There are two main approaches to the analysis of establishing an equilibrium price: L. Walras and A. Marshall. The main difference in A. Marshall's approach is the difference between prices P1 and P2 (Fig. 6). A. Marshall believed that sellers primarily respond to the difference between the demand price and the offer price. The higher this gap, the more profitable it is for the manufacturer, the more incentives can be found to change the supply. A change in the supply reduces this difference and thus contributes to the achievement of the equilibrium price.
According to L. Walras, in conditions of lack of goods, i.e. shortage, buyers are active, and in conditions of a surplus of goods - sellers. In contrast, A. Marshall believed that important role manufacturers play a role in shaping the market conditions. The equilibrium price is usually lower than the maximum price assumed by buyers by the amount of consumer surplus, which is the surplus primarily for wealthy consumers who could purchase the product above the equilibrium price PE up to the maximum Pmax, but purchase the product at the market price.
Rice. 6.
Thus, from the above it follows that if the price in the market is not equal to the equilibrium, then the actions of buyers and sellers move it towards the equilibrium. If the supply volume is not equal to the equilibrium one, then, focusing on the demand price, sellers increase or decrease the supply volumes to an equilibrium level, at which the equilibrium price is also established. Modern economic theory operates with the supply and demand functions of L. Walras and the graphs of these functions by A. Marshall, but this does not affect the results of the analysis of the interaction between supply and demand.
Since, according to L. Walras, prices are the instrument for building equilibrium in the market, the model he built characterizes the situation that is developing on the market in the short term. Market processes in the long run, when you can change the volume of output and sales by increasing or decreasing the number of factors used, are better described by the Marshall model.
The market automatically, with the support of the "invisible hand" mechanism, contributes to the formation of equilibrium prices. The excess of the demand price over the supply price leads to a redistribution of resources in favor of enterprises that produce products with high effective demand. Relatively high prices testify to the relative rarity of goods, prompting an increase in the volume of their production and, thereby, a better satisfaction of needs. Since the equilibrium price significantly exceeds the costs of those industries whose costs are below average, it contributes to the redistribution of resources from inefficient to efficient producers. This improves the efficiency national economy generally.
Walrasian equilibrium
Marshall equilibrium
The equilibrium price is formed for the following reasons:
The demand price coincides with the offer price in the case of an equilibrium volume of demand and supply.
16. General concept of elasticity. Elasticity Formula
Elasticity- the degree of response of one quantity to a change in another.
Elasticity coefficient- assessment of elasticity in percentage terms; the ratio of the percentage change in one quantity to the percentage change in another.
The elasticity of demand- elasticity can be measured using the coefficient. elastomer
Elasticity =((Q1 – Q2) / (Q1+Q2)) / ((P2 – P1) / (P1 + P2)). P1 is the price before the change, P2 is the price after the change, Q1 is the demand before the change, Q2 is the demand after the change.
Price elastic demand (P): the change in demand for a product depends on a change in its price. Three types of price elasticity:
1) Elastic demand (with a slight drop in price, the volume of sales rises). E>1.
2). Unit elasticity (price change in % is equal to % change in sales). E=1.
3). Inelastic demand (when the price changes, there are no significant changes in sales.). E<1
Factors of elastic demand.
1. Irreplaceability - if there is a substitute, then demand will be more elastic).
2. The importance of goods for the consumer. - (inelasticity is the demand for essential goods).
3. Share in income and expenses. (Goods are elastic if a significant share of the funds is spent on them).
4. Time frame - elasticity increases in the long term and becomes less elastic in short periods of time.
The change in total revenue with the same changes in the price of goods. with different elastomer. demand:
1. With elastic demand, a fall in price causes such an increase in sales volume, which leads to an increase in total revenue.
2. When demand is unity, elasticity is an increase in sales volume with a decrease in prices so that the total revenue remains unchanged.
3. With inelastic demand, a fall in prices leads to a small increase in sales, the volume of total revenue decreases.
Elast. demand by income- as the ratio of the percentage change in the volume of demand for goods to the percentage change in income (I): E D =Q\Q: I\I. Since the consumer changes the demand for different goods in different ways when income changes, the indicator can also have different positive and negative values. If the consumer increases the volume of purchases with an increase in income, then elast. income is positive (E I >0; we are talking about a standard normal product, for example, an extra pair of shoes). If demand growth outpaces income growth high elast. by income (E I >1; durable goods: cars, computer - people spend on their savings or take out a loan). If, with an increase in income, demand decreases E I<0 - аномальные или низкокачественные товары (дешевые сорта колбасы).
