2-1p. The function of the population's demand for a given product: Qd=7-R. Suggestion function: Q s \u003d -5 + 2P,where Qd- volume of demand in million pieces per year; Qs- volume of supply in million pieces per year; R - price in thousands of rubles. Plot supply and demand graphs for a given product, plotting the quantity of the product on the x-axis (Q) and on the y-axis - the price of a unit of goods (R).
Solution
Since the given functions reflect a linear relationship, each of the graphs can be built using two points.
2-2p. Determine the market demand function based on individual demand data:
Q(1) = 40-8R at Р ≤ 5 and 0 at P > 5,
Q(2) = 70-7P at Р ≤ 7 and 0 at P>7,
Q(3) = 32-4P at Р ≤ 8 and 0 at P > 8.
a) Derive the demand curve equation analytically.
b) Which of the indicated groups of consumers do you think is richer? Is it possible to draw an unambiguous conclusion?
Solution
a) Q=Q(1)+Q(2)+Q(3) = 142-19P at 0 ≤ P ≤ 5,
Q \u003d Q (2) + Q (3) \u003d 102-11P at 5 < Р ≤ 7 ,
Q=Q(3)=32-4P at 7 < P ≤ 8 ,
Q=0 at P > 8.
b) The third group of consumers is willing to pay the highest prices. For example, when P=7.5 the first two groups will stop buying, and the buyers of the 3rd group will buy 2 units. (32-4x7.5=2). But it is impossible to make an unambiguous conclusion that the third group includes the richest buyers, since we do not know either their income or other direct and indirect signs of wealth.
2-3p. The demand for VCRs is described by the equation:
Qd=2400-100R, and the supply of video recorders - by the equation Qs=1000+250Р, where Q- number of VCRs bought or sold per year; R - the price of one video recorder (in thousand rubles).
a) Determine the equilibrium parameters in the VCR market.
b) How many VCRs would be sold at a price of 3,000 rubles?
c) How many VCRs would be sold at a price of 5000 rubles?
Solution
a) In order to determine the equilibrium parameters, we equate the volume of demand to the volume of supply:
Qd=Qs, or 2400-100P=1000+250P.
Solving the equation, we find the equilibrium price:
1400=350P; Pe \u003d 4000 rubles.
Substituting the found price into the equation describing demand, or into the equation describing supply, we find the equilibrium quantity Qe.
Qe = 2400-100 x 4 = 2000 PCS. in year.
b) To determine how many VCRs 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 = 2400 - 100 X 3 = 2100 PCS. in year;
Qs = 1000 + 250 X 3 = 1750 PCS. in year.
This shows that at a price below the equilibrium price, consumers will want to buy more VCRs than manufacturers are willing to sell. (Qd>Qs). In other words, consumers will want to buy 2100 units. video recorders, but they can buy exactly as much as the sellers sell them, that is, 1750 pieces. This is the correct answer.
c) We substitute the price of 5000 rubles in each of these equations:
Qd = 2400 - 100 X 5 = 1900 PCS. in year;
Qs = 1000 + 250 X 5 = 2250 PCS. in year.
At a price above the equilibrium price, producers will want to sell 2250 units. VCRs, but consumers will only buy 1,900 units. video recorders, therefore, only 1900 pcs. VCRs and will be sold at a price of 5,000 rubles.
Answer: a) equilibrium parameters: Pe=4000 rub., Qe=2000 PCS. in year.
b) when P=3000 rub. will be sold Q=1750 PCS. in year.
c) at P=5000 rub. will be sold Q=1900 PCS. in year.
2-4p. The gas demand function has the form: Qd g \u003d 3.75 R n -5 R g, and the function of its sentence: Qs g \u003d 14 + 2R g + 0.25R n,where R n, R g are the prices of oil and gas, respectively.
Define:
a) at what prices for these energy carriers the volumes of demand and supply of gas will be equal to 20 units;
b) by what percentage will the volume of gas sales change with an increase in the price of oil by 25%.
Solution
A) To determine at what prices for these energy carriers the volumes of demand and supply of gas will be equal to 20 units. solve the system of equations:
3.75R n -5R g \u003d 20
14 + 2R g + 0.25R n \u003d 20Þ P n =8; R g =2.
