Debreu Gerard (1921-2004) American economist of French origin. Reformer of the theory of economic equilibrium Gerard Debreu Nobel Prize

Debra Gerard

Debreu Gerard (1921 - 2004)

Gérard Debré was born in Calais, France, in 1921. He received his mathematics education at the University of Paris, graduating in 1946. He was a member of the Bourbaki group that existed in France in the post-war period. The members of the group were young French mathematicians who set out to reconstruct the logical foundations of mathematical science, publishing all their work jointly, under the pseudonym of the non-existent genius Nikolai Bourbaki. Since 1948, he studied in the USA on a Rockefeller Foundation scholarship, and in 1948 he became a member of the Coles Commission at the University of Chicago (see Marshak Y.). He began collaborating with Kenneth Arrow. Together they published the landmark work “The Existence of Equilibrium in a Competitive Economy” ( Existence of an Equilibrium for a Competitive Economy , 1954), which presented a rigorous mathematical proof of the existence of general equilibrium, using topological methods hitherto unknown to economists. One can treat this and other attempts to prove the uniqueness of the general equilibrium in a system of many markets with irony. Clearly, in the real world, the equilibrium prices and quantities in all markets are determined in some way, and perhaps economists are better off studying how markets find these equilibrium quantities than studying whether a certain system of equations has a mathematical solution. However, the theory of general economic equilibrium applies in all areas modern science, and unless one has proof of the existence of general equilibrium, it is impossible to use this theory with confidence. In addition, evidence for the existence of a solution to a general equilibrium system depends on certain constraint conditions that can shed light on how equilibrium in multiple markets is actually achieved in the real world. Arrow-Debreu's article did highlight some of these aspects of real competition (see also Khan F.).

In 1955, Debreu moved with the other members of the Coles Commission to Yale University, where he remained as a visiting professor until 1960. In 1959, he published his masterpiece, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Axiomatic Analysis of Economic Equilibrium, Wiley, 1959; Yale University Press, 1971), a small book that showed highest level the mathematical sophistication that economists can achieve; using set theory and topology instead of calculus and matrices, he successfully arrived at the traditional results of competitive price theory with minimal effort and maximum accuracy; this work makes no allowance for those who prefer a non-mathematical mode of discussion, but nevertheless has significantly influenced the verbal presentation of ideas in economics textbooks.

After this, Debreu published a significant number of purely mathematical papers on problems of the so-called "existence theorem", seeking to relax the strict assumptions necessary to prove the existence of a general equilibrium under competitive conditions. In these articles he also tried to answer the question at what speed real economies reach a general equilibrium? Some of these papers are reprinted in Mathematical Economics: Twenty Papers of Gerard Debreu, ed. W. Hildebrand, Cambridge University Press, 1981.

Debreu left Yale in 1960 and is now a professor of economics and mathematics at the University of California, Berkeley. He was president of the Econometric Society from 1969 to 1971, a member of the American Association for the Advancement of Science since 1970, and president of the American Economic Association in 1990. The award that gave him the most satisfaction was probably the French Legion of Honor, which he received in 1976 g., because despite living in America for many years, it is impossible not to notice a Frenchman in Debra by his pronunciation, gastronomic habits and personal charm. But this success was offset by the Nobel Prize in Economics, which he received in 1983.

Literature

G. Debreu, Random Walk and Life Philosophy, in the book . Eminent Economists: Their Life Philosophies edited by M. Szenberg (Cambridge university Press, 1992).

Prize Lecture. Lecture to the memory of Alfred Nobel, December 8, 1983

Murray Millgate.

prominent French economist. Contributed huge contribution in the theory of general equilibrium, in the theory of welfare, the theory of utility and demand. Debreu is the 1983 Nobel laureate in economics for his "contributions to the understanding of the theory of general equilibrium and the conditions under which general equilibrium exists." Debre developed jointly with K. Arrow modern theory general equilibrium. This theory turns the theory of interest into a special case of the theory of the price of “future goods”, so that interest becomes an element in the ratio of prices of future goods relating to different points in time, and capital becomes the present embodiment of future consumer goods.

Excellent definition

Incomplete definition ↓

Gerard DEBREUX

Nobel Prize in Economics 1983

American economist Gerard Debreu was born in Calais, France. His parents were Camille and Fernard (née Desharnais) Debray. Both his grandfathers and father were the owners of a small lace production enterprise, traditional in those places.

D. studied at college in Calais and received a bachelor's degree in 1939. He was going to study mathematical sciences in Paris, but the 2nd World War ruined these plans. In 1939-1940 D. first attends preparatory school in the town of Amber, then in 1940-1941. the so-called Lycée in Grenoble, organized during wartime. Until the summer of 1941, D. remained in the unoccupied zone - the Vichy Republic, formed after the defeat of France in 1940. Then he entered the Higher Pedagogical School at the University of Paris "Ecole Normale Superiere", where he remained until the liberation of the city in 1944. After this, D. enlists in the French army, undergoes training at an officer school in Algeria and serves in Germany in the ranks of the French army until mid-summer 1945.

