Equilibrium price and equilibrium volume. Forward and reverse demand functions

The demand function for the product has the form: Qd \u003d 15 - 2p

Suggestion Function Qs \u003d -2 + 3p

Define:

1. Equilibrium price and sales.

2. The government introduced a goods tax in the amount of 1 thousand rubles. per unit of production. The tax is paid by sellers of goods. Define new equilibrium demand volume and price.

3. Calculate the amount of cash receipts from the state budget from tax. Who will the introduction of the industrial tax will have a greater impact - on sellers or buyers. Why?

1. To determine the equilibrium price and the equilibrium sales volume, it is necessary to use the condition of market equilibrium:

In our example:

15 - 2p \u003d -2 + 3p,

Thus, the equilibrium price will be equal to 3.4 thousand rubles. per unit of goods. In our example, the equilibrium sales volume can be determined by substituting the equilibrium price into the demand or supply function.

Equilibrium volume \u003d 15 - 2x3.4 \u003d 8.2 thousand units. in Week.

2. Since the seller pays the tax, the offer function will change. She will take the form:

Qs \u003d -2 + 3 (p - 1) \u003d -5 + 3p

To determine the new equilibrium price and sales volume, it is necessary to use the condition of market equilibrium:

5 + 3r \u003d 15 -2r

P \u003d 4 thousand rubles. per unit - a new equilibrium price.

Q \u003d 15 - (2 x 4) \u003d 7 thousand units. a week - a new equilibrium volume.

3. The total amount of tax that will go to the state budget will be equal to 7 thousand units. x 1ty.rub. \u003d 7 million rubles

The price that buyers pay is 4 thousand rubles. per unit

The price that the seller will receive will be 4 - 1 \u003d 3 thousand rubles. per unit

From 1 thousand rubles. tax - 0.6 thousand rubles. buyers will pay, and 0.4 thousand rubles. paid by seller

Determine if the budget is scarce if public procurement is 60 million rubles, transfer payments are 10 million rubles, interest payments are 15% per annum on government debt equal to 30 million rubles, tax revenues are 20% of GDP, equal to 360 million rubles.

360 x 0.2 - (60 + 10 + 30 x 0.15) \u003d 72 - 74.5 \u003d - 2.5 million rubles. - deficit of the state budget.

3. Which of the following benefits should, in your opinion, be received by citizens through the market, and which should be provided by the state:

a) food; b) education; d) housing;

e) healthcare; e) television; g) wine and vodka products. Explain the answer.

4. Lotteries are an important source of government revenue. What are the pros and cons of this income-raising tool?

5. Suppose you purchased a foreign car. You have to pay customs duty, the value of which depends on the volume of the car engine. What are the main elements of tax in this situation: tax subject, tax carrier, tax object, source, unit of taxation, tax rate.

6. What measures to increase budget revenues could you suggest?

Related Information:

1. III part. The installation of a third company (3 TS) consists of three modules, the latter having a redundant element that cannot be replaced

2-1p.  The function of population demand for a given product: Qd \u003d 7-P.  Suggestion Function: Qs \u003d -5 + 2P,Where Qd -  volume of demand in million units per year; Qs -  supply volume in million units per year; R -  price in thousands of rubles. Build graphs of supply and demand for this product, putting the quantity of goods on the abscissa axis (Q)  and on the ordinate axis - unit price (R).

Decision

Since the given functions reflect a linear dependence, then each of the graphs can be built on two points.

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

Q (1) \u003d 40-8P  at P ≤ 5  and 0   at P\u003e 5,

Q (2) \u003d 70-7P  at P ≤ 7  and 0   at P\u003e 7,

Q (3) \u003d 32-4P  at   P ≤ 8and 0   at   P\u003e 8.

a) Derive the equation of the demand curve analytically.

