Supply and demand are represented by equations. Equilibrium price and equilibrium volume. Tasks for the application of formulas for calculating the equilibrium price and equilibrium sales volume

Task 1.1.In a conventional economic system, two types of products are produced: X and W. For the production of 1 unit. products X requires 50 units. resource, products U - 25 units. The total volume of a completely interchangeable resource that the economic system has is 400 units.

Determine the opportunity cost of producing the last unit of the product X.

Decision.

First of all, we note that the opportunity costs for the manufacture of any unit of production, as X, and Y are unchanged, since the resource from which they are made is completely interchangeable. Taking this into account, we calculate the volumes (quantities) of output of both types of products, dividing the value of the available volume of the resource (400 units) by the corresponding standards of its costs for the manufacture of products X and W. As a result, we get 8 units. products X and 16 units. products U. Further, using the definition of opportunity costs (the amount of another type of product that must be donated to increase the volume of production of this product per unit), we calculate the sought opportunity costs associated with the manufacture of the last unit of production X:16/8 \u003d 2 units. products of W.

Task 1.2.By plane from the city AND in town IN can be reached for 1 h, and by bus - 5 hours. The cost of a plane ticket is 500 den. units, by bus - 100 den. units

Calculate the minimum hourly earnings, starting from which movement will become profitable (in work time) by plane.

Decision.

Since economic costs are the sum of explicit (accounting) costs, as well as the opportunity costs of missed opportunities, the condition of equal benefits of the considered options for moving from one city to another can be written as follows: 500 + x = 100 + 5x, Where x - hourly earnings of the "traveler".

This means that travel by plane becomes economically viable if the hourly earnings exceed 100 den. units

Task 1.3.The farmer has three fields, each of which is uniform, although their yield is not the same. Wheat and potatoes are grown in these fields. In the first field, the farmer can grow either 40 tons of wheat or 100 tons of potatoes, on the second - 100 and 150, respectively, and on the third - 50 and 100.

Plot the farmer's production capability curve.

Decision.

To plot a farmer's production capability curve, the opportunity cost of growing wheat and potatoes must be calculated. It is advisable to present the calculations in tabular form, which for the example under consideration will have the following form.

On the abscissa we plot the volumes of potatoes grown, and on the ordinate - wheat. Then, taking into account the provisions of the law of increasing opportunity costs, as well as the productivity of the corresponding fields, the curve of the production capabilities of the farmer will have the following form.

Task 1.4.Suppose there are two people working in a small trouser workshop: a foreman and his assistant.

The productivity of their labor for cutting and sewing trousers (with the same quality of work) is as follows:

Type of work	Time spent on units. goods, h
Type of work		assistant
Cut fabrics
Sewing trousers

Without division of labor, 28 trousers (20 by a foreman and 8 by an assistant) can be sewn in a workshop in a month (120 hours of working time).

What should be the division of the pile between the foreman and the assistant to minimize the production volume in the workshop?

Decision.

Workers should specialize in accordance with the principle comparative advantagesdetermined by the minimum opportunity costs

to perform the work under consideration.

The calculation results for this example are shown below.

The assistant should be engaged in cutting (12 pants per month). For the same time, the master will be able to cut 18 and sew 30 trousers.

So, only due to the optimal distribution of responsibilities, labor productivity in the workshop will increase by 7% (30 trousers instead of 28).

Task 1.5. The demand and supply of a specific product in some underdeveloped country were characterized by analytical dependencies Q D \u003d 200 - P and (I s \u003d \u003d -100 + 2 R.

In order to protect the poorest layers of the population, the government of the country has fixed the price of this product at a level below the equilibrium level. The result of these actions of the government was a reduction in the expenses of the population for the purchase of the product in question by 28%.

Determine the price level fixed by the government.

Decision.

Let us find the initial equilibrium state of the market for the product under consideration and the corresponding consumer costs:

In terms of a fixed price (P,), the costs of consumers of this product, and hence the income of its producers, amounted to 72,000 den. units

Determining the volume of supply of goods in the conditions under consideration as 72,000 / P, we write the equation 72,000 / P, \u003d -100 + 2P, solving which, we find: P, \u003d 90 den. units

Task 1.6. The demand function for a certain product has the form (Ooh) \u003d 400 - YR. The supply function of this product is linear, and the equilibrium sales volume is 100 units. products. It is also known that in the conditions under consideration, the consumers 'gain is 2 times higher than the producers' gain.

Determine the size of the deficit (overproduction) of products, if a fixed price level is set for the goods - 28 den. units

Decision.

It is advisable to illustrate the solution to this problem using the graphical model presented below.

Consumer surplus corresponds to the area of \u200b\u200bthe triangle P e P 2 E and can be defined as follows: 0.5 (P 2 - P E) 100. In turn, the equilibrium price P E can be found from the equation 400 - 10P f \u003d 100, resulting in P E \u003d 30 days sd. R 2 can be calculated similarly: 400 - 10P 2 \u003d 0, whence R 2 \u003d 40 days units

The consumer surplus will thus amount to 500 den. units From the formula for calculating the producers' surplus, equal to 250 den. units, we find: 1 \u003d 25 days units :: 0.5 (P E -P t)? 100 = 250.

As a result, we get Q s \u003d -500 + 20R.

Since the result of price fixing R at 28 den. units the emergence of a deficit, we define it by the formula:

Task 1.7. The supply and demand functions for a certain product have the form Q n = 1000 - 5R and (Y \u003d -100 + 2.5 R.

As a result of fixing the price of a product, a deficit arose, to eliminate which measures were taken to increase the supply of this product by 100%.

Determine the volume (in units of production) of the eliminated deficit.

Decision.

Let us use the graphic illustration of the solution presented below, which greatly facilitates the understanding of its process.

1) Q 5 i \u003d 2Q S \u003d -200 + 5P;
2) 1000 - 5P \u003d -200 + 5P, P \u003d 120, Q \u003d 400;
3) deficit \u003d Q D - Q s =1100- 7,5P \u003d 1100 - 7.5 120 \u003d 200 units. products.

Task 1.8.The supply and demand functions for a specific product are: Q ° \u003d 8 - R and 0 s \u003d -4 + 2R.

Determine how the equilibrium sales volume will change if a tax is imposed on the product in the amount of 30% of the price, which is paid (entered into the budget) by the manufacturer.

Decision.

The equilibrium volume of sales of a product before the introduction of a tax on it is determined from equation 8 - R \u003d -4 + 2Р, whence Р is equal to \u003d 4, Qp aBll \u003d 4.

The function of the supply of this product after the introduction of tax on it will take the form: Q ’9 i \u003d -4 + 2 (Р-0, ЗР).

Equating the supply function to the demand function, we find the volume of sales of the goods in terms of its taxation: it will be 3 SD., I.e. will decrease by 25%.

