Model zagalnoї rivnovagi Walras. Walras' law
(nxm) elements, similar to V. Leontiev - a square matrix (nxm) of elements. In addition, in the Leontief model of structuring, the gross output (wine is added to the industrial and final product), the indication of the gerel variability is added to the vartost, it is divided into the balance with the characteristics of the secondary element of the final product and the distribution is redistributed to income. But still, the best idea of the model of wickerwork - the release has already been made at the visnovkas of Walras.
Por_vnyuyuchi number nevіdomih (2m + 2n - 1) і kіlkіst іvnyan, scho de stink zbіgayutsya і ekonomіchnomu sensі unbalanced. Walras get out of position, turning on one equal model. As a result, the equivalence of the number of equivalences of the number of nevіdomih comes out. The system of equalization is gaining economic sense of equal importance. This, obviously, does not mean that the language will be pronounced, even if it is necessary to bring the reason, unity and positiveness of the decision. From a practical point of view, it is also unlikely that a solution to the system of equalization is possible, for which there would be dozens of millions of product names with specific indications of the effects of vitrates on their selection. Therefore, the sense of Walras's model itself is theoretical - it shows the market in an ideal way.
In order to understand that such an ideal macro-economy is equal to the market type, Walras and Pareto introduced the most important ideas. The Walrasian model has become the starting point for new horizons in the analysis of equivalence.
To complete the change, the model of Walras is modified, as it is understood as a synthesis of models of the behavior of firms, spozhivachіv and global economic zeal. New model
Wisnovki with Walras model
The Walrasian model is a simplified, sensible picture of national government. Vaughn looks, how to be restored to the level of development, dynamics. They don’t worry about a lot of factors that develop in practice, for example, psychological motives, ochіkuvannya. The model looks at the markets that have developed, are tired and meet the needs of the market infrastructure.
DESIGN 2. Walras Model
Section 2. Walras Model 221
Section 2. Walras Model 223
Section 2. Walras Model 225
In such a manner, in retrospect, if the curve of the popu is negative, and the curve of the proposition is positive, the models of Walras and Marshall are reduced to that very stable position of jealousy. Prote chi crooked drink and propositions may look like this Let's see fig. 6a from the section 2 lectures 1, de depicted as "the curve that bends", the propositions of practice. The upper part of the curve has a negative nahil. Negative impudence can also be characterized by crooked propositions on the foreign exchange market (the supply chain will be looked at in the upcoming issues of our publication). Now let's look at the market from a negatively chiseled curve of propositions, to marvel at how to bring us the models of Walras and Marshall to the same trend.
In this manner, the models of Walras and Marshall produce, although from a theoretical point of view, the stability of jealousy to the minds of the minds. The reason for these powers is the difference in the state of affairs about the functioning of the market mechanism, which underlies the models, as we can see. It can be said that the Walrasian model correctly describes the function of the market mechanism, while the Marshall model describes it incorrectly (otherwise). In fact, the process of establishing equalness in a short period is more briefly described using the additional Walrasian model, if, for example, it is too much to drink to increase the value to an equally important value.
In the theory created by him and K. Errow in the 50th century, both descriptions are gaining intellect, which guarantee the basis of total jealousy and for less suvorih, lower for the Walras model, omissions (Errow-Debré theorem). Ale yogo doslіdzhennya did not become obese without nutritional reasons for jealousy. Vіn analyzed and yogo normative characteristics and unity. K. Yerrow and J. Debré formulated the mind, for some kind of price mechanism in order to increase the efficiency of resource recovery. Developing the theory of global equivalence, Debre created new methods of economic analysis, like victorious at once a lot of economists.
This theoretical plan has a new classic - a modified version of the Walrasian model. Modification, about
In the Walrasian model, all information is valid for prices, moreover, prices are equal. Vidhilennya in the system in the case of rіvnovag may be less than the last of various inaccuracies (due to the inaccuracy of information to the innocence of prices and zatrimo in the reaction of people to the outrageous storm)4.
Now let's take a look at what the assertion "about the role of two-fold estimates in the framework of the Walras-Wald model in the framework of the Walras-Wald model is similar to, but not inconsistent assertions in the framework of the optimal planning model (3.P).
On the basis of the theoretical conception, the Walrasian model, the model of global economic revival, was inspired, a kind of one-time sign of national statehood in a pure look. If I become jealous, then out, for Walras-su, I convey the presence of three minds
In short, apparently, vin having developed an innovative model from the development of a primitive mathematical apparatus. Cournot (ournot), a master mathematician, lower Walras, and a man, like a great infusion hit the new one, eluded the solution of the problem through її over the top difficulties. Irrespective of those that the model of Walras constantly exchanged glances with and thoroughly, її zagalnaya kontseptsіya dosi zasivaetsya nezmennoy. In his history of economic analysis (1954) Schumpeter (Shumpeter) writing Walras, in my opinion, was the greatest of all economists.
