Equilibrium price and equilibrium quantity. A set of economic and legal procedures that allow people to exchange their labor services for wages and other benefits - document Tasks for graphical definition of market equilibrium

07.05.2022

3. Market equilibrium. Market volume of sales and market revenue. Deficiency and surplus of goods. The impact of changes in supply and demand on the market equilibrium.

Complexity

Task №3.1.1

Determine the price at which buyers will completely buy all the goods?

Answer: at P = 1 p.

Task №3.1.2

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

What: reverse or direct?

Answer. Reverse.

Task №3.1.3

A man who sighs about an avocado near an avocado and vows to taste it sooner or later, does this show his demand for avocados or not? Explain.

Answer. No. Demand implies not only the desire to acquire some good, but also the (solvent) willingness to do so.

Task №3.1.4

What does a linear demand function look like?

Answer. Qd(P) = a – bP.

Task №3.1.5

Does the quantity demanded have any dimension?

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

Task №3.2.1

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

Build supply and demand graphs 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 built using two points.

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

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

Please note that from the point of view of mathematics, the graphs described by these functions can also be located in the plane with negative numbers. However, from an economic point of view, supply and demand curves can only be located in the area of positive values, since neither price nor quantity can be negative.

Task №3.2.2

Qd (P) = 20 - 2P is a direct function of demand. Write an inverse demand function.

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

Task №3.2.3

Recall the standard way of finding the coefficients of a linear demand function, which will be required in most problems that do not give the demand function itself, but indicate that it has a linear form.

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

Task №3.2.4

What do we need to find in order to compose a system of two equations for finding the coefficients of a 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.

Task №3.2.5

How to start plotting a linear demand function graph?

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

Task №3.3.1

The volume of demand for product 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 product A.

Find the equilibrium price and the equilibrium quantity sold.

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

Task №3.3.2

The market demand for the product is given by the function: QD = 9 - 3P.

The quantity of goods that is put up for sale is 6 units.

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

B) What will happen if the price of the product is 2 rubles, provided that the quantity of the product offered for sale remains unchanged?

A) at P \u003d 1 p.

B) there will be a surplus of goods in the market in 3 units. (6 - (9 - 3 × 2)).

Task №3.3.3

Review the chart carefully.

Based on the results of the economic analysis of the graph, formulate answers to the following questions:

1. What is the economic meaning of the intersection of curves in t. E?

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

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

Task №3.3.4

Explain what could be the reason for such a situation in the market:

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 №3.4.1

The demand for bananas is described by the equation: Qd = 2400 - 100R, and the supply of bananas is described by the equation Qs = 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, we equate the value of demand to the value of supply:

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

Solving the equation, we find the equilibrium price:

1400 = 350 R; Р = 4 (thousands of rubles).

Substituting the found price into the equation describing demand, or into the equation describing 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 3,000 rubles (i.e., at a price below the equilibrium price), you need to substitute this price value into both the demand equation and the supply equation:

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

Qs = 1000 + 250 3 = 1750 kg per day.

This shows that at a price below the equilibrium, consumers will want to buy more bananas than producers will agree to sell (Qd > Qs). In other words, consumers will want to buy 2100 kg of bananas, but will be able to buy exactly as many as the sellers will sell them, i.e. 1750 kg. This is the correct answer.

3) We substitute the price of 5000 rubles in each of these equations:

Qd = 2400 - 100 5 = 1900 kg per day;

Qs = 1000 + 250 5 = 2250 kg per day.

It is clearly seen that at a price above 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 the 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.

Task №3.5.1

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

What happens to the equilibrium if the quantity demanded decreases by 1 unit at any price level?

Answer. The equilibrium price is 5.75, the equilibrium sales volume is 8.25.

Task №3.5.2

Demand function for product X: Qd = 16 - 4Р, supply function Qs = -2 + 2Р.

Determine the equilibrium in the market for this good.

What happens to the equilibrium if the quantity supplied increases by 2 units at any price level?

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

Task №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 the 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 increases.

How will the total income of sellers of oranges change?

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

The supply curve for tangerines has shifted to the left. This increased the equilibrium price in that market and decreased the equilibrium quantity sold.

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

b) With an increase in the supply of tangerines, 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 the price in this market.

A decrease in the price of tangerines will reduce the demand for oranges, and the demand curve for this conjugate 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 sellers of oranges will decrease compared to the original.

Task №3.5.4

The population demand function for this product Qd = 7 - P, the supply function of this product Qs = -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 c.u. e.

Determine the equilibrium price and the equilibrium quantity sold.

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 = 4 c.u. (equilibrium price); Qd = 7 – 4 = 3 mln. (equilibrium volume).

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

Task №3.5.5

The price of milk has gone up. 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.

By what percent did the volume of sour cream sales change?

Answer. Decreased by 20%.

Task №3.6.1

The function of the population's demand for a given product: Qd = 7 - P.

Offer function: QS=-5+2P,

Using the available data, determine (graphically and analytically) the parameters of the market equilibrium, i.e., the equilibrium price and the equilibrium quantity of the product.

a) It can be seen from the graph that the supply and demand curves intersect at a point with coordinates: Q = 3 and P = 4. This intersection point is the market equilibrium point. So: 3 million pieces - the equilibrium quantity of goods; 4000 rubles is the equilibrium price.

b) The analytical way of solving is that the quantity of the requested good should be equated to the quantity of the offered good in algebraic form:

Qd = Qs i.e. 7 - P = -5 + 2 P.

Solving this equation for P, we get:

7 + 5 = 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:

Therefore, the equilibrium volume is 3 million pieces.

Task №3.6.2

The price of apples has gone up. As a result, the price of apple juice changed by 20%, and the annual revenue from its sales increased from 400 to 408 thousand rubles.

By what percent did the volume of apple juice sales change?

Answer: decreased by 15%.

Task №3.6.3

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

By what percent did the volume of lemonade sales change?

Answer: increased by 20%.

Task №3.7.1

What does this chart show?

Answer. Change in revenue.