Since from the first equation R n \u003d (20 + 5R g) / 3.75, Let's substitute this expression into the second equation.
14+2P g +0.25(20/3.75)+0.25(5P g/3.75)=20,
2R g +0.25 (5R g / 3.75) \u003d 20-14-0.25 (20 / 3.75),
2R g +0.33R g \u003d 6-1.33,
2.33P g \u003d 4.67,
R g =2.
P n \u003d (20 + 5 X 2)/3,75=8.
b) If the price of oil rises to 10 den. units, then the equilibrium in the gas market will be subject to the following equality:
3,75 X 10 - 5R g \u003d 14 + 2R g + 0.25 X 10 Þ
37.5-5R g \u003d 14 + 2R g + 2.5Þ
-5R g - 2R g \u003d 14 + 2.5-37.5Þ
-7P g \u003d -21,
R g \u003d 3, Q g \u003d 37.5 - 5 X 3 = 22,5.
those. gas sales will increase by 12,5%.
Answer: a) if the volumes of demand and supply of gas are equal 20 units. oil and gas prices will be equal respectively P n =8; R g =2.
b) with an increase in the price of oil by 25% , the volume of gas sales will increase by 12,5%.
2-5p. There are three sellers and three buyers in the real estate market. The functions of the offer at the price of sellers are known:
Qs 1 =2P-6; Qs 2 =3P-15; Qs 3 \u003d 5P.
and the demand function at buyers' price:
Qd 1 =12-P; Qd 2 =16-4P; Qd 3 \u003d 10-0.5 R.
Determine: the parameters of market equilibrium, as well as the volume of the transaction of each trade participant at the equilibrium price.
Present a graphical and analytical solution.
The demand function for a product has the form: Qd = 15 – 2p
Offer function Qs = -2 + 3p
Define:
1. Equilibrium price and sales volume.
2. The government introduced a commodity tax on goods in the amount of 1 thousand rubles. per unit of production. The tax is paid by the sellers of the goods. Determine the new equilibrium quantity demanded and the price.
3. Calculate the amount of cash receipts to the state budget from paying taxes. Who will be more affected by the introduction of a flat tax - sellers or buyers. Why?
1. To determine the equilibrium price and the equilibrium sales volume, it is necessary to use the market equilibrium condition:
In our example:
15 - 2p = -2 + 3p,
Thus, the equilibrium price will be equal to 3.4 thousand rubles. per unit of goods. The equilibrium sales volume in our example can be determined by substituting the equilibrium price into the supply or demand function.
Equilibrium volume \u003d 15 - 2x3.4 \u003d 8.2 thousand units. in Week.
2. Since the seller pays the tax, the supply function will change. It will take the form:
Qs \u003d -2 + 3 (p - 1) \u003d -5 + 3p
To determine the new equilibrium price and sales volume, it is necessary to use the market equilibrium condition:
5 + 3p = 15 -2p
P \u003d 4 thousand rubles. per unit is the new equilibrium price.
Q \u003d 15 - (2 x 4) \u003d 7 thousand units. per week - the new equilibrium volume.
3. The total amount of tax that will go to the state budget will be equal to 7 thousand units. x 1ty.rub. = 7 million rubles
The price that buyers will pay is 4 thousand rubles. per unit
The price that the seller will receive will be equal to 4 - 1 = 3 thousand rubles. per unit
Out of 1 thousand rubles. tax - 0.6 thousand rubles. buyers will pay, and 0.4 thousand rubles. the seller will pay
Determine if the budget is in deficit state procurements are 60 million rubles, transfer payments are 10 million rubles, interest payments are 15% per annum on a public debt of 30 million rubles, tax revenues are 20% of GDP, equal to 360 million rubles.
360 x 0.2 - (60 + 10 + 30 x 0.15) \u003d 72 - 74.5 \u003d - 2.5 million rubles. - deficit of the state budget.
3. Which of the following benefits, in your opinion, should citizens receive through the market, and which should be provided by the state:
a) food; b) education; d) housing;
e) healthcare; e) television; g) wine and vodka products. Explain the answer.
4. Lotteries are an important source of government revenue. What are the arguments for and against this means of increasing revenues you could offer?