Upon returning to Ecole Normale in 1946, D. passed the competition and received the qualification of a mathematics teacher. At the same time, he develops an interest in economic theory, and he gets a job as a research assistant at the National Center for Scientific Research, where he works for two years. In the summer of 1948, D. studied for several weeks in Austria, at the Salzburg Seminar on Economic Research, led by V. Leontiev. For the next year and a half, as a Rockefeller Foundation fellow, he interned at the economics departments of leading US universities (Harvard, Chicago, California and Columbia), and in 1950, for four months at universities in Sweden and Norway. Upon completion of his studies, D. worked for five years as a research assistant at the Coles Commission on economic research at the University of Chicago. In 1955-1956 for six months he worked in Paris for the French Electricity Service. In 1956, the University of Paris awarded him the degree of Doctor of Science. In 1955-1961 D. was a professor at Yale University and also worked at the Coles Foundation and Stanford University until he moved to the University of California at Berkeley in 1962 as a professor of economics. In 1975 he was also appointed professor of mathematics.

D.'s scientific interests are primarily related to the development of one of the central areas of modern economic theory - the theory of general equilibrium, the foundations of which were laid by A. Smith. Smith first posed the problem of how, in a decentralized market system, decisions made independently of each other at the level of individual consumers and firms are coordinated in such a way that as a result, sellers find a market for their products and buyers realize their needs. A. Smith believed that the market price system itself, built on the laws of supply and demand, automatically ensures the necessary coordination individual plans. IN late XIX V. French mathematician L. Walras formulated this idea in mathematical terms in the form of a system of equations. He is credited with creating the theory of general equilibrium.

D. first became acquainted with the problem of general equilibrium while studying at Ecole Normale through the works of M. Allais, who gave a new formulation of this theory in the book “In Search of Economic Discipline” (“A la Recherche dune Discipline Economique*, 1943”). In 1952, while working for the Coles Commission, D. published his first article on this topic.Two years later, in the journal Econometrica, he, together with K. Arrow, came up with a classic article, “The Existence of Equilibrium for a Competitive Economy.” " ("Existence of an Equilibrium for a Competitive Economy"), where they proposed a mathematical model market economy, in which various producers plan the marketing of their products and services, as well as the demand for factors of production, in such a way as to maximize profits. The model contained, on the one hand, the supply of goods and the demand for production factors, and on the other, all prices. Having made additional assumptions regarding consumer behavior, D. and K. Arrow obtained demand functions, i.e. the relationship between prices, on the one hand, and the quantity of goods supplied and demanded, on the other. In this model they were able to prove the existence of equilibrium prices.

These ideas received further development in published in the late 50s. D.'s book "The Theory of Value: An Axiomatic Analysis of Economic Equilibrium". D. extended the "proof of existence" of equilibrium to more general cases, considering many solutions for which equilibrium is achievable. The Theory of Value, which contains D.'s mathematical analysis of general equilibrium, is today considered a classic economic work of the 20th century. This book, which, like many of D.'s other works, is distinguished by its universality, unsurpassed elegance of presentation and mathematical rigor, reflects his contribution to various areas economic theory, such as welfare theory, utility theory, derivative demand functions.

D.'s theory allows for many far-reaching interpretations and areas of application. His concept of “goods,” for example, is formulated so broadly that it can be used in the analysis of purely static equilibrium, in the study of the spatial distribution of production and consumption activities, and in other areas. Within the framework of the same model, the theory of general equilibrium of economics includes the theory of allocation, the theory of capital, and the theory of economic behavior under conditions of uncertainty. D. used mathematical tools to study such a purely practical problem as, for example, a decrease in the level of well-being as a result of a certain taxation policy. He also considered problems of economic uncertainty, including the problem of future commodity markets, and also examined the conditions under which prices in a system tend to their equilibrium values. The axiomatic method used by D. and his colleagues has become a standard tool economic analysis. In the 50s this method was used in the analysis of general equilibrium theory, utility theory and production theory. In the 80s these same techniques were adopted in macroeconomic research, when studying industrial organization, public finance and in many other areas.

D.'s largest work, published in the 80s, is a collection of articles "Mathematical Economics" ("Mathematical Economics", 1983), devoted to the theory of equilibrium. The 20 articles-chapters of the collection summarize the main economic developments D.. It included both newly written chapters and articles previously published in economic journals: “New Concepts and Techniques for Equilibrium Analysis”, 1962), “Economics with Equilibrium conditions of restrictions" ("Economies with a Finit Set of Equilibria", 1970), "Four Aspects of the Mathematical Theory of Economic Equilibrium", 1974).

D.'s works are distinguished by a high degree of abstraction of presentation and complex mathematical apparatus, which makes them difficult to understand and use even among economists. Many of D.'s assumptions about how the market system functions and what determines the behavior and actions of people may seem divorced from real life, and his results are inapplicable to economic reality. Nevertheless, the works of D. and his followers made a huge contribution to the progress of economic science.

