. The title of this chapter is quite long because a matrix equation can be solved by many different algorithms. The only ones we discuss are Gaussian elimination and a variant which is faster in certain circumstances. Frequently in physical systems...

Words: 399 - Pages: 2

Premium Essay

Trade Between Developed and Developing Nation

...International Investment and International Trade in the Product Cycle Author(s): Raymond Vernon Source: The Quarterly Journal of Economics, Vol. 80, No. 2 (May, 1966), pp. 190-207 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/1880689 . Accessed: 19/10/2014 12:59 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly Journal of Economics. http://www.jstor.org This content downloaded from 82.219.188.189 on Sun, 19 Oct 2014 12:59:41 PM All use subject to JSTOR Terms and Conditions INTERNATIONAL INVESTMENT AND INTERNATIONAL TRADE IN THE PRODUCT CYCLE* RAYMONDVERNON Location of new products, 191.- The maturing product, 196.- The standardized product, 202. Anyone who has soughtto understandthe shifts in international trade and internationalinvestmentover the past twenty years has chafed from time to time under an acute sense of the inadequacy of the available analytical tools. While...

Words: 7781 - Pages: 32

Premium Essay

Lit Review Household/Carbon Footprint

...economic activity and “explore the variation in carbon footprints across different segments of society.” Druckman and Jackson found that affluence was a big factor in determining carbon emission disparities but it was not the only factor. Using a Local Area Resource Analysis (LARA) model, they realised that dwelling type and household composition also played a part. Using a variety of different methods and data, Druckman and Jackson tried to understand the variations in the UK’s carbon emissions. Examples of the different types of data in the literature were: “Allocation table for high level functional uses”, trends in CO2 and household expenditure in the UK and “CO2 emissions attributable to Supergroups”. In almost all research projects there are assumptions and limitations and this was also the case in this literature. Druckman and Jackson are attempting to understand emissions linked to consumption, something that requires a great amount of data collecting due to embedded consumption. This consumption accounting requires Environmental Input-Output modelling which has not been used in the UK since 1995. Druckman and Jackson therefore have to use alternative methods (in this case, the “1995 Leontief Inverse and Imports...

Words: 1020 - Pages: 5

Free Essay

Human Resource Management and Safety: Technical Efficiency and Economic Incentives

...Upjohn Institute Press Book Chapters Upjohn Research home page 2005 Human Resource Management and Safety: Technical Efficiency and Economic Incentives Richard J. Butler Brigham Young University Yong-Seung Park Kyung Hee University Citation Butler, Richard J., and Yong-Seung Park. 2005. "Human Resource Management and Safety: Technical Efficiency and Economic Incentives." In Safety Practices, Firm Culture, and Workplace Injuries. Kalamazoo, MI: W.E. Upjohn Institute for Employment Research, pp. 1-12. http://research.upjohn.org/up_bookchapters/33 This title is brought to you by the Upjohn Institute. For more information, please contact ir@upjohn.org. 1 Human Resource Management and Safety Technical Efficiency and Economic Incentives More U.S. workers die each year on the job than were killed in the U.S. military cumulatively from 1998 through November 2004, even after including self-inflicted and accidental military deaths (DIOR 2005). In 2001, there were 8,786 job-related fatal injuries (5,900 not counting the fatalities caused by the terrorist attacks of September 11), or about 3.7 fatal injuries per 100,000 workers. Workers made 2.1 million trips to the emergency room for injuries sustained from accidents at work (Centers for Disease Control and Prevention 2004). Workers’ compensation insurance, which covers all medical expenses and part of lost wages associated with injuries, cost employers $63.9 billion in 2001 (Williams, Reno, and Burton 2003). The...

Words: 4381 - Pages: 18

Free Essay

Econ864

...60 Other 50 Value added 40 Total Input 200 Manufacturing Services 80 40 40 60 25 20 30 60 125 70 300 250 Other 30 90 25 100 155 400 Table 1: Interindustry Transaction Matrix (Values)   1.39 0.51 0.46 0.33 0.67 1.49 0.65 0.57  Leontief Inverse:  0.56 0.33 1.34 0.27 0.73 0.48 0.67 1.61 Question 1. See Lecture Notes Week 4, the textbook Section 5.7, and Chapter 12 Introduction to Mathematical Economics, (Dowling 2001). Use Table 1 and the given Leontief inverse to answer the following. 1.1 [1 Mark] Determine the value of the agriculture goods required to produce $1 dollars worth of manufacturing. 1.2 [1 Mark] Determine the increase in the size of the economy caused by a $1 increase in the final demand for manufacturing.   50 100 1.3 [2 Marks] Determine the total outputs vector x1 for final demands given by y1 =  . The 100 140 amount for each sector should be rounded to the nearest integer. ∂xi 1.4 [2 Marks] See section 7.5 pages 173 – 175 in the textbook. Observe that denote the partial ∂d j derivative of the total output from sector i with respect to final demand from sector j and that ∂x = ∂d j ∂x1 ∂d j ∂x2 ∂d j ∂x3 ∂d j ∂x4 ∂d j T denotes the vector of partial derivatives from each sector with respect to final demand from ∂x3 ∂x sector j. Determine and . ∂d2 ∂d4 Printed on September 6, 2014 Page 2 of 7 ECON864 Early Semester Quiz Question 2. (See Lecture Notes Week 3) Consider the following macroeconomic model. Commodity Market...