Revenue (total income) is the area of the rectangle: the product of price and quantity. When the price rises, we add to the area of the specified rectangle the area of the rectangle directly above it, approximately equal to qDp, but subtract from its area the area of the rectangle adjacent to it from the side, equal to approximately pDq.

Task №3.7.2

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

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

Task №3.7.3

Can a 15% increase in price lead to a 19% increase in revenue? Can revenue increase by 19% with a price decrease of 15%? How much should the volume of sales change in each case (if possible)? All other factors are considered unchanged. Assume no shortage.

Task №3.8.1

Show the size of the "dead weight" and explain what it is.

Answer. Loss of dead weight due to the imposition of a tax.

Area B + D measures the loss of dead weight due to the imposition of the tax.

Task №3.8.2

Let us be given two countries with domestic markets for a certain product. For each country, domestic supply and demand are indicated. 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 commodity characterized by supply and demand curves. The equilibrium in country A is characterized by a lower price than country B. PA< PB.

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

When the markets of both countries are open, goods will flow from the economy where prices are lower to the economy where prices are higher. 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, an equilibrium world price of 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 an excess supply in country A at the world price of PM. Imports in country B correspond to excess demand in country B at the world price of PM. As shown in the graph, the oversupply band in country A is equal to the excess demand band in country B, i.e. exports equal imports.

Task №3.9.1

The function of the population's demand for a given product: Qd = 7 - P.

Offer function: QS=-5+2P,

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

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

Substitute the new price value into the demand function and into the supply function:

Qd \u003d 7 - 6 \u003d 1,

Qs = -5 + 26 = 7

This shows that at the new price equilibrium in the market will not be achieved, since the quantity of the offered goods will be 7 million pieces, while the quantity of the requested goods will be only 1 million pieces.

Consequently, there will be an excess of goods in the market.

The amount of excess goods will be 6 million pieces: 7 - 1 = 6.

Task №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 shortage is 30.

Find the equilibrium price and equilibrium volume in the market.

Let's display what we are given on the graph:

This problem has only a graphical solution.

On the chart, we see two similar triangles (upper and lower). Recall that in similar 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.

Where P* = 60.

We also note that it is impossible to determine the equilibrium volume from these data.

Task №3.10.1

The demand function for a product has the form Qd = 150 + bP. It is known about the supply that at P = 10, the volume of supply is 100, at P = 15 - the volume of supply is 150. The revenue of producers of goods in conditions of market equilibrium is 1000 den.un.

Find the quantity demanded at a price equal to 8.

Task №3.10.2

Solve the problem (from Ravichev).

Somehow the King called the Economist and complained:

- My treasury is dying. We need to fill it up. And the income tax and so be healthy - 25%. And here's the thought that came to me. My boar hunters are completely unrestrained. They have gone silly from market freedom and have taken a year, you understand, to sell at 72 dollars per kg - this is at a cost price of 22 dollars! And just a few people offer them $68 or less, and in general, no one wants to sell. I'll impose an excise tax on them. A small one - $ 2 per kg. And I will replenish the treasury, and I will press the hunters. Calculate 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 boars? he politely inquired.

- This I can say to answer, - the King said proudly and cast as a spell:

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

“Oh yes,” the Economist thought, but what about the offer?

“I can't help here. I only know that we have a straight supply curve.

The king sighed and left.

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 revenues will DECREASE by $28.

Task №3.10.3

The function of the population's demand for a given product: QD = 9 - P.

The supply function of this product: Qs = -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) Assume that a commodity tax paid by the seller in the amount of 1.5 rubles has been introduced for this product. per piece. Determine the equilibrium price (with and without tax included), the equilibrium sales volume. Make a drawing.

b) Assume that a commodity 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. Make 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. Make a drawing.

d) Assume that a commodity tax is introduced on this product, paid by the seller, in the amount of 1.5 rubles. a piece. At the same time, the government set a fixed retail price (including tax) of 5 rubles. Define excess demand. Make a drawing.

Tasks for building supply and demand curves goods

Task 1

Formulation of the problem:

Draw a demand curve for this good and show how it changes if buyers prefer to buy 20 kg more at each price level?

Technology for solving the problem: First, let's draw a coordinate system and choose a scale, then put the points corresponding to the values of the quantity demanded at a certain price. By connecting the dots, we get the demand curve. An increase in demand by 20 units will change the preferences of consumers, which will manifest itself in an increase in the volume of demand. So, at a price of $ 20, buyers will be ready to purchase 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)	Volume of demand (Qd 1) (kg)	Volume demanded (Qd 2) (kg)

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

Task 2

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

Price (P) (thousand rubles)	Volume of demand (Qd) (pcs.)

Draw a demand curve for this product.

Task 3

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

Technology for solving the problem: First, let's draw a coordinate system and draw a demand curve (in this case, the curve should not be very flat, since there are few substitutes for this production).

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

Task 4

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

Technology for solving the problem: BUT

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

Task 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 of good Y increases (goods X and Y are substitutes).

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

If the price of good Y increases, then the demand for it will fall and some consumers will switch to the consumption of substitute goods, including goods 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 goods. This can be represented by moving the point BUT 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 entered the market.

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

If new buyers enter the market for product A, then the demand curve will shift to the right to position d 2, which leads to an increase in demand for the product. This can be represented 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 .

Task 7

Formulation of the problem: VCR prices have dropped. Show on graphs 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.

A decrease in prices will increase the demand for VCRs, which is represented by point A moving to B on the demand curve as the price factor changes. The volume of demand at the same time increases from Q 1 to Q 2 .

Since VCRs and video cassettes are complementary goods (mutually complementing each other), the video cassette market will also change. As the demand for VCRs has increased, so will the demand for VCRs.

Let's look at this on a chart:

The demand curve for video cassettes shifts to the right as the non-price factor changes, and at the same price P 1 the quantity demanded will increase from Q 1 to Q 2 .

Task 8

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

Technology for solving the problem: First, let's draw a coordinate system and draw a demand curve d 1 . If the season of consumption of the goods 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.