Task 1.9.Syroe for some product is characterized by the equation Q D \u003d 120 - P, and the offer of the same product - by the equation Q s \u003d -30 + 2Р.

Determine what the minimum tax per unit of goods sold must be established in order to receive 600 den. To the state budget. units

Decision.

Denoting through N the required amount of tax, we determine the price of a unit of goods in terms of taxation: 120 - P \u003d -30 + 2 (P - N), whence P \u003d 50 + 2/3 N.

Substituting in the found expression P (N) into function Q D, find: Q (N) = = 70 - 2/3N. The total tax in this case is: (70 - 2/3 N) A7 \u003d 600. Having solved this equation, we find: N \u003d 9,4.

Task 1.10. The market for a certain product is characterized by the following supply and demand functions: Q D = 740 - 2R and Q? \u003d-100 + R.

The government has established a single tax on this product, which maximizes the total amount of tax revenues to the state budget.

Determine how much of the tax burden fell on the shoulders of consumers of the product in question.

Decision.

The algorithm for solving this problem can be as follows:

1) define the equilibrium price in terms of tax (N):

2) calculate the sales volume:

3) determine the amount of tax:

4) set the equilibrium price in the absence of tax:

5) determine the amount of overpayment for each unit of goods purchased by consumers in terms of tax payment:

6) calculate the total tax burden of consumers of the product in question:

Task 1.11. The supply and demand functions for a product, producers (sellers) of which are subject to a single tax on each unit of the product, have the form: Q D = 800 - 3R and Q s \u003d -250 + 2R.

The total amount of tax revenues to the state budget is 4250 den. units

Determine by how many units the volume of supply of this product will increase when the tax imposed on it is canceled.

Decision.

The problem under consideration can be solved in the following sequence:

1) define the parameters of equilibrium in the conditions of taxation of goods:

2) calculate the amount of tax:

3) we get the equation of the supply function after tax abolition:

4) define the parameters of equilibrium after the tax is canceled:

5) calculate the increase in sales of the product in question after the abolition of tax on it:

Task 1.12.The market for a certain product, operating under the conditions of taxation of its producers, is characterized by a demand function with unit price elasticity and a supply function: Q 51 \u003d -20 + 2 R. The equilibrium sales volume was 10 units. goods. When the tax was canceled, the price of the goods was reduced by 1/3. What will be the sales volume of this product after tax cancellation?

Decision.

Let's consider a graphical illustration of this task.

1. Determine the equilibrium price of the goods in terms of tax payment: 10 \u003d -20 + + 2Р, whence R = 15.
2. After the abolition of the product tax, the price decreased by 10 dei. units
3. Since for all points of the unit demand function PQ \u003d const, we find the sales volume in the conditions of tax abolition: 15 units. products.

Task 1.13.Marginal utilities for goods L, B and FROM are equal to 10, 20 and 18 units, respectively. The prices of goods are also known L and C: R A \u003d 5 days units., P with \u003d 9 days units

At what level of product price IN will the consumer be in equilibrium?

Decision.

In a state of equilibrium, the ratios of marginal utilities to the prices of the corresponding goods must be equal. In our case, the condition must be satisfied

whence it follows that P in \u003d 10 den. units

Task 1.14. The consumer's utility function is: U (A, B, C) = 6a ++ 8b + 4c. Prices of goods are known AND and B: R l \u003d 3 days units., P in \u003d 4 den. units

Determine the price of the item FROM, if the consumer is in equilibrium.

Decision.

The marginal utility is equal to the partial derivative of the utility of the given commodity, therefore, Mf / 4 \u003d b, MU B \u003d 8 and MU C = 4.

Then, according to the consumer equilibrium condition

Task 1.15. Determine consumer choice, if known: utility function U \u003d 2XY, Where X, Y- volumes of goods; commodity prices P x \u003d 8 days units., P Y \u003d 5 days units; disposable income M \u003d 96 den. units

Decision.

It is necessary to find such quantitative values X and Y, at which the utility function reaches its maximum for the given budget constraints. The sequence for solving the problem can be as follows:

1) define the marginal utilities of goods:

2) formalize the budget constraint equation:

3) let's make a formalized record of the principle of the equilibrium state of the consumer:

4) solve the system of equations:

Answer: X \u003d b, Y \u003d 9.6, 17 \u003d 115.2.

Task 1.16. The demand for a certain conditional product is characterized by the function Q "\u003d 60 - 3 R.

The equilibrium state of the market for a given product corresponds to a point with a unit price elasticity of demand. It is also known that the price elasticity of supply at the equilibrium point E s \u003d 1 2 / h- The government decided to fix prices at 8 den. units

Determine what will be observed in the considered economic system.

Decision.

Let's define the coordinates of the equilibrium point:

Find the parameters of the offer function Q s \u003d a + LR Y using the formula for calculating the point elasticity of supply:

For our initial data, we get 5/3 \u003d ^ 10 / 3o\u003e 0TC UD a B \u003d 5.

Let's define the parameter and: 30 = and + 5 10, whence a \u003d -20.

So, the sentence function has the form Q s \u003d -20 + 5P.

Since the price is fixed at a level below the equilibrium level, there will be a deficit, the volume of which should be calculated as follows:

Deficit \u003d [(60 - 30 8) - (-20 + 5 8)] \u003d 16 units.

Task 1.17.It is known that the supply and demand functions for a certain commodity are linear, and in addition, the supply function passes through the origin and a point with unit price elasticity of demand.

Determine what will be observed in the considered economic system.

Decision.

For a linear demand function (Q D = and- Bp) the coordinates of a point with unit elasticity are

Then the slope of the supply curve passing through the given point under the conditions of the problem is equal to

For the demand line.

Since the condition \u003d -7 ^ 7 is satisfied, we can conclude about the indif-

the market availability of this product.

Task 1.18.The market for a certain product, operating under the conditions of taxation of its producers, is characterized by a demand function with unit price elasticity and a supply function 0 s = -20 + 2R. Equilibrium sales volume with 10 units. goods.

With the abolition of the tax, the supply of goods increased by 15 units. for any price level. What will be the sales volume of this product after tax cancellation? Decision.

We will illustrate the solution to this problem using a graphical model.

1. Let's define the equilibrium price of the goods in terms of tax:
10 \u003d -20 + 2 P, whence P E - 15.
2. Let us determine the equilibrium quantity of goods in the conditions of the abolished tax: Q e \u003d 15 10 / R E.
3. Solve the equation -rr- \u003d -5 + 2P, whence we find P E \u003d 10 and Q E \u003d 15.

Task 1.19. The demand for a specific product can be formalized using the equation Q D = 600 - 2R.

The revenue of manufacturers (sellers) of day products amounted to 45,000 den. units

Determine the coefficient of price elasticity of demand, which led to the specified amount of revenue of manufacturers.