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

Decision

a) Q \u003d Q (1) + Q (2) + Q (3) \u003d 142-19P  at 0 ≤ P ≤ 5,

Q \u003d Q (2) + Q (3) \u003d 102-11P  at 5 < Р ≤ 7 ,

Q \u003d Q (3) \u003d 32-4P  at 7 < P ≤ 8 ,

Q \u003d 0  at P\u003e 8.

b) The third group of consumers agrees to pay the highest prices. For example, when P \u003d 7.5  the first two groups will stop buying, and the buyers of the 3rd group will buy 2 units. (32-4x7.5 \u003d 2). But an unequivocal conclusion that the richest buyers are in the third group cannot be made, since we do not know either their income or other direct and indirect signs of wealth.

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

Qd \u003d 2400-100Pand the offer of VCRs is given by the equation Qs \u003d 1000 + 250Pwhere Q -  the number of video recorders bought or sold per year; R -  the price of one VCR (in thousand rubles).

a) Determine the equilibrium parameters in the market of video recorders.

b) How many video recorders would be sold at a price of 3,000 rubles?

c) How many video recorders would be sold at a price of 5,000 rubles?

Decision

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

Qd \u003d Qs,  or 2400-100P \u003d 1000 + 250P.

Solving the equation, we find the equilibrium price:

1400 \u003d 350P; Pe \u003d 4000 rub.

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

Qe \u003d 2400-100x 4 = 2000   PCS. in year.

b) To determine how many video recorders will be sold at a price of 3,000 rubles (i.e., at a price below the equilibrium price), you need to substitute this price value in both the demand equation and the supply equation:

Qd = 2400 - 100 x 3 = 2100 pCS. in year;

Qs \u003d 1000 + 250x 3 = 1750 pCS. in year.

This shows that at a price below equilibrium, consumers will want to buy more VCRs than manufacturers agree to sell (Qd\u003e Qs).  In other words, consumers will want to buy 2100 pcs. VCRs, nosmogut can buy exactly as much as sellers will sell them, i.e. 1750 pcs. This is the correct answer.

c) Substitute the price of 5000 rubles in each of these equations:

Qd \u003d 2400 - 100x 5 = 1900   PCS. in year;

Qs \u003d 1000 + 250x 5 = 2250   PCS. in year.

At a price above the equilibrium, manufacturers will want to sell 2250 units. VCRs, however consumers will buy only 1,900 pcs. VCRs, therefore, only 1,900 pcs. VCRs and will be sold at a price of 5000 rubles.

Answer: a) equilibrium parameters: Pe \u003d 4000 rub., Qe \u003d 2000  PCS. in year.

b) when P \u003d 3000 rub.will be sold   Q \u003d 1750  PCS. in year.

c) when P \u003d 5000 rub.will be sold   Q \u003d 1900  PCS. in year.

2-4p.  The gas demand function has the form: Qd g \u003d 3.75P n -5P g, and the function of his sentence: Qs g \u003d 14 + 2P g + 0.25P n,Where R n, R g  - respectively, oil and gas prices.

Define:

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

b) how much percent will change the volume of gas sales with an increase in oil prices by 25%.

Decision

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

3.75P n -5P g \u003d 20

14 + 2P g + 0.25P n \u003d 20Þ P n \u003d 8; P g \u003d 2.

Since from the first equation P n \u003d (20 + 5P g) / 3.75,we substitute this expression into the second equation.

14 + 2P g +0.25 (20 / 3.75) +0.25 (5P g / 3.75) \u003d 20,

2P g +0.25 (5P g / 3.75) \u003d 20-14-0.25 (20 / 3.75),

2P g + 0.33P g \u003d 6-1.33,

2.33P g \u003d 4.67,

P g \u003d 2.

P n \u003d (20 + 5x 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 x   10 - 5P g \u003d 14 + 2P g + 0.25x 10 Þ

37.5-5P g \u003d 14 + 2P g + 2.5Þ

-5P g - 2P g \u003d 14 + 2.5-37.5Þ

-7P g \u003d -21,

P g \u003d 3, Q g \u003d 37.5 - 5x 3 = 22,5.

