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 labor market, 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 of them 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 an excess work force in the amount 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 data of the 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 for this market labor?
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. Other equal conditions a shift to the left of the demand curve for the labor of workers in the 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.
A 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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Topics: Demand, elasticity of demand, market equilibrium
Task 1. Determine equilibrium price and TV sales volume on regional TV. Plot the supply and demand curves using the supply and demand functions. Answer the questions:
1) What are the equilibrium price and the equilibrium volume of purchase and sale? Check the graphic solution with analytical calculations.
2) If the price of a good rises to P1, what is the excess of the good in that market?
3) If the price of the good is P2, then what is the amount of the deficit?
1) Equilibrium condition:
200 - 5P = 50 + P
Pp \u003d 25 monetary units.
2) Price Р 1 = 30 UAH
Qd 1 \u003d 200 - 5P 1 \u003d 200 - 5 × 30 \u003d 50 units
Qs 1 \u003d 50 + P 1 \u003d 50 + 30 \u003d 80 units;
The surplus is:
ΔQ \u003d Qs 1 - Qd 1 \u003d 80 - 50 \u003d 30 units;
3) Price Р 2 = 25 UAH
Qd 1 \u003d 200 - 5P 2 \u003d 200 - 5 × 25 \u003d 75 units
Qs 1 \u003d 50 + P 2 \u003d 50 + 25 \u003d 75 units;
the shortage of goods is:
ΔQ \u003d Qs 2 - Qd 2 \u003d 75 - 75 \u003d 0 units;
Task 2. The demand function for product X has the form: Q x =10-2P x +0.5P y . Determine the coefficients of direct and cross elasticity of demand for product X at P x = 3 UAH, P y = 10 UAH, to which group of goods (complements, substitutes or neutral) goods X and Y belong.
1. Find the direct elasticity of demand for product X:
2. Find the cross elasticity of demand for product X:
Conclusion: these are substitute goods.
Task 3.
The supply and demand functions are given in the table.
1) Determine the coefficient of price elasticity of demand at the point of equilibrium of supply and demand.
2) At what volume of sales will the seller's revenue be maximum? What will be the price of the goods?
3) Draw demand and revenue curves. What is the relationship between these curves?
1) Equilibrium condition:
200 - 5P = 50 + P
Pp \u003d 25 monetary units.
Qp = 200 - 5Pp = 200 - 5×25 = 75 units
2) Coefficient of price elasticity
At the point of equilibrium, demand is elastic.
3) Determine the point of unit elasticity
5P = 200 - 5P 10P = 200 P1 = 20 units
The seller's revenue will be maximum at the point of unit elasticity.
Qd 1 \u003d 200 - 5P 1 \u003d 200 - 5 × 20 \u003d 100 units.
TR = Qd 1 × P 1 = 20 × 100 = 2000 units.
4) Let's represent demand and revenue graphically in the figure.
Task 4. Demand and supply in the market are described by the equations given in the table. The state has established a per-product tax on the manufacturer in the amount of UAH T. per unit of production. Define:
1) elastic and inelastic segments of demand;
2) how the equilibrium price and volume of production will change (graphically and analytically) after the introduction of the tax;
3) what is the income of the state from the introduction of this tax;
4) tax amounts attributable to the share of the consumer and the producer;
5) excessive tax burden.
Solution
1. Equilibrium condition: Qd=Qs; 100-2R=-20+2R
equilibrium parameters before the introduction of the tax.
Price elasticity coefficient:
The elastic section is determined by the condition Ed>1
P>25. At P>25 - elastic area;
At R<25 – неэластичный участок.
2. Equilibrium parameters at T=2.
If a tax is introduced, then the S curve shifts to the left and up by 2 units. along the P axis. In this case, P + \u003d P - + T. New supply and demand equations:
100-2P + = -24 + 2P +;
P + \u003d 31 - the price of the new equilibrium (the price of the seller)
Q + \u003d 100 - 2 × 31 \u003d 38 units.
3. State income from the introduction of this tax
Tgos-va \u003d Q + × T \u003d 38 × 2 \u003d 76 monetary units.
4. The amount of tax attributable to the share of the consumer
Тconsumption \u003d Q + × (P + - Pp) \u003d 38 × (31 - 30) \u003d 38 units
5. The amount of tax attributable to the share of the manufacturer
Tpr \u003d Q + × (T - (P + - Pp)) \u003d 38 × (2 - (31 - 30)) \u003d 38 units
6. Excessive tax burden
Tizb \u003d 0.5 T × (Qp - Q +) \u003d 0.5 × 2 × (40 - 38) \u003d 2 units.
Task 5. Demand and supply in the market are described by the equations given in the table. The government introduces subsidies per unit of goods in the amount of UAH T. Determine graphically and analytically:
1) the equilibrium price and the equilibrium sales volume before and after the introduction of the subsidy;
2) the total amount of expenses for subsidizing the goods;
3) the consumer's gain and the producer's gain from the introduction of the subsidy.
Solution
1. Equilibrium condition:
200 - 0.5R \u003d -50 + 2R
equilibrium parameters before the introduction of the subsidy.
2. Equilibrium parameters at S=50.
If a subsidy is introduced, then the S curve shifts to the right and down by 50 units. along the P axis. In this case, P + \u003d P - -T. New supply and demand equations:
200 - 0.5P + \u003d 50 + 2P +;
P + = 60 - the price of the new equilibrium (seller's price)
Q + \u003d 200 - 0.5 × 60 \u003d 170 units.
