Equilibrium price and equilibrium volume. Demand. Demand functions. The law of demand Topic: "Theory of supply and demand"

Typical tasks

Problem 1

The function of the population's demand for this product has the form: Q D = 7 - –P.

The supply function of the given product: Q S = 5 + 2P, where Q D and Q S are, respectively, the volume of demand and the volume of supply in million pieces per year, P is the price in den. units

a) Determine the equilibrium price and equilibrium sales.

b) Suppose a tax is imposed on this product, paid by the seller in the amount of 1.5 den. units for a unit.

Determine the equilibrium sales volume and equilibrium prices for

buyer (P e +) and seller (P e -).

Solution

Hence: 7 - P = - 5 + 2P, P e = 4.

Q D = 7 - 4 = 3, Q S = - 5 + 2 × 4 = 3, Q e = 3.

b) Since the seller pays the tax, the price for him will be P - = P + - 1.5.

Hence: Q D = 7 - P +,

Q S = - 5 + 2P - = - 5 + 2 (P + - 1.5).

therefore: 7 - P e + = - 5 + 2P e + - 3.

Hence: P e + = 5; P e - = 3.5; Q e = 2.

In the figure, this position can be represented as follows:

Task 2

Equilibrium was established in the market for this product at a price of 4 den. units per piece and sales volume of 18 thousand pieces per day. In this case, the coefficient of direct elasticity of demand (e D) is 0.05, and supply (e S): + 0.1.

Determine the equilibrium price for a product in the event of a decrease in demand for it by 10%, based on the assumption that the supply and demand functions are linear.

Solution

In the case of linear supply and demand functions:

Q D = a - bP; Q S = m + nP,

hence,
a

Because
a
then in a state of equilibrium:

- 0.05 = - b × 4/18, that is, b = 0.225.

0.1 = n × 4/18, that is, n = 0.45.

Now we can define parameters a and m:

a = 18 + 0.9 = 18.9; m = 18 - 1.8 = 16.2.

Hence,

Q D = 18.9 - 0.225P; Q S = 16.2 + 0.45P.

With a decrease in demand by 10%, the condition of equilibrium in the market for a given product takes the form: 0.9Q D = Q S; that is

0.9 (18.9 - 0.225P) = 16.2 + 0.45P.

Hence: P = 1.23.

Tasks

1. The demand function for this product has the form: Q D = 5 - P. Supply function: Q S = - 2 + P.

Determine the equilibrium price and volume of sales, as well as the surplus of the seller and the buyer. Sellers received a subsidy of 3 den. units per piece sold. Calculate the equilibrium volume, price and surplus. How was the subsidy distributed between buyers and sellers?

Determine the equilibrium price and sales volume. The state introduced a subsidy for consumers in the amount of 3 den. units per unit. Determine the new equilibrium sales volume and price. How much subsidy should the government allocate?

3. The demand function for this product has the form: Q D = 12 - P. Supply function: Q S = - 3 + 4P.

Determine the equilibrium price and sales volume. The excise tax on sellers was introduced in the amount of 20% of the sales volume. Determine the new equilibrium sales volume and price. How much tax will the state receive?

4. The coefficient of price elasticity of demand is - 0.2, and the coefficient of price elasticity of supply is + 0.2. In equilibrium, 10 units of good are sold at a price of 5 den. units

Determine the equilibrium volume and price with the introduction of a 1 den commodity tax. unit, which producers pay. (Assume supply and demand functions are linear.)

5. In what situation will most of the tax burden fall on

manufacturers?

a) Q D = 5 - 2P, Q S = P + 1;

b) Q D = 5 - P, Q S = 1 + P;

c) Q D = 5 - P, Q S = 1 + 2P.

6. The demand function for this product has the form: Q D = 8 - 2P. Supply function: Q S = 4 + P.

Determine the per-product subsidy that must be allocated to producers in order for the product to be distributed as a “free good”. How much of the product will be distributed in this case?

7. The demand function for this product is: Q D = 2 - 3P. Supply function: Q S = - 0.5 + 2P.

Determine the social benefit arising from the production and sale of the good (the sum of the surplus of buyers and sellers).