Decision.

The revenue of manufacturers (sellers) of these products can be calculated as follows: PQ \u003d P (600 - 2 R) \u003d 45,000, whence R \u003d 150 and Q = 300.

Task 1.20. Market equilibrium of some commodity with an equilibrium price P \u003d\u003d 100 den. units and the equilibrium amount of sales Q \u003d 400 units characterized by the elasticity of demand at a price equal to E ° \u003d -0.5. It is known that the demand function for the product under consideration is linear.

Determine the maximum possible amount of revenue that a manufacturer of this product could receive in the conditions of monopolization of the market for the product in question.

Decision.

To solve this problem, it is necessary to determine the parameters in an explicit form of an unspecified demand function: Q D \u003d a - bp. This can be done as follows.

dQ D P p _ , 100 , „

" E ° -Zha'- 0 - 5 - b WA, kuyu - 2

2. 400 = and - 2 100, therefore a \u003d 600.

In this case, the corresponding price is calculated according to the formula P \u003d ^ - \u003d ^^ \u003d 150, then Q \u003d 600 - 2 150 = 300. 1b 11

4. PQ \u003d 45,000 den. units

Task 1.21. It is known that the market sells 100 units weekly. product by price P \u003d 8 days units Under the condition of equilibrium in the market, a decrease in prices by 1% causes an increase in demand for goods by 0.8%.

Determine the demand function for the product in question, assuming that it is linear.

Decision.

In accordance with the economic meaning of the coefficient of price elasticity of demand, let us set its value: -0.8. Then

from where b \u003d 10. Then from the equation 100 \u003d ^ -10-8 we determine the parameter a: a \u003d 180. As a result, we get: Q D \u003d 180 - YR.

Task 1.22. Determine the point elasticity of demand for a product based on its price if it is known that a 5% decrease in price led to a 2% decrease in revenue. Decision.

We use the symbols P, Q and P V Q V indicating prices and quantities before and after the change in the price of the goods.

Then, based on the initial data, you can write:

We divide both sides of the equation na PQ and after simple arithmetic transformations we get A Q / Q = 0,0316.

3. Market equilibrium. Market volume of sales and market revenue. Shortage and excess of goods. The impact of changes in supply and demand on market equilibrium.

Complexity

Task number 3.1.1

Determine at what price will buyers buy the entire product?

Answer: with P \u003d 1 p.

Problem number 3.1.2

The law of demand states that there is a relationship between the level of price (P) for a product and the amount of demand for it (Qd).

Which: backward or forward?

Answer. Reverse.

Problem number 3.1.3

A person who sighs at an avocado for an avocado, and vows to taste it sooner or later, is this showing his demand for an avocado or not? Explain.

Answer. Not. Demand implies only a desire to acquire some good, but also a (solvent) willingness to do it.

Problem number 3.1.4

What does the linear demand function look like?

Answer. Qd (P) \u003d a - bP.

Problem number 3.1.5

Does the quantity demanded have any dimension?

Answer. Yes. It is measured in units of the good in question.

Task number 3.2.1

where Qd is the volume of demand in million units per year; Qs - volume of supply in million units per year; P is the price in thousands of rubles.

Plot the graphs of supply and demand for a given product, plotting the quantity of the product (Q) on the abscissa and the unit price of the product (P) on the ordinate.

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

For the demand curve: if P \u003d 0, then Qd \u003d 7; if Р \u003d 7, then Qd \u003d 0. Connect these points with a straight line, and the graph is ready (see figure).

For the supply curve: if P \u003d 3, then Qs \u003d 1; if P \u003d 6, then Qs \u003d 7. Connecting these points with a straight line, we obtain a supply curve.

Note that from a mathematical point of view, the graphs described by these functions can be located in a plane with negative numbers. However, from the economic point of view, supply and demand curves can be located only in the area of \u200b\u200bpositive values, since neither price nor quantity can be negative.

Problem number 3.2.2

Qd (P) \u003d 20 - 2P - direct demand function. Write the inverse demand function.

Answer. Pd (Q) \u003d 10 - 0.5Q - inverse function demand.

Task number 3.2.3

Recall 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.

Answer. Since we have two unknowns, to find them it is necessary to compose a system of at least two equations.

Task number 3.2.4

What do we need to find in order to compose a system of two equations to find the coefficients of the linear demand function?

Answer. To do this, you need to find the coordinates (Q, P) of two points that correspond to a given demand function.

Problem number 3.2.5

Where to start plotting a linear demand function?

Answer. From finding the coordinates of the intersection of our lines with the axes Q and P. To do this, we substitute in each function first Q \u003d 0, and then P \u003d 0. This principle works well when constructing linear demand functions.

Task number 3.3.1

The volume of demand for product A for this market is determined by the formula Qd \u003d 9 - Р, the volume of supply - by the formula Qs \u003d –6 + 2Р, where Р is the price of goods A.

Find the equilibrium price and equilibrium sales.

Answer: the equilibrium price is 5 den. units, sales volume - 4 USD e.

Task number 3.3.2

Market demand for a product is given by the function: QD \u003d 9 - 3P.

The quantity of goods that is offered for sale is 6 units.

A) Determine at what price the buyers will completely buy all the goods?

B) What happens if the price of the goods is 2 rubles, provided that the quantity of the goods put up for sale remains unchanged?

A) with P \u003d 1 p.

B) a surplus of goods of 3 units will appear on the market. (6 - (9 - 3x2)).

Task number 3.3.3

Analyze the chart carefully

According to the results economic analysis schedule, formulate the answers to the following questions:

1. What is the economic meaning of the intersection of the curves at point E?

2. What does the KL segment mean at the price of P3?

3. What is the economic interpretation of the segment MN at the price P2?

Task number 3.3.4

Explain what this market situation might be related to:

Answer. We see a situation of excess. Most likely, we are talking about state intervention in the economy through the establishment of a fixed price higher than the equilibrium one.

Task number 3.4.1

The demand for bananas is described by the equation: Qd \u003d 2400 - 100R, and the supply of bananas is described by the equation Qs \u003d 1000 + 250R, where Q is the number of kilograms of bananas bought or sold per day; P - the price of 1 kg of bananas (in thousand rubles).

1) Determine the equilibrium parameters in the banana market (equilibrium price and quantity).

2) How many bananas would be sold at a price of 3000 rubles? for 1 kg?

3) How many bananas would be sold at a price of 5000 rubles? for 1 kg?

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

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

Solving the equation, we find the equilibrium price:

1400 \u003d 350 R; P \u003d 4 (thousand rubles).

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

Q \u003d 2400 - 100 4 \u003d 2000 kg of bananas per day.