Task 9

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

Technology for solving the problem:

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

2nd way. First, draw a coordinate system and choose a scale. Then we determine the points corresponding to the values quantity demanded at zero price and price at volume equal to zero. By connecting the dots, we get the demand curve.

Task 10

Formulation of the problem:

Draw a supply curve for this product.

Technology for solving the problem: First, let's draw a coordinate system and choose a scale, then put points corresponding to the values of the supply volume at a certain price. By connecting the dots, we get the supply curve.

Task 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 happens to the supply curve for a given good if producers increase the supply of good 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 select the scale, then put the points corresponding to the values of the supply volume at a certain price. Connecting the dots, we get the supply curve s 1 . Then we construct a new supply curve s 2 corresponding to new supply values at different prices.

Task 12

Formulation of the problem: The product supply function Y is given by the formula Qs = -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 of the supply volume at a certain price (for example, P=5, Qs=0; P=10, Qs=100, etc.). By connecting the dots, we get the supply curve.

2nd way. First, draw a coordinate system and choose a scale. Then we determine the points corresponding to the values of the supply volume at zero price (Qs = -100 + 20 * 0 = -100) and the price at the supply volume equal to zero (0 = -100 + 20 * P, P = 5). By connecting the dots, we get the supply curve.

Task 13

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

Technology for solving the problem: BUT, 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 therefore the volume of supply of goods on the market will also decrease. The supply curve will shift to the left (up), and at the same price, the supply will decrease to Q 2 .

Task 14

Formulation of the problem: The price of good A has risen. Show on the graph what will happen to the supply of this product.

Technology for solving the problem: First, let's draw a coordinate system and draw a supply curve (in this case, the type of curve does not matter). Take any price P 1 and mark a point on the supply curve BUT, 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 producer will increase the production of this product, therefore, the volume of supply of the product on the market will increase. At the same time, the supply curve does not change, since the price factor changes, which will be reflected in the curve itself. The point will move to position B, the volume of supply will increase to Q 2 .

Task 15

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

Technology for solving the problem: First, let's draw a coordinate system and draw a supply curve (in this case, the type of curve does not matter). Take any price Р 1 and mark a point on the supply curve s 1 a, which is typical for this price, while the volume of supply will be Q a . The introduction of a tax will lead to a decrease in income, so the manufacturer will reduce the production of this product, and therefore, the volume of supply of goods on the market will decrease. In this case, the supply curve will shift to the left 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 decrease to Q c.

Task 16

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

Technology for solving the problem: First, draw a coordinate system and depict the supply curve s 1 (in this case, the type of the curve does not matter). Take any price and mark a point on the supply curve a, 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 income will increase, so 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

Problem 17

Formulation of the problem: Draw an arbitrary supply curve for product A. Show the change in supply if new sellers entered the market.

Technology for solving the problem: First, let's draw a coordinate system and draw a supply curve (in this case, the type of curve does not matter). Take any price and mark a point on the supply curve a, 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 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 c.

Tasks for graphical determination of market equilibrium

Problem 18

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

Technology for solving the problem: X at- commodity prices.

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

Answer: The price is 18 dollars, the volume of sales is 6 pieces.

Problem 19

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

Technology for solving the problem: Draw a coordinate system. Axis X we plot the values of the volume of supply and demand, along the axis at- commodity prices.

At the equilibrium point (E), an equilibrium price of $18 and an equilibrium sales volume of 16 units are established. Since the price settled at $14, the balance is broken. The quantity demanded is 15 and the quantity supplied is 18 units. A difference of 3 units is the shortage of good X.

Answer: a deficit of 3,000 pieces of good X.

Problem 20

Formulation of the problem: The volumes of demand and supply of 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: Draw a coordinate system. Axis X we plot the values of the volume of supply and demand, along the axis at- commodity prices.

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

Answer: a surplus of 2,000 pieces of product A.

Problem 21

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

Technology for solving the problem: Draw a coordinate system. Axis X we plot the values of the volume of supply and demand, along the axis at- commodity prices.

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

Answer: Equilibrium price $20, sales volume 27 pieces.

Problem 22

Formulation of the problem: The table presents data on prices, volumes of supply and demand for product Y. Draw supply and demand curves and determine the equilibrium point. Find what the equilibrium will be like if supply rises.

Technology for solving the problem: Draw a coordinate system. Axis X we plot the values of the volume of supply and demand, along the axis at- commodity prices.

At the equilibrium point (E), an equilibrium price of $180 and an equilibrium sales volume of 6,000 liters are established. Consider the change in the proposal in the table:

Price (USD)	Volume demanded (Qd)	Supply volume (Qs 1)	Supply volume (Qs 2)

Let's construct a new supply curve s 2 . The equilibrium price will now be $140, and the equilibrium sales volume is 8,000 liters.

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

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

Problem 23

Formulation of the problem: The volume of demand for product 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 product A. Find the equilibrium price and equilibrium sales volume.

Technology for solving the problem: In equilibrium, the volume of demand and volume of supply are equal, therefore, it is necessary to equate their formulas: 9 - Р = -6 + 2Р, hence the equilibrium price is 5. To determine the equilibrium sales volume, it is necessary to substitute the equilibrium price in any formula: Qd = 9 - 5 = 4 or: Qs = -6 + 2*5 = 4.

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

Problem 24

Formulation of the problem: The demand function for the good Qd = 15 - P, the supply function Qs = -9 + 3P. Determine the equilibrium in the market for this good. What happens to the equilibrium if the quantity demanded decreases by 1 unit at any price level?

Technology for solving the problem: Under equilibrium conditions, the volume of demand and volume of supply are equal, therefore, it is necessary to equate their formulas: 15 - Р = -9 + 3Р, hence, the equilibrium price is 6. To determine the equilibrium sales volume, it is necessary to substitute the equilibrium price in any formula: Qd = 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) - P \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 - P \u003d -9 + 3P, P \u003d 5.75, the sales volume is 8.25.

Answer: equilibrium price 5.75, equilibrium sales volume 8.25.

Problem 25

Formulation of the problem: 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 the equilibrium if the quantity supplied increases by 2 units at any price level?

