consumer balance. Methods for finding the equilibrium point

A point at rest is said to be in equilibrium if the resultant of the forces applied to it is zero. If a point remains in equilibrium for some period of time, then it is at rest during that period.

Thus, a necessary and sufficient condition for a point at rest to be in equilibrium under the action of forces applied to it is that the resultant R of these forces be equal to zero. If the force projections are R, then this condition can be written analytically in the form of three algebraic equations:

146. The case when there is a force function.

If there is a force function for the resultant of forces applied to a point, then the three previous equations take the form:

A function is said to have a maximum or minimum at a point if its value at that point is greater or less than at any other point sufficiently close to it. According to this, the three previous conditions are the necessary conditions for the maximum or minimum of the function . From this we conclude that in the presence of a force function, those points in space where the function reaches its maximum or the smallest value, the essence of the equilibrium position: a point, being placed in one of these positions without an initial velocity, will remain in this position.

147. Stability of equilibrium. Lejeune-Dirichlet theorem.

When a point is in a position of equilibrium, it may happen that the slightest shock or displacement from this position imparted to the point will be sufficient to set it in motion, which will be more and more intensified, so that the point will eventually move to a final point. distance from its equilibrium position. In this case, the equilibrium is said to be unstable. Conversely, equilibrium is stable if the point deviates arbitrarily little from its own

equilibrium position, provided that the initial deviation and speed are sufficiently small.

Lejeune-Dirichlet theorem. - The equilibrium positions of the moving point, in which the force function reaches its maximum, are the positions of stable equilibrium.

Let a, b, c be the coordinates of the point A, at which the force function has a maximum; this means that the function at point A reaches a value greater than at any other sufficiently close point.

Let us prove that A is a position of stable equilibrium, i.e., that point M will not leave the sphere with center A and with radius arbitrarily small, provided that the initial position of the point is sufficiently close to A and the initial velocity is sufficiently small.

Since the function o is defined only up to a constant, we can choose this constant in such a way that it vanishes at the point A and, therefore, is negative near this point, i.e., inside and on the surface of the sphere (with the exception of points A) with center Ls radius , which can be set as small as desired. In particular, since it is negative on the surface of the sphere S, one can choose a positive number (also arbitrarily small together with , satisfying at any point x, y, z of this surface the condition

After this is done, we give the point M an initial position close enough to A to satisfy the condition

and initial speed small enough for the inequality

Establishing an equilibrium price occurs in a competitive market under the influence of general trends and specific features of both supply and demand. On fig. 1 shown in most general view dynamic processes that occur in the sphere of movement of goods and prices.

Rice. one. Graph of the market balance of supply and demand

Equilibrium market priceis the price at which there is no surplus or shortage for any given commodity. It is established as a result of balancing supply and demand as the monetary equivalent of a strictly defined quantity of goods.

Supply and demand are balanced under the influence of the competitive market environment, as a result of which the price and the quantity of the commodity sold at that price are the result of the balance of supply and demand. Other equal conditions the price corresponds to the quantity that buyers are willing to buy and sellers are willing to sell.

Intersection pointE is the point of balance between supply and demand. As shown in the equilibrium graph, any surplus of a commodity brought to market "pushes" the price of the commodity down towards the equilibrium point. And vice versa, if there is a shortage on the market, a shortage of any goods, then an upward trend arises, which “presses” the price of the missing goods upwards, towards the same equilibrium point.

Ultimately, an equilibrium price P e will be established, at which Q e goods will be sold in this market in each this moment time. At each subsequent moment of time (during the day, week, month, year) the market equilibrium can be established as a certain new value of the equilibrium price and the number of sales of goods at this price.

However, equilibrium- this is a state of the market in which Q d = Q s . Any deviation from this state sets in motion forces that can return the market to a state of equilibrium: eliminate the shortage (Q d > Q) or excess goods on the market (Q s< Q d).

The balancing function is performed by the price, stimulating the growth of supply with a shortage and "unloading" the market from surpluses, holding back supply. If demand grows, a new, higher equilibrium price level and a new, larger supply of goods are established. Conversely, a decrease in demand leads to the establishment of a lower equilibrium price and a smaller supply volume (Fig. 2, a, b).