5. Suppose you have purchased a foreign-made car. You have to pay customs duty, the value of which depends on the engine size of the car. What are the main elements of the tax in this situation: the subject of the tax, the bearer of the tax, the object of the tax, the source, the unit of taxation, the tax rate.
6. What measures could you suggest to increase the state budget revenues?
Related information:
- III part. The installation of a third company (3 TS) consists of three modules, the latter having a redundant element that cannot be replaced
ANSWER: You must enter the number 1.
Task number 4.
The demand function is given by the equation Qd = 50 - 2Р,
and sentences Qs = 5 + 3P. Determine consumer surplus.
Quantity Q
Answer options:
Consumer surplus is the difference between the maximum price a consumer is willing to pay for a unit of a good and the actual price he actually paid. The area of a triangle bounded by the demand curve and the equilibrium market price equals the consumer surplus. Therefore, we need to find the sides AB and AC.
Qs \u003d Qd or 50 - 2P \u003d 5 + 3P, hence 5P \u003d 45 or P \u003d 9,
those. the equilibrium price (or point A) is 9.
Qd \u003d 50 - 2P \u003d 50 - 2 * 9 \u003d 50 - 18 \u003d 32, that is, AC \u003d 32
We find point B by equating Qd \u003d 0 or 50 - 2P \u003d 0, hence P \u003d 25 or point B \u003d 25
AB=25 - 9=16
Area of triangle ABC = ½ × 32 × 16 = 256 Answer : 256
ANSWER: option 2, i.e. 256
Task number 5
The figure shows the consumer's indifference curve and its budget line. Write the equation of the budget line if the price of product Y is P = 6 rubles
| |
Answer options:
1) Qy \u003d 10 - 1.5 Qx
2) Qy \u003d 15 - 0.67Qx
3) Qy \u003d 10 - 0.67 Qx
4) Qy \u003d 15 - 1.5 Qx
SOLUTION:
An indifference curve is a curve showing different combinations of 2 products that have the same utility for the consumer.
A budget line is a curve showing different combinations of quantities of two goods that a consumer can buy, given the budget allocated for the purchase of these goods and their prices. At the point where the budget line touches the indifference curve, the consumer's optimum is determined, but for this problem, the touch point does not matter.
If the consumer spends all his money only on good Y, then he can buy a maximum of 10 units; if he spends all his money on good X, he can buy a maximum of 15 units.
A consumer can buy 10 units of product Y by spending his entire budget, so his budget is 6 rubles × 10 units = 60 rubles.
Then the price of goods X=60 rubles/15 units=4 rubles. for 1 item X.
Now we can write the equation for the budget line.
6 rub. × Qy + 4 rub. × Qx = 60 or otherwise Qy \u003d 10 - 0.67Qx
Answer: option 3.
Task number 6
If the production function is defined by the equation Q=100+12 K²+10L, then the equation for the marginal product of capital is
Answer options:
2) MPK=100 +24K
SOLUTION:
The marginal product of capital is equal to the first derivative of the production function with respect to capital, i.e. we take the derivative of Q:
(Q)"=(100+12 K² +10L)"=100"+(12K²)"=10 L"=0+12×2K+0=24K
You can check this solution with the following reasoning:
Let K1 be the previous value of capital, and K2 be the subsequent value of capital after increasing it by one unit., ∆K = K2 - K1; ∆Q = Q2 - Q1.
Then ∆Q =100+12 (K2)²+10L – =
12 (K2)²- 12 (K1)²=12(K2 ─K1)× (K2+ K1);
MRK=∆Q / ∆K=12(K2 ─K1)× (K2+ K1) / (K2 - K1)=12 (K2+ K1)
Since with an infinitesimal increment K2 = K1, then MRC=24 K
Answer: option 4.
