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

Task 1.1. In a conditional economic system, two types of products are produced: X and U. For the production of 1 unit. products X 50 units required. resource, products U - 25 units. The total amount of a completely fungible resource that the economic system has is 400 units.

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

Solution.

First of all, we note that the opportunity cost of manufacturing any unit of output, 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 U. As a result, we get 8 units. products X and 16 units. products U. Next, using the definition of opportunity costs (the amount of another type of product that must be sacrificed to increase the volume of production of this product per unit), we calculate the required opportunity costs associated with the manufacture of the last unit of production X: 16/8 = 2 units products U.

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

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

Solution.

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

This means that traveling 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 varies. These fields grow wheat and potatoes. On 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 possibilities curve.

Solution.

To construct a farmer's production possibilities curve, it is necessary to calculate the opportunity costs associated with growing wheat and potatoes. It is advisable to present the calculations in tabular form, which for the example under consideration will have the following form.

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

Task 1.4. Let's assume that two people work in a small trouser-tailoring workshop: the master and his assistant.

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

Type of work	Time spent per unit goods, h
Type of work		assistant
Cutting fabric
Tailoring of trousers

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

What should be the division of the pile between foreman and assistant in order to minimize the amount of output in the workshop?

Solution.

Workers should specialize in accordance with the principle comparative advantage determined by the minimum of opportunity costs

to carry out the work in question.

The calculation results for this example are shown below.

The assistant should be engaged in cutting (12 trousers per month). During 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 grow by 7% (30 trousers instead of 28).

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

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

Determine the price level fixed by the government.

Solution.

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

Under the conditions of a fixed price (P,), the expenses 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/Р, we write the equation 72,000/Р, = -100 + 2Р, solving which, we find: Р, = 90 den. units

Problem 1.6. The demand function for some product has the form (U)= 400 - JUR. The supply function of this product is linear, and the equilibrium sales volume is 100 units. products. It is also known that under the conditions under consideration, the payoff of consumers is 2 times higher than the payoff of producers.

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

Solution.

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

Consumer surplus corresponds to the area of the triangle P e R 2 E and can be defined as follows: 0.5 (P 2 - R E) 100. In turn, the equilibrium price R E can be found from the equation 400 - 10P f = 100, as a result P E = 30 den. sd. R 2 can be calculated similarly: 400 - 10P 2 = 0, from where R 2= 40 den. units

The consumer surplus will therefore be 500 den. units From the formula for calculating the surplus of producers, equal to 250 den. units, we find: 1 = 25 den. units : : 0.5 (P E -P t) ? 100 = 250.

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

Since the result of price fixing R at the level of 28 den. units there will be a shortage, we determine it by the formula:

Problem 1.7. The supply and demand functions for some commodity have the form Qn = 1000 - 5R and (Y = -100 + 2.5 R.

As a result of fixing the price of the goods, a shortage 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.

Solution.

Let's use the graphical illustration of the solution presented below, which greatly facilitates the understanding of its process.

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

Problem 1.8. The supply and demand functions for a particular product have the form: Q° = 8 - R and 0 s = -4 + 2R.

Determine how the equilibrium sales volume will change if a tax of 30% of the price is introduced on the product, which is paid (introduced to the budget) by the manufacturer.

Solution.

The equilibrium volume of sales of goods before the introduction of a tax on it is determined from equation 8 - R= -4 + 2P, whence P equals = 4, Qp aBll = 4.

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

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

Problem 1.9. The yield for some product is characterized by the equation Q D = 120 - P, and the offer of the same product - by the equation Qs\u003d -30 + 2P.

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

Solution.

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

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

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

The government has set this product single tax, 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.

Solution.

The algorithm for solving this problem can be as follows:

1) determine 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 a 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:

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

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

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

Solution.

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

1) determine the equilibrium parameters in terms of taxation of goods:

2) calculate the amount of tax:

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

4) determine the equilibrium parameters after the abolition of the tax:

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

Problem 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 in this case was 10 units. goods. With the abolition of the tax, the price of goods decreased by 1/3. What will be the volume of sales of this product after the abolition of the tax on it?

Solution.

Consider a graphical illustration of this problem.

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

Problem 1.13. Marginal utilities for goods L, V and FROM equal to 10, 20 and 18 units, respectively. The prices of goods are also known L and S: R A= 5 den. units, R s= 9 den. units

At what price level AT the consumer will be in equilibrium?