D. was awarded the Alfred Nobel Prize in Economics for 1983 “for his contribution to the development of the theory of general equilibrium and the conditions under which it is carried out in a certain abstract economy.” According to a member of the Royal Swedish Academy of Sciences, K. G. Mehler, in his works on the theory of general equilibrium, D. “not only tells us about the price mechanism, but also introduces new analytical methods, new tools of analysis into the arsenal of economists.” D.'s insightful analysis of models of abstract economies gave economists a general theory that can be applied to a wide variety of situations.

In 1945, D. married Françoise Bled; they have two daughters, Chantal and Florence. In 1975, D. became a US citizen. Unlike many of his colleagues, D. constantly rejected offers to work in industry or government. He continues to teach at Berkeley. Gifted students and economists from all over the world come there to conduct joint research, and his popular lectures are considered outstanding for their mathematical rigor, virtual absence of verbal explanations, and the same elegance of presentation that distinguishes all his scientific works. Every year D. conducts dozens of seminars in a wide variety of audiences - for economists, mathematicians and interested people in other professions. He is truly tireless in his service to mathematical economics.

D. has been a holder of the French Legion of Honor since 1976. He was a Guggenheim Fellow at the Center for Operations Research and Econometrics at the Université catholique de Louvain (Belgium, 1968-1969 and 1971-1972); Erskine Foundation Fellow at Canterbury Christchurch University ( New Zealand, summer 1969); Foreign Fellow of Churchill College, Cambridge (Spring 1972). He is a member of the American Academy of Arts and Sciences, the American National Academy of Sciences, the American Economic Association, and the American Association for the Advancement of Science. In 1969-1971 he was vice-president and then president of the Econometric Society. D. was awarded honorary degrees by Bonn, Lausanne, Northwestern (USA) universities and the Toulouse University of Social Sciences.

Major works: Market Equilibrium//Proceedings of the National Academy of Sciences. 1956. N 42, pp. 876-878; Theory of Value: An Axiomatic Analysis of Economic Equilibrium. New York, 1959; Professor Debreus "Market Equilibrium" Theorem: An Expository Note. West Lafayette, 1973; Mathematical Economics: Twenty Papers of Gerard Debreu. Cambridge, 1983.

About the winner: New York Times. 1983, October 18; Time. N 122. 1983, October 31, p. 93; Samuelson P. The 1983 Nobel Prize in Economics//Science. N 222. 1983, December 2, pp. 987-989; Varian H. R. Gerard Debreus Contributions to Economics//Scandinavian Journal of Economics. 1984. Vol. 86. N 1, pp. 4-16; Hildenbrand W., Mas-Colell A. (eds.). Contributions to Mathematical Economics in Honor of Gerord Debreu. 1986.

Literature in Russian: Marketing. 1993. N 1. ss. 101-105.

Excellent definition

Incomplete definition ↓

Nobel Prize in Economics 1983

American economist born in Calais, France. His parents were Camille and Fernard (née Desharnais) Debreu. Both his grandfathers and father were the owners of a small lace production enterprise, traditional in those places.

D. studied at college in Calais and received a bachelor's degree in 1939. He was going to study mathematical sciences in Paris, but the outbreak of World War II disrupted these plans. In 1939-1940 D. first attends preparatory school in the town of Amber, then in 1940-1941. the so-called Lycée in Grenoble, organized during wartime. Until the summer of 1941, D. remained in the unoccupied zone - the Vichy Republic, formed after the defeat of France in 1940. Then he entered the Higher Pedagogical School at the University of Paris "Ecole Normale Superiere", where he remained until the liberation of the city in 1944. After this, D. enlists in the French army, undergoes training at an officer school in Algeria and serves in Germany in the ranks of the French army until mid-summer 1945.

Upon returning to Ecole Normale in 1946, D. passed the competition and received the qualification of a mathematics teacher. At the same time, he developed an interest in economic theory, and he got a job as a research assistant at the National Center for Scientific Research, where he worked for two years. In the summer of 1948, D. studied for several weeks in Austria, at the Salzburg Seminar on Economic Research, led by V. Leontiev. For the next year and a half, as a Rockefeller Foundation fellow, he interned at the economics departments of leading US universities (Harvard, Chicago, California and Columbia), and in 1950, for four months at universities in Sweden and Norway. Upon completion of his studies, D. worked for five years as a research assistant at the Coles Commission for Economic Research at the University of Chicago. In 1955-1956 for six months he worked in Paris for the French Electricity Service. In 1956, the University of Paris awarded him the degree of Doctor of Science. In 1955-1961 D. was a professor at Yale University and also worked at the Coles Foundation and Stanford University until he moved to the University of California at Berkeley in 1962 as a professor of economics. In 1975 he was also appointed professor of mathematics.

D.'s scientific interests are primarily related to the development of one of the central areas of modern economic theory - the theory of general equilibrium, the foundations of which were laid by A. Smith. Smith first posed the problem of how, in a decentralized market system, decisions made independently of each other at the level of individual consumers and firms are coordinated in such a way that as a result, sellers find a market for their products and buyers realize their needs. A. Smith believed that the market price system itself, built on the laws of supply and demand, automatically ensures the necessary coordination of individual plans. At the end of the 19th century. French mathematician L. Walras formulated this idea in mathematical terms in the form of a system of equations. He is credited with creating the theory of general equilibrium.