Words: 1340 - Pages: 6

Premium Essay

International Risks

...Political environment, which is more important especially large international business, requires high investment. More consumers sought after more goods, more service and besides last pay back time. The political systems have two types namely; democracy and totalitarianism. Economic environment, which is required in home country, host country and world economics, are supporting or objection for international business and relation to suppliers. Economic growth affects on politics social and lows, the found political system and situation politics in country, and the world has direct affects on economic and business. Social and culture are foundation of living and work for humans, they has an impact on characteristic to work and every day life. For lows, it is convention for country activities including economic activities and business. Therefore economics, political, social and lows are closely bound in terms of relationship. Technology environment refers to new knowledge factor in the world such as sciences or engineering and including strategic management because marketing competition enforce each country to invent new knowledge or know-how benefit for its own business development. Each country that has new knowledge must create new products; have low capital and high efficiency in order to keep pace with the international competitors and to respond the customers’ needs in the international market. When the country enters into international business, they must encounter...

Words: 2079 - Pages: 9

Premium Essay

Minor Las Period 1 Overview

...Fundamentals of Logistics Management International Business period 1 LAS: International Business period 1 overview 1 Fundamentals Schedule of Logistics Management Week Content number 1 World of International Business, International Business environment , theories on and types of international Trade, Project Traid and International business, cultural analyses Cultural analysis, Porter Porter, Risk analyses Risk analysis, CSA / FSA analysis CSA / FSA analysis Overflow 2 3 4 5 6 7 DO NOT FORGET Rugman H1, H2 H3, H5, H6 H5, H13, DO NOT FORGET LAS: International Business period 1 overview 2 THEORIES ON INTERNATIONAL TRADE • Absolute and competitive advantage • Heckscher and olin’s theorem • The leontief-paradox • The flying geese model LAS: International Business period 1 overview 3 THEORY OF ABSOLUTE ADVANTAGE (Adam Smith) Each nation should specialize in producing goods it has a natural or aquired advantage in and therefore can produce more efficiently LAS: International Business period 1 overview 4 THEORY OF COMPETITIVE ADVANTAGE (David Ricardo) It is advantageous for two countries to trade if the cost ratio between the two countries differ (If producing x, expressed in y, is cheaper in country 1 than in country 2, while producing y in country 2 is cheaper than in country 1 , country 1 exports x and country 2 exports y) LAS: International Business period 1 overview 5 HECKSCHER – OHLIN • Two production factors...

Words: 3034 - Pages: 13

Premium Essay

Stoplet-Samuelson Theorem

...I. Stoplet-Samuelson Theorem In order to understand the Stoplet-Samuelson Theorem we need to understand the Hekscher-Ohlin model first, as the theorem is within the context of that model. In that model there are two countries with different factor endowments, one capital abundant and the other one labor abundant. There are two products, one capital intensive and the other one labor intensive. There are two factors, one is labor and the other one is capital. In this context, the theorem shows that there is a positive relationship between the changes of the price of an output and the changes in the price of input factor used in a higher percentage (intensively) (for example: labor intensive or capital intensive) in producing the final product. And there is a negative relationship between changes in the price of an output and changes in the price of the factor not used intensively in producing that product. To explain the theorem, we can have a look at the real world and think about what happens when the U.S. ( a capital abundant and labor scarce country) takes part of the international trade. Would the high-waged labor lose because of international trade? This is the first thing I would ask myself, and it seems to be logical that labor will lose competitiveness with other labor abundant countries, and therefore labor would lose because of international trade. Samuelson and Stolper demonstrated that free trade lowers the real wage of the scarce factor and raises that of...

Words: 1051 - Pages: 5

Premium Essay

Begrepp

...700 Viktiga begrepp 2003 Ricardian model. - enkel modell - visar hur skillnader mellan länder ger upphov till handel och vinster av handel. - arbetskraft enda produktionsfaktorn - länder skiljer sig bara vad gäller arbetskraftens produktivitet i olika branscher. - tar inte hänsyn till: skalekonomier, resursskillnader i handelshinder. Även om vissa av den rikardianska modellens prognoser är klart orealistiska så har dess grundläggande prognos – att länder exporterar varor där de har en relativt hög produktivitet –bekräftats av ett antal studier. Terms of trade (ToT) - priset på export dividerat med priset på import (Pe/Pi) - ökning i ToT innebär välfärdsökning och tvärtom för en minskning Leontief paradox - motsäger Heckscher Ohlin-modellen - visade att de varor som exporterades av USA var mindre kapitalintensiva än de som importerades ❑ - Första empirska testet av H-O ❑ - Wassily Leontief med Amerikanska data för 1947 ❑ - USA mest kapitalintensiva landet i världen ❑ förväntaning: export kapitalintensiva varor, import arbetskraftsintensiva ❑ resultat: tvärtom Leontief paradox: The Heckscher-Ohlin (factor-proportions) theory states that countries export those goods whose production is intensive in factors with which they are abundantly endowed. One would expect the United States, which has a high capital/labor ratio relative to the rest of the world, to export capital-intensive...

Words: 3300 - Pages: 14