LECTURE No. 12. The theory of general economic equilibrium

1. General equilibrium model including production; the problem of the existence of a solution and the process of "tatonnement"

The general equilibrium model of Leon Walras (1834-1910) includes production at a certain level of factors, which is specified in advance. Suppose that in the economy there are consumers who are independent of each other, and producers who own factors of production for sale to independent firms. Since consumers' budgets are always limited, they have to maximize what they find useful, which determines everyone's demand. This demand depends on prices and consumer income.

If supply and demand are expressed in the same conventional units, then the aggregate supply will be equal to the aggregate demand. Such a formulation is essentially the law of Jean-Baptiste Say, expressed in mathematical language. In addition, the law so formulated does not make it possible to understand what is more important: supply or demand. But Jean-Baptiste Say, in his work on this topic, clearly explained that supply dominates demand.

Leon Walras did not try to derive rigorous mathematical conditions under which equilibrium exists. He just demonstrated a possible mechanism of movement towards equilibrium. This process has been called "tatonnement".

According to Walras, there are two types of such a process.

1. To begin with, it is possible to make an exchange incorrectly, that is, when some participants in the transaction won, while others lost this time. Since the principle of individual maximization has been violated, it is possible to cancel the transaction and accordingly offer new prices for the conclusion of a new transaction. In this way, balance can be reached through a long process of trial and error.

2. To find the balance, this option is more suitable than the previous one. Someone alone controls this process. First, he collects applications with offers and demand. Then, based on these orders, it adjusts prices, repeating the first action in theory. After the equilibrium prices are deduced, a deal is usually made.

You can take a more complex model (production model) as a basis. Suppose there is an increase in demand for a particular product. There is a shortage of this product. Then the manufacturer will be able to afford to raise the price of this product, therefore, to get more profit at the same cost. The emergence of a larger increase in profits allows the manufacturer to expand its production. More of this commodity appears on the market, and it ceases to be a shortage. Then the production rate automatically decreases. In the end, the equilibrium in the market will be restored. If capital accumulation is also included in this model, then the interest rate will also change.

2. The theory of general equilibrium in the XNUMXth century: the contribution of A. Wald, J. von Neumann, J. Hicks, C. Arrow and J. Debre

General equilibrium theory in the XNUMXth century. developed in two directions.

The first of these areas can, perhaps, be attributed to microeconomics. Such scientists as A. Wald, J. von Neumann, J. Hicks, K. Arrow and J. Debre are associated with this direction. The largest contributions have been made since the late 1920s. until the early 1960s.

The second direction is more like macroeconomic. This direction was initiated when there was a general interest in such problems as unemployment and money. The analysis of these problems is closely connected with the methodological problem of the representatives of the second direction. For them, the main question is how macro- and micro-approaches relate to each other. O. Lang, D. Patinkin, R. Klauer, R. Barrow, G. Grossman belong to this direction. You can also name John Maynard Keynes, although he refuted this approach, but after he identified problems for future researchers in this area.

No matter how different these directions may seem, they have many of the same interests and goals. These interests relate to issues such as expectation, uncertainty, limited information, etc.

In 1936, the most famous of A. Wald's series of papers on rigorous general equilibrium analysis was published. He was the first to be able to give a clear and rigorous definition of competitive equilibrium. Wald was also the first to prove that in the Leon Walrasian system, under certain conditions, there is a positive price vector, in which demand equals supply is established due to the actions of buyers and producers, each of which tries to satisfy its needs as much as possible.

Wald also investigated the problem of the uniqueness of the solution, therefore, he proposed using the insufficiently strong axiom of revealing preferences for market demand functions, as well as the conditions for gross substitution of all goods. These conditions later became the main problem of his further research.

In 1937, J. von Neumann presented to the public the proof of the existence of an equilibrium trajectory for a proportionally expanding economy. In this work, he used the concept of equilibrium, which can be applied to a constantly changing economy. He is also the first to use the tools of game theory in proofs. According to him, a model of this type, like that of Leon Walras, can be interpreted as a game. Therefore, the solutions of the game are found equilibria.