Rice. 2. (a) Equilibrium level with changing demand and constant supply

Figure 2. (b) Equilibrium level with changing supply and constant demand

As can be seen from the graph, the balancing function of price reveals its influence both through demand with unchanged supply, and through supply with unchanged demand.

With a changing supply and a constant demand, a different level of market equilibrium will also be established. Thus, an increase in supply will give a new point of lower equilibrium price with an increasing number of sales of goods. In the event of a decrease in supply, equilibrium will be established for more than high level with fewer product sales.

Equilibrium- the law for each competitive market, which allows you to keep the balance of the entire economic system generally.

Example of calculating the equilibrium price

On the Moscow market household appliances the offer of domestic refrigerators looked like: Q s = 15 000 4- + 2.4P, whereR- price, thousand rubles for 1 refrigerator; Q s - volume of offer, pcs. in a year. The demand for these refrigerators looked like this: Q d = 35 000 - 2.9R.

The equilibrium price of domestic refrigerators can be established by balancing the supply and demand for this product (Q s = Q d ).

The balance of supply and demand. Equilibrium price.

Equilibrium - This is a situation in the market when supply and demand are the same or equivalent at an acceptable price for the consumer and the producer.

Market equilibrium arises as a result of the interaction of supply and demand. To find out how this happens, you need to combine the supply and demand curve on the same graph.

This graph expresses the simultaneous behavior of supply and demand for a particular product and shows at what point the two lines intersect (i.e. E). At this point, equilibrium is reached. point coordinates E are the equilibrium price R E and equilibrium volume . The dot characterizes equality Q E = Q s = Q D , where - the volume of the offer QD- demand volume.

The equilibrium point shows that here supply and demand, being opposing market forces, are balanced. The equilibrium price means that as many goods are produced as required by buyers. Such an equilibrium is an expression of the maximum efficiency of a market economy, because in a state of equilibrium the market is balanced. Neither the seller nor the buyer has internal motivations to violate it. Conversely, at any other price other than the equilibrium price, the market is not balanced, and buyers and sellers tend to change the situation in the market.

Thus, the equilibrium price is the price that balances supply and demand as a result of the action of specific forces.

If the real price is greater than the equilibrium (), then at such a price, the quantity demanded will be less than the quantity supplied Q2. In this case, producers will prefer to reduce the price than to continue to produce output in a volume that significantly exceeds the volume of demand. The excess supply will put downward pressure on the price.

If the real market price is below the equilibrium price (R 2), then the volume of demand on the graph Q4 and the commodity will become scarce. Some buyers will choose to pay a higher price. As a result, excess demand will put pressure on the price.

This process will continue until it reaches an equilibrium level. R E, where supply and demand are equal.

Equilibrium is the law of every competitive market. Thanks to the equilibrium in each market, the equilibrium of the economic system as a whole is maintained.

It is important to emphasize that the equilibrium price is set in competitive market conditions. However, it is impossible to meet all the conditions of competition. The mechanism of market price equilibrium is the mechanism of approaching perfection, which is never fully achieved.

Yet in practice, according to the law of supply and demand balance, the price of any commodity. All commodity markets are close to competitive equilibrium, if there are no elements of monopoly intervention in the market mechanism that change the model of competitive equilibrium.

Market price. Market equilibrium

The functions of supply and demand considered by us earlier interact in the commodity market. Under the influence of the competitive environment of the market, supply and demand are balanced, as a result of which the market price and quantity of the purchased goods are established.

Market price is considered the equilibrium price when it determines the level at which the seller still agrees to sell, and the buyer already agrees to buy the goods.

Graphically, the state of equilibrium in the market for a particular product can be represented by combining the supply and demand curves in one figure (Fig. 4.1).

Rice. 4.1. Market balance of supply and demand.

Point of intersection of curves E is the point of balance between supply and demand. Then for a given quantity of goods QE the maximum price at which it can be purchased by buyers (bid price RD), coincides with the minimum acceptable price for sellers (bid price Ps), which will mean the establishment of a stable equilibrium price in this market RE, at which the equilibrium quantity of goods will be bought and sold Q.E.