Solution.

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

whence it follows that R in = 10 den. units

Problem 1.14. The utility function of the consumer has the form: U(A, B, C) = 6a ++ 8b+ 4s. Goods prices are known BUT and B: R l= 3 den. units, P in = 4 den. units

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

Solution.

Marginal utility is equal to the partial derivative of the utility of this product, therefore, Mf / 4 = b, MU-B= 8 and MU C = 4.

Then, according to the equilibrium condition of the consumer

Problem 1.15. Determine consumer choice if known: utility function U= 2xy, where X, Y- volumes of goods; commodity prices P x = 8 days units, P Y = 5 days units; disposable income M = 96 den. units

Solution.

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

1) define the marginal utilities of goods:

2) we formalize the budget constraint equation:

3) we will 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.

Problem 1.16. Demand for some conditional product is characterized by the function Q" = 60 - 3 R.

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

Determine what will be observed in the considered economic system.

Solution.

Let's determine the coordinates of the equilibrium point:

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

For our initial data, we get 5 / 3 = ^ 10 /zo> 0TK UD a b = 5.

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

So the offer function is Q s = -20 + 5R.

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

Shortage = [(60 - 30 8) - (-20 + 5 8)] = 16 units

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

Limit what will be observed in the considered economic system.

Solution.

For a linear demand function (Q D = a- 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 = -7 ^ 7 is satisfied, we can conclude that the individual

fsrentnost the market for this product.

Problem 1.18. The market for a certain good, operating under conditions of taxation of its producers, is characterized by a demand function with unit price elasticity and a supply function 0s = -20 + 2R. The equilibrium sales volume is 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 volume of sales of this product after the abolition of the tax on it? Solution.

We will illustrate the solution of this problem with the help of a graphical model.

1. Let's determine the equilibrium price of the goods in terms of the tax:
10 \u003d -20 + 2 P, from where R E - 15.
2. Let us determine the equilibrium quantity of goods under the conditions of the abolished tax: Q e = 15 10/R E.
3. We solve the equation -gg- \u003d -5 + 2P, from where we find P E = 10 and Q E = 15.

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

The proceeds of producers (sellers) of this product amounted to 45,000 den. units

Determine the coefficient of price elasticity of demand, which determined the specified amount of revenue for producers.

Solution.

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

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

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

Solution.

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 in the following way.

dQ D R p _ , 100 , „

" E °-Zha’- 0 - 5 - b Sh' a, kuyu b - 2

2. 400 = a- 2 100, therefore, a = 600.

In this case, the corresponding price is calculated by the formula Р = ^- = ^^ = 150, then Q= 600 - 2 150 = 300. 1b 11

4. PQ= 45 000 den. units

Problem 1.21. It is known that 100 units are sold in the market every week. goods by price P = 8 days units Assuming equilibrium in the market, a 1% decrease in price causes an increase in the volume of demand for a product by 0.8%.

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

Solution.

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

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

Problem 1.22. Determine the point elasticity of demand for a good at its price if it is known that a 5% decrease in price led to a 2% decrease in revenue. Solution.

We use R Q and P V Q V denoting prices and quantities before and after a change in the price of a commodity.

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

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

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 function demand.

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 quantity demanded for good A this market is determined by the formula Qd \u003d 9 - P, the supply volume - by the formula Qs \u003d -6 + 2P, where P is the price of goods 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 goods is 2 rubles, provided that the quantity of the goods put up for sale remains unchanged?

A) at P = 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.

According to the results economic analysis graph, provide 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 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 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 units per year, Qs is the volume of supply in million units 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 volume of sales and equilibrium price 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 market equilibrium, i.e., the equilibrium price and the equilibrium quantity of the good.

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 risen. 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 the price and the 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 adjoining 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 free trade, that is, buyers of each country can choose between domestic and foreign producers, and 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 a 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

From this it is clear that at 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 under market equilibrium conditions 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 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 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 manufacturer will increase the production of this product, and therefore, the volume of supply of the product on the market will increase. The supply curve does not change, because there is a change price factor, which will affect 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, 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 supply and demand curves and, on the graph, determine what will happen in the market if the price is set 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 items 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: In equilibrium, 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 = 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?