Technology for solving the problem: Under equilibrium conditions, the volume of demand and volume of supply are equal, therefore, it is necessary to equate their formulas: 16 - 4Р = -2 + 2Р, hence, the equilibrium price is equal to 3. To determine the equilibrium sales volume, it is necessary to substitute the equilibrium price in any formula: Qd = 16 - 4 * 3 \u003d 4 or: Qs \u003d -2 + 3 * 2 \u003d 4. If the supply increases by 2 units, then the supply 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 = -2 + 2P, P = 2.33, the sales volume is 6.68.

Answer: equilibrium price 2.33, equilibrium sales volume 6.68.

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Theory

Labor market- a set of economic and legal procedures that allow people to exchange their labor services for wages and other benefits.

Features of the labor market:

A. The labor market is not a market of primary demand (primary demand is in the markets for goods and services), but a derivative demand.

Derived demand - demand for factors of production generated by the need to use them for the production of goods and services.

B. Demand in the labor market is not for labor services in general, but for services of a certain type and complexity (for example, not for the services of drivers in general, but for the services of bus drivers with a certain level of qualification and experience).

C. Along with the national one, there are local labor markets (for example, the labor market of the Ivanovo region or the labor market of the Krasnodar Territory), where the ratio of demand for labor services of the same type and their supply can vary significantly.

D. The supply of labor services may vary due to the fact that people are able to change professions by acquiring a different skill.

Thus, the labor market connects people who want to sell their labor services and organizations that want to buy these services. The latter are usually referred to as "employers" or "employers".

Labor market

(labor services)

Buyers Sellers

Employers Employees

Demand Offer

2. Demand is the volume of labor services offered by employers at specific wage rates.D.

3. Supply - the volume of labor services offered by employees at specific wage rates -S.

4. Wage rate - the amount of money paid to an employee for a certain amount of time worked (a certain amount of work -W.

5. Demand scale - a table that shows the wage rate and the amount of demand.

Scale of demand for labor services.

6. The offer scale is a table that shows the wage rate and the amount of the offer.

Scale of supply for labor services.

7. The demand curve is a line showing the relationship between the wage rate and the quantity demanded.

8. The supply schedule is a line showing the relationship between the wage rate and the supply.

Demand and supply schedules for labor services.

9. The demand curve has a negative slope: the higher the wage rate, the lower the demand for labor services and vice versa.

10. The supply curve has a positive slope: the higher the wage rate, the greater the supply of labor services and vice versa.

11. The Law of Demand - The higher the wages that workers demand for their work, the fewer employers are willing to hire.

12. The Law of Supply - The higher the wages employers are willing to pay for a particular job, the more people are willing to do that job.

13. Equilibrium in the labor market This is a situation in the labor market that satisfies both the employer and the employee.

14. Equilibrium wage rate– We = 50 rubles/hour. This is the wage for which a certain number of employees are willing to work and for which the same number of employees are willing to hire employers.

15. Equilibrium number of workers– Qe = 300 people. The number of people who are willing to work for a certain wage and who are willing to be hired by employers for the same wage.

16. An excess of labor services in the labor market- this is a situation in which the number of employees who are ready to sell their labor services for a certain fee exceeds the number of workers to whom employers are ready to provide work, i.e. supply exceeds demand.

17. Deficit (shortage) of labor services in the labor market - this is a market situation in which the number of workers that employers are willing to hire for a certain fee exceeds the number of workers willing to sell their labor services for this fee, i.e., demand exceeds supply.

18. Factors affecting the change in supply and demand in the labor market.

1. Price factor: change the wage rate.

2. Non-price factors: demand for goods and services;

the level of prices for manufactured products;

prestige of work; - change

complexity, burden of work;

labor productivity;

the level of social security;

having free time.

Practical tasks:

Working with charts and scale of supply and demand.

1) Based on the scale of demand and the scale of supply, determine:

A. the number of workers required - demand (persons) and the number of workers offering their labor services at different wage rates.

Scale of supply and demand for labor services.

Wage rate

(rub/hour)

Number of required

workers, pers.

The number of workers offered

providing services, pers.

Offer, S

At a wage rate of 30 rubles per hour, the demand for labor services is 500 people, and the supply is 100 people.

At a wage rate of 60 rubles per hour, the demand for labor services is 200 people, and the supply is 400 people.

B. the wage rate if the demand for labor services is 100 people and the supply is 500 people.

With a demand of 100 people and a supply of 500 people, the wage rate will be 70 rubles per hour.

2) Based on the scale of supply and demand, draw a demand schedule and a supply schedule.

Demand schedule and supply schedule for labor services.

3) Using supply and demand charts, answer the questions:

What is the point of intersection of the graphs called?

The point of intersection of supply and demand graphs is called the equilibrium point - E.

What is the wage rate at equilibrium called?

At the equilibrium point, the wage rate is called the equilibrium wage rate.

What is the equilibrium wage rate?

The equilibrium wage rate is 50 rubles per hour.

What is the equilibrium number of workers willing to sell their labor services and the number of workers required at the equilibrium wage rate?

The equilibrium number is 300 people.

Can supply and demand change in the labor market?

Supply and demand can change under the influence of various factors:

1. The price factor - changes in the wage rate.

What happens if the wage rate increases to 60 rubles per hour?

The supply will rise to 400 people, and the supply curve will shift to the right.

Demand will decrease to 200 people, while the demand curve will shift to the left.

There will be a labor surplus of 200 people.

What happens if the wage rate decreases to 30 rubles per hour?

The supply will decrease to 100 people, while the supply curve will shift to the left.

Demand will increase to 500 people, while the demand curve will shift to the right.

What situation will arise in this regard in the labor market?

There will be a labor shortage of 400 people.

non-price factors.

How will the demand for labor services change if the demand for goods and services increases?

If the demand for goods and services increases, then the demand for labor services will also increase, while the demand curve will shift to the right and vice versa.

How will the demand for labor services change if the prices of manufactured products increase?