Analytically, using the familiar supply and demand functions, equilibrium state in the commodity market can be written as follows:

It should be noted that at the same time, both buyers and sellers will be satisfied with the situation that has developed on the market at the moment. A price decrease below the equilibrium level will be unprofitable not only for sellers, but also for buyers, since this will reduce the quantity of goods offered, and a price increase above the equilibrium level will not suit not only buyers, but also sellers, since it will reduce the purchased volume of goods.

Other things being equal, the market price corresponds to the quantity of goods that buyers want to buy, and sellers agree to sell, i.e. for each particular product there is neither surplus nor shortage. Thus, the equilibrium of the market is its state when the condition Qd = Qs. Deviation from this state will set in motion forces seeking to return the market to a state of equilibrium, i.e. to eliminate the surplus (when Qd< Qs) or lack of goods on the market (Qd > Qs).

In analytical form, for the supply and demand functions, the equality of the volume of demand QD volume of supply QS at a given equilibrium price RE will look like this:

In order to more clearly imagine the mechanism of establishing a market price under the influence of supply and demand, let us return to our example characterizing the situation in the potato market.

Let's combine our two tables on potato consumption into one (Table 4.1).

Table 4.1. Potato demand and supply

The table shows that only at a price of 7.50 rubles. for 1 kg of potatoes, supply and demand are balanced. Let's transfer this data to the graph (Fig. 4.2).

Rice. 4.2. Equilibrium price.

The point reflects the coincidence of interests of sellers and buyers at a price of 7.50 rubles. Therefore, 7.50 rubles. (PE) is the equilibrium market price. At a higher price there is excess supply over demand. For example, at a price of 10 rubles. only 5 tons of potatoes will be bought, and Utah will offer, therefore, the surplus will be 5 tons. This surplus, as a result of the competition of sellers, will help to reduce the price. At a price below the balancing price, demand exceeds supply and there is deficit goods on the market. In this case, excess demand and buyer competition will drive up the price.

Equilibrium mechanism

Let us consider the mechanism for establishing market equilibrium, when, under the influence of changes in supply or demand factors, the market leaves this state. There are two main variants of the disproportion between supply and demand: excess and shortage of goods.

Excess(surplus) of a good is a situation in the market when the supply of a good at a given price exceeds the demand for it. In this case, competition arises between manufacturers, the struggle for buyers. The winner is the one who offers more favorable conditions for the sale of goods. Thus, the market tends to return to a state of equilibrium.

deficit goods - in this case, the quantity demanded for the goods at a given price exceeds the quantity offered. In this situation, competition already arises between buyers for the opportunity to purchase a scarce product. The winner is the one who offers the highest price for this product. The increased price attracts the attention of manufacturers, who begin to expand production, thereby increasing the supply of goods. As a result, the system returns to a state of equilibrium.

Thus, the price performs a balancing function, stimulating the expansion of production and supply of goods with a shortage and restraining supply, ridding the market of surpluses.

The balancing role of price is manifested both through demand and through supply.

Suppose that the equilibrium established in our market was disturbed - under the influence of any factors (for example, income growth) there was an increase in demand, as a result, its curve shifted from D1 in D2(Fig. 4.3 a), and the proposal remained unchanged.

If the price of a given commodity did not change immediately after the shift in the demand curve, then following the growth in demand, a situation will arise when, at the previous price, P1 the amount of goods that each of the buyers can now purchase (QD) exceeds the volume that can be offered at a given price by the producers of a given goods (QS). The amount of demand will now exceed the amount of supply of this product, which means that shortage of goods at the rate of Df = QD – Qs in this market.

The shortage of goods, as we already know, leads to competition between buyers for the opportunity to purchase this product, which leads to an increase in market prices. According to the law of supply, the response of sellers to an increase in price will be to increase the volume of goods offered. On the chart, this will be expressed by the movement of the market equilibrium point E1 along the supply curve until it intersects with the new demand curve D2 where the new equilibrium of the given market will be reached E2 s equilibrium quantity of goods Q2 and equilibrium price P2.

Rice. 4.3. Equilibrium price point shift.

Consider a situation where the equilibrium state will be violated on the supply side.

Suppose that under the influence of some factors there was an increase in supply, as a result of which its curve shifted to the right from the position S1 in S2 and demand remained unchanged (Fig. 4.3 b).