P 
cross elasticity.
Eсross=Q A \Q A: P B \P B . Q A - volume of demand for product A, P B - price of product B
Supply elasticity- the sensitivity of the volume of supply to a change in the market price, or - the degree to which the quantity of goods and services offered for sale changes in response to a change in the market price.
Factors: time factor, raw material prices, salary level, etc.
Price elasticity coefficient of supply (Es) = Qa\Q: P\P
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The first economist to build a mathematical model using a system of equations to prove the possibility of the existence of a general equilibrium was the Swiss economist Léon Walras (1834-1910). He suggested that the national economy consists of consumers using n interrelated goods, the production of which is carried out using m different factors of production. Under conditions:
Given the utility functions of each consumer and his budget,
Equality of the budget of the consumer of the value of his factors of production,
If the volume of its factors of production is fixed (the absolute inelasticity of their supply), it is possible to construct the demand function of the i-th consumer for the j-th good:
M i is the budget of the i-th consumer,
P j , r t - prices of goods and factors, respectively, j = 1,2,..n, t=1,2,...m,
F S i , t is the given volume of the t-th factor belonging to the i-th consumer.
For the sake of simplicity, let us assume that each firm produces only one kind of good. With a given technology and known prices for goods and factors of production, a profit maximizing firm forms a supply function for a good and a demand function for factors. The sum of the offers of all firms producing the same good forms the industry supply:
The total demand of these firms for factors is the industry demand for each of the factors:
On the basis of functions (6)-(8), a microeconomic general equilibrium model is constructed, consisting of three groups of equations:
1. equilibrium conditions in the goods market:
2. equilibrium conditions in the markets for factors of production:
3. budgetary restrictions of firms in the market of perfect competition in the form of equality of total revenue to total costs:
The system of equations (9)-(11) contains 2n+m unknowns and the same number of equations. But only 2n+m-1 equations are independent. This is due to the budget constraint of consumers, due to which the total excess demand of any consumer is equal to zero.
Assume that there are only 2 markets for goods and 1 market for factors. The budget constraint (equation) of the th consumer has the form:
This equality says that the expenses of the th consumer (left side) should be equal to his income from the sale of his goods and factors of production (right side).
In parentheses - excess demand of the th consumer in each of the markets, i.e. the equality of the total excess demand to zero for any consumer is only another form of representation of his budget constraint. Let us sum up the budget equations of all participants in market transactions:
It follows from equality (13) that if the system of prices P 1 , P 2 , r ensures equilibrium in any two markets, then the equilibrium will also be in the third one. This conclusion, which is true for any number of markets, is called Walras' law.
In accordance with Walrasian law the system of equations (9)-(11) contains 2n+m-1 independent equations. At the time of Walras, there was no mathematical apparatus for solving it. Walras took the path of grouping equations, and considered the movement towards equilibrium as a gradual process - a “groping search” for the correct proportions of exchange, especially at the stage of a preliminary contract.
In order for the system to have a solution, one more independent equation must be added, or the number of unknowns must be reduced by 1. The first option - macroeconomic - introduces an additional equation for the equilibrium of supply and demand in the money market. The second - the microeconomic price of the chosen good is taken as 1, and the system of relative prices is sufficient to explain microeconomic phenomena.
General equilibrium under conditions of pure exchange with limited resources and goods provides a solution to the economic problem - the placement of a limited number of goods among consumers. One of the best ways of such placement is the box (box) of Francis Edgeworth (English economist, 1845-1926), in 1891. Wrote Mathematical Psychology.
The search for market equilibrium in the Walrasian model begins with an analysis of scarcity. Let's assume that the price P 1 is established. At this price, producers are limited to supply Q 1 . And buyers at this price demand Q 2 . There is an excess demand or shortage. Consumers begin to compete, and this leads to higher prices. Producers move up along the supply line S, reacting to the mood of the buyer. Οʜᴎ meet at point E. Demand equals supply. Market equilibrium is established, the deficit disappears. The Walrasian model is better suited to characterize the process of establishing equilibrium in a short period.