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

Qd \u003d 2400 - 100 3 \u003d 2100 kg per day;

Qs \u003d 1000 + 250 3 \u003d 1750 kg per day.

This shows that at a price below the equilibrium price, consumers will want to buy more bananas than producers agree to sell (Qd\u003e Qs). In other words, consumers will want to buy 2,100 kg of bananas, but will be able to buy exactly as much as the sellers will sell them, i.e. 1,750 kg. This is the correct answer.

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

Qd \u003d 2400 - 100 5 \u003d 1900 kg per day;

Qs \u003d 1000 + 250 5 \u003d 2250 kg per day.

It is clearly seen that at a price higher than the equilibrium price, producers will want to sell 2250 kg of bananas, but consumers will buy only 1900 kg of bananas, therefore, only 1900 kg of bananas will be sold at a price of 5000 rubles.

Note. Despite its apparent simplicity, this task is insidious. Many schoolchildren, solving it, experience difficulties, because they substitute the value of non-equilibrium prices in only one of the equations (either in the demand equation or in the supply equation), which gives them one correct and one incorrect answer.

Problem number 3.5.1

The demand function for the good is Qd \u003d 15 - Р, the supply function is Qs \u003d -9 + 3Р.

What happens to equilibrium if the volume of demand decreases by 1 unit at any price level?

Answer. Equilibrium price 5.75, equilibrium sales 8.25.

Problem number 3.5.2

The demand function for product X: Qd \u003d 16 - 4P, supply function Qs \u003d -2 + 2P.

Determine the equilibrium in the market for this good.

What happens to equilibrium if supply increases by 2 units at any price level?

Answer. After the supply change, the equilibrium price is 2.33, the equilibrium sales volume is 6.68.

Task number 3.5.3

Suppose that both oranges and tangerines are sold by their producers in the same national market. Answer the following questions:

a) Suppose tangerine groves are damaged by pests.

How will this affect the equilibrium prices and volumes of tangerines and oranges?

b) Suppose the supply of tangerines is increasing.

How will the total income of orange sellers change?

a) Mandarin groves have been damaged by pests and this has led to a decrease in the supply of tangerines.

The supply curve for mandarins has shifted to the left. This increased the equilibrium price in the given market and decreased the equilibrium sales volume.

Oranges and tangerines are interchangeable goods, therefore, an increase in the price of tangerines will lead to an increase in demand for oranges, and the demand curve in the orange market will move from left to right. Accordingly, the equilibrium price and sales volume in the orange market will increase.

b) When the supply of tangerines increases, the supply curve in the tangerine market shifts to the right, and this leads to an increase in the equilibrium volume of sales and a decrease in prices in this market.

A decline in the price of tangerines will reduce demand for oranges, and the demand curve in this related market will shift to the left. Accordingly, the volume of sales of oranges and the price of one kilogram of these fruits will decrease.

Consequently, the total income of the orange sellers will decrease compared to the initial one.

Task number 3.5.4

The demand function of the population for this product is Qd \u003d 7 - P, the supply function of this product is Qs \u003d -5 + 2P, where Qd is the volume of demand in million pieces per year, Qs is the volume of supply in million pieces per year, P is the price in USD. e.

Determine the equilibrium price and equilibrium sales.

What happens if the price is set at $ 3?

To determine the equilibrium sales volume and equilibrium price, we equate the demand function with the supply function. At the equilibrium point P \u003d 4 c.u. (equilibrium price); Qd \u003d 7 - 4 \u003d 3 million pcs. (equilibrium volume).

If P is equal to $ 3, then there will be a deficit, which will amount to 3 million units. To find the size of the deficit, we substitute P \u003d 3 into the functions of demand (Qd \u003d 7 - P) and supply (Qs \u003d -5 + 2P) that we have by condition, and then we find the difference between the amount of demand and the amount of supply.

Problem number 3.5.5

Milk has risen in price. As a result, the price of sour cream changed by 10%, and the revenue of sour cream producers decreased from 200 thousand rubles to 176 thousand rubles.

How much has the sour cream sales volume changed?

Answer. Decreased by 20%.

Problem number 3.6.1

Population demand function for this product: Qd \u003d 7 - P.

Suggestion function: QS \u003d -5 + 2P,

Using the available data, determine (graphically and analytically) the parameters market equilibrium, that is, the equilibrium price and the equilibrium quantity of goods.

a) The graph shows that the supply and demand curves intersect at a point with coordinates: Q \u003d 3 and P \u003d 4. This intersection point is the point of market equilibrium. So: 3 million pieces is the equilibrium quantity of goods; 4000 rubles is the equilibrium price.

b) The analytical solution is that the quantity of the requested product should be equated to the quantity of the offered product in algebraic form:

Qd \u003d Qs i.e. 7 - P \u003d -5 + 2 P.

Solving this equation for P, we get:

7 + 5 \u003d 2 P + P,

So, the equilibrium price is 4000 rubles. To find the equilibrium quantity, you need to substitute the resulting price value into any of the equations:

Consequently, the equilibrium volume is 3 million pieces.

Task number 3.6.2

Apples have risen in price. As a result, the price of apple juice changed by 20%, and the annual proceeds from its sales increased from 400 to 408 thousand rubles.

How much has the apple juice sales volume changed?

Answer: decreased by 15%.

Task number 3.6.3

Sugar has dropped in price. As a result, the price of lemonade changed by 10%, and the annual proceeds from its sale increased from 200 million rubles. up to 216 million rubles.

How much has the lemonade sales volume changed?

Answer: grew by 20%.

Problem number 3.7.1

What does this graph show?

Answer. Change in revenue.

Revenue (total revenue) is the area of \u200b\u200bthe rectangle: the product of price and quantity. When the price rises, we add to the area of \u200b\u200bthe indicated rectangle the area of \u200b\u200bthe rectangle lying directly above it, approximately equal to qDp, but subtract from its area the area of \u200b\u200bthe rectangle adjacent to it, equal to approximately pDq.

Task number 3.7.2

It is known that 5 thousand spectators will come to the concert with free admission, and an increase in the ticket price for each ruble reduces their number by 10 people.

What ticket price should organizers set if they want to maximize revenue?

Task number 3.7.3

Could a 15% price increase lead to a 19% increase in revenue? Could revenue increase 19% when prices go down 15%? How much should the sales volume change in each case (if possible)? All other factors are considered unchanged. Assume no deficit.

Problem number 3.8.1

Show the size of the deadweight and explain what it is.

Answer. Loss of dead weight due to tax imposition.

Area B + D measures the dead weight loss resulting from the imposition of the tax.

Task number 3.8.2

Let us be given two countries with internal markets for a certain product. Domestic supply and demand are shown for each country. It is required to determine who will be the importer and who will be the exporter when establishing trade relations between countries. Why?