As long as the market price remains the same (R1) an increase in supply will lead to excess goods in size Sp = Qs–QD. As a result, there is vendor competition, leading to a decrease in the market price (with P1 before P2) and an increase in the volume of goods sold. On the chart, this will be reflected by the movement of the market equilibrium point E1 along the demand curve until it intersects with the new supply curve, resulting in a new equilibrium E2 with parameters Q2 and P2.

Similarly, it is possible to identify the effect on the equilibrium price and the equilibrium quantity of goods of a decrease in demand and a decrease in supply.

AT educational literature four rules for the interaction of supply and demand are formulated.

1. An increase in demand causes an increase in the equilibrium price and the equilibrium quantity of goods.
2. A decrease in demand causes a fall in both the equilibrium price and the equilibrium quantity of goods.
3. An increase in supply entails a decrease in the equilibrium price and an increase in the equilibrium quantity of goods.
4. A decrease in supply entails an increase in the equilibrium price and a decrease in the equilibrium quantity of goods.

Using these rules, you can find the equilibrium point for any changes in supply and demand.

The following circumstances can mainly prevent the price from returning to the market equilibrium level:

1. administrative regulation of prices;
2. monopolism producer or consumer, allowing to keep the monopoly price, which can be either artificially high or low.

State regulation of market processes with the help of taxes and subsidies

Intervention external forces in the operation of the law of supply and demand can affect the formed market equilibrium. One of the levers for regulating the market system that does not violate the law of supply and demand are taxes. They do not change the conditions for the flow of market processes and do not limit the freedom of action of market entities. However, both consumers and producers of goods perceive the increase in taxes extremely negatively, since any tax, direct or indirect, is necessarily included in the price of the goods sold. An increase in price, inevitably following an increase in tax, causes a decrease in both consumer purchases and the supply of taxed goods.

Graphically, this situation can be represented as follows. As a result of the introduction of a new tax or an increase in the interest rates of existing taxes, the supply curve S1 move left and up by the tax amount T, since the seller is now forced to charge a higher price for the goods in order to receive the same revenue. In response to this reduction in supply, the market equilibrium point will move along the demand curve from E1 up to the intersection with the new supply curve S2, i.e. to the point E2. As a result, a new equilibrium will be established on the market, in which the volume of goods will decrease from Q1 before Q2 and the price will increase with P1 before R2(Fig. 4.4).

Rice. 4.4. Consequences of imposing a tax.

Despite the fact that formally the tax is paid directly to the state budget by the manufacturer or seller of goods, however, most of it is shifted to consumers who buy goods that are taxed.

In this way, negative effect tax increases - a general decrease in the production of goods and a decrease in the consumption of their buyers due to their rise in price.

The opposite result is achieved by providing a subsidy (they can be considered as negative taxes) to both the buyer and the seller.

Shifting supply and demand curves by the amount of the subsidy G will be the opposite of their taxation bias.

For example, the receipt of a subsidy by the seller will be tantamount to a reduction in his costs and, on the graph, will lead to a downward shift in the supply curve by the amount G(Fig. 4.5), which will lead to an increase in the equilibrium quantity of goods with Q1 before Q2 and at the same time reduce the equilibrium price from P1 before P2.

Rice. 4.5. Consequences of the introduction of subsidies.

If the buyer receives the subsidy, then by the amount G the demand curve will move, not the supply curve.

State influence on market processes through price regulation

Equilibrium prices that have been established in the market at a certain moment, due to various circumstances, do not always suit society.

1. The market price is considered the equilibrium price when it determines the level at which the seller still agrees to sell, and the buyer already agrees to buy the goods. Graphically, the state of equilibrium in the market for a particular product can be represented by combining the supply and demand curves in one figure. The point of intersection of the curves is the point of equilibrium between supply and demand.

2. When deviating from the state of equilibrium, i.e., in the presence of a shortage or surplus of goods on the market, the price plays a balancing role, stimulating the growth of supply in case of a shortage and restraining it in case of overstocking.