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

Answer: a) with equal volumes of gas supply and demand 20 units. oil and gas prices will be equal respectively P n \u003d 8; P g \u003d 2.

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

2-5p.  There are three sellers and three buyers in the real estate market. The seller’s offer features are known:

Qs 1 \u003d 2P-6; Qs 2 \u003d 3P-15; Qs 3 \u003d 5P.

and demand functions at the price of buyers:

Qd 1 \u003d 12-P; Qd 2 \u003d 16-4P; Qd 3 \u003d 10-0.5P.

Determine: the parameters of market equilibrium, as well as the volume of transactions of each trading participant at the equilibrium price.

Present a graphical and analytical solution.

Typical Tasks

Task 1

The population demand function for this product has the form: Q D \u003d 7 - –P.

The supply function of this product: Q S \u003d 5 + 2P, where Q D and Q S are, respectively, the volume of demand and supply in million units per year, P is the price per day. units

a) Determine the equilibrium price and the equilibrium sales volume.

b) Suppose a tax is introduced 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

the buyer (Pe +) and the seller (Pe +).

Decision

Hence: 7 - P \u003d - 5 + 2P, Pe \u003d 4.

Q D \u003d 7 - 4 \u003d 3, Q S \u003d - 5 + 2 × 4 \u003d 3, Q e \u003d 3.

b) Since the seller pays the tax, the price for it will be P - \u003d P + - 1.5.

Hence: Q D \u003d 7 - P +,

Q S \u003d - 5 + 2P - \u003d - 5 + 2 (P + - 1,5).

therefore: 7 - P e + \u003d - 5 + 2P e + - 3.

Hence: P e + \u003d 5; P e - \u003d 3.5; Q e \u003d 2.

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

Task 2

In the market for this product equilibrium was established at a price of 4 den. units per unit and sales volume of 18 thousand units 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 of a product in the event of a 10% reduction in demand for it, based on the assumption that the supply and demand functions are linear.

Decision

In the case of linear supply and demand functions:

Q D \u003d a - bP; Q S \u003d m + nP,

hence,
a

As
a
then in equilibrium:

- 0.05 \u003d - b × 4/18, i.e. b \u003d 0.225.

0.1 \u003d n × 4/18, i.e. n \u003d 0.45.

Now we can determine the parameters a and m:

a \u003d 18 + 0.9 \u003d 18.9; m \u003d 18 - 1.8 \u003d 16.2.

Hence,

Q D \u003d 18.9 - 0.225P; Q S \u003d 16.2 + 0.45P.

With a decrease in demand by 10%, the equilibrium condition in the market for this product takes the form: 0.9Q D \u003d Q S; i.e

0.9 (18.9 - 0.225P) \u003d 16.2 + 0.45P.

Hence: P \u003d 1.23.

Tasks

1.   The demand function for this product has the form: Q D \u003d 5 - P. Supply function: Q S \u003d - 2 + P.

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

2.

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

3.   The demand function for this product has the form: Q D \u003d 12 - P. Supply function: Q S \u003d - 3 + 4P.

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

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

Determine the equilibrium volume and price when introducing a commodity tax of 1 den. units paid by manufacturers. (Assume that the supply and demand functions are linear).

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

manufacturers?

a) Q D \u003d 5 - 2P, Q S \u003d P + 1;

b) Q D \u003d 5 - P, Q S \u003d 1 + P;

c) Q D \u003d 5 - P, Q S \u003d 1 + 2P.

6.   The demand function for this product has the form: Q D \u003d 8 - 2P. Suggestion function: Q S \u003d 4 + P.

Determine the amount of the production subsidy that needs to be allocated to producers so that the goods begin to spread as a “free good." How much product will be distributed?

7.   The demand function for this product has the form: Q D \u003d 2 - 3P. Suggestion function: Q S \u003d - 0.5 + 2P.

Determine the public benefit arising from the production and sale of goods (the amount of surplus buyers and sellers).