In two countries (A and B), there are domestic markets for a certain product, characterized by supply and demand curves. Equilibrium in country A has a lower price than country B. PA< PB.

Countries open their markets to unimpeded trade, that is, buyers in each country can choose between domestic and foreign producers, and sellers in each country can choose between domestic and foreign markets.

With the markets of both countries open, the commodity will flow from the lower-price economy to the higher-price economy. That is, country A, where the domestic price was lower, will export the goods, and country B will import. As a result of trade between countries, such an equilibrium world price PM will be established, at which the volume of exports from country A will be equal to the volume of imports to country B. Exports in country A correspond to the excess supply in country A at the world price PM. Country B's imports correspond to excess demand in Country B at the world price PM. As shown in the graph, the segment of excess supply in country A is equal to the segment of excess demand in country B, that is, exports are equal to imports.

Task number 3.9.1

Population demand function for this product: Qd \u003d 7 - P.

Suggestion function: QS \u003d -5 + 2P,

where Qd is the volume of demand in million units per year; Qs - volume of supply in million units per year; P is the price in thousands of rubles.

What happens if the country's government sets the price at 6,000 rubles per unit of goods and does not allow sellers to sell their goods at a lower price?

Plug the new price into the demand function and the supply function:

Qd \u003d 7 - 6 \u003d 1,

Qs \u003d -5 + 26 \u003d 7

Hence, it is clear that with the new price, the market balance will not be achieved, since the quantity of the offered product will be 7 million pieces, while the quantity of the requested product is only 1 million pieces.

Consequently, there will be a surplus of goods on the market.

The amount of surplus goods will be 6 million pieces: 7 - 1 \u003d 6.

Task number 3.9.2

Supply and demand are described by linear functions.

At a price of 100, the surplus is 60, and at a price of 40, the deficit is 30.

Find the equilibrium price and equilibrium volume in the market.

Let's display what is given to us on the chart:

This task has only a graphical solution.

On the chart, we see two similar triangles (upper and lower). Recall that in such figures, the proportion of the ratio of similar elements is preserved.

In this case, the ratio of the bases of the triangles is equal to the ratio of their heights.

Whence P * \u003d 60.

Also note that the equilibrium volume cannot be determined from these data.

Problem number 3.10.1

The demand function for the product has the form Qd \u003d 150 + bP. It is known about the supply that at P \u003d 10, the supply volume is 100, at P \u003d 15 - the supply volume is 150. The income of the producers of the goods in the conditions of market equilibrium is 1000 monetary units.

Find the quantity demanded at a price equal to 8.

Problem number 3.10.2

Solve the problem (from Ravichev).

The King called the Economist somehow and complained:

- My treasury is withering. We need to replenish it. And the income tax and so be healthy - 25%. And this is what I thought was born. My boar hunters are completely loose. They have gone nuts from the freedom of the market and what a year they have taken, you know, the manner of selling at $ 72 per kg - this is at a cost price of $ 22! And if anyone offers them $ 68 or less, no one wants to sell at all. I will impose an excise tax on them. A small one - $ 2 per kg. And I will replenish the treasury, and I will squeeze the hunters. Count how much I will replenish the treasury. Any questions?

Well, what could the Economist ask? Of course, about the demand:

- And what, excuse me, is the demand for these very wild boars? He asked politely.

“That I can say to answer,” said the King proudly and spoke like an incantation:

Q \u003d - 4P + 304. Well, what will be the proposals?

“Oh yeah,” the Economist dawned, but what about the offer?

“I can’t help you here. I only know that our supply curve is straight.

The king sighed and departed.

So how much will the King replenish the treasury if he introduces an excise tax on the sale of wild boars?

Answer. After the introduction of the excise tax, tax revenues will REDUCE by $ 28.

Problem number 3.10.3

Population demand function for this product: QD \u003d 9 - P.

Offer function of this product: Qs \u003d -6 + 2P,

where QD is the volume of demand in million units, QS is the volume of supply in million units, P is the price in rubles.

a) Suppose a product tax is imposed on this product, paid by the seller, in the amount of 1.5 rubles. per piece. Determine the equilibrium price (with and without tax included), the equilibrium sales volume. Draw a drawing.

b) Suppose a product tax is imposed on this product, paid by the seller, in the amount of 25% of the price paid by the buyer. Determine the equilibrium price (with and without tax included), the equilibrium sales volume. Draw a drawing.

c) Suppose that for each unit of goods sold, producers receive an additional 1.5 rubles. from the state budget. Determine the equilibrium price (with and without subsidies), the equilibrium sales volume. Draw a drawing.

d) Suppose that a per-product tax paid by the seller in the amount of 1.5 rubles is introduced on this product. a piece. At the same time, the government set a fixed retail price (including tax) at 5 rubles. Identify excess demand. Draw a drawing.

Tasks for plotting supply and demand curves goods

Problem 1

Formulation of the problem:

Draw a demand curve for a given product and show how it will change if customers choose to buy 20 kg more at each price level?

Technology for solving the problem:First, we draw a coordinate system and choose a scale, then we put points corresponding to the values \u200b\u200bof the volume of demand at a certain price. By connecting the dots, we get the demand curve. An increase in demand by 20 units will change consumer preferences, which will manifest itself in an increase in demand. So, at a price of $ 20, buyers will be ready to buy not 320 kg, but 340, at a price of $ 30 - 300 kg, at $ 40 - 260. Let's build another column in the table:

Price (P) (USD)	Demand volume (Qd 1) (kg)	Demand volume (Qd 2) (kg)

As a result, the demand curve will also shift, it will be located to the right of d 1.

Problem 2

Formulation of the problem:The dependence of the volume of demand for goods X on its price is presented in the table.

Price (P) (thousand rubles)	Demand volume (Qd) (pcs.)

Draw a demand curve for a given product.

Problem 3

Formulation of the problem:A demand curve d 1 for dry cleaning services is given. Show how demand will change if a dry cleaner announces a tariff increase for its services.

Technology for solving the problem: First, we draw a coordinate system and depict the demand curve (while the curve should not be very flat, since this production has few substitutes).

An increase in tariffs leads to a decrease in demand for services, which is represented by the movement of point A to B along the demand curve as the price factor changes. At the same time, the volume of demand will decrease from Q 1 to Q 2.

Task 4

Formulation of the problem:Given the demand curve d 1 for product X. Show the change in demand if the product becomes more fashionable.

Technology for solving the problem: AND

If product X becomes fashionable, then the demand curve will shift to the right to position d 2, which will increase the demand for the product. This can be depicted by moving the point AND exactly B

Problem 5

Formulation of the problem:Initially, the demand curve for good X was at position d 1. Show the change in demand if the price for product Y increases (product X and Y are substitutes).