With an increase in the price of manufactured products, the demand for labor services will decrease, while the demand curve will shift to the left and vice versa.

How will the supply of labor services change if work becomes unprestigious?

If the job becomes unprestigious, then the supply of labor services will decrease, while the supply curve will shift to the left and vice versa.

How will the demand for labor services change if labor productivity increases?

With an increase in labor productivity, the demand for labor services will decrease, while the supply curve will shift to the left and vice versa.

Thus, a change in non-price factors leads to an increase or decrease in the volume of supply and demand and to a shift in the supply and demand curves, to the emergence of a shortage or excess of labor in the labor market.

Problem solving.

The supply of labor in some industry is described by the equation L s =20*W,

and the demand for labor is described by the equation L d \u003d 1200 - 10 * W, where W is the daily wage rate in rubles, and L is the number of workers requested by firms and offering the services of their labor in one day.

How many workers will be hired?

L s = 20*W B (.)E

L d \u003d 1200 - 10 * W L s \u003d L d \u003d L e

We = ? 20 * W e \u003d 1200 - 10 * W e

W s = W d = W e

Le \u003d 1200 - 10 * We

L e \u003d 1200 - 10 * 40 \u003d 800

Answer: 40 rubles / hour; 800 people.

Assignments for independent work.

Suppose the following data represent the magnitude of the supply and demand for labor in a particular industry.

Wage rate

(USD/hour)

Number of required

Number of workers

offering services,

1. Determine, using the given supply and demand scale, the equilibrium wage rate and the number of workers offering their labor services.

2. Suppose that as a result of signing a collective agreement, wages were $5 per hour.

(a) What will be the demand for labor services at the new wage level?

b) how many people will offer their labor services?

c) what is the situation on the labor market?

d) which workers will benefit and which will lose as a result of the new higher wages?

Based on the data presented in the supply and demand scale, build supply and demand graphs.

What factors and how can affect the change in supply and demand in this labor market?

Test tasks.

Choose the correct one from 4 answer options.

1. On the labor market they buy:

A) labor itself

B) labor services;

C) both answers are correct;

D) both answers are wrong.

2. The supply of labor services depends on:

A) from the level of salary;

B) from remoteness from work;

B) from labor productivity;

D) all of the above.

3. With an increase in wages, the demand for labor:

A) is growing

B) falls

B) can rise and fall;

D) does not change.

When hiring new employees, employers tend to pay more and more attention to:

B) education;

B) physical condition;

D) nationality.

A shift in the demand curve for labor can be caused by a variety of reasons, except:

A) demand for the firm's products

B) labor productivity;

C) labor prices;

D) capital prices (machinery and equipment).

6. The firm's demand for labor services is:

A) derived from the demand for products;

B) derived from the supply of products;

C) there is no correct answer;

D) both answers are correct.

7. The demand curve for labor services has:

A) positive slope

B) negative slope;

C) can have both positive and negative slope;

D) has no slope.

8. In Russia, in the transition to a market economy, the demand for accountants has increased. At the same time, there has been an increase in the number of certified public accountants offering their services. As a result:

A) the equilibrium wage rate of accountants and their equilibrium number have decreased;

B) the equilibrium wage rate of accountants and their equilibrium number have increased;

C) the equilibrium wage rate of accountants and their equilibrium number have increased.

D) the equilibrium number of accountants has increased, and nothing definite can be said about the equilibrium wage rate.

9. Ceteris paribus, a shift to the left of the demand curve for the labor of workers in an industry can be associated with:

A) an increase in the price of a substitute resource;

B) a decrease in demand for products manufactured using the labor of industry workers;

C) a decrease in the price of a complementary resource;

D) an increase in demand for products manufactured using the labor of industry workers.

10. If the level of social protection of workers increases, then:

A) the supply of labor services will decrease;

B) the supply of labor services will increase;

D) the supply of labor services will not change;

C) there is no correct answer.

Task.

In the labor market, the market demand for labor is described by the equation L d = 100 - 2*W, and the market supply of labor is described by the equation L s =40 +4*W, where W is the daily wage rate in rubles, and L is the number of workers requested firms and offering the services of their labor in one day.

Determine the equilibrium wage rate in this labor market.

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... on the mine fear and risk my economic and legal ... allowing rally of people around the interests of the organization, its goals. Combination of formal planning with others ... services 7) Expenses on the wages 8) Accruals on the salary fee ...

The task

Demand and supply of the firm in the market are described by the equations: Q d =200-5R; Q s =50+P. Determine the parameters of market equilibrium.

Decision

Market equilibrium is achieved when the volumes of demand Q d and supply Q s are equal:

Substituting the supply and demand functions into equality, we get:

200 - 5P = 50 + P
200 - 50 \u003d P + 5P
P = 25

In order to determine the equilibrium volume, it is necessary to substitute the equilibrium price into the demand or supply equation:

200 - 5 × 25 = 75 units

Thus, the equilibrium price is 25 den. units, and the equilibrium volume is 75 units.

Task 2. Calculation of market equilibrium parameters when introducing a tax on consumers

The task

The demand curve is described by the equation Q d \u003d 70-2P, and the supply curve - by the equation Q s \u003d 10 + P. The government introduced a consumer tax of $9 per item. Define:

the extent to which consumers and producers will suffer from the imposition of this tax.

Decision

Before the introduction of the tax, market equilibrium was achieved at the price Р 0 and the volume Q 0 (in the figure - at the point of intersection of the demand curves D and supply S). Calculate the equilibrium parameters:

70 - 2P \u003d 10 + P
3P=60
R=20 USD
Q 0 \u003d 30 units.

As a result of the introduction of the tax, the following changes will occur:

Consequences of the introduction of the tax

Since a tax is introduced on consumers, the price for them will increase and will be P d . The quantity of goods that consumers will purchase at a given price will be Q 1 (in the figure - the point of intersection of the demand curve D and price P d).
The net price that producers will receive will be P s . The quantity of goods that is produced at a given price P s will be Q 1 (in the figure - the point of intersection of the supply curve S and price P s).