Von Neumann's rejection of the result allows us to consider the important aspect of equality, which is not manifested in the Walrasian model, and the most equal - the maximum output of a penny-MIII and the minimum income of factors. Tsej vysnovok є i.fazheinoe іnshoy movoy sverdzhennja Smіta about іvnіst cost-i і roblenї produktsії і on sumi dovodіv ekonomіki.
Lange and Lerner propagandized a model to Deak, that I would support a decentralized economy, that would be formed from state-owned enterprises, supporting and supporting the Central Committee for planning. Remaining actually BJ vykonu the role of the auctioneer from the model of Walras, rozrakhovuyut, optimal prices, us in front of the prices of variant factors, for deyakoї umoglyadnoї ekonomіki, and zadaє їх ekonomіchnym subjects. Managers of state-owned enterprises independently make decisions, focusing on the parameters of the task price. When tsimu stench keruyutsya two rights
It is obvious that the Walrasian model cannot be used to explain some of the mechanisms, as they are taken as a violation of macroeconomic proportions. As new classics are being solidified, it is impossible to introduce macroeconomic imbalance out of microeconomic revival.
The Keynesians rightly pointed out that the new classics were judged within the framework of the Walrasian model, as they turn off some false signals that are badly related to the real behavior of people. Well, it’s obvious that people are not only talking about price signals in their minds, but the wild picture of the economy is just like a Walrasian, so it’s painted by new classics.
The first economist, who inspired a mathematical model for an additional system of equalization to prove the possibility of establishing a global equalization, was the Swiss economist Leon Walras (1834-1910). Vіn admitting that the statehood is built up from spozhivachіv, vikoristovuyut n mutually beneficial goods, the production of which is carried out from the stagnation of various factors of virobnitstva. For wits:
Data on the functions of the skin spasm and budget,
Equity to the budget of saving the value of yoga factors
The fixation of the commitment of the th factor of variation (absolute inelasticity of the їх propositions), it is possible to induce the function of drinking the i-th benefit for the j-th good:
M i - the budget of the i-th employee,
P j , r t
F S i , t
With the method of forgiveness, it is acceptable, the leather company only produces one kind of benefits. Given the given technology and the cost of benefits, the factor of production of the firm, which maximizes profits, forms the function of the proposition of the benefit and the function of the benefit on the factor. The sum of the propositions of all firms, which achieve one and the same good, satisfies Galuzev's proposition:
Sumarniy drink tsikh firms on the factor to install galuzevy drink on the skin of the factors:
On the basis of functions (6)-(8) there will be a micro-economical model of global equity, which consists of three groups of equity:
1. be smart about the market of goods:
2. wash your jealousy in the markets of factors of production:
3.budgetary exchanges of firms over the market thoroughly compete as a equivalence of the gross income to the gross costs:
Rivnyan system (9)-(11) Ale independent є less than 2n + m-1 equal. Tse z budgetary exchanges of relief, after all, such a sumar superfluous drink of skin relief is almost zero.
Let's assume that there are only 2 markets of goods and 1 market of factors. Budgetary obmezhennya (rіvnyannya) -go spozhivacha may look:
Tsya equanimity to certify that vytrati th spozhivacha (left part) is responsible for increasing his income from the sale of the benefits and factors of production (the right of the part).
In round temples - superfluous demand for the th skin s rinkiv, tobto. the equivalence of the total oversupply to zero, whether there is any savings, is only another form of manifestation of the yogo budgetary subsistence. Depending on the budgetary balance of all participants in the market areas:
It is evident from the equality (13) that if the system of prices P 1 , P 2 r guarantees equality in any two markets, then it will be equal in the third one. Tsey visnovok, virny for whether there is a large number of rinkiv, may be called Walrasian law
Valid until Walrasian law equalization system (9)-(11) revenge 2n+m-1 independent equalities. During the hours of Walras, a daily mathematical apparatus for cherry blossoms. Walras was on the way to the grouping of equals, and Rukh looked at the step-by-step process - "poshuk on the dotik" of the upper proportions of the exchange, especially at the stage of the contract ahead of the contract.
So the system is small solution, it needs to add one independent equal, or change by 1 number of unknowns. The first variant - macroeconomic - to introduce supplementary equalization of the equal amount of drinking and propositions on the penny market. The other is the microeconomic price of the return of the good is taken for 1, and the system of visual prices is sufficient for explaining microeconomic phenomena.