D. first became acquainted with the problem of general equilibrium while studying at Ecole Normale through the works of M. Allais, who gave a new formulation of this theory in the book “In Search of Economic Discipline” (“A la Recherche dune Discipline Economique*, 1943”). In 1952, while working for the Coles Commission, D. published his first article on this topic.Two years later, in the journal Econometrica, he, together with K. Arrow, came up with a classic article, “The Existence of Equilibrium for a Competitive Economy.” " ("Existence of an Equilibrium for a Competitive Economy"), where they proposed a mathematical model of a market economy in which various producers plan the distribution of their products and services, as well as the demand for factors of production, in such a way as to maximize profits. The model contained, with on the one hand, the supply of goods and the demand for production factors, on the other - all prices. Having made additional assumptions regarding consumer behavior, D. and K. Arrow obtained demand functions, i.e. the relationship between prices, on the one hand, and the quantity of goods supplied and demanded, on the other. In this model they were able to prove the existence of equilibrium prices.

These ideas were further developed in the book published in the late 50s. D.'s book "The Theory of Value: An Axiomatic Analysis of Economic Equilibrium". D. extended the "proofs of existence" of equilibrium to more general cases, considering many solutions for which equilibrium is achievable. The Theory of Value, which contains D.'s mathematical analysis of general equilibrium, is today considered a classic economic work of the 20th century. This book, which, like many of D.'s other works, is distinguished by its universality, unsurpassed elegance of presentation and mathematical rigor, reflects his contribution to various areas of economic theory, such as welfare theory, utility theory, derived demand functions.

D.'s theory allows for many far-reaching interpretations and areas of application. His concept of “goods,” for example, is formulated so broadly that it can be used in the analysis of purely static equilibrium, in the study of the spatial distribution of production and consumption activities, and in other areas. Within the framework of the same model, the theory of general equilibrium of economics includes the theory of allocation, the theory of capital, and the theory of economic behavior under conditions of uncertainty. D. used mathematical tools to study such a purely practical problem as, for example, a decrease in the level of well-being as a result of a certain taxation policy. He also considered problems of economic uncertainty, including the problem of future commodity markets, and also examined the conditions under which prices in a system tend to their equilibrium values. The axiomatic method used by D. and his colleagues has become a standard tool of economic analysis. In the 50s this method was used in the analysis of general equilibrium theory, utility theory and production theory. In the 80s these same techniques have been adopted in macroeconomic research, in the study of industrial organization, public finance, and in many other areas.

D.'s largest work, published in the 80s, is a collection of articles "Mathematical Economics" ("Mathematical Economics", 1983), devoted to the theory of equilibrium. The 20 articles-chapters of the collection summarize the main economic developments of D. It includes both newly written chapters and articles previously published in economic journals: “New Concepts and Techniques for Equilibrium Analysis ", 1962), "Economies with a Finit Set of Equilibria", 1970), "Four Aspects of the Mathematical Theory of Economic Equilibrium", 1974) .

D. was awarded the Alfred Nobel Prize in Economics for 1983 “for his contribution to the development of the theory of general equilibrium and the conditions under which it is carried out in a certain abstract economy.” According to a member of the Royal Swedish Academy of Sciences, K. G. Möhler, in his works on the theory of general equilibrium, D. “not only tells us about the price mechanism, but also introduces new analytical methods, new tools of analysis into the arsenal of economists.” D.'s insightful analysis of models of abstract economies gave economists a general theory that can be applied to a wide variety of situations.

D. has been a holder of the French Legion of Honor since 1976. He was a Guggenheim Fellow at the Center for Operations Research and Econometrics at the Université catholique de Louvain (Belgium, 1968-1969 and 1971-1972); Erskine Foundation Fellow at Canterbury Christchurch University (New Zealand, summer 1969); Foreign Fellow of Churchill College, Cambridge (Spring 1972). He is a member of the American Academy of Arts and Sciences, the American National Academy of Sciences, the American Economic Association, and the American Association for the Advancement of Science. In 1969-1971 he was vice-president and then president of the Econometric Society. D. was awarded honorary degrees by Bonn, Lausanne, Northwestern (USA) universities and the Toulouse University of Social Sciences.

Literature in Russian: Marketing. 1993. N 1. ss. 101-105.

View value Gerard Debreu in other dictionaries

Proudhon Pierre Gerard (1809-1865)— - French philosopher, sociologist, economist, theory of anarchism. The basis of P.’s teaching is the assertion that what is acquired without labor (rent, profit), for the protection of which........ exists.
Political dictionary

De Toni-Debre-Fanconi Syndrome- (G. de Toni, born in 1895, Italian pediatrician; A. R. Debre, born in 1882, French pediatrician; G. Fanconi, born in 1892, Swiss pediatrician; synonym: glucoaminophosphate diabetes, Debre de Toni-Fanconi syndrome, Fanconi-Debreu-De........
Large medical dictionary

Debra- de Toni-Fanconi syndrome (A. R. Debre, born in 1882, French pediatrician; G. de Toni, born in 1895, Italian pediatrician; G. Fanconi, born in 1892, Swiss. pediatrician) - see De Toni-Fanconi syndrome.
Large medical dictionary

Debre-fibiger Syndrome- (A. R. Debre, born in 1882, French pediatrician: J. A. G. Fibiger, 1867-1928, Danish pathologist) see Adrenogenital syndrome with loss of salts.
Large medical dictionary

Debra— (Debray) Henri Jules (1827-88) - French inorganic chemist. Together with A. Saint-Clair Deville, he developed methods for purifying platinum (1855-59). In 1872 they also received an alloy of iridium and platinum........