8.   The demand function for this product has the form: Q D \u003d 7 - 2P. Suggestion function: Q S \u003d P - 5.

Determine the equilibrium price and sales volume. Calculate the amount of commodity subsidies necessary to promote the product on the market and achieve a sales volume of 3 units.

9.   The demand function for this product has the form: Q D \u003d 12 - P. Supply function: Q S \u003d - 3 + 4P.

Determine the equilibrium price and sales volume. Introduced tax on the manufacturer in the amount of 2 den. units per unit sold. Calculate the new equilibrium sales and price, as well as net social losses.

10.   The demand function for this product has the form: Q D \u003d 12 - P. Supply function: Q S \u003d - 3 + 4P.

Determine the equilibrium price and sales volume. An excise tax has been introduced on buyers in the amount of 20% of sales. Define 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 \u003d 5 - P. Supply function: Q S \u003d - 1 + P.

Determine the equilibrium price and sales, as well as surplus

sellers and buyers. A customer tax of 3 den. units per unit. Determine the equilibrium volume, price, surplus of sellers and buyers, as well as the net loss of society.

12.   There are three demand functions and their corresponding functions.

offers:

a) Q D \u003d 12 - P, Q S \u003d - 2 + P;

b) Q D \u003d 12 - 2P, Q S \u003d - 3 + P;

c) Q D \u003d 12 - 2P, Q S \u003d - 24 + 6P.

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

13.   The demand function for this product has the form: Q D \u003d 6 - 2P. Suggestion function: Q S \u003d - 2 + 2P.

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

14.   The demand function for this product: Q D \u003d 7 - P, the supply function of this product: Q S \u003d - 5 + 2P.

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

15.   The demand function for this product: Q D \u003d 16 - 4P, the supply function of this product Q S \u003d - 2 + 2P.

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

16.   The demand function for this product: Q D \u003d 7 - P, the supply function of this product: Q S \u003d - 5 + 2P.

At what tax rate (in den. Units per unit of goods) will the total amount of the tax charge be the maximum?

17.   In a state of equilibrium in the market 120 pieces of goods A are for sale

at the price of 36 den. units It is known that the demand and supply function of this good are straightforward and at the same time e D \u003d - 0.75, and e S \u003d + 1.5.

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

18.   The market is characterized by the following supply and demand functions: Q D \u003d 12 - P; Q S \u003d 2P - 3.

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

19.   Suppose an excise tax on cigarettes of 25 den. units per pack, which caused a shift in the supply curve from S 1 to S 2, as shown in the figure. Answer the following questions:

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

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

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

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

20.   The gas demand function has the form: Q r D \u003d 3.75P n - 5P g, where P n, P g are the oil and gas prices, respectively, the gas supply function is: Q g S \u003d 14 + 2P g + 0.25P n

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

21.   The product demand function has the form: Q D \u003d 5 - P, the product supply function has the form: Q S \u003d - 1 + 2P. Suppose that a quota for the production of this product is set at 2 thousand units.

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

22.   In region I, the demand function for a certain product has the form: Q D1 \u003d 50 - 0.5P 1, the supply function: Q S1 \u003d - 10 + P 1, where Q D1, Q S1 are the demand volume and the supply volume in region I, respectively P 1 - market price in region I (den. Units / kg). For region II

demand function for the same product: Q D2 \u003d 120 - P 2, supply function: Q S2 \u003d - 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) Suppose transportation is permitted. Shipping costs are negligible. Define the same as in paragraph a. In addition, determine the volume of production in each region, the volume of traffic.

Who benefits from the lifting of the ban on transportation, who does not benefit from it? Does the overall benefit of lifting the ban increase or not?

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

Define the same as in paragraph b.

d) Transportation is allowed. Shipping costs are negligible. The government of Region I has established 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 established not by the government of the first region, but by the government of the second region (an “import” duty of 10 den. units per 1 kg of imported products)?