Now, let's answer the questions posed in the problem point by point.

1. How will the equilibrium price and volume of production change? Market equilibrium is reached when the producer's sales equal the consumer's purchases:

The equilibrium sales volume Q 1 after the introduction of the tax corresponds to the price P d on the demand curve and the price P s on the supply curve. The difference between the purchase price P d and the sale price P s is the amount of tax t:

Since the demand, supply and tax curves are given, the market equilibrium parameters after the introduction of the tax can be found from the equations:

Q d \u003d 70 - 2P
Q s \u003d 10 + P
Q d = Q s
P d - P s = 9

Substituting the first two equations into the third one, we get:

70 - 2P = 10 + P

The introduction of a tax on consumers will lead to an increase in the selling price. It will be P d \u003d P s + 9. We substitute P d into the equation and get:

70 - 2(Ps + 9) = 10 + Ps
70 - 2 Ps - 18 = 10 + Ps
3 Ps = 42
P s = 14
P d = 23

Substituting the equilibrium price P s into the supply equation, we obtain the equilibrium volume Q 1:

Q 1 \u003d 10 + 14 \u003d 24

The same result can be obtained by substituting the purchase price P d into the demand equation:

Q 1 \u003d 70 - 2 × 23 \u003d 24

After the introduction of a tax on consumers in the amount of $ 9 per unit. the equilibrium volume in the market will be 24 units. at an equilibrium price (P s) of $14 per unit. Thus, the introduction of a tax on consumers will lead to a reduction in the equilibrium volume by 6 units. (30 - 24) and the equilibrium price for $6 (20 - 14).

2. What is the income of the state from the introduction of the tax? For each unit of goods sold, the government will receive $9. The total amount of taxes received by the government will be:

D g \u003d Q 1 × t \u003d 24 × 9 \u003d $ 216

Graphically, the total amount of government revenue is represented in the figure by the total area of rectangles A and D.

3. To what extent will consumers and producers suffer from the introduction of this tax? In order to determine how the tax burden is distributed between buyers and producers, it is necessary to determine the amount of their losses as a result of the introduction of the tax. The volume of purchases of consumers as a result of the introduction of the tax decreased from 30 units. to 24 units, and the purchase price increased from $20 to $23. The total loss to consumers (as a result of price increases and reduced volume of purchases) with the introduction of the tax is graphically represented by the total area of figures A and B. Under the tax, each unit of goods costs consumers $3 is more expensive than no tax, i.e. they spend extra:

Q 1 × 3 = 24 × 3 = $72

Thus, the part of tax revenue paid by consumers will be $72 (in the figure - the area of rectangle A). As a result of the introduction of the tax, the selling price was reduced from $20 to $14 per unit. , which means that for each unit of goods, the manufacturer will receive $ 6 less. Its losses as a result of price reduction will be:

Q 1 × 6 = 24 × 6 = $144

The part of tax revenues paid by producers is graphically represented in the figure by the area of rectangle D. The results of the calculation indicate that when a tax on consumers is introduced, producers pay 2 times more of the tax revenues than consumers themselves.

Task 3. Calculation of market equilibrium parameters when introducing a tax on producers

The task

Suppose that the demand curve is described by the equation Q d \u003d 400 - P, and the supply curve - by the equation Q s \u003d 100 + 2P. The government introduced a tax on producers in the amount of $15 per unit of output.

Define:

how will the equilibrium price and volume of production change;
what is the income of the state from the introduction of this tax;
the extent to which consumers will suffer from the imposition of this tax.

Decision

1. The problem is solved similarly to the previous one (see Problem 2), with the only difference being that not consumers are taxed, but producers. We determine the parameters of the market equilibrium before the introduction of the tax:

400 - P d \u003d 100 + 2 (P d - 15)
3Pd=330
P d = 110 den. units
P s \u003d 110-15 \u003d 95 den. units
Q 1 \u003d 400 - 110 \u003d 290 units.

The parameters of market equilibrium after the introduction of the tax are determined using the equations:

Q d \u003d 400 - P
Q s \u003d 100 + 2P
Q d = Q s
P d - P s = 15

By imposing a tax on producers, the net price they receive will decrease. The introduction of a tax on producers will not affect the purchase price P d , and the sale price will be equal to P s = P d - 15. Having made all the necessary substitutions, we obtain:

400 - P d \u003d 100 + 2 (P d - 15)
3 P d = 330
Pd = $110
Ps = 110 - 15 = $95
Q 1 \u003d 400 - 110 \u003d 290 units.

After the introduction of the tax on producers, the equilibrium quantity was 290 units, and the equilibrium price was $110. Thus, the equilibrium quantity decreased by 10 units, and the equilibrium price increased by $10.

2. For each unit of goods sold, the government will receive $15. The total amount of taxes received by the government will be:

D g \u003d Q 1 × t \u003d 290 × 15 \u003d $ 4350

3. Under the tax on producers, each unit of goods costs consumers $10 more (before the tax, the purchase price was $100, with the tax -$110). The portion of tax revenue paid by consumers will be:

Q 1 × 10 = 290 × 10 = $2900

Before the introduction of the tax, the selling price was $100, and after the introduction of the tax, it was $95, i.e. under the tax, manufacturers receive $5 less for each unit sold. The portion of tax revenue paid by producers will be:

Q 1 × 5 = 290 × 5 = $1450

Thus, when introducing a tax on producers, buyers pay 2 times more of the tax revenue than producers.

Task #4

According to Table 1. characterizing various situations in the market of canned green peas, it is necessary:

a) Draw a supply and demand curve

b) If the market price for a can of peas is 1 gr. 60 kopecks, what is typical for this market - a surplus or a deficit? What is their volume?

c) If the market price for a can of peas is 3 gr. 20 kop. What is typical for this market - a surplus or a shortage? What is their volume?

d) What is the equilibrium price in this market?

e) Rising consumer spending increased the consumption of canned peas by 30 million cans at each price level. What will be the equilibrium price and equilibrium output?

Table 1.

Task 5.