Technology for solving the problem: First, we draw a coordinate system and draw the demand curve for product X (the shape of the curve does not matter). Take any price and mark the point on the demand curve AND, which is typical for this price, while the volume of demand will be Q 1.

If the price of product Y increases, then the demand for it will fall and some consumers will switch to the consumption of substitute products, including product X. In this case, the demand curve for product X will shift to the right to position d 2, which leads to an increase in demand for the product. This can be depicted by moving the point AND exactly B on a new demand curve at the same price P 1. The volume of demand will increase from Q 1 to Q 2.

Task 6

Formulation of the problem:Draw an arbitrary demand curve for product A. Show the change in demand if new buyers come to the market.

Technology for solving the problem: First, we draw a coordinate system and draw the demand curve (the shape of the curve does not matter). Take any price and mark the point on the demand curve A, which is typical for this price, while the volume of demand will be Q 1.

If new buyers come to the market of good A, then the demand curve will shift to the right to position d 2, which leads to an increase in demand for the good. This can be depicted by moving the point A exactly B on a new demand curve at the same price P 1. The volume of demand will increase from Q 1 to Q 2.

Problem 7

Formulation of the problem:VCR prices have dropped. Show on the charts what will happen in the VCR market and the video cassette market.

Technology for solving the problem: First, let's draw a coordinate system and plot the demand curve for VCRs.

Lower prices will increase demand for VCRs, which is depicted by moving point A to B along the demand curve as the price factor changes. At the same time, the volume of demand increases from Q 1 to Q 2.

Since VCRs and videotapes are complementary products (complementary to each other), the market for videotapes will also change. As the demand for VCRs has grown, so will demand for videotapes.

Consider this in the graph:

The demand curve for videotapes shifts to the right, since the non-price factor changes, and at the same price P 1, the volume of demand will increase from Q 1 to Q 2.

Problem 8

Formulation of the problem:Given a demand curve d 1 for good A. Show how the position of this curve will change if the season for the consumption of goods ends.

Technology for solving the problem: First, we draw the coordinate system and draw the demand curve d 1. If the season for the consumption of a good is over, then the demand for it will fall and the demand curve will shift to the left (down), while the volume of demand at the same price P 1 will decrease from Q 1 to Q 2.

Problem 9

Formulation of the problem:The demand function is given by the formula Qd \u003d 7-P. Plot the demand curve.

Technology for solving the problem:

1st way... Let's draw a coordinate system and choose a scale, then put points corresponding to the values \u200b\u200bof the volume of demand at a certain price. (For example, P \u003d 1, Qd \u003d 6; P \u003d 2, Qd \u003d 5, etc.) By connecting the dots, we get the demand curve.

2nd way.First, let's draw a coordinate system and choose a scale. Then we define the points corresponding to the values volume of demand at zero price and price at volume equal to zero. By connecting the dots, we get the demand curve.

Problem 10

Formulation of the problem:

Draw a supply curve for a given product.

Technology for solving the problem:First, we draw a coordinate system and select a scale, then we put points corresponding to the values \u200b\u200bof the supply volume at a certain price. By connecting the dots, we get the supply curve.

Assignment 11

Formulation of the problem:The dependence of the volume of supply of goods A on its price is presented in the table:

Show on a graph what will happen to the supply curve for a given product if manufacturers increase the supply of product A by 10 units at each price level.

Technology for solving the problem:First, let's draw a new table to show the changes in the product offer.

Now let's draw a coordinate system and choose a scale, then put points corresponding to the values \u200b\u200bof the supply volume at a certain price. Connecting the points, we get the supply curve s 1. Then we construct a new supply curve s 2 corresponding to the new supply values \u200b\u200bat different prices.

Assignment 12

Formulation of the problem:The product supply function Y is given by the formula Qs \u003d –100 + 20Р. Draw a supply curve.

Technology for solving the problem:

1st way... Let's draw a coordinate system and choose a scale, then put points corresponding to the values \u200b\u200bof the supply volume at a certain price (for example, P \u003d 5, Qs \u003d 0; P \u003d 10, Qs \u003d 100, etc.). By connecting the dots, we get the supply curve.

2nd way.First, let's draw a coordinate system and choose a scale. Then we define the points corresponding to the values \u200b\u200bof the supply volume at zero price (Qs \u003d –100 + 20 * 0 \u003d –100) and the price at the supply volume equal to zero (0 \u003d –100 + 20 * Р, Р \u003d 5). By connecting the dots, we get the supply curve.

Assignment 13

Formulation of the problem: The supply curve for product X is given. Show the change in supply if more expensive raw materials are used in production.

Technology for solving the problem: AND, which is typical for this price, while the volume of supply will be Q 1. The use of more expensive raw materials will lead to an increase in production costs, the volume of production will decrease, and hence the volume of supply of goods on the market will decrease. The supply curve will move to the left (up), and at the same price, the supply will decrease to Q 2.

Assignment 14

Formulation of the problem: The price of item A has increased. Show on the graph what will happen with the offer of this product.

Technology for solving the problem:First, we draw a coordinate system and draw the supply curve (the shape of the curve does not matter). Take any price P 1 and mark the point on the supply curve AND, which is typical for this price, while the volume of supply will be Q 1. An increase in price will lead to an increase in income, so the manufacturer will increase the production of this product, therefore, the volume of supply of the product in the market will increase. The supply curve does not change, since there is a change price factor, which will be reflected in the curve itself. The point will move to position B, the supply will increase to Q 2.

Assignment 15

Formulation of the problem:The state introduced a tax on goods A. Show on the graph what changes will occur in the supply of goods.

Technology for solving the problem: First, we draw a coordinate system and draw the supply curve (the shape of the curve does not matter). Take any price P 1 and mark the point on the supply curve s 1 and, which is typical for this price, while the volume of supply will be Q a. The introduction of the tax will lead to a decrease in income, so the manufacturer will reduce the production of this product, therefore, the volume of supply of the product on the market will decrease. In this case, the supply curve will shift to the left to position s 2, since the non-price factor changes. The point will move to position in, the volume of supply will decrease to Q in.

Assignment 16

Formulation of the problem:The state introduced a subsidy for the production of goods X. How will the position of the supply curve for this product change?

Technology for solving the problem:First, we draw a coordinate system and draw the supply curve s 1 (the shape of the curve does not matter). Take any price and mark a point on the supply curve and, which is typical for this price, while the volume of supply will be Q a. Receiving a subsidy will reduce the costs of the enterprise, and the income will increase, therefore, production will increase, and the volume of supply of goods on the market will also increase. The supply curve will then shift to the right to position s 2. The point will move to position in

Assignment 17

Formulation of the problem:Draw an arbitrary supply curve for item A. Show the supply change if new sellers enter the market.