The following options for changing the equilibrium price are possible:

1. an increase in demand causes an increase in the equilibrium price and the equilibrium quantity of goods;
2. a decrease in demand causes a fall in both the equilibrium price and the equilibrium quantity of goods;
3. an increase in supply entails a decrease in the equilibrium price and an increase in the equilibrium quantity of goods;
4. a decrease in supply entails an increase in the equilibrium price and a decrease in the equilibrium quantity of goods;
5. one of the levers of regulation of the market system are taxes. Such regulation does not violate the principles of formation of an equilibrium price according to the laws of supply and demand, does not change the conditions for the course of market processes and does not limit the freedom of action of market entities;
6. state intervention in market pricing by setting fixed prices affects the very operation of market mechanisms, changing the process of achieving equilibrium. The consequences of price controls, especially if they are applied for a long time, have a negative effect both in the social and economic spheres.

To do this, you need to use the supply and demand functions and determine at what value of the price the supply and demand functions will give the same values. We can solve this problem in two ways.

1. If the supply and demand functions are expressed using tables, then we just need to find the price for which the values ​​of the columns containing the supply and demand volumes coincide. Table 2.4.1 provides supply and demand information for the bun market, compiled from tables 2.2.1 and 2.3.1. It is easy to see that the price of 15 rubles per bun gives the same supply and demand volumes equal to 2=800 buns. At a price of 20 rubles, supply exceeds demand (3=600 > 2=000), and at a price of 10 rubles, on the contrary, demand exceeds supply (2=000< 4=150).

Table 2.4.1

2. Now let's try to determine the market equilibrium using charts . To determine the equilibrium price and equilibrium quantity, we simply need combine demand curve and supply curve on the same graph and find intersection point.

Let us use the already constructed demand and supply curves from § 2 and § 3. Suppose that the curve D in fig. 2.4.1 is the consumer demand curve for buns in the market for this good. A curve S is the supply curve of rolls by their producers.

Curves intersect at some point BUT(in other words, have a common point BUT), which shows the equilibrium values ​​of price and quantity in this market. The point at which the supply and demand curves intersect is called balance point.

In this case, the equilibrium price is the price of 15 rubles, and the equilibrium quantity is 2=800 buns.

Note that no other price is the equilibrium price. Any price above 15 rubles will cause a supply volume in this market exceeding 2 = 800 rolls, since manufacturers interested in additional profit will want to increase output. And the quantity demanded will be lower than 2 = 800 rolls, since the increased price will force some consumers to partially or completely refuse to consume this good, and therefore the total quantity of demand will decrease somewhat. As a result, there will be oversupply(part of the total supply that will not be able to find a buyer). In this case, the sellers, whose product it turns out to be, will be forced to suffer losses.

For example, at a price of 20 rubles, the quantity supplied will be 3=600 buns, while the quantity demanded is only 2=000 buns. As a result, 3=600=v=2=000===1=600 buns will remain unsold.

Accordingly, at any value of the price below the equilibrium one, the opposite picture will be observed. Sellers will want to reduce the amount of supply somewhat, since lowering the price means reducing the profitability of production. A==customers will want to increase their consumption, since a lower price means an increase in their purchasing power and a reduction in the "difficulty" of purchasing the buns. As a result, there will be supply shortage(excess demand) = there will be consumers left in the market who would like to buy some more rolls at this price, while all the rolls brought by the producers have already been sold.

For example, at a price of 10 rubles, the quantity demanded will be 4=150 buns, while the quantity supplied is only 2=000. As a result, a certain number of consumers in the market who "did not have time" to buy rolls will remain with an excess volume of demand 4=150 v 2=000 = 2=150 rolls.

Only the price of 15 rubles causes such a volume of supply of rolls and such a volume of demand for them that the market cleared, and all participants in transactions remain satisfied with this state of affairs and do not want to change their behavior.

At the same time, we can calculate the cost of all transactions if we find the product of price and sales volume. In this case, it is 15=T=2=800 = 42=000 (rubles). This means that in total buns were sold for 42 = 000 rubles, and this amount was transferred from buyers to sellers. Each buyer paid some part of this amount, and each seller also got some part of it. In Fig.=2.4.1, this sum corresponds to the shaded rectangle.

Note that at this equilibrium price, some sellers and buyers may have refused to trade at all. There could be "failed" sellers and buyers who were not at all satisfied with given price and they refused to buy or sell even one bun. Of course, there may be no such thing if every buyer bought and every seller sold at least one bun.