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: 16 - 4Р = -2 + 2Р, hence, the equilibrium price is 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.

print version

Solve Problem 1. Supply in the labor market in some industry is described by the equation LS=20*w, and industry demand for labor is described by the equation Ld =1200 - 10*w, where w is the daily rate wages(thousand rubles), and L is the number of workers asked by firms and offering the services of their labor in one day. A) Draw the demand and supply curves for labor on a graph.

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

Solve the problem Supply in the labor market in some industry is described by the equation LS=20*w, and industry demand for labor is described by the equation Ld =1200 - 10*w, where w is the daily wage rate (thousand rubles), and L is the number workers asked by firms and offering the services of their labor in one day. B) determine the equilibrium number of employees and the equilibrium wage rate in this labor market (using graphical and analytical methods)

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

Analytical solution Supply LS=20*w demand Ld =1200 - 10*w where w is the daily wage rate (thousand rubles) and L is the number of employees Solution: LS = Ld 20*w = 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 employees is 800 people.

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

Decision 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 = 800 L 1 L 2 L (number of people per day)

Solve problems number 2. Why canals and dams are built with great use in India labor resources, and in the Netherlands - with a large use of machines and mechanisms? Which construction method is more efficient? #3 Sylvester Stallone received $15 million plus a percentage of the box office for his role in Rocky 4. Why do you think Stallone makes so much money?

Homework Suppose the following data represent the magnitude of the supply and demand for labor in a particular industry. Wage rate (USD per hour) Number of workers required (persons) 1 5000 Number of workers offering their services (persons) 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 at a perfect competitive market labor. 2. Suppose that as a result of signing collective agreement union representatives and entrepreneurs, the salary was $5 per hour. A) What will be the demand for labor at the new level of wages? How many workers will offer services and ore at the new salary level? What will be the unemployment rate? B) Which workers will lose and which will benefit as a result of the new, higher salary level? 3. Display the results graphically.

Examples of solving problems on the topic

"Market and Market Equilibrium"

Task 1. What is the equilibrium price level and equilibrium volume sale 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 market situation develop if the price is administratively set equal to: a) CU 8, b) CU 12?

Solution . At the point of market equilibrium, the amount of demand is equal to the amount of supply, therefore 30-2P = 4P - 30, hence P = 10 DU,Q= 10 pcs.

At P=8Q D \u003d 30 - 2 8 \u003d 14 pieces, andQ S = 4 8 - 30 = 10 pcs. BecauseQ D > Q S , there will be a situation of excess demand (deficit) in the market in the amount of 14-10 = 4 pcs.

At P= 12Q D \u003d 30 - 2 12 \u003d 6 pieces, andQ S \u003d 4 12 - 30 \u003d 18 pcs. BecauseQ D < Q S , there will be a situation of excess supply (surplus of goods) in the market in the amount of 18-6 = 12 pcs.

Task 2.

Solution . At a price of 6 sous, the quantity demanded = 1100 liters and the quantity supplied = 800 liters. Consequently, there will be a shortage of milk in the market in the amount of = 1100-800=300 liters.

Task 3.

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

At the point of maximum market price, the quantity demanded is zero, so 50-2P=0, whence P Max = 25 MU.

The length of the leg along the abscissa axis is 32 pcs. The length of the leg along the ordinate axis is 25-9 = 16 DU.

The consumer's surplus is equal to the area of the triangle: 0.5 16 32 = 256 DU

Task 4. With Q d = 1200-5R and Q s = 500 + 5R. The state gives a subsidy to the producer in the amount of CU10. per unit of production. How will the equilibrium price and equilibrium quantity change after the subsidy is introduced? What will be the selling price of the product for the manufacturer?

Solution. After the introduction of a subsidy of 10 CU per unit of production, the offer 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 = 500 + 5(P +10), hence P 0 ’ \u003d 65 MU,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 = 500 + 5R, therefore R 0 =70 MU,Q 0 = 850 pcs.

As can be seen from the calculations, the equilibrium market price decreased by 5 MU, and the equilibrium volume increased by 25 pcs.

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

Task 5. With request and offer are given by functions: Q d = 100 – R and Q s = 2R - 50. The state introduces a 10% sales tax. What will be the consequences of this?

Solution. After the introduction of the tax, the offer will change, as 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= 2 P 0.9 - 50

We equate the demand, which has remained unchanged, to the new expression for the supply:

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

Before the introduction of the tax: 100-P = 2P - 50, therefore, P 0 =50 MU,Q 0 = 50 pcs.

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

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