Technology for solving the problem: First, we draw a coordinate system and draw the supply curve (the shape of the curve does not matter). Take any price and mark a point on the supply curve and, which is typical for this price, while the volume of supply will be Q a. The appearance of new sellers on the market will lead to an increase in the volume of supply of goods on the market. In this case, the supply curve will shift to the right to position s 2, since there is a change in the non-price factor. The point will move to position in, the volume of supply will increase to Q in.

Tasks for the graphical determination of market equilibrium

Assignment 18

Formulation of the problem: prices, volumes of demand and supply of goods X. Draw the curves of supply and demand and determine the equilibrium point.

Technology for solving the problem: x at - product prices.

At the equilibrium point (E), an equilibrium price of $ 18 and an equilibrium sales volume of 6 pieces are established.

Answer:Price $ 18, sales volume 6 pieces.

Assignment 19

Formulation of the problem:The table provides data on prices, volumes of demand and supply of goods X. Draw the supply and demand curves and on the graph determine what will happen in the market if the price settles at $ 14.

Technology for solving the problem:We draw a coordinate system. Axis x we postpone the values \u200b\u200bof the volume of demand and supply, along the axis at - product prices.

At the equilibrium point (E), an equilibrium price of $ 18 and an equilibrium sales volume of 16 pieces are established. Since the price has settled at $ 14, the equilibrium is upset. The volume of demand is 15, and the volume of supply is 18 units. The difference of 3 units is a shortage of goods X.

Answer:a deficit in the amount of 3 thousand pieces of goods X.

Assignment 20

Formulation of the problem:The volumes of supply and demand for goods A are presented in the table. Draw supply and demand curves and determine the equilibrium point. What happens in the market if the price settles at $ 30?

Technology for solving the problem:We draw a coordinate system. Axis x we postpone the values \u200b\u200bof the volume of demand and supply, along the axis at - product prices.

At the equilibrium point (E), an equilibrium price of $ 28 and an equilibrium sales volume of 6 pieces are established. If the price is set at $ 30, then the demand will be 5 units and the supply will be 7 units. Thus, there will be a surplus of 2 units in the market.

Answer: a surplus of 2 thousand pieces of A.

Assignment 21

Formulation of the problem:The table presents data on prices, volumes of demand and supply of goods X. Draw the curves of supply and demand and determine the equilibrium point. How will the equilibrium change if the volume of demand increases by 2 units at each price level.

Technology for solving the problem:We draw a coordinate system. Axis x we postpone the values \u200b\u200bof the volume of demand and supply, along the axis at- product prices.

At the equilibrium point (E), an equilibrium price of $ 18 and an equilibrium sales volume of 26 are established. If demand increases, then the curve moves to the right by two units. A new equilibrium will be established at a price of $ 20 and a sales volume of 27.

Answer:Equilibrium price $ 20, sales volume 27.

Assignment 22

Formulation of the problem:The table presents data on prices, volumes of demand and supply of goods U. Draw the curves of supply and demand and determine the equilibrium point. Find out what the balance will be if the supply rises.

Technology for solving the problem:We draw a coordinate system. Axis x we postpone the values \u200b\u200bof the volume of demand and supply, along the axis at - product prices.

At the equilibrium point (E), an equilibrium price of $ 180 and an equilibrium sales volume of 6 thousand liters are established. Consider the change in the offer in the table:

Price (USD)	Demand volume (Qd)	Supply volume (Qs 1)	Supply volume (Qs 2)

We construct a new supply curve s 2. The equilibrium price will now be $ 140, and the equilibrium sales volume is 8 thousand liters.

Answer: The new equilibrium price is $ 140, the sales volume is 8 thousand liters.

Tasks for the application of formulas for calculating the equilibrium price and equilibrium sales volume

Assignment 23

Formulation of the problem:The volume of demand for good A in this market is determined by the formula Qd \u003d 9 - P, the volume of supply - by the formula Qs \u003d –6 + 2P, where P is the price of good A. Find the equilibrium price and the equilibrium sales volume.

Answer: the equilibrium price is 5 den. units, sales volume - 4 USD e.

Assignment 24

Formulation of the problem:The demand function for the good is Qd \u003d 15 - Р, the supply function is Qs \u003d –9 + 3Р. Determine the equilibrium in the market for this good. What happens to equilibrium if the volume of demand decreases by 1 unit at any price level?

Technology for solving the problem:Under equilibrium conditions, the volume of demand and the volume of supply are equal, therefore, it is necessary to equate their formulas: 15 - Р \u003d –9 + 3Р, hence, the equilibrium price is 6. To determine the equilibrium volume of sales, it is necessary to substitute the equilibrium price in any formula: Qd \u003d 15 - 6 \u003d 9 or: Qs \u003d - 9 + 3 * 6 \u003d 9. If demand decreases by 1 unit, then the demand function will change: Qd 1 \u003d (15 - 1) - Р \u003d 14 - P. To find a new equilibrium price, it is necessary to equate the new volume of demand and the volume of supply 14 - Р \u003d –9 + 3Р, Р \u003d 5.75, the sales volume is 8.25.

Answer:equilibrium price 5.75, equilibrium sales volume 8.25.

Assignment 25

Formulation of the problem: The demand function for product X: Qd \u003d 16 - 4P, supply function Qs \u003d –2 + 2P. Determine the equilibrium in the market for this good. What happens to equilibrium if supply increases by 2 units at any price level?

Technology for solving the problem:Under equilibrium conditions, the volume of demand and the volume of supply are equal, therefore, it is necessary to equate their formulas: 16 - 4P \u003d –2 + 2P, hence, the equilibrium price is 3. To determine the equilibrium volume of sales, it is necessary to substitute the equilibrium price in any formula: Qd \u003d 16 - 4 * 3 \u003d 4 or: Qs \u003d –2 + 3 * 2 \u003d 4. If the offer increases by 2 units, the offer function will change: Qs 1 \u003d (–2 + 2) + 2P \u003d 2P. To find a new equilibrium price, it is necessary to equate the new volume of demand and the volume of supply 16 - 4P \u003d –2 + 2P, P \u003d 2.33, the sales volume is 6.68.

Answer:equilibrium price 2.33, equilibrium sales volume 6.68.

print version

Solve problem No. 1. Supply on the labor market in a certain industry is described by the equation LS \u003d 20 * w, and the sectoral demand for labor is described by the equation Ld \u003d 1200 - 10 * w, where w is the daily rate wages (thousand rubles), and L is the number of employees requested by firms and offering their labor services in one day. A) Draw the supply and demand curves of labor on a graph.