Gerard— (Gerhardt) Charles Frederic (1816-56) - French chemist. He distinguished (1842) the concepts of molecule, equivalent and atom. Proposed (1851) a generalized theory of types, according to which all compounds........
Large encyclopedic dictionary

Fanconi Debre de Toni Syndrome- (G. Fanconi, born in 1892, Swiss pediatrician; A. R. Debre, born in 1882, French pediatrician; G. de Toni, born in 1895, Italian pediatrician) see De Tony-Debreu-Fanconi syndrome.
Large medical dictionary

Debra- (Débré), Michel (b. 15.I.1912) - French. state and political activist A lawyer by training. In 1938 he was an employee of the office of the Min. finance P. Reynaud. At the beginning of the 2nd World War he was mobilized........
Soviet historical encyclopedia

Jaco, Gerard— (Jacquot), bronze master in St. Petersburg. under Al I. (1809 he worked for decoration. Kazan.

Kugelchen, Gerard- portrait painter; favorite painter of Alexander I. Engraved his portrait with etching. See my Detailed Dictionary of Portraits. No.
Large biographical encyclopedia

De Toni - Debra - Fanconi Syndrome-I
De Toni - Debre - Fanconi syndrome (G. de Toni, Italian pediatrician, born in 1895; A.R. Debrt, French pediatrician, born in 1882; G. Fanconi, Swiss pediatrician, born........
Medical encyclopedia

Debre - De Toni - Fanconi Syndrome— (A.R. Debré, born 1882, French pediatrician; G. de Toni, born 1895, Italian pediatrician; G. Fanconi, born 1892, Swiss pediatrician)

Medical encyclopedia

Debre - Fibiger Syndrome— (A.R. Debré, b. 1882, French pediatrician; J. A.G. Fibiger, 1867-1928, Danish pathologist)
see Adrenogenital syndrome with loss of salts.
Medical encyclopedia

Fanconi - Debra - De Toni Syndrome— (G. Fanconi, born 1892, Swiss pediatrician; A.R. Debre, born 1882, French pediatrician; G. de Toni, born 1895, Italian pediatrician)
see De Toni - Debra - Fanconi syndrome.
Medical encyclopedia

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Posted on http://www.allbest.ru

Ministry of Education and Science of the Russian Federation

Federal State Budgetary Educational Institution

higher professional education

"St. Petersburg State

the University of Economics"

Department of World Economy

and international economic relations

by discipline

"Theories of Nobel laureates in economics"

"Gerard Debreu. Equilibrium and the conditions under which it exists"

Completed:

student gr. No. 1311

R. D. Khomkov

Scientific director

Candidate of Economic Sciences, Associate Professor O. A. Kuzakova

Saint Petersburg

Introduction

Economic equilibrium is the point at which the quantity demanded and the quantity supplied are equal.

In economics, economic equilibrium characterizes the state in which economic forces are balanced and, in the absence of external influences, the (balanced) values of economic variables will not change.

The relevance of the research topic lies in the fact that equilibrium in the economy is one of the main mechanisms for the existence of a successful economic situation, so it is necessary to understand the factors and conditions of its operation.

The purpose of this work is to study the influence of the work of Gerard Debreu on the development of the theory of equilibrium and the conditions of its existence.

To achieve this goal, it is necessary to complete a number of tasks:

Study the activities of Gerard Debreu and the factors that influenced his work;

Consider the general equilibrium model;

Analyze the shortcomings and suggest ways to eliminate them;

Consider the features of equilibrium in Russia.

The main sources of information were recorded lectures by Debreu, as well as textbooks by Allais and Leontiev, who mentored the young Gerard. The equilibrium structure in Russian economy, and also discusses the shortcomings and suggests ways to eliminate them.

Chapter 1. Life and work

1.1 Curriculum Vitae

Gerard Debreu is an American economist and Nobel Prize winner in 1983. Born in the city of Calais in France. In 1939? defended his bachelor's degree in mathematics. After the war he returned to work at his own university as a teacher. At the same time, he develops an interest in economic theory, which subsequently captivates him completely.

Fig.1 Activities of J. Debreu

1.2 Activities and mentors

For the first time, Debreu became acquainted with the problem of joint equilibrium while studying at Ecole Normale through the works of M. Allais, who gave a new formulation to this issue in his work “In Search of Economic Discipline” (“A la Recherche d"une Discipline Economique” , 1943). In 1952, while working on the Coles Commission, Debreu published his first article on this topic. Two years later, in the journal Econometrica, he, together with K. Arrow, published the now traditional article “Equilibrium in competitive economy" ("Existence of an Equilibrium for a Competitive Economy"), where they proposed a mathematical model of a market economy in which all producers strive to maximize their profits, while planning their sales and demand for factors of production. The model contained, on the one hand , supply of goods and demand for production factors, on the other - all prices. Having made additional assumptions regarding consumer behavior, Debreu obtained demand functions, i.e. the relationship between prices, on the one hand, and the quantity of goods supplied and demanded, on the other. In this model, he was able to prove the existence of equilibrium prices.