J. von Neumann proved that the model of an expanding economy can be imagined if we assume that there are two players whose sum of money is zero. The first of them tries to maximize its payoff (the growth rate of the economy under the condition of limited supply). The second tries to minimize his loss (percentage subject to profit limitation). He also substantiated that under certain certain conditions there is a solution to this game, which is characterized by the equality of the values ​​of these functions. The equality of the growth rate and the percentage is the equilibrium point.

One of the most important roles in improving the methods of proving the existence of an equilibrium is assigned to Kakutani's theorem on a point that never moves.

In the mid-1950s, based on this theorem and new research in the field of linear programming, several scientists, including Nobel laureates K. Arrow (1972) and J. Debre (1983), created their own versions of the existence theorem for a unique solution for Walrasian models, and much simpler than Walda proposed in his time. Now the Arrow-Debré model (1954) is considered to be classical in the theory of general equilibrium. This model is a modified version of the Walrasian model. These scientists also proved that there is still a competitive equilibrium. In their opinion, this balance should be maintained on the following foundations:

1) the maximum possible profit at the price that was set;

2) the price of the excess supply of goods is equal to zero;

3) the maximum possible utility of the product at a certain given price and profit share;

4) prices are only positive.

J. Debret is also known as the author of "The Theory of Value".

In the 1930s J. Hicks and P. Samuelson began to study the problem of equilibrium stability. They are considered to be the founders in the field of research of this problem. Subsequently, such studies were taken up by such scientists as K. Arrow, F. Khan, T. Nigishi, L. Mackenzie.

According to Hicks' assumption, an increase in the price of a good creates conditions for a decrease in demand for this good. Such an effect is likely to be stronger than the effect that is associated with an indirect change in the prices of other goods. Demand for such goods may change due to the rise in price of this product. These products include both replacement and complementary products. (If a certain model of a car rises in price, then there may be a decrease in demand for components for this model, and also an increase in demand for a similar model from another manufacturer.)

Authors: Eliseeva E.L., Ronshina N.I.

<< Back: Marginalism (The theory of marginalism. Methodological principles of marginalism. The marginalist theory of value and its advantages. The marginalist revolution. The causes and consequences of the marginalist revolution. The theory of utility of William Stanley Jevons. The theory of exchange of William Stanley Jevons. The theory of labor supply of William Stanley Jevons. The theory of exchange of Francis Isidro Edgeworth)

>> Forward: Alfred Marshall (A. Marshall - leader of the Cambridge school of marginalists. Alfred Marshall's partial equilibrium method. Alfred Marshall's analysis of utility and demand. Alfred Marshall's analysis of costs and supply. Alfred Marshall's equilibrium price and the influence of the time factor)

We recommend interesting articles Section Lecture notes, cheat sheets:

▪ Marketing. Crib

▪ Insurance law. Lecture notes

▪ Russian literature of the XX century in brief. Crib

See other articles Section Lecture notes, cheat sheets.

Read and write useful comments on this article.

<< Back

Latest news of science and technology, new electronics:

The existence of an entropy rule for quantum entanglement has been proven 09.05.2024

Quantum mechanics continues to amaze us with its mysterious phenomena and unexpected discoveries. Recently, Bartosz Regula from the RIKEN Center for Quantum Computing and Ludovico Lamy from the University of Amsterdam presented a new discovery that concerns quantum entanglement and its relation to entropy. Quantum entanglement plays an important role in modern quantum information science and technology. However, the complexity of its structure makes understanding and managing it challenging. Regulus and Lamy's discovery shows that quantum entanglement follows an entropy rule similar to that for classical systems. This discovery opens new perspectives in the field of quantum information science and technology, deepening our understanding of quantum entanglement and its connection to thermodynamics. The results of the study indicate the possibility of reversibility of entanglement transformations, which could greatly simplify their use in various quantum technologies. Opening a new rule ... >>