Marshall model.
In the second model, the focus is on the reaction of market entities to the prices themselves. Let's assume that the ask price is higher than the offer price. With the quantity supplied Q1 and the price P2, sellers will increase the quantity supplied as the market price rises. If the demand price turned out to be less than the supply price, on the contrary, the supply will decrease until the market equilibrium is reached at point E. The Marshall model is more suitable for analyzing the process of achieving equilibrium in a long period, when the supply volume is able to respond to a high demand market price.
The state influences the functioning of the market system and participates in economic relations. The main economic functions of the state:
1. Development of a legal framework for the effective functioning of the economy, which includes the creation of legal norms, the development of a system for regulating relations between economic entities and the definition of property rights.
2. Protection of competition. It provides for the demonopolization of the economy, the stimulation of competition by introducing restrictions and permits.
3. Production of goods for public use. Those. goods that the market system does not intend to produce.
4. Redistribution of income and wealth. These are taxation and transfer payments (payments not related to the current economic activity of the recipient (social insurance payments ...)).
5. Allocation of resources for public goods.
6. Stabilization of the economy (ᴛ.ᴇ. implementation of measures to smooth out the cyclical nature of the development of the economy). This is the containment of unemployment, inflation, support for economic growth and control over the equilibrium of the circulation of income and expenses.
Walras model. - concept and types. Classification and features of the category "Walras Model." 2017, 2018.
This model is an attempt to present all the equations describing the general equilibrium in the economy, in order to compare the number of these equations with the number of variables they include. If the number of equations is equal to the number of variables, then general equilibrium is possible.
Let us imagine an economy with the following characteristics: in any market of this economy there is perfect competition (a large number of buyers and sellers, complete information, no costs for entry and exit from the market, each consumer and firm act independently of the others); it also assumes the absence of externalities and public goods.
There is T types of consumer goods, each of which is produced under conditions of perfect competition by many independent firms. Each firm maximizes its profit.
The farm has P types of resources that are owned by consumers and are provided by the latter firms at certain prices. Each consumer can own any number of types of resources and does not necessarily offer for sale the entire amount of the available resource. Consumers distribute the received income among different consumer goods, maximizing their utility functions.
Let a fixed amount of each resource be needed to produce a unit of each good. Thus, there is a matrix of size pht, separate element ats, which shows the amount of resource j, necessary for the production of a good /:
Thus, in total in the economy there is P resource markets and T markets for consumer goods. In every market, there are two variables - price and quantity. In the market for a particular good, this is P, and Q t , and in the market of a separate resource -pj and qj. In total it turns out 2 P + 2t unknown.
Let us now determine the number of equations describing the economic system. There are four groups of equations that describe different types of functional dependencies in the economy: 1) equations for the demand for consumer goods, 2) equations for the supply of resources, 3) equations for equilibrium in the industry, 4) equations for the demand for resources. The first two groups describe the equilibrium of consumers, the second two define the equilibrium of producers.
1. Consumer demand equations
The individual consumer's demand for each good is defined as a function of the prices of all consumer goods 
i prices of all resources
Since the demand of each consumer depends on these variables, it can be said that the market demand is defined as the sum of the individual demands. Therefore, to write down the market demand function for a good, you need to write down the following equality:
where qi- the volume of production of the good;
- the total demand of all consumers in the market
good I.
Because we have T markets for goods, we have exactly T such demand equations.
2. Resource supply equations
Because consumers must also choose the amount of supply of resources they possess, one must write down their supply functions. The individual supply of a resource also depends on the prices of consumer goods. (P, P t) and prices of all resources (p h p „). It is these two series of values that make it possible to estimate the benefits from the sale of resources. Since the individual supply of each consumer is defined similarly, we can represent the market supply function of an individual resource as a function of all prices on the farm and write the following equation:
where q, - sales volume in the resource market j;
Resource suggestion function j all household consumers.
Since the economy has P resource markets, we have exactly P such offer functions.
Note that one price vector defines volumes
demand and supply at once in all markets of goods and resources, since the choice of an individual consumer consists in the simultaneous determination of his demand and supply in all markets of the economy at given prices.
In addition, in this vector of prices, it is the ratio of prices of various goods and resources that is important, and not their absolute value. A proportional change in all prices will not cause a change in supply and demand in all markets. For example, if both the prices of goods and the prices of resources increase by exactly 2 times, no consumer will have an incentive to change his behavior.