According to table 2. characterizing various situations in the electric drill market, it is necessary:

a) Draw supply and demand curves

b) What is the equilibrium price in the market for electric drills?

c) What is the equilibrium volume of purchase and sale of electric drills?

d) If the price of an electric drill is 30 UAH. , what is the magnitude of the deficit in this market?

e) If the price of an electric drill rises to UAH 60, what is the excess in this market?

Volume (thousand / pieces)

Task 6.

The demand function is expressed by the equation y \u003d 5 - 1 / 2p

a) Determine the quantity of goods that buyers can purchase at prices p = 1; p = 2; p = 3;

b) Set the value of the saturation volume and prohibitive price;

c) Plot the demand function in a coordinate system R:Q.

Task 7.

For product Q on the market, the following values of the function are set:

Suggestion function: p = l+3/2Q

Demand function: p = 5-l/2Q

a) What quantity of goods will the seller offer at the price p = 3; p = 6; p = 9

b) What quantity of goods will the seller offer at the price p = 1

c) Present both functions graphically and determine the equilibrium price and equilibrium quantity

2) Why prices p = 4.5 and p = 3 are not equilibrium

Solving problems on supply and demand.

Task 4. - solution:

A) (See fig. 3)

quantity (million/cans)

b) a deficit equal to 30 million cans per year d) The equilibrium price is 2 UAH. 40 kop.

c) an excess of 130 million cans per year e) The equilibrium price will be 3 UAH. 20 kop.

equilibrium volume 60 million cans

Task 5

a) see fig. 4.

b) 50 d) Shortage equal to 14 thousand pieces

c) 16 e) Excess equal to 7 thousand pieces

Task 6.

a) If we substitute the price values into the demand function, then the values of the quantity of goods will be as follows: Q = 8 with P = 1; Q = 6 at P = 2; Q = 4 at P = 3;

b) Saturation volume Q, will be carried out at Р = 0; Q = 10. The prohibitive price is the price at which the quantity in demand is zero;

Task 7.

a) If these prices are substituted into the supply function, then we get the following quantities of goods offered in each individual case:

Q = 11/3 at P = 3

Q = 31/3 at P = 6

Q = 51/3 at P = 9

b) at P = 1 sellers do not offer anything at all. The reason is that their costs were higher than the price

X = 2 demand

The point of intersection will be at the intersection of both curves. If we compare the function of supply and demand, we get: l + 3 / 2Q \u003d 5-l / 2Q Q \u003d 2; P \u003d 4.

d) None of these prices can indicate the equilibrium price, because the quantity of goods offered and in demand in this case is different. At a price of P = 4.5, the proposed quantity of goods will be Q = 7 / 3, and the quantity in demand - Q = 1, i.e., there is an excess supply. The opposite is the situation at P - 3. The proposed quantity will be Q = 1 / 3, and the demanded Q - 4, i.e., there is an excess of demand. Both quantities cannot exist for a long time if prices are set freely.

Task number 8. Calculation of the buyer's price and the seller's price, the amount of tax, surpluses, net losses

Supply and demand

The demand function of the population for this product has the form:

Suggestion function:

Assume that this product is subject to a tax paid by the seller in the amount of 1 den. units

Define:

a) the price for the buyer and the price for the seller, including tax;

b) the total amount of tax paid to the budget;

c) buyer's surplus and seller's surplus before and after the introduction of the tax;

d) net loss to society.

a) Find the equilibrium price and volume before the introduction of the tax.

After the introduction of the tax, the supply curve will shift up by the amount of the tax. Find the equilibrium price and volume after the introduction of the tax:

This is the buyer's price.

In order to determine the seller's price, we substitute the equilibrium volume after the introduction of the tax into the original supply function.

- seller's price.

Point A will have coordinates (3,4).

b) Determine the total amount of tax paid to the budget. It will be numerically equal to the area of the rectangle (5, E2, A, 4):

c) To find the buyer's surplus and the seller's surplus before and after the introduction of the tax, we use the graph:

Let's find the intersection point of the graph of the demand function with the y-axis:

The buyer's surplus before the tax is numerically equal to the area of the triangle (4.33; E1; 8):

The buyer's surplus after the introduction of the tax is numerically equal to the area of the triangle (8; 5; E2):

Let's find the intersection points of the graphs of supply functions with the y-axis:

The seller's surplus before the introduction of the tax is numerically equal to the area of the triangle (4.33; E1; 2.5):

The seller's surplus after the introduction of the tax is numerically equal to the area of the triangle (5; E2; 3.5):

d) The net losses of society are numerically equal to the area of the triangle (A, E1, E2):

Task number 9. Determining the change in income with an increase in sales of products by one unit

The firm has a demand curve:

Knowing that P=100, determine the change in income with an increase in sold products by one unit.

The increase in income with an increase in sales by one unit is called marginal revenue (MR - marginal revenue).

Marginal revenue can be represented as the partial derivative of total revenue with respect to the quantity of the good.

In addition, price and volume are interconnected by a functional relationship: Р = f(Q).

It is easy to see that the second term in brackets is the inverse of the demand elasticity:

Determine the price elasticity of demand:

Thus, an increase in the number of products sold by one unit will reduce the firm's income by 200 units.

Task number 10. Revenue calculation

The demand curve for the monopolist's products is described by the equation

The monopolist has set a price for the product at which the elasticity of demand for it is (-2). Determine the profit of the monopolist.

Let us write the equation of the demand curve in the usual form: we express the quantity of demand Q in terms of the price P.

The elasticity of demand in the case of a continuous function is calculated by the formula:

And equal by condition

Task number 11. Price elasticity of demand

The function is given by the equation

a) Derive the formula for the elasticity of this demand.

b) At what price will the price elasticity of demand be -0.5?

c) At what price in the price range from 200 to 300 will elasticity be maximum in absolute value?

a) Since we are given a continuous function in the condition of the problem, we will use the point elasticity coefficient to derive the formula for the elasticity of this demand.

At the point (P 0 ,Q 0), the point elasticity is calculated as

is the derivative of the demand function at this point.

c) The larger P, the greater the elasticity in absolute value. Therefore, in the price range from 200 to 300, it reaches a maximum at the point Р=300.