8. The demand function for this product has the form: Q D = 7 - 2P. Supply function: Q S = P - 5.

Determine the equilibrium price and sales volume. Calculate the per-product subsidy required to market a product and achieve a sales volume of 3 units.

9. The demand function for this product has the form: Q D = 12 - P. Supply function: Q S = - 3 + 4P.

Determine the equilibrium price and sales volume. A manufacturer tax of 2 den has been introduced. units per unit sold. Calculate the new equilibrium sales volume and price, and the net social loss.

10. The demand function for this product has the form: Q D = 12 - P. Supply function: Q S = - 3 + 4P.

Determine the equilibrium price and sales volume. An excise tax has been introduced on buyers in the amount of 20% of sales. Determine the new equilibrium sales volume and price. How much tax will the state receive?

11. The demand function for this product has the form: Q D = 5 - P. Supply function: Q S = - 1 + P.

Determine the equilibrium price and volume of sales, as well as the surplus

sellers and buyers. Customer tax imposed at 3 den. units per unit. Determine the equilibrium volume, price, sellers 'and buyers' surpluses, and the net loss to society.

12. There are three demand functions and their corresponding functions

suggestions:

a) Q D = 12 - P, Q S = - 2 + P;

b) Q D = 12 - 2P, Q S = - 3 + P;

c) Q D = 12 - 2P, Q S = - 24 + 6P.

The state introduces a subsidy to producers in the amount of 3 den. units for each piece. When will consumers receive most of the subsidy? Why?

13. The demand function for this product has the form: Q D = 6 - 2P. Supply function: Q S = - 2 + 2P.

Determine the excess demand at a price of 1 den. units Determine the equilibrium sales volume if the government sets a fixed price a) 1.5 den. units; b) 2.5 den. units

14. The demand function for this product: Q D = 7 - P, the supply function of this product: Q S = - 5 + 2P.

Determine the equilibrium price and equilibrium sales. Suppose the fixed price is determined at the level: a) 5 den. units for a unit; b) 3 days units for a unit. Analyze the results obtained. In which of these cases will the volume of consumption be the largest?

15. The demand function for this product: Q D = 16 - 4P, the supply function for this product Q S = - 2 + 2P.

Find the equilibrium price and equilibrium sales volume. Determine the sales tax rate at which the equilibrium sales volume is 2 units.

16. The demand function for this product: Q D = 7 - P, the supply function of this product: Q S = - 5 + 2P.

At what tax rate (in monetary units per unit of goods) will the total tax levy be the maximum?

17. In a state of equilibrium, 120 pieces of good A are sold in the market

at a price of 36 den. units It is known that the function of supply and demand for this good are straightforward and at the same time e D = - 0.75, and e S = + 1.5.

Determine what the price of good A will equal if its supply is reduced by 25%.

18. The market is characterized by the following supply and demand functions: Q D = 12 - P; Q S = 2P - 3.

Determine how much the equilibrium price will change if a 50% turnover tax (on sales volume) is introduced.

19. Let's assume that the excise tax on cigarettes is 25 den. units per bundle, which caused the supply curve to shift from S 1 to S 2, as shown in the figure. Answer the following questions:

a) What are the tax revenues to the budget if the demand curve is D 1? D 2?

b) Explain why the equilibrium price of cigarettes does not rise by 25 den. units?

c) At what demand (D 1 or D 2) will the introduction of the tax lead to the largest reduction in the number of smokers?

d) Suppose that instead of imposing a tax, the government decided to limit the sales of cigarettes in the country to 4 million packs per period. Where it leads?

20. The gas demand function has the form: Q r D = 3.75P n - 5P g, where P n, P g are the prices of oil and gas, respectively, the gas supply function is: Q g S = 14 + 2P g + 0.25P n.

At what prices for these energy carriers will gas demand and supply be balanced at the level of 20 units?

21. The demand function for the product has the form: Q D = 5 - P, the product supply function has the form: Q S = - 1 + 2P. Suppose there is a production quota of 2,000 units for this product.

What will be the consequences of this decision? Calculate the surplus of the seller and the buyer before and after the introduction of the quota.