Solution W (thousand rubles) - daily wage rate Ld \u003d 1200 - 10 * w 100 90 80 70 60 50 40 30 20 10 0 LS \u003d 20 * w 100 200 400 500 700 800 1000 1200 L (number of people per day )

Solve the problem The supply in the labor market in a certain industry is described by the equation LS \u003d 20 * w, and the sectoral demand for labor is described by the equation Ld \u003d 1200 - 10 * w, where w is the daily wage rate (thousand rubles), and L is the quantity workers asked by firms and offering their services in one day. B) determine in a given labor market the equilibrium number of employees and the equilibrium wage rate (using graphical and analytical methods)

Solution W (thousand rubles) - daily wage rate Ld \u003d 1200 - 10 * w 100 90 80 70 60 50 40 30 20 10 0 LS \u003d 20 * w Equilibrium point 100 200 400 500 700 800 1000 1200 L (number of people in a day)

Analytical solution Supply LS \u003d 20 * w demand Ld \u003d 1200 - 10 * w where w is the daily wage rate (thousand rubles), and L is the number of employees Solution: LS \u003d Ld 20 * w \u003d 1200 - 10 * w, 30 * w \u003d 1200, W \u003d 40 thousand rubles. in a day. LS \u003d 20 * 40 \u003d 800, or, Ld \u003d 1200 - 10 * 40 \u003d 800 The equilibrium number of employed is 800 people.

Solve the problem The supply on the labor market in a certain industry is described by the equation LS \u003d 20 * w, and the sectoral demand for labor is described by the equation Ld \u003d 1200 - 10 * w, where w is the daily wage rate (thousand rubles), and L is the quantity workers asked by firms and offering their services in one day. C) Suppose that for some reason the industry demand for labor has increased. Show this on a graph. What will happen to the salary rate and the amount of employment? Will this change the total income received by all workers in the industry?

Solution What factors can increase (decrease) the demand wage rate W (thousand rubles) - daily for labor services? L d 1 L d 2 LS W 2 W 1 0 L 1 \u003d 800 L 1 L 2 L (number of people per day)

Solve Problem # 2. Why India Build Canals and Dams with High Use labor resources, and in Holland - with a large use of machines and mechanisms? Which construction method is more efficient? # 3. Sylvester Stallone received $ 15 million plus box office interest for his role in Rocky IV. Why do you think Stallone makes so much money?

Homework Suppose the following data represent the amount of labor supply and demand in a particular industry. Salary rate (dollars per hour) Number of workers required (people) 1 5000 Number of workers offering their services (people) 1000 2 3 4 5 6 4000 3000 2000 1000 0 2000 3000 4000 5000 6000

Homework 1. Determine, using the data in the table, the equilibrium wage rate and the number of workers offering their services for a completely competitive market labor. 2. Suppose that as a result of signing collective agreement trade union representatives and entrepreneurs salary was $ 5 per hour. A) What will be the value of the demand for labor at the new level of wages? How many workers will offer t ore services at the new salary level? What will be the unemployment rate? B) Which workers will lose and which will gain as a result of a new, higher level of salary? 3. Display the results obtained graphically.

Examples of solving problems on the topic

"Market and Market Equilibrium"

Objective 1.What is the equilibrium level of prices and the equilibrium volume of sales of goods on the market, if supply and demand are described by the equations: Q D \u003d 30 - 2P and Q S \u003d 4P - 30? How will the situation on the market develop if the administrative price is set equal to: a) 8 CU, b) 12 CU?

Decision ... At the point of market equilibrium, the value of demand is equal to the value of supply, therefore 30-2P \u003d 4P - 30, hence P \u003d 10 DE,Q \u003d 10 pcs.

When P \u003d 8Q D \u003d 30 - 2 8 \u003d 14 pcs., AndQ S \u003d 4 8 - 30 \u003d 10 pcs. AsQ D > Q S , the market will have a situation of excess demand (deficit) in the amount of 14-10 \u003d 4 pcs.

When P \u003d 12Q D \u003d 30 - 2 12 \u003d 6 pcs., AndQ S \u003d 4 12 - 30 \u003d 18 pcs. AsQ D < Q S , the market will have a situation of excess supply (surplus goods) in the amount of 18-6 \u003d 12 pcs.

Objective 2.

Decision ... At a price of 6 sous, the amount of demand \u003d 1100 liters, and the amount of supply \u003d 800 liters. Consequently, there will be a milk deficit on the market in the amount of \u003d 1100-800 \u003d 300 liters.

Objective 3.

Decision ... At the point of market equilibrium: 50-2P \u003d 5 + 3P, therefore, P 0 \u003d 9 DE,Q 0 \u003d 32 pcs.

At the point of the maximum market price, the demand value is zero, therefore 50-2Р \u003d 0, whence Р max \u003d 25 DE.

The length of the leg along the abscissa is 32 pcs. The length of the leg along the ordinate is 25-9 \u003d 16 DE.

The consumer surplus is equal to the area of \u200b\u200bthe triangle: 0.5 16 32 \u003d 256 DE

Problem 4.C Q d = 1200-5R and Q s = 500 + 5R.The state gives a subsidy to the manufacturer in the amount of CU 10. per unit of production. How will the equilibrium price and equilibrium volume change after the introduction of the subsidy? What will the manufacturer's selling price be equal to?

Decision. After the introduction of a subsidy of 10 CU per unit of production, the proposal will change:Q S (P) → Q S (P+10), i.e. the new sentence will be described by the expression:Q s = 500 + 5(P +10)

1200-5P \u003d500 + 5(P +10), therefore P 0 ’ \u003d 65 DE,Q 0 ’ \u003d 1200-5 65 \u003d 875 pcs.

Before the introduction of the subsidy, the market was characterized by the following parameters:1200-5P \u003d500 + 5P, hence P 0 \u003d 70 DE,Q 0 \u003d 850 pcs.

As can be seen from the calculations, the equilibrium market price decreased by 5 CU, while the equilibrium volume increased by 25 units.

The manufacturer's price will be: R S \u003d P 0 ’ +  H \u003d 65 + 10 \u003d 75 CU, which is 5 CU higher than the initial equilibrium level (R 0 \u003d 70 DE).

Problem 5.Crequest and offer are set by the functions: Q d = 100 – Rand Q s = 2R - 50.The state introduces a 10% sales tax. What are the consequences of this?

Decision. After the introduction of the tax, the proposal will change, since 10% of the price will have to be paid in the form of tax. Consequently, the enterprise will have 0.9 P, then the supply function will be described by the expression:Q s \u003d 2 P 0.9 - 50

The demand, which remains unchanged, is equated to a new expression for the proposal:

100-P \u003d 2 P 0.9 - 50, therefore P 0 ’ \u003d 54 DE,Q 0 ’ \u003d 46 pcs.

Before the introduction of the tax: 100-P \u003d 2P - 50, therefore, P 0 \u003d 50 DE,Q 0 \u003d 50 pcs.

As can be seen from the calculations, the equilibrium market price increased by 4 units, while the equilibrium volume decreased by 4 units.

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