Zagalna rіvnovaga in the minds of a net exchange with the exchange of resources and goods for the safety of the solution of the economic problem - the placement of the exchanged number of goods in the middle of the savings. One of the shortest ways of such placement is the box (box) of Francis Edgeworth (English economist, 1845-1926), 1891r. writing Mathematical Psychology.
The Swiss economist-mathematician Leon Walras (1834-1910) having looked at the question of food: how do markets and sectors of the economy function in the most savage (pure) way? On the basis of some principles, the interdependence of prices, vitrates, obsyagiv pita and propositions on different markets is established? Chi accepts the interdependence of the form of "equal importance" or the market mechanism, which directs the reverse?
Walras realized that the solution to the problem can be reached with the aid of the mathematical apparatus. The entire economic world of wines was divided into two great groups: firms and households. Firms enter the market of factors as buyers and on the market of fast goods as sellers. Home governments - the rulers of the factors of production - act in the role of their sellers and at the same time as buyers of goods. The roles of sellers and buyers are constantly changing. In the course of the exchange, the expenses of the workers of the goods are converted to the income of the households, the costs of the exchanges of the households - to the incomes of the workers (firms).
The prices of economic officials should be deposited in the form of obsyagiv vrobnitstv, drink, also, in the vіd tsіni of the viroblenі commodities. Have your own money, prices for goods that are released into the suspension, lie down in the prices at the factories of the factory. Remain to be able to confirm the vitrates of firms. At that very hour, the firms can come up with witrats of households.
Prompted to complete the collaborative system of mutually equitable, Walras argued that the system of equalization can be achieved as an “ideal”, such a competitive market. The camp, which took away the name of the Walrasian law, to say: the camp has a equal market price more expensive than the border crossings. In this way, the variability of the suspension product is more expensive than the market variance of the varieties for the release of the varietal factors; the sukupny will drink more than the sukupny rechennyu; the price and the cost of the change do not change and do not change.
On the basis of the theoretical conception, the Walrasian model, the model of global economic revival, was inspired, a kind of one-time sign of national statehood in a pure look. If I become jealous, then, after Walras, I convey the presence of three minds:
In the first place, that proposition of factors will drink equal; a fixed price is fixed on them;
In another way, that proposition of goods (services) will also be realized on the basis of fast, stable prices;
Thirdly, the prices of goods should be given to the vitrates of the selection.
Rіvnovagi є stіykimi, more on the market there are forces (persh for everything, prices for factors of production and for goods), which virіvnyuyut vіdhilennya that vіdnovlyuyut “equanimity”. It turns out that “incorrect” prices are step by step turned off, shards of this sprya are completely free to compete.
Wisnovki with Walras model
The main visnovok, which is in Walras's model, is interdependence and mutual investment of all prices as a regulatory tool, moreover, as a market of goods, and in general markets. Prices for spare goods are set at mutual and mutual modalities with prices for factories of production, prices for labor force - with the improvement and influx of prices for products too.
Rіvnovazhnі tsіni vnaslіdok zaєmopov'yazannosti vsіh rinkіv (rіnіv vіdovіv, pratі, fіnansovіh rіnіv, rіnkіv tsіnnih paperіv).
In this model, the possibility of establishing equally important prices at once in all markets can be mathematically explained. To tsієї rivnovagi by virtue of the authoritative їy mekhanіzmu pragne market economy.
From the theoretically feasible economic level of viplya vysnovok schodo vіdnoї stіykostі system of market vіdnosin. The establishment (“naming”) of equally important prices is found on all markets and, it is permissible, to bring such propositions to them.
The revival of the economy does not lead to a revival of the exchange, to a market revival. From the theoretical concept of Walras, the principle of mutuality of the main elements (markets, spheres, sectors) of the market economy is clear.
The Walrasian model is a simplified, sensible picture of national government. Vaughn looks, how to be restored to the level of development, dynamics. They don’t worry about a lot of factors that develop in practice, for example, psychological motives, ochіkuvannya. The model looks at the markets that have developed, are tired and meet the needs of the market infrastructure.
The peculiarities of the mechanism of formation of the market rіvnovagi are those that are not controlled by anything known and purposefully directed. The subject of the market is independent of one type of one, following the authorities' interests. With all the competitive forces that work on the side of sellers and on the side of buyers, match the synchronization of prices to drink that proposition, which, in its line, to bring to evenness obsyagiv drink that proposition. Forming an equal value, in such a way, leading to the achievement of the market equal.