22. In region I, the demand function for a certain product has the form: Q D1 = 50 - 0.5P 1, the supply function: Q S1 = - 10 + P 1, where Q D1, Q S1 are the volume of demand and the volume of supply in region I, respectively, P 1 - market price in region I (monetary units / kg). For region II

demand function for the same product: Q D2 = 120 - P 2, supply function: Q S2 = - 20 + P 2.

a) Suppose the transportation of this product between two regions is prohibited.

Determine market prices, sales in each region. Determine the surplus of consumers, the surplus of producers for each region, the total surplus for each region, the total surplus for two regions.

b) Let's say that transportation is allowed. Shipping costs are negligible. Define the same as in point a. In addition, determine the volume of production in each region, the volume of traffic.

Who benefits from lifting the ban on transportation? Who benefits from it? Is the overall benefit of lifting the ban increasing or not?

c) Carriage is permitted. Transportation costs are 10 den. units per 1 kg transported from one region to another.

Define the same as in point b.

d) Carriage is permitted. Shipping costs are negligible. The government of Region I has set an "export" duty of 10 den. units per 1 kg of exported products.

Define the same as in paragraph c. In addition, determine the total surplus of each region, including the tax received.

e) What will change if the duty is set not by the government of the I region, but by the government of the II region (“import” duty in the amount of 10 monetary units per 1 kg of imported products)?

23. Below are data on the volumes of supply and demand at various values of the price of this product:

a) If the price of the goods is 6 den. units per unit, how many units of goods

will be offered for sale? How many units would people want to buy? How much will the product actually be sold?

b) If the price of the goods rises to 12 den. units per unit, how many units will be offered for sale? What will be the volume of demand? How many units will be sold in this case?

c) Determine the equilibrium price and equilibrium sales.

d) Draw all the options graphically.

24. The following supply and demand functions are given:

a) Q D = 10 - P, Q S = 2P - 2;

b) Q D = 10 - P, Q S = 2 + P;

c) Q D = 10 - P, Q S = 4 + 0.5P;

What situation corresponds to stable equilibrium, unstable equilibrium, uniform fluctuations in the conditions of a cobweb-like model.

25. Four consumers are ready to purchase this product at individual prices equal to 8, 7, 5 and 2 den. units The supply prices of the goods from four manufacturers (each produces a unit of this good) are equal: 6, 4, 3 and 2 den. units

What is the maximum possible total surplus? How many goods will be produced and at what price? (Solve the problem graphically.)

26. Equilibrium in the market for this product was established at P = 5 and Q = 15. The coefficient of direct elasticity of demand with respect to price is –0.05, and the coefficient of direct elasticity of supply with respect to price is +0.2.

a) What will be the price of a product if the demand for it increases by 15%, and supply - by 10%, provided that the supply and demand functions are linear.

b) Present the solution to the problem on the graph.

27. The supply and demand functions for this product are as follows: Q D = 32 - 2P, Q S = –2 + 3P.

a) What is the maximum tax amount that can be collected if it is levied on each unit sold? The seller pays the tax.

b) Plot the Laffer curve.

28. The demand function for hairdressing salon services has the form: Q D = P 2 - 4P + 10. Service supply function: Q S = 6P - P 2.

a) Determine the equilibrium values of price and volume.

b) Plot the dependence of the number of services offered on its price.

c) Determine at what price the total income of the hairdressing salon will be maximum.

29. At a price of 3, the demand for the good is 30, and at a price of 4, it is 12. The demand function is linear.

Determine the maximum bid price.

30. The demand function for cabbage is: Q Dt = 200 - P t. The sentence function has the form: Q St = - 10 + 0.5 , where - the price of cabbage in period t, "expected" by farmers at the time they make decisions about the size of production. Let's assume: = P t-1.

a) Determine the sales volume and prices for cabbage in periods 1, 2, ..., 6, if P 0 = 200.

31. The demand function for carrots is: Q Dt = 200 - 0.5 ... The sentence function has the form: Q St = - 10 + 0.5 , where = P t - 1.

a) Determine the sales volumes and prices for carrots in periods 1, 2, ..., 6, if P 0 = 145.

b) Determine the equilibrium price and equilibrium sales. Can this equilibrium be called stable? Draw a drawing.

c) What changes, in your opinion, can occur in the mechanism of formation of expectations?