These ideas were further developed in the 50s. in The Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Debreu was able to formalize the theory from particular cases to general ones, while exploring various situations, at which equilibrium is achievable. The theory of value, in which Debreu reached the peak of his analysis of mathematical equilibrium, is now considered one of the most authoritative works in this field of the 20th century. Like most of Gerard Debreu's books, it is distinguished by mathematical rigor and rigidity of writing, which causes difficulties in mastering for an untrained user.

Despite the fact that Debreu's theory is abstract and quite difficult to apply in practice, it allows for many interpretations, and at the same time, areas of application. His concept of “goods,” for example, is formulated so broadly that it can be applied in the analysis of purely static equilibrium, as well as in the study of the distribution of production and consumption work, as well as in other areas.

Within the framework of one and the same model, general equilibrium theory includes several concepts.

Rice. 2 Concepts of general equilibrium theory

Debreu used various mathematical research tools to study various practical problems, such as the decline in welfare resulting from a particular taxation system. It is worth noting that this is not the first and far from the last Nobel laureate who was critical of taxes, considering them destructive.

Basically, his work is based on the study of financial uncertainty under which the market operates, as well as the method of its independent settlement and stabilization. The axiomatic method used by Debreu and his colleagues has become a classic tool of economic analysis. In the 50s this method was used in the analysis of general equilibrium theory, utility theory and production theory. In the 80s these same techniques have been applied to macroeconomics, industrial organization, public finance, and a variety of other fields.

Debreu's largest and at the same time culminating work was the collection “Mathematical Economics” (1983), published in the 80s and dedicated to the theory of equilibrium. The main economic developments of Gerard were summarized in 20 chapter articles. It included completely new articles and studies, as well as old and modified ones: “New Concepts and Techniques for Equilibrium Analysis” (1962), “Economics with Equilibriums under Constraints” (“Economies with a Finit Set of Equilibria", 1970), "Four Aspects of the Mathematical Theory of Economic Equilibrium", 1974.

Chapter. 2 General equilibrium theory

2.1 From Walras to Debreu

While still a student, Gerard Debreu became interested in the works of the famous economist Walras. It was from Walras's study of equilibrium that Debreu began to build. It is worth noting that the theory of equilibrium described by Walras has a number of shortcomings. Let's analyze each theory in detail.

Walras's model is based on the criterion of absolute competition, when no single buyer (client) or single trader has every chance to specifically influence market prices. The purpose of this model is to derive general laws of operation of the price system in the presence of a large number of markets. Continuous economic equilibrium, according to Walras’s definition, “is a situation in which the effective supply and effective demand for productive services are equalized in the services market; the effective supply and effective demand for products are equalized in the commodity market and, in the end, the purchasing value is equal to the cost of production manifested in productive services.” An analysis of supply and demand is carried out in two product markets - productive services and consumer goods. In the main market, the sellers are manufacturers offering their services to businessmen, and in the other market they become customers of consumer goods. As a result of free competition, prices are set, and the economy reaches an equilibrium position when the demand for consumer products and the reasons for making are equal to their proposal. Walras believed that it was possible to establish a system of supply and demand equations in every market. In this case, the number of equations is equal to the number of variables in the system of equations, which means that there is a single conclusion - the set of goods “C”, at which equilibrium develops. Economic sense the last equality is that the cost of all purchased consumer goods equal to the cost of all factors of production sold. Based on the above, Walras's law is formulated: the total amount of demand for all goods and services must be equal to the total amount of their supply under any price system. However, this model does not take into account lending and savings, but securities are considered one of the types of goods.

Arrow-Debreu general equilibrium model. It is assumed that n products (outputs) are created in the economy and m reasons for production are used. There is 100% competition and prices are set by the market. Every company is a customer in the market for factors of production and a trader in the market for products and services, seeking to maximize revenue.

The Arrow-Debreu general equilibrium model illustrates a fundamental economic fact: given random, non-equilibrium values, the decisions made by different participants economic actions, will be inconsistent, i.e., economically ineffective. This means that certain types of products will be produced in excess, while demand for others will exceed supply, prices for certain products will rise or fall for some time. This will not happen if the economic system is in a state of equilibrium.

Equilibrium in the Arrow-Debreu model is a set of such prices of products and reasons for production, production volumes of products and acquired reasons for production in the criteria for fulfilling economical restrictions (subject to technological restrictions), such that the joint demand for any type of product (reason for production) is equal to their total prescription.

The Arrow-Debreu equilibrium has many optimal properties, in particular it is Pareto optimal. This means that any attempt to improve the fortunes (increase profits or utility) of any participant economic process compared to the equilibrium one, even if existing restrictions are ignored, inevitably leads to a deterioration in the condition of some other participant. That is, Pareto-optimal (Pareto optimal) is an equilibrium when, with constant locality of resources and a constant level of income, it is impossible to increase the well-being of some economic entities without worsening the well-being of others.