Task 1

Formulation of the problem:

Draw a demand curve for this good and show how it changes if buyers prefer to buy 20 kg more at each price level?

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

Task 2

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

Price (P) (thousand rubles)	Volume of demand (Qd) (pcs.)

Draw a demand curve for this product.

Task 3

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

Task 4

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

Technology for solving the problem: BUT

Task 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 of good Y increases (goods X and Y are substitutes).

Task 6

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

Task 7

Formulation of the problem: VCR prices have dropped. Show on graphs 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.

Let's look at this on a chart:

The demand curve for video cassettes shifts to the right as the non-price factor changes, and at the same price P 1 the quantity demanded will increase from Q 1 to Q 2 .

Task 8

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

Task 9

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

Technology for solving the problem:

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

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

Task 10

Formulation of the problem:

Draw a supply curve for this product.

Task 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 happens to the supply curve for a given good if producers increase the supply of good 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.

Task 12

Formulation of the problem: The product supply function Y is given by the formula Qs = -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 of the supply volume at a certain price (for example, P=5, Qs=0; P=10, Qs=100, etc.). By connecting the dots, we get the supply curve.

Task 13

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

Task 14

Formulation of the problem: The price of good A has risen. Show on the graph what will happen to the supply of this product.

Task 15

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

Task 16

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

Problem 17

Formulation of the problem: Draw an arbitrary supply curve for product A. Show the change in supply if new sellers entered the market.

Microeconomics

Suppose that supply and demand in the market for product A are represented by the equations: Qd= 50 - P; Q s = P - 10, where Q d - the volume of demand for product A, units; Q s - the volume of supply of goods A, units; P - the price of goods A, rub.

Determine the equilibrium price and equilibrium quantity of the good in the market.

We write the equilibrium condition:

Qd = Qs

50 - P = P - 10

P - P = -10 - 50

2P = -60

P==30

Knowing that Qd = Qs, we substitute the value of P into any function to calculate the equilibrium volume of goods

Qs = P - 10 = 30 - 10 = 20

So, Re = 30, Qe = 20

At a price below the equilibrium price by 10 r. those. P \u003d 30-10 \u003d 20 rubles.

Qd = 50-20=30, Qs = 20-10=10, i.e. Qd > Qs.

There is a shortage of goods on the market (equal to 20 units), since the volume of demand is greater than the volume of supply.

2. The functions of supply and demand in the market of educational services are represented by the equations: Qd = 1000 – 35P; Qs = 5P + 600, where

Qd, Qs - volumes, respectivelysupply and demand (in hours); P – market price per hour (conventional unit).

The state has introduced a fixed price for the product in the amount of 3 conventional units. for 1 hour. Determine the consequences of this step for consumers and producers.

Decision

1000-35p=5p+600

40p=400

p=10 - equilibrium price

Q=1000-35*10=650 - equilibrium volume

Q=1000-35*3=895 - volume of demand

Q= 5*3+600=615 - supply volume

895-615=280 - product shortage

3. Two consumers (A and B) have different individual demand functions: A: Qd = 5 - P; B: Qd \u003d 10 - 2P.

Determine the market demand if A and B are the only consumers.

Decision

Two consumers have different individual demand functions: QD1 = 5 - P and QD2 = 10 - 2*P. Determine the market demand if these two consumers are the only ones in the market.

Answer: Q= 15-3r market demand

4. Demand and supply are presented as: Qd= 6 – P; Qs = -12 + 2P. Determine the balance parameters and explain the situation.

Decision

Qd = Qs

6 - P = -12 + 2P.

3P=-12-6

3P=-18

3P=18

5. The product supply function has the form: Qs=-4+0.5Р. The state provided subsidies to the manufacturer in the amount of 4 den. units per unit products.

1) What will be the volume of supply at a price of 8 den. units?

2) What was the volume of supply before the introduction of the subsidy?

Decision

Let's define the equilibrium price Qd = Qs 8 – P = - 4 + 2P 12 = 3P P = 4 monetary units. – equilibrium price 2. determine the equilibrium volume of sales for given parameters, before subsidies Qd = 8 – 4 QD = 4 units QS = - 4 + 2 * 4 QS =4 units3. we determine the price with a subsidy from the budget 4 + 2 = 6 units. 4. Determine the surplus of goods on the market Qd = 8 - 6 QD = 2 units QS = 4 + 2 * 6 QS = 8 units. Surplus \u003d 8 - 2 \u003d 6 units.

Answer: the equilibrium volume of sales before the subsidy will be 4 units, after the introduction of the subsidy, a surplus of 6 units is formed on the market.

Topic: Elasticity of supply and demand

1. The original price of the book was 120 rubles, the sales volume was 100 copies per day. With an increase in price to 160 rubles. 90 copies were sold. in a day. Calculate the price elasticity of demand for the book.

Decision

The price of the goods increased from 4.5 to 6 den.un. The volume of demand for the goods was reduced from 3000 to 300 pieces. What is the direct elasticity coefficient?

To solve the problem, the central point formula is used

Ed x =(Pav./Qav.)x(∆Q /∆P)

(120+160)/2 x 90-100 = -0.4

(100+90) /2 160-120

Answer: -0.4

Topic: Theory of production and costs

1. A sportswear company rents a room for 100,000 rubles. per year, utility bills - 50 thousand rubles. per year, the salary of 5 employees is 600 thousand rubles. per year, raw materials and materials cost the company 450 thousand rubles. per year, entrepreneurial income is assumed to be at least 300 thousand rubles. in year. The market price of the costume is 4 thousand rubles. The estimated output of one employee is at least 80 suits per year. What is the firm's accounting profit? What economic profit will the firm earn?

Equilibrium price and equilibrium quantity. A set of economic and legal procedures that allow people to exchange their labor services for wages and other benefits - document Tasks for graphical definition of market equilibrium

Tasks for building supply and demand curves goods

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Tasks for graphical determination of market equilibrium

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

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