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.

a) Determine the sales volumes and prices for carrots in periods 1, 2, ..., 10, if P 0 = P t -1 = 250.

b) Draw the price dynamics in the figure.

c) Determine the equilibrium price and equilibrium sales. Can this equilibrium be called stable?

2. The rate of economic growth.

3. A simplified description of some aspects or properties of the economic system.

4. Competitiveness.

5. The need for something.

6. The desire of economic agents to maximize benefits under existing constraints.

7. Resources spent on production.

8. One of the possible options.

9. One of the properties of economic resources.

Topic: "Theory of supply and demand"

1. How will the position of your CD demand curve be affected by the following events (all other things being equal):

a) increase in income;

b) you are tired of listening to music at home alone - it is better to go with friends to concerts and discos more often;

d) CD player prices have gone down;

e) prices for cassette recorders have risen;

f) your friends believe (and you tend to think so) that due to the surplus of CDs on the market, their price will gradually decrease;

g) the cost of sound recording has increased.

2. The table presents data on the individual volumes of demand of consumers A, B, C.

Define:

a) the volume of market demand

b) build graphs of individual and market demand

3. There are three consumers in the market for a certain product: A, B, C. Individual demand curves are presented in the graphs. Plot the market demand curve.

4. Market demand for notebooks is characterized by the following demand scale: at a price of 10 rubles. the amount of demand is equal to 700 pieces, at a price of 20 rubles. the amount of demand decreases to 600 pieces, and at a price of 30 rubles. reduced to 500 pcs. Determine the market demand function for notebooks.

5. The initial price is P1 = 10, and the volume of demand is Q1 = 450. Due to the increase in price to P2 = 40, the volume of demand has decreased to Q2 = 300.

Define:

a) demand function

b) the amount of demand at P = 20

6. The demand function of an individual consumer is:

QD1 = 5 - 0.5P

Determine the market demand function ("Marshallian" type) if there are 5 firms on the market.

7. The functions of individual demand are given:

QD1 = 100 - P1

QD3 = 20 - 2P3

Define the aggregate demand function and graph it.

8. The individual offer function looks like:

Determine the function of the market supply if 8 identical firms operate on the market. ("Marshallian" look)

9. What impact will each of the following items have on the demand for product B, on the equilibrium volume and equilibrium price for a given amount of supply?

a) product B becomes more fashionable;

b) the price of product C, a substitute for product B, is reduced;

c) consumers expect lower prices and higher incomes;

(d) Population is growing rapidly.

10. For a given value of demand, how will each of the positions affect the supply, equilibrium price and quantity of goods B:

a) a decrease in the price of product A, in the production of which the same technologies and resources are used, which are required for the production of product B;

b) the introduction of a tax on sales of goods B;

c) granting a subsidy to the manufacturer of product B;

d) technical progress in the production of product B;

e) reduction in the number of firms producing the product;

f) an increase in the prices of inputs for the production of product B.

11. Patties replace buns in consumption and butter complements. What happens in the respective markets if the price of buns goes down?

a) the price of pies and butter will go down;

b) the price of pies will go up and the butter will go down;

c) the price of pies will go down and butter will go up;

d) the price of pies and butter will rise

12. Player supply and demand are described by the following equations:

Qd = 300 - 20P, Qs = 20 + 50P.

a) draw the supply and demand curves, and determine the equilibrium price and quantity;

b) due to a change in mode, demand changes according to the equation:

Qd = 510 - 20P. What happens to the demand curve? Find a new balance.

13. There are 2 sellers and 2 consumers on the market.

The buyers' demand functions, respectively, have the form:

QD1 = 10 - P, QD2 = 15 - 3P

The seller's offer functions are as follows:

QS1 = 2P - 6, QS2 = 4P

Determine the equilibrium price and volume of the transaction for each trader. Provide a graphical solution to the problem.

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16. The demand function has the form: Qd = 20 - 3P. The sentence function is: Qs = -3 + 6P. Determine the type of balance by the given functions. (Stable or unstable)

17. Consumer surplus is 15, producer surplus is 5, demand price (Pd) = 10, supply price (Ps) = 2

Determine the equilibrium values of price and quantity (PE-? And QE-?)