I can overcome the disadvantages of the Arrow-Debreu model (the existence of a solution and its uniqueness) with the help of more modern approaches to general equilibrium theory, in particular, using the input-output model and mathematical programming methods.

2.2 Arrow-Debreu model

Manufacturers

In the economy there are firms producing types of products. The technological set of the th company is denoted by. They are assumed to be closed and limited and include a zero vector, that is, the probability of a firm’s inactivity in the market. The Minkowski sum (the sum of vectors of activity/inactivity of firms) of technological sets of firms represents the general economic technological set, which is nothing more than a convex set.

This is the price vector. Then - the profit of the th firm with net output. Firms strive to maximize their profits. The dependence of the solution to this problem on a given price vector is a function of supply. So the function aggregate supply equal. Sentence functions are homogeneous equations of degree zero.

Consumers

But the economy cannot exist without consumers, so there are also individuals (consumers) with an initial supply of goods and utility functions, where is a -dimensional vector of consumption, which is a subset. Debreu assumed that all utility functions have all partial derivatives and for any deterministic set of vectors will be such that the set is strictly convex.

In this case, the consumer’s income consists of the cost of his initial reserves and income from participation in companies

where is the fixed share of participation (in the income) of the th consumer in the th firm.

Each consumer solves the problem of maximizing utility under a loose budget constraint. Solutions to this problem, depending on the price vector, turn out to be functions of individual consumer demand, and their sum is a function aggregate demand. Demand functions are homogeneous equations of degree zero.

Excess demand function

The aggregate excess demand function is defined as

where is the total initial inventories of consumers.

According to Walras’s law (the sum of excess demand in all markets/excess supply in all markets must be equal to zero), with a non-negative price vector the equality must be satisfied:

The model assumes that all goods markets exist and utility functions and technological sets depend on them. Also, all markets are connected, that is, goods can be freely exchanged. It is assumed that everyone economic entity“small enough”, that is, subjects cannot form the structure of prices and goods (for each of them the price vector is given exogenously, by external reasons) - a condition for perfect competition in markets. Each subject has complete information regarding the structure of price formation and the characteristics of goods. In addition, it is assumed that there are no transaction costs of externalities, that is, there is no impact on third parties not mediated by the market.

In Arrow-Debreu economics, a situation is called equilibrium if, for an equilibrium price vector, individual demand and supply for consumers and firms, respectively, are solutions to the corresponding optimization problems at equilibrium prices, Walras’ law is satisfied at equilibrium prices, and there is no shortage of goods in the economy, that is

The Arrow-Debreu theorem is that under the described assumptions in this model there is always an economic (static) equilibrium (a non-negative vector of prices that satisfies the equilibrium conditions). The proof of the theorem is based on Kakutani's theorem on the fixed point of a multivalued (point-set) mapping.

It is worth noting that there is a so-called exchange economy, which is a simplified Arrow-Debreu model, but without taking into account product manufacturers. Initially, it was she who was considered by Gerard as an object of study, or rather, it was a prerequisite for the development of the theory of general equilibrium. The exchange economy was described in detail in the works of Walras, and the law of equilibrium in the exchange economy was also reflected in it.

Chapter. 3 Debreu model and the real economic situation

3.1 Disadvantages of the model

jungle equilibrium nobel economist

One of the main problems in Gerard's theories, in my opinion, is excessive abstraction from the real economic situation. Firstly, the consumer, like the manufacturer, simply physically cannot have all the available information about the market. Secondly, even the same information can be interpreted in different ways by both firms and private users of this information.

But what confuses me most about the model is the non-participation of the state in the economy, or rather the complete absence of state intervention in activities economic markets. As I mentioned above, Debreu spoke on the topic of destructiveness tax policy state, criticized the structure of the state, etc. However, one cannot deny or ignore the fact that this moment(and at the time of work on the theory of equilibrium, that is, in the post-war period, even more so) the economy is clearly integrated into the state and at this moment it is virtually impossible to imagine the work of the economy, markets and its subjects without state intervention.

It is worth noting that Debreu clearly distinguished between macroeconomics and microeconomics and, it seems to me, put microeconomics, as can be seen from his Nobel lecture, as well as from his work: all microeconomic indicators were taken into account, down to age and the amount of savings (Added Arrow). Having become acquainted with the activities of Edward Prescott as another Nobel laureate, I realized that considering economics within the framework of global theories (for example, as the theory of general equilibrium), based on only one of the parts general economy- means not allowing your own ideas to come true. Time has shown that Debreu's theories have found partial application in practice, albeit in many cases. Is it worth mentioning that the main goal of Gerard Debreu was to generalize and formalize equilibrium and the conditions for its existence in economics.

In other words, ideal equilibrium cannot exist.

Fig. 3 Types of balance

3.2 Leontief’s theory as a method for eliminating the shortcomings of Debreu’s theory

In order to fully reveal the topic of the abstract, one cannot help but consider ways to solve the shortcomings of the Debreu model.