23. Below are data on the volumes of supply and demand for various values \u200b\u200bof 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 will people want to buy? How much will the actual product 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 the equilibrium sales volume.

d) Display all options graphically.

24.   The following supply and demand functions are given:

a) Q D \u003d 10 - P, Q S \u003d 2P - 2;

b) Q D \u003d 10 - P, Q S \u003d 2 + P;

c) Q D \u003d 10 - P, Q S \u003d 4 + 0.5P;

What situation corresponds to stable equilibrium, unstable equilibrium, uniform fluctuations in 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 goods from four manufacturers (each produces a unit of this product) are: 6, 4, 3 and 2 den. units

What is the maximum possible total surplus? How much product and at what price will be produced? (The problem is solved graphically.)

26.   The equilibrium in the market of this product was established at P \u003d 5 and Q \u003d 15. The coefficient of direct elasticity of demand at a price is –0.05, and the coefficient of direct elasticity of supply at a price of +0.2.

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

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

27.   The supply and demand functions for this product are of the form: Q D \u003d 32 - 2P, Q S \u003d –2 + 3P.

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

b) Build a Laffer curve.

28.   The demand function for the services of a hairdresser has the form: Q D \u003d P 2 - 4P + 10. The function of the service offer: Q S \u003d 6P - P 2.

a) Determine the equilibrium values \u200b\u200bof price and volume.

b) Build the dependence of the quantity of service offer on its price.

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

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

Determine the maximum bid price.

30.   The demand function for cabbage has the form: Q Dt \u003d 200 - P t. The offer function has the form: Q St \u003d - 10 + 0.5 where - the price of cabbage in the period t, "expected" by farmers at the time they make decisions on the size of production. Suppose: \u003d P t-1.

a) Determine the sales volume and prices of cabbage in periods 1, 2, ..., 6, if P 0 \u003d 200.

31.   The demand function for carrots has the form: Q Dt \u003d 200 - 0.5 . The offer function has the form: Q St \u003d - 10 + 0.5 where \u003d P t - 1.

a) Determine the sales volumes and prices of carrots in periods 1, 2, ..., 6, if P 0 \u003d 145.

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

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

d) ††††††††††††††††††††††††††††††††††††††† ME e ar e e ea ††††††††††††††††††††††††††††††† follow-t-tau e-ea †††††††††††††††††††††††††††††† Check ††† ††††††††††††††††††††††††††††††††††††††† †† †††††††††† † ††††††††††††††††††††††††††††††††††† †† †††††††††††††where - the price of carrots in period t, “expected” by farmers at the time they make decisions on the size of production. Suppose: =
.

a) Determine the sales volumes and prices of carrots in periods 1, 2, ..., 10, if P 0 \u003d P t -1 \u003d 250.

b) Depict the dynamics of price changes in the figure.