Mini air conditioner Sony Reon Pocket 5 09.05.2024

Summer is a time for relaxation and travel, but often the heat can turn this time into an unbearable torment. Meet a new product from Sony - the Reon Pocket 5 mini-air conditioner, which promises to make summer more comfortable for its users. Sony has introduced a unique device - the Reon Pocket 5 mini-conditioner, which provides body cooling on hot days. With it, users can enjoy coolness anytime, anywhere by simply wearing it around their neck. This mini air conditioner is equipped with automatic adjustment of operating modes, as well as temperature and humidity sensors. Thanks to innovative technologies, Reon Pocket 5 adjusts its operation depending on the user's activity and environmental conditions. Users can easily adjust the temperature using a dedicated mobile app connected via Bluetooth. Additionally, specially designed T-shirts and shorts are available for convenience, to which a mini air conditioner can be attached. The device can oh ... >>

Energy from space for Starship 08.05.2024

Producing solar energy in space is becoming more feasible with the advent of new technologies and the development of space programs. The head of the startup Virtus Solis shared his vision of using SpaceX's Starship to create orbital power plants capable of powering the Earth. Startup Virtus Solis has unveiled an ambitious project to create orbital power plants using SpaceX's Starship. This idea could significantly change the field of solar energy production, making it more accessible and cheaper. The core of the startup's plan is to reduce the cost of launching satellites into space using Starship. This technological breakthrough is expected to make solar energy production in space more competitive with traditional energy sources. Virtual Solis plans to build large photovoltaic panels in orbit, using Starship to deliver the necessary equipment. However, one of the key challenges ... >>

Random news from the Archive Tyrannosaurus Air Conditioner 06.09.2019 Scientists from the United States said that in the skull of the tyrannosaurus rex there were two holes that served as a kind of "air conditioner". They were needed because the giant and active pangolin quickly overheated. Previously, it was thought that these holes contained muscle tissue, but now researchers have concluded that they were actually covered with a network of blood vessels. It is known that large animals need additional cooling mechanisms, since in the heat their body can quickly overheat. During the study, scientists used thermal imagers to observe alligators at a farm at the Florida Zoo. It turned out that in the alligator's skull there are holes filled with blood vessels. "The body temperature of an alligator depends on the environment. We noticed that when it got colder and the alligators were trying to warm up, the thermal imagers recorded large heat spots in the upper part of their skull, which indicate an increase in body temperature. However, as the day became warmer, these spots darkened, as if they were turned off to reduce the temperature, "said study co-author Kent Vliet. After studying the fossilized remains and three-dimensional models of the skull of tyrannosaurs, scientists found that they had similar openings. It was previously thought that these holes contained muscle tissue, but Holliday says that "it is strange to see muscles that rise up from the jaw, then turn 90 degrees and continue under the cranial vault."

Other interesting news:

▪ Preparations for the Chinese lunar mission

▪ Grasshopper oil

▪ 75" 4K MicroLED TV

▪ Billiard cue with laser sight

▪ Intercity travel by car

News feed of science and technology, new electronics

Interesting materials of the Free Technical Library:

▪ site section Electric meters. Article selection

▪ article by Erich Fromm. Famous aphorisms

▪ article Can you see the sunrise and sunset of the Earth on the moon? Detailed answer

▪ article Working with a piston-mounting gun. Standard instruction on labor protection

▪ article Subwoofer Thunder V-150. Encyclopedia of radio electronics and electrical engineering

▪ article 12/1000 volt voltage converter. Encyclopedia of radio electronics and electrical engineering

Leave your comment on this article:

All languages ​​of this page

Arabic	Hebrew	Polish
Bengali	Hindi	Portuguese
Chinese	Italian	Spanish
English	Japanese	Turkish
French	Korean	Ukrainian
German	Malay	Vietnamese

Home page | Library | Articles | Website map | Site Reviews

www.diagram.com.ua
2000-2024