Currency "href =" / text / category / denezhnaya_edinitca / "rel =" bookmark "> currency. Draw the situation graphically and define:

1) how the equilibrium values of price and volume have changed;

2) consumer and producer surpluses before and after the introduction of the tax;

3) state income from the introduction of the tax;

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Section II. FOUNDATIONS OF THE THEORY OF MICROECONOMICS

This section provides an introduction to the study of microeconomics. The section provides general concepts that describe behavior in a market economy, without which it is impossible to study an advanced course in microeconomics. The section begins with a study of the basic concepts of microeconomics - demand, supply, equilibrium. Further, the concept of elasticity is revealed, which will subsequently be used not only in the course of microeconomics, but also in macroeconomics and the world economy. The section ends with the study of the foundations of the behavior of the subjects of the modern market economy.

Chapter 5. DEMAND: SUPPLY AND MARKET BALANCE

It is known from the previous chapters that the connection between producers and consumers in the commodity economy is carried out indirectly, indirectly - through the market. A specific form of implementation of commodity relations is a market mechanism, the main elements of which are demand, supply, price.

The purpose of the analysis of this chapter is the mechanism of interaction between supply and demand, i.e. the supply-demand model, which performs analytical and descriptive functions and is the most useful and important tool in the arsenal of an economist.

The supply and demand model, on the basis of which prices are formed, has been the core of economic theory for more than a century. Despite the fact that in the conditions of modern methods of regulating the market economy, equilibrium is achieved not only due to the interaction of market forces, but also with an active economic policy of the state, this model simply and convincingly leads to explicit and unambiguous conclusions that can be used to analyze various economic problems. ... It describes in a simple form some of the forces at work in the economy and thus reflects important aspects of real life.1

Demand. Demand functions. Demand law

Demands in a market economy appear in the form of demand. Market demand is an indirect reflection of people's need for a given product or service.

Human needs are known to be unlimited. Can we talk about unlimited demand? What is the difference between these concepts? The fact is that demand is a form of expression of the need presented on the market and secured with money, that is, demand is a solvent need. It is not enough to desire to purchase a product, it is necessary that the consumer has a certain amount of money in order to realize his desire. The market does not respond to insolvent needs. More precisely, the category of demand can be expressed by the term magnitude or demand volume.

The amount (volume) of demand- this is the amount of goods that consumers are willing and able to purchase at a certain price from a number of possible for a certain period of time.

It is important to distinguish between the terms "demand volume" and "actual purchase volume". The volume (value) of demand is determined only by the buyer, and the volume of the actual purchase is determined by both the buyer and the seller. For example, government price caps can cause significant increases in demand. At the same time, the volume of sales (“volume of actual purchase”) is likely to be low as a result of the manufacturer's disinterest in selling at fixed prices.

What determines the amount of demand? Various factors affect the desires and capabilities of a particular consumer to purchase a certain amount of goods. These include:

Product price P (price)

Consumer income I (income)

Tastes, fashion T (tastes)

Prices for related goods: interchangeable (substitutes) P S or complementary (complements) P C

Number of buyers N

Expectation of future prices and incomes W

Other factors X

So, in its most general form, the demand function is written as follows:

Q d = f (P, I, T, P S, P C, N, X)

Attempts to investigate the nature of the change in the value of demand Q d under the influence of all factors at once will not give a positive result. In this case, in order to identify the nature of the change in the value of demand Q d, it is first necessary to fix the values of all variables except one and to study the relationship between Q d and this variable. This method means that we investigate the dependence of the quantity of demand on each variable. all other things being equal.

The amount of demand for a product, first of all, depends on the price. If all factors, except for the price, are taken as unchanged for a given period, then price demand function will look:

The inverse dependence of the price on the amount of demand is called inverse demand function and has the form:

All other things being equal, a decrease in price leads to an increase in the amount of goods purchased by buyers; an increase in price causes a reverse reaction: the purchase of goods is reduced. Thus, the specified property of demand reflects the inverse relationship between the change in price and the amount of demand. The inverse relationship between the price and the amount of demand (other parameters are unchanged) is universal and reflects the operation of one of the fundamental economic laws - the law of demand.

Antoine Augustin Cournot(1801-1877) - the creator of the mathematical theory of demand. A. Cournot was, first of all, a talented mathematician, but he was bored in the world of pure mathematics, and with its help he tried to take a fresh look at the problems of other sciences and find connections between them.