In economic theory, there are two main approaches to the analysis of the mechanism of establishing a market economy: the Swiss economist Leon Walras (1834-1910) and the English economist Alfred Marshall (1842-1924).
L. Walras, explaining the establishment of a market rіvnovagi at the sight of the colivannya tsіn. Vіdpovіdno poglyadіv L.Walras, vіdhilennya tsіni vіd іnоvno important іvnі umovlyuє viniknennya raznіnіnі і іnіdіnі і pіtu іnіdіnії propositionsії, scho vіdіnja іn establishment konkurentsії mіzh vіzh vіzh vіzh vіzh purchasі, pozdzhuyuyu tsіm tsіm vіd.rіvіnі vіnі 7. At the time of installation of cіni, more importantly (P1> PE), there is too much product on the market (QS1> QD1). In the situation, not all sellers deprive them of the opportunity to sell their products, since a small number of buyers are ready to buy goods at a high price. Blame the competition among the sellers, they will win those, if they are able to reduce the price of the goods. As a result, the price may have a downward trend, so it is not of equal importance. The process of lowering the price and increasing the sales volume to the point of equalization (E).
In another case, with a reduced price lower than equal to equal (Р2<РЕ), на рынке образуется дефицит товара (QD2>QS2), but the price is low, which does not encourage more sellers to promote their goods for sale. Blame the competition among buyers, not all of them can buy cheap goods. Deficiency in goods that bazhannya yogo buy sponukaє a part of the purchase will be pogodzhuvatisya on the bіsh visokі cіni, vnaslіdok of which the price of the cіna zbіshuєtsya, to pragne the rіvnovázhny rіvnya. Growing prices are accompanied by short-term values of drinking and advancing obligatory propositions. This process is to be continued until the market reaches the point of equality, if that proposition is able to become balanced again.
In this way, in both ways, the difference between the prices of the equally important equal and the unstable ones, the shards of the internal market forces have sprung up the recognition of the equally important market.
Rice. 7.
A. Marshall considered the other mechanism of market revival (Fig. 8). In the event of damage to the market, sellers manipulate not prices, but generally promoted products. Be-yaky obsyag to the goods, which are promoted to the market, lower than the rіvnovo important (Q1< QE), порождает ситуацию, когда цена спроса превышает цену предложения (PD1>PS1). This situation is viable for sellers, who sell goods at a price that is richly outweighing their average costs, sellers take a significant profit. A high profit of spontaneous sellers, which are on the market, increase the number of proponated products and attract new sellers. As a result, the propositions become larger, having risen between the price of drink and the price of the proposition, it shortens. This process is three until the establishment of a market price, for which the difference is equal to the price, for which you are ready to pay for the goods of the buyer and the price, for which you are able to sell the goods to the seller (PD = PS), as well as the difference between the value of the drink and the value of the proposition QS) (Q=D) .
In the opposite direction, if on the market proponuєtsya nadmіrna kіlkіst commodities, cіna propozicії perevishuvatime cіnu drink (PS2>PD2). Not otrimuyuchi vіd goods bazhany income, part of the sellers will be stunned to quickly kіlkіst zaproponovanoї produktsії, іnsha part of the sellers will deprive the market. As a result, the propositions will change, and the market price will increase, even more important. In this rank, the equally important camp of the market will be renewed.
Rice. 8.
Looking directly at the analysis of the establishment of the market balance, it is fair to stop until different hourly intervals. L.Walras’ pidkhid is more acceptable to a short-line period, if it is necessary to change the task, and the cost of the price is to accept the renewal of the market level. The position of A.Marshall more adequately reflects the situation in the pre-stroke period, which is sufficient for the fact that virobniks, focusing on a high or low level of the market price, have little opportunity to attach their products to the needs of buyers.
Por_vnyalna characteristic of two approaches:
In such a manner, in retrospect, if the curve of the popu is negative, and the curve of the proposition is positive, the models of Walras and Marshall are reduced to that very stable position of jealousy. Prote chi crooked drink and propositions can look like that? Let's guess from the previous material that the curve of the speech can mother a negative frailty (individual proposition of practice, exchange of resources). The upper part of the curve has a negative nahil. Negative impudence can also be characterized by curved propositions on the currency market. Now let's look at the market from a negatively hacked-up curve of proposition, to marvel at how to bring us the models of Walras and Marshall to the same trend.
We can look at the back of the head, if the crooked speech is straightened down and the cut of the crooked speech is steeper than the crook of the crooked drink. Let's go back to Walras's argumentation (Fig. 9a). Let the first variance P0. At this price, Q1Q2 will be too much and the price will move up to point E. Rivnavaga stay.