3. Equilibrium equations in the industry
According to the logic already used, we would now have to write down the supply functions in the market for each good on the basis of the supply function of an individual firm. But we cannot do this due to the assumption of fixed coefficients. After all, fixed coefficients mean no economies of scale and no diminishing marginal productivity. The supply function of any good in this situation must have infinite elasticity, and the size of the firm turns out to be indeterminate.
In this situation, we can ignore the supply functions as such and write down another condition for the equilibrium of an individual producer in a particular market - the equality of profit to zero. Since there is perfect competition in all markets, the general equilibrium will be reached if the profitability of the production of all goods is the same and equal to zero. Or, what is the same, the average cost will be equal to the price of the good. Thus, we have
those. the price of a good i is broken down into the cost of acquiring resources to produce a unit of the good. Since every good must be produced under similar conditions, we have T such equations. Here, too, only the ratio of prices is essential: their proportional change does not violate equality (67.3).
4. Demand equations for resources
In determining the demand for resources, we are faced with the same problem as when considering the equation of equilibrium in the industry. Since the production coefficients are constant, the resource demand functions will have infinite elasticity. But as in the previous case, we can cheat and write down the general equilibrium condition - the demand for each resource will be presented in such an amount that is necessary to produce an equilibrium set of goods according to the existing production coefficients. Formally, this is also a demand function for a resource, in which not the prices of goods and resources are written as arguments, but already selected quantities of goods produced. Therefore, we can write
where qi- the volume of production of the good i.
Since this equality must hold for all resources, we also have P such equations.
Since we are analyzing relative prices and abstracting from their absolute values, in order to measure prices, we need to choose one good that will serve as a unit of account. The price of this good is taken equal to one and therefore is not unknown. So the number of unknowns is 2p + 2t - 1.
Now we can sum up. In total, our system has 2 P + 2t equations and 2p + 2t- 1 unknown. As you can see, there are fewer unknowns than equations, and this shows that one of the equations is redundant. If it can be excluded from the system by proving its dependence on the rest, then the general equilibrium is possible.
One equation can be eliminated based on the following consideration. In general equilibrium, all the income received by consumers from the sale of resources is spent in the markets for consumer goods. This means that the total cost of resources must be equal to the total cost of goods. Therefore, in conditions of general equilibrium, knowing the prices and quantities in all markets for resources and goods, except for the market for the good chosen as the unit of account, we can calculate the volume of demand in this market in a residual way. As a result of this, one of the demand equations turns out to be dependent on all other equations in the system, and it can be excluded. Remains 2 P + 2t- 1 independent equations.
Thus, the number of equations turns out to be equal to the number of unknowns, and this means the possibility of achieving a general equilibrium in the economy.
The necessity of equality of the number of unknowns to the number of equations to achieve general equilibrium in the economy does not mean the sufficiency of this condition. First, if the functions are non-linear, then the system of equations may have several solutions. This means that there are several equilibrium points (supply and demand curves in individual markets may intersect more than once). Secondly, as a result of solving this system of equations, we can get negative prices and quantities for individual goods, which will not make economic sense, and the general equilibrium with such absurd prices and quantities will be impossible.
The first rigorous proof of the existence of general equilibrium was carried out in the 1930s. German mathematician and statistician A. Wald. Subsequently, this proof was improved in the 1950s. K. Arrow and J. Debre. As a result, it was shown that there is a unique general equilibrium state with non-negative prices and quantities, if two conditions are met: 1) there is a constant or decreasing returns to scale of production; 2) for any good there is one or more other goods that are with him in relation to substitution.
To prove the possibility of achieving a general equilibrium, it is necessary to determine the mechanism for achieving equilibrium prices and volumes in each market. Walras himself used the theory of groping to prove the achievement of equilibrium, which is as follows.
First, it is necessary to answer the question of whether the system will move towards equilibrium prices and volumes. This is proved "by contradiction": if one imagines that at first some arbitrary price vector is realized, which does not correspond to the equilibrium one, this will mean a surplus in some markets and a shortage in others. This condition will lead to higher prices in markets where there is a shortage, and lower prices in those markets where there is a surplus. The change in prices will continue until the equilibrium vector of prices is "groped".