In 1838, Cournot published his most famous book today, A Study of the Mathematical Principles of Wealth Theory. In fact, this was the first conscious and consistent attempt to apply a serious mathematical apparatus for the study of economic processes. From this sprout a whole area of science grew - mathematical economics.

It was A.Courno who was the first to deeply analyze the relationship between demand and price in various market situations. This made it possible for him to formulate the law of demand and bring economics close to understanding the concept of “elasticity of demand” (A. Marshall picked up the ideas of A. Cournot and brought them to their logical conclusion). Cournot was able to mathematically rigorously prove that the highest sales proceeds are often provided by far from the highest price.

Why does demand behave this way? This happens for a number of reasons that argue the law of demand and take into account the following circumstances:

Common sense and life experience directly influence the volume of purchases depending on the price. The lower the price, the more purchases - this is a psychological moment.

Of course, at low prices, the volume of purchases increases, but sooner or later the consumer reaches the limit when each next unit of goods will deliver less and less pleasure, no matter how much the price decreases. After a certain level of saturation of the need, the satisfaction received from the product or service begins to decrease. Economists call this effect the law of diminishing marginal utility. The decline in marginal utility explains why low prices stimulate demand. Goods sold at a high price are usually not bought for the future or "at random". But if the price is low and affordable, then, most likely, the buyer purchases this product even a little more than he needs.

The action of the law of demand can be explained based on two interrelated effects - income effect and substitution effect.

Obviously, at a lower price, the buyer can afford to buy more of a given product without giving up purchasing other products. He feels richer because a price cut increases his real purchasing power, or real income with the same value of his monetary income. it income effect.

Income effect(as a result of price changes) - a change in the value of demand for a product, due to the fact that a change in its price leads to a change in the real income of the consumer.

The extent of the income effect depends mainly on how much of the income is spent on the purchase of a given product. The more income is spent on a product, the more the effect of price increases on the consumer's real income will influence and the more consumption will decrease.

On the other hand, the consumer is inclined to replace more expensive goods with cheaper analogs, which leads to an increase in the value of demand for these goods. it substitution effect.

Substitution effect- the desire of consumers to buy a product in greater quantities when its relative price decreases (replacing others with this product) and to consume it in smaller quantities when its relative price rises (to replace this product with others). It is this effect that determines the negative slope of the demand curve.

The magnitude of the substitution effect depends mainly on the quantity and availability of substitute goods.

The income effect combined with the substitution effect form a general the effect price changes.

The functional relationship between the amount of demand and the price can be expressed in various ways:

1. Tabular- in the form of a table or a scale of demand (table 5.1):

Table 5.1

The ratio of the price of goods X and the quantity X for which demand is presented.

2-1p. Population demand function for this product: Qd = 7-P. Suggestion function: Q s = -5 + 2P,where Qd - demand volume in million units per year; Qs - supply volume in million units per year; R - price in thousands of rubles. Plot supply and demand graphs for a given product, plotting the quantity of the product on the abscissa (Q) and on the ordinate - the unit price (R).

Solution

Since the given functions reflect a linear relationship, each of the graphs can be plotted using two points.

2-2p. Determine the market demand function based on individual demand data:

Q (1) = 40-8P at P ≤ 5 and 0 at P> 5,

Q (2) = 70-7P at P ≤ 7 and 0 at P> 7,

Q (3) = 32-4P at P ≤ 8 and 0 at P> 8.

a) Derive the equation of the demand curve analytically.

b) Which of these consumer groups do you think is richer? Is it possible to draw an unambiguous conclusion?

Solution

a) Q = Q (1) + Q (2) + Q (3) = 142-19P at 0 ≤ P ≤ 5,

Q = Q (2) + Q (3) = 102-11Р at 5 < Р ≤ 7 ,

Q = Q (3) = 32-4P at 7 < P ≤ 8 ,

Q = 0 at P> 8.

b) The third group of consumers agree to pay the highest prices. For example, for P = 7.5 the first two groups will stop buying, and the buyers of the third group will buy 2 units. (32-4x7.5 = 2). But it is impossible to draw an unambiguous conclusion that the third group includes the richest buyers, since we do not know either their income or other direct and indirect signs of wealth.