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

GUIDELINES

Example 1  There are three demand functions and the corresponding supply functions:
   a) QD \u003d 12 - P, Qs \u003d - 2 + P;
   b) QD \u003d 12 - 2P, Qs \u003d - 3 + P;
   c) QD \u003d 12 - 2P, Qs \u003d - 24 + 6P.
   The state introduces a subsidy to producers in the amount of 3 den. units for each piece. In which case will consumers receive most of the subsidies? Why?
Decision:
   We determine the equilibrium price and volume of sales in each case. To do this, we equate the supply and demand function:
   a) 12 - P \u003d -2 + P \u003d\u003e P \u003d 7, Q \u003d 5;
   b) 12 - 2P \u003d -3 + P \u003d\u003e P \u003d 5, Q \u003d 2;
   c) 12 - 2P \u003d -24 + 6P \u003d\u003e P \u003d 4.5, Q \u003d 3.
   If a subsidy to producers is introduced, sellers will be able to reduce the offer price by the amount of the subsidy. We express the offer price, taking into account the subsidy:
   a) Ps \u003d Qs + 2 - 3 \u003d Qs - 1;
   b) Ps \u003d QS + 3 -3 \u003d Qs;
   c) Ps \u003d QS / 6 + 4 - 3 \u003d Qs / 6 + 1.
   Hence the new offer function:
   a) Qs \u003d 1 + P;
   b) Qs \u003d P;
   c) Qs \u003d - 6 + 6P.
   We find a new state of equilibrium:
   a) 12 - P \u003d 1 + P \u003d\u003e P \u003d 5.5; Q \u003d 6.5;
   b) 12 - 2P \u003d P \u003d\u003e P \u003d 4, Q \u003d 4;
   c) 12 - 2P \u003d -6 + 6P \u003d\u003e P \u003d 2.25, Q \u003d 7.5.
   Answer: Thus, consumers will receive most of the subsidy in option c) of the supply and demand functions: the price will decrease by 2.25 den. units, i.e. 50% of the initial value, while the volume of sales will grow 2.5 times.
Example 2 The equilibrium price of grain in the world market is P \u003d 1.5 dollars per pound. Q \u003d 720 million pounds of grain is sold annually. The price elasticity of demand for grain is equal to EP (D) \u003d -0.8. Define a linear function of demand for grain.
Decision:
   It should be noted that the price elasticity coefficient of demand is the tangent of the slope of the demand graph to the abscissa. Given the above, we will draw up a linear equation of the dependence of demand on price. The linear relationship model is as follows:
   QD \u003d a + EP (D) × P,
   where QD is demand, P is price, EP (D) is the linear coefficient of demand elasticity of price.
   Knowing that P \u003d $ 1.5 per pound, q \u003d 720 units. (million pounds), EP (D) \u003d -0.8, we find an unknown parameter in this model:
   720 \u003d a - 0.8 × 1.5; a \u003d 721.2.
   Thus, the model of the dependence of demand on price is as follows: QD \u003d 721.2 - 0.8P.
Example 3  The cross elasticity between the demand for kvass and the price of lemonade is 0.75. What products are we talking about? If the price of lemonade increases by 20%, how will the demand for kvass change?
Decision:
   Kvass and lemonade are interchangeable products, since the coefficient of cross elasticity of demand EA, B has a positive value (0.75).
   Using the formula of the coefficient of cross elasticity EA, B, we determine how the demand for kvass will change with an increase in the price of lemonade by 20%.
   If we take the change in demand for kvass for x, and the change in the price of lemonade for y, then we can write the equation EA, B \u003d x / y; where x \u003d EA, B × y or
   x \u003d 0.75y \u003d 0.75 × 20% \u003d 15%.
   Thus, with a 20% increase in the price of lemonade, the demand for kvass will increase by 15%.
Example 4Given the functions of supply and demand for goods:
   QD \u003d 150 - 3P, QS \u003d - 70 + 2P.
   The state introduced a tax on goods in the amount of 7.5 cu with each unit of products sold. Determine the equilibrium price and the equilibrium volume before and after the introduction of the tax. What part of the tax will be paid by the manufacturer and the buyer?
Decision:
   The initial market equilibrium will be in t. E (Pe, Qe), where QD \u003d QS. 150 - 3P \u003d -70 + 2P; 220 \u003d 5P; Pe \u003d 44 c.u.
   We substitute the equilibrium price (Pe) into the demand or supply function and find the equilibrium sales volume Qe \u003d -70 + 2 × 44 \u003d 18 units.
   After the introduction of the tax, the market equilibrium will move to t. E1 (the intersection point of the old demand function Qd \u003d 150 - 3Р and the new supply function QS1 \u003d - 70 + 2 (P - t) \u003d -70 + 2P - 15 \u003d -85 + 2P.
   Thus, the new equilibrium is calculated as follows:
   QD \u003d QS1: 150 - 3P \u003d -85 + 2P; 235 \u003d 5P; Pe1 \u003d 47 c.u.
The new equilibrium sales volume is Qe1 \u003d 150 - 3 × 47 \u003d 9 units.
   The amount of tax paid by the buyer:
   tD \u003d Pe1 - Pe \u003d 47 - 44 \u003d 3 c.u.
   The amount of tax paid by the seller:
   tS \u003d Pe - (Pe1-t) \u003d 44 - (47 - 7.5) \u003d 4.5 c.u.
   Since demand is more elastic than supply, in this case the tax burden will fall more on the shoulders of the seller than the buyer.