3. Government spending on subsidies
Sgos-va \u003d Q + × S \u003d 170 × 50 \u003d 8500 den.
4. Subsidy amount attributable to the consumer
Spr \u003d Q + × (Рр - Р +) \u003d 170 × (100 - 60) \u003d 6800 units
5. Amount of subsidy attributable to the share of the producer
Spr \u003d Q + × (S - (Рр - Р +)) \u003d 170 × (50 - (100 - 60)) \u003d 1700 units
Task 6. The demand function for product X has the form Q dx \u003d 14 - P X + 0.1P Y; P X = 6; PY=10. Determine the cross elasticity of demand for good X at the price of good Y. What is the relationship between goods X and Y?
Solution
1) Cross elasticity formula
2) The volume of demand for product X
Q dx \u003d 14 - P X + 0.1P Y \u003d 14 - 6 + 0.1 × 10 \u003d 9.
3) Ed(xy) = = 0.1 × = 0.11
Because Ed(xy)≥0, then goods X and Y are goods substitutes or substitutes.
Task 7. Determine the income elasticity of demand if it is known that with an income of 4000 den. units per month, the volume of demand will be 20 units, and with an income of 5000 den. units - 18 units Which product group does this product belong to?
Solution
1) The income elasticity of demand is the ratio of the relative change in demand to the change in the income of the population.
E = 
= -0.105÷0.222 = -0.473
Because the elasticity index is less than zero, then the product is of poor quality.
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 from which it will be profitable to travel (during working hours) 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 |
|
|
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 of comparative advantage, determined by the minimum opportunity cost.
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 established a single tax on this product, maximizing 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 (QD = 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.
The equilibrium price is the price at which the quantity demanded in the market equals the quantity supplied. Expressed as Qd(P) = Qs(P) (see basic market parameters).
Service assignment. This online calculator is aimed at solving and checking the following tasks:
- Equilibrium parameters of the given market (determination of the equilibrium price and equilibrium volume);
- Coefficients of direct elasticity of supply and demand at the equilibrium point;
- Consumer and seller surplus, net social gain;
- The government introduced a commodity subsidy from each sold unit of goods in the amount of N rubles;
- The amount of the subsidy directed from the state budget;
- The government introduced a commodity tax on each sold unit of goods in the amount of N rubles;
- Describe the consequences of the government's decision to fix the price of N above (below) the equilibrium price.
Instruction. Enter the supply and demand equations. The resulting solution is saved in a Word file (see the example of finding the equilibrium price). A graphical solution of the problem is also presented. Qd - demand function, Qs - supply function
Example. Demand function for this product Qd=200–5P , supply function Qs=50+P .
- Determine the equilibrium price and equilibrium sales volume.
- Suppose that the city administration decided to set a fixed price at the level of: a) 20 den. units per piece, b) 30 den. units a piece.
- Analyze the results. How will this affect the behavior of consumers and producers? Present the solution graphically and analytically.
Solution.
Find the equilibrium parameters in the market.
Demand function: Qd = 200 -5P.
Offer function: Qs = 50 + P.
1. Equilibrium parameters of a given market.
At equilibrium Qd = Qs
200 -5P = 50 + P
6p=150
P equals = 25 rubles. - equilibrium price.
Q equals = 75 units. is the equilibrium volume.
W \u003d P Q \u003d 1875 rubles. - income of the seller.
Consumer surplus measures how much better an individual lives on average.
consumer surplus(or gain) is the difference between the maximum price he is willing to pay for the good and the price he actually pays. If we add up the surpluses of all consumers who purchase this product, then we get the size of the total surplus.
Producer Surplus(win) is the difference between the market price and the minimum price for which producers are willing to sell their product.
Seller's surplus (P s P 0 E): (P equals - Ps) Q equals / 2 = (25 - (-50)) 75 / 2 = 2812.5 rubles.
Buyer's surplus (P d P 0 E): (Pd - P equal) Q equal / 2 = (40 - 25) 75 / 2 = 562.5 rubles.
Net social gain: 2812.5 + 562.5 = 3375
The knowledge of surpluses is widely used in practice, for example, when distributing the tax burden or subsidizing industries and firms.
2) Suppose that the city administration decides to set a fixed price of 20 den. units a piece
P fix = 20 rubles.
Volume of demand: Qd = 200 -5 20 = 100.
Supply volume: Qs = 50 + 120 = 70.
After fixing the price, the volume of demand decreased by 25 units. (75 - 100), and the deficit of producers decreased by 5 pieces. (70 - 75). There is a shortage of goods in the market in the amount of 30 pcs. (70 - 100). 
Suppose the city administration decides to set a fixed price of 30 denier. units a piece.
P fix = 30 rubles.
Volume of demand: Qd = 200 -5 30 = 50.
Supply volume: Qs = 50 + 1 30 = 80.
After fixing the price, the volume of demand increased by 25 units. (75 - 50), and the producers' surplus increased by 5 units. (80 - 75). There is a surplus of goods in the market in the amount of 30 pieces. (80 - 50). 
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 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.
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 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 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 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 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 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 a product with 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, i.e. buyers of each country can choose between domestic and foreign producers, and sellers of each country can choose between domestic and overseas market sales.
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
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.
AT this case the ratio of the bases of the triangles is equal to the ratio of their altitudes.
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.