2-3p. The demand for VCRs is described by the equation:

Qd = 2400-100R, and the offer of video recorders - by the equation Qs = 1000 + 250Р, where Q - the number of VCRs bought or sold during the year; R - the price of one VCR (in thousand rubles).

a) Determine the equilibrium parameters in the VCR market.

b) How many VCRs would have been sold at a price of 3000 rubles?

c) How many VCRs would have been sold at a price of 5,000 rubles?

Solution

a) In order to determine the parameters of equilibrium, let us equate the volume of demand to the volume of supply:

Qd = Qs, or 2400-100P = 1000 + 250P.

Solving the equation, we find the equilibrium price:

1400 = 350P; Pe = 4000 rub.

Substituting the found price into the equation describing the demand, or into the equation describing the supply, we find the equilibrium quantity Qe.

Qe = 2400-100 x 4 = 2000 PCS. in year.

b) To determine how many VCRs will be sold at a price of 3000 rubles (i.e. at a price below the equilibrium one), you need to substitute this price value in both the demand equation and the supply equation:

Qd = 2400 - 100 NS 3 = 2100 PCS. in year;

Qs = 1000 + 250 NS 3 = 1750 PCS. in year.

This shows that at a price below the equilibrium price, consumers will want to buy more VCRs than manufacturers will agree to sell (Qd> Qs). In other words, consumers will want to buy 2,100. VCRs, but they can buy exactly as much as the sellers will sell them, i.e. 1750 pcs. This is the correct answer.

c) Substitute the price of 5,000 rubles into each of these equations:

Qd = 2400 - 100 NS 5 = 1900 PCS. in year;

Qs = 1000 + 250 NS 5 = 2250 PCS. in year.

If the price is higher than the equilibrium price, the producers will want to sell 2,250 units. VCRs, but consumers will only buy 1,900. VCRs, therefore, only 1900 pieces. VCRs and will be sold at a price of 5,000 rubles.

Answer: a) equilibrium parameters: Pe = 4000 rubles, Qe = 2000 PCS. in year.

b) at P = RUB 3000 will be sold Q = 1750 PCS. in year.

c) at P = RUB 5000 will be sold Q = 1900 PCS. in year.

2-4p. The gas demand function has the form: Qd g = 3.75P n -5P g, and the function of its proposal is: Qs g = 14 + 2P g + 0.25P n,where R n, R g- oil and gas prices, respectively.

Define:

a) at what prices for these energy carriers the volumes of gas demand and supply will be equal to 20 units;

b) by what percentage the volume of gas sales will change with an increase in oil prices by 25%.

Solution

A) To determine at what prices for these energy carriers the volumes of gas demand and supply will be equal to 20 units. we solve the system of equations:

3.75R n -5R g = 20

14 + 2P g + 0.25P n = 20Þ R n = 8; P g = 2.

Since from the first equation P n = (20 + 5P g) / 3.75, substitute this expression into the second equation.

14 + 2P g +0.25 (20 / 3.75) +0.25 (5P g / 3.75) = 20,

2P g +0.25 (5P g / 3.75) = 20-14-0.25 (20 / 3.75),

2P g + 0.33P g = 6-1.33,

2.33P g = 4.67,

P g = 2.

R n = (20 + 5 NS 2)/3,75=8.

b) If the price of oil rises to 10 den. units, then the equilibrium in the gas market will be subject to the following equality:

3,75 NS 10 - 5P g = 14 + 2P g + 0.25 NS 10 Þ

37.5-5P g = 14 + 2P g + 2.5Þ

-5P g - 2P g = 14 + 2.5-37.5Þ

-7P g = -21,

P g = 3, Q g = 37.5 - 5 NS 3 = 22,5.

those. gas sales will increase by 12,5%.

Answer: a) if the volumes of demand and supply of gas are equal, 20 units. oil and gas prices will be equal respectively R n = 8; P g = 2.

b) with an increase in the price of oil by 25% , the volume of gas sales will increase by 12,5%.

2-5p. There are three sellers and three buyers in the real estate market. The functions of the offer at the price of sellers are known:

Qs 1 = 2P-6; Qs 2 = 3P-15; Qs 3 = 5P.

and the demand function for the buyers' price:

Qd 1 = 12-P; Qd 2 = 16-4P; Qd 3 = 10-0.5R.