The equilibrium price is the price at which the volume of demand in the market is equal to the volume of supply. It is expressed as Qd (P) \u003d Qs (P) (see main market parameters).

Service purpose. This online calculator is aimed at solving and checking the following tasks:

1. The equilibrium parameters of a given market (determination of equilibrium price and equilibrium volume);
2. Coefficients of direct elasticity of supply and demand at the equilibrium point;
3. Surplus consumer and seller, net public gain;
4. The government introduced a cash subsidy from each unit of goods sold in the amount of N rub .;
5. The amount of subsidies allocated from the state budget;
6. The government introduced a goods tax on each unit of goods sold in the amount of N rub .;
7. Describe the consequences of the decision by the state to fix the price of N above (below) the equilibrium.

Instruction Enter the supply and demand equations. The resulting solution is saved in a Word file (see the example of finding the equilibrium price). A graphical solution to the problem is also presented. Qd - demand function, Qs - supply function

An example. The demand function for this product Qd \u003d 200–5P, the supply function Qs \u003d 50 + P.

1. Determine the equilibrium price and the equilibrium sales volume.
2. Suppose that the city administration decided to set a fixed price at: a) 20 den. units apiece, b) 30 den. units a piece.
3. Analyze the results. How will this affect consumer and producer behavior? The decision to present graphically and analytically.

Decision.
Find the equilibrium parameters in the market.
Demand Function: Qd \u003d 200 -5P.
Suggestion function: Qs \u003d 50 + P.
1. The equilibrium parameters of this market.
At equilibrium, Qd \u003d Qs
200 -5P \u003d 50 + P
6P \u003d 150
P equal \u003d 25 rubles. - equilibrium price.
Q equ \u003d 75 units. - equilibrium volume.
W \u003d P Q \u003d 1875 rub. - seller’s income.

Consumer surplus shows how much better individuals live on average.
Consumer surplus  (or gain) is the difference between the maximum price that he is ready to give for the goods and the one he really pays. If we add up the surplus of all consumers who purchase this product, then we get the size of the total surplus.
Producer surplus  (gain) - this difference between the market price and the minimum price for which manufacturers are willing to sell their goods.
Seller's surplus (P s P 0 E): (P equal - Ps) Q equal / 2 \u003d (25 - (-50)) 75/2 \u003d 2812.5 rub.
Buyer's surplus (P d P 0 E): (Pd - P equal) Q equal / 2 \u003d (40 - 25) 75/2 \u003d 562.5 rub.
Net public gain: 2812.5 + 562.5 \u003d 3375
The knowledge of surpluses is widely used in practice, for example, in distributing the tax burden or subsidizing industries and firms.

2) Suppose that the city administration decided to set a fixed price at 20 den. units a piece
P fix \u003d 20 rubles.
Demand: Qd \u003d 200 -5 20 \u003d 100.
Supply volume: Qs \u003d 50 + 1 20 \u003d 70.
After fixing the price, the volume of demand decreased by 25 units. (75 - 100), and the shortage of manufacturers decreased by 5 pcs. (70 - 75). The market has a shortage of goods in the amount of 30 pcs. (70 - 100).


Suppose that the city administration decided to set a fixed price at 30 den. units a piece.
P fix \u003d 30 rubles.
Demand: Qd \u003d 200 -5 30 \u003d 50.
Supply volume: Qs \u003d 50 + 1 30 \u003d 80.
After fixing the price, the volume of demand increased by 25 units. (75 - 50), and the surplus of manufacturers increased by 5 pcs. (80 - 75). In the market surplus goods in the amount of 30 pcs. (80 - 50).