It is now necessary to follow Marshall's mind (Fig. 9b). Let the first proposition be good Q0. The price of the drink outweighs the price of the proposition (P2> P1), the proposition increases, and the price of the drink more shifts the price of the proposition. Rukh is in direct contact with the opposite position of jealousy. Equity is not stable.
Rice. nine.
ale nestia for Marshall (b).
Now let the crooked river straighten down again, but steeper kut the crooked crooked drink (Fig. 10).
Rice. 10. Rivnavaga, nestia after Walras (a), ale staid after Marshall (b).
In this manner, the models of Walras and Marshall produce, even from a theoretical point of view, to the minds of stamina and jealousy. The reason for these powers is the difference in the state of affairs about the functioning of the market mechanism, which underlies the models, as we can see. Can you say that the Walras model correctly describes the function of the market mechanism, and the Marshall model - incorrectly (otherwise)? Definitely no. In fact, the process of establishing equality in a short period is more accurately described for the additional model of Walras, if, for example, the superworld drinks water up to an increase in price to an equally important value.
At that very hour, for the analysis of the reach of the equal in the old period, the Marshall model is more successful, and the price of the proposition grows, so the price of the drink outweighs the price of the proposition.
It is significant that the models of Walras and Marshall have one joint power, as if they were different from the pavutino-like model. In the pavutinopodіbnіy model, the hour was divided into intervals of the same trivality, and the stretching of the skin interval changed the models were left constant. The price in the spider-like model was changed by haircuts from the forward period to the onset. In a different way on the right in the models of Walras and Marshall.
Here the hour is changing, which is constantly changing, and the price is constantly changing. In the pavutinopodіbnіbnіbnіbnіbnіbnіbіbnіbnіy modelіvіv propositionії vіdnomі periodі vіznaієєєєєє prodіvіїії іn the previous period. Tsya the situation calls out to its own line the theoretical possibility of inconsistency of jealousy to inspire for a "normal" kind of crooked drink and proposition (the curve of the proposition may be positive, and the crooked drink can be negative). The models of Walras and Marshall have this option turned off.
The first economist, who incited the model of a global jealousy, JI. Walras. The people's statehood, after Walras, is formed from the first domestic statehood, which accumulates various blessings, for the preparation of which, various factors of production are stagnated.
Likening home governments to good things and factors of variation given by their functions of value. Budget spozhivachacha formed in the aftermath of the sale of nelezhnyh yoma chinnikіv vrobnitstva. The market curves of drinking and propositions are settled in the aftermath of the folding of individual functions.
On the basis of the findings of the functions of cost, budgetary obmezheni, market value and propositions, Walras presented the model of global equity, which consists of three groups of equity, which show:
1) wash your jealousy in the market of goods: , de Q j - kіlkіst j-th good (j = 1, n) provided by us by domestic governments;
2) wash the equivalence on the markets of factors of variance: , de F t - number of the t-th factor of variance ( t\u003d 1, m), which is in all home states;
3) budgetary exchange of firms for the minds of thorough competition, as the equalness of the gross income to the gross costs:
P j = g w:val="EN-US"/>
Rivnyan revenge system (2 n + m- 1) independent country. As soon as you see the income of the spontaneous, then, having presented the real value of the pennies from the equal, we will take the number of goods and services that are exchanged. J.I. Walras, violating the system of rivnyan, having created two important visnovki:
1) for the total amount of economic surpluses in some markets, the increase in the amount of deficits in others;
2) just as the system of prices ensures the reliability on any three markets, then it will be reliable on the fourth market. Tsei visnovok otrimav name Walras's law.
Let's look at the Walras model on a specific butt.
Butt 9.2
It is acceptable that one product is being rotated - crackers, moreover, their release is stained less borosno and tsukor. Drinking on crackers is significant through Q, and the price of crackers is assumed to be equal to one. Technological coefficients of tasks in tables.
Obsyagi propositions are borosna and zukra given by formulas
q 1 \u003d 2 + r 1; q 2 = 6+2 r 2 .
Vykhodyachi s data, what is in the problem, we write:
a) the equalization of the equal galuse with the variation of crackers: 1 \u003d 0.25 r 1 + 0.5 r 2;
b) equal to drink on borosno and tsukor: q 1 = 0.25 Q q 2 \u003d 0.5Q. Virishima system from five equals, vvazhuchi, scho obsyag
products and resources in thousands of tons. As a result, it is taken into account that 16 ths. tons of crackers, with which 4 yew are glassed. tons of flour and 8 yew. t zucru.