Determine: the parameters of the market equilibrium, as well as the volume of the transaction of each participant in the trade at the equilibrium price.

Provide a graphical and analytical solution.

1. Direct and inverse demand functions

Condition: It is known that consumers are ready to purchase 20 units of a good for free; with each increase in price by 1, the amount of demand decreases by 2 units. Write down the forward and backward views of the demand function describing the given situation.

Solution: Since a price change by 1 always changes Q by 2 units, we are dealing with a linear demand function. (The direct form of the demand function is the dependence of the demand value (Q) on the price (P) - Qd (P); and the reverse form of the function, on the contrary, is the dependence of the price on the demand value - Pd (Q)).

In general, a direct linear demand function is written as: Q d (P) = a - bP, where a and b are the coefficients that we need to find. We know that for P = 0 the value of demand is 20 units, from which it follows that a = 20... Moreover, the coefficient b = 2... Thus, the direct demand function can be written as Qd(P) = 20 - 2P.

To obtain the inverse demand function, we express the price from the previously obtained expression: Pd(Q) = 10 - 0.5Q.

Answer: Q d (P) = 20 - 2P- direct demand function ; P d (Q) = 10 - 0.5Q- inverse demand function .

Note: both types of demand function are equally often used in solving problems, however, it does not matter if you forget which of the types is called.

2. Reconstruction of the linear demand function

Condition: At a price P 0 = 10, consumers want and can buy 5 units of products. If the price rises by 50%, then the amount demanded will fall by 40%. Write down the demand function for a given good, if it is known that it has a linear form.

Solution: In general, the linear demand function can be written as Q d (P) = a - bP, where a and b are the coefficients that we need to find. Since we have two unknowns, to find them it is necessary to compose a system of at least two equations. To do this, we find the coordinates (Q, P) of two points that correspond to the given demand function.

When P 0 = 10, consumers are ready to buy 5 units of the good, that is, the value of demand Q 0 is equal to 5 - these are the coordinates first point... If the price rises by 50%, the price will be equal to 15; and the value of demand after falling by 40% will be equal to 3 units. So the coordinates second point is (3, 15). Let's write down the system of equations:

5 = a - b * 10

3 = a - b * 15

The system is solved when a = 9 and b = 0.4.

Answer: Q d (P) = 9 - 0.4P.

Note: this is the standard way of finding the coefficients of a linear demand function, which will be required in most problems in which the demand function itself is not given, but it is indicated that it has a linear form.

3. Plotting a linear demand function

Condition: The functions of demand for some good are given: Q d1 (P) = 20 - 2P and P d2 (Q) = 5 - Q. Let the demand, expressed by the first function, decreased by 5 units. at each price level, and demand, expressed by the second function, increased by 60%. Plot the original and modified demand functions.

Solution: To begin with, we write down the demand functions in direct form, that is, we express Q through P: Q d1 (P) = 20 - 2P and Q d2 (Q) = 5 - P. To build any linear function, it is enough to find the coordinates two points. The further these points are from each other, the more accurately the line can be drawn. The ideal option is if we find the coordinates of the intersection of our lines with the Q and P axes. To do this, we substitute in each function first Q = 0, and then P = 0. This principle works well when constructing linear demand functions; in other cases, its application can be limited:

Now we will find new demand functions, calculated taking into account the changes. The first demand decreased by 5 units. at each price value, that is Q new d1 (P) = Q d1 (P) - 5: Q new d1 (P) = 15 - 2P. On the graph, the new demand curve is obtained by shifting the original curve to the left for 5 units. - this is red line D 3... The second demand increased by 60% at each price level. So, with P 1 = 5 and Q 1 = 0, no change will occur, since 60% of 0 is 0. At the same time, with P 2 = 0 and Q 2 = 5, the change in demand will be maximum and will be 0.6 * 5 = 3 units Thus, the new demand function will be Q new d2 (P) =Q d2 (P) +Q d2 (P) * 0.6:Q new d2 (P) =8 - 1.6P. Let us check the result obtained by substituting the already known points (0.5) and (8.0) into the function. Everything is being done, this demand is displayed on the graph blue line D 4.

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