It is not surprising that Gerard became interested in equilibrium - many factors contributed to this: the difficult years of the country's economic recovery after the war, the widespread criticism of Smith and Keynes. And also acquaintance and work under the leadership of Leontiev, who, in my opinion, resolved the shortcomings of the Debreu general equilibrium model exactly 10 years before the presentation of the Gerard Prize for his work.

The input-output theory has been most widely used as a tool for solving problems of planning, forecasting and managing the state economy.

A financial project or monitoring can be represented as a numerical conclusion of a certain system of joint equilibrium equations. The output of products and services in each individual sector and branch of the economy is considered unknown. A large number of technologies that are similar to each other allow them to be created at different cost levels. Everything is drawn up in the form of a matrix of costs and output.

A system of joint equilibrium equations using input-output tables allows us to determine what output and costs should be in each sector. In order to guarantee the creation of the intended final product of a given size and structure, while following Walras' law, it is necessary to qualitatively examine disturbances and deviations in the equilibrium of the economy, and make a choice between various options optimal and competent development of events.

3.3 Features of equilibrium and disequilibrium in the Russian economy

Russia, like the USSR, has some specific features regarding balance. For example, the USSR was characterized by a constant excess of demand over supply. Prices were set “from above” and increased inconsistently, but in conditions of constant increase in demand, prices systematically found themselves at a level lower than the one that could balance supply and demand. As a result, at the moment it is no secret that there was a chronic shortage of the vast majority of goods. The Soviet-style economy was quite rightly called an “economy of scarcity.”

Among the features of the formation of the Russian balance, the following should be highlighted:

Rice. 4 Features of the Russian balance

Conclusion

The purpose of the abstract was to study the influence scientific work Gerard Debreu in the development of the theory of general equilibrium and its shortcomings.

To achieve this goal, a number of tasks were completed:

The activities of Gerard Debreu and the factors that influenced his work were studied;

A general equilibrium model is considered;

The shortcomings are analyzed and ways to eliminate them are proposed;

The features of equilibrium in Russia are considered.

Taking into account the above, we can conclude that Gerard Debreu had a strong influence on the development of the theory of general equilibrium and drew attention to the factors of its existence:

Equilibrium is a dynamic, variable state and a necessary but insufficient condition for optimality;

A particular equilibrium ensures the optimal distribution of goods and services in a certain period of time;

Competitive equilibrium is Pareto optimal.

The theory of general equilibrium has had a great influence on the development of understanding of the workings of pricing and markets. With the help of Debreu's model, it became clear that optimal equilibrium is achieved at a certain point in time and cannot be long-term. Gerard showed that changes in supply strictly affect the structure of demand and vice versa. It is difficult to underestimate the contribution of Gerard Debreu to the development of economic science.

Bibliography

Larionov I.K., Aliev A.A. Economic theory: tutorial//. - M., Dashkov and K, 2012 - 408 p.

Nikolaeva I.P. Economic theory: textbook //I.P. Nikolaeva -M., Dashkov and K, 2013 - 328 p.

Rogova N.V., Ulyanova O.Yu. Course of economic theory: conceptual approach: textbook//. - Volgograd, VolgGASU, 2011. 147 p.

V. P. Busygin, E. V. Zhelobodko, A. A. Tsyplakov. Microeconomics - third level: textbook//. - Novosibirsk, 2003, 694 p.

V. Leontyev. Intersectoral economics // Preface. and scientific ed. A.G. Grandberg. M.: Economics, 1997 (series: Economists - Nobel Prize laureates);

K. Arrow Information and economic behavior // Questions of Economics. 1995. No. 5. 106 pp.;

Alle M. Economics as a science. M.. 1955;

V.E. Manevich. RUSSIAN ECONOMY AND KEYNESIAN THEORY: article//. - 2006, 14 p.

ECONOMIC THEORY IN THE MATHEMATICAL MODE by Gerard Debreu[ Electronic resource]:Nobel Prize.- Access mode: http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1983/debreu-lecture.pdf Access date: 01/17/2015

Gerard Debreu. Lectures of Econ theory. [Electronic resource]: YouTube.com.- Access mode: https://www.youtube.com/watch?v=FfztV7HQf_8 Access date: 02/19/2015

Arrow-Debreu model. Electronic resource. Wikipedia.- Access mode: https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C_%D0%AD%D1%80 %D1%80%D0%BE%D1%83_%E2%80%94_%D0%94%D0%B5%D0%B1%D1%80%D1%91 Date of access: 02/17/2015

THEORY OF VALUE. An Axiomatic Analysis of Economic Equilibrium. Electronic resource. Cowles Foundation for Research in Economics.- Access mode: http://cowles.econ.yale.edu/P/cm/m17/ Access date: 02/17/2015

Posted on Allbest.ru

Debreu Gerard (1921-2004) American economist of French origin. Reformer of the theory of economic equilibrium Gerard Debreu Nobel Prize

Gerard DEBREUX

View value Gerard Debreu in other dictionaries

Send your good work in the knowledge base is simple. Use the form below

Similar documents

Best of the day