Task number 7
Using the data in the table, calculate the marginal cost of producing the first unit of output:
| Volume of production, units | |||
| Medium fixed costs, rub. | |||
| Medium variable costs, rub. |
Enter your answer:
SOLUTION:
General costs equal to the sum of constants and variables: TC=FC+VC
Marginal cost (MC)=TC2 - TC1 =VC2 - VC1 since FC1=FC2
Since it is about marginal cost first units, then the previous value of the volume of production is 0. At zero volume of production, fixed costs are 60, and variables are 0. For the first (one) unit, the average and total values \u200b\u200bare the same, therefore MC \u003d 100 - 0 \u003d 100
ANSWER: MS for the first unit = 100
Task number 8
The company manufactures and sells 100 valves per month. If production costs are 12,000 den. units, and the average profit is 50 den. units, then the gross income of the firm is equal to:
Enter your answer:
SOLUTION:
In economic theory, gross income (GD) is understood as income from the production and sale of products, i.e. the product of the quantity of goods sold and the unit price of the product. (it should be borne in mind that in the Soviet models of self-support, gross income was understood as part of the proceeds minus material costs). Gross income includes both cost of production and profit. We find the total profit by multiplying average profit on the number of products.
ECONOMIC THEORY
1. The demand for a product is represented by the equation P = 5 - 0.2Q d , and the supply P = 2 + 0.3Q s . Determine the equilibrium price and the equilibrium quantity of the good in the market. Find the elasticity of supply and demand at the equilibrium point.
Solution:
At the point of equilibrium Q d = Q s . Therefore, 5 - 0.2Q d = 2 + 0.3Q s .
Let's make calculations and determine the equilibrium price and the equilibrium quantity of goods on the market: Q E = 6; PE = 3.8.
By the condition of the problem, P = = 5 - 0.2Q d , hence Q d = 25 - 5P. The derivative of the demand function (Q d) / = -5.
At the equilibrium point P e = 3.8. Let's determine the elasticity of demand at the equilibrium point: E d (3.8) = -(3.8 / 6) · (-5) = 3.15.
Similarly, the elasticity of supply at the point is determined: Е s = - (P 1 / Q 1) · (dQ s p / dP), where dQ s p / dP is the derivative of the supply function at the point Р 1 .
By the condition of the problem, P = 2 + 0.3Q s , hence Q s = 10P/3 - 20/3. Derivative of the supply function (Q s) / = 10/3.
At the equilibrium point P e = 3.8. Calculate the elasticity of supply at the equilibrium point: E s (3.8) = -(3.8 / 6) · (10/3) = 2.1.
Thus, the equilibrium price is P e = 3.8; equilibrium quantity - Q e \u003d 6; elasticity of demand at the equilibrium point - E d (3.8) = 3.15; elasticity of supply at the point of equilibrium - E s (3.8) = 2.1.
2. The demand function for this product is given by the equation Q d \u003d - 2P + 44, and the supply function Q s \u003d - 20 + 2P. Determine the price elasticity of demand at the equilibrium point of the market for this product.
Solution:
At the point of equilibrium Q d = Q s . Let's equate the supply and demand functions: - 2P + 44 = -20 + 2P. Accordingly, P e = 16. Let's substitute the resulting equilibrium price into the demand equation: Q d = - 2 16 + 44 = 12.
Substitute (for verification) a certain equilibrium price in the supply equation: Q s = - 20 + 2 16 = 12.
Thus, in the market for this product, the equilibrium price (P e) will be 16 monetary units, and 12 units of the product (Q e) will be sold at this price.
The elasticity of demand at a point is determined by the formula of point price elasticity and is equal to: E d \u003d - (P 1 / Q 1) · (ΔQ d p / ΔP), where ΔQ d p / ΔP is the derivative of the demand function at point P 1.
Since Q d \u003d -2P + 44, then the derivative of the demand function (Q d) / \u003d -2.
At the equilibrium point P e = 3. Consequently, the price elasticity of demand at the equilibrium point of the market for this product will be: E d (16) = -(16 / 12) · (-2) = 2.66.
3. The demand for product X is given by the formula Q d \u003d 20 - 6P. An increase in the price of good Y caused a change in the demand for good X by 20% at each price. Define a new demand function for product X.
Solution:
According to the condition of the problem, the demand function: Q d 1 = 20 - 6P. An increase in the price of good Y causes a change in the demand for good X by 20% at each price. Accordingly, Q d 2 = Q d 1 + ΔQ; ΔQ \u003d 0.2Q d 1.
In this way, new feature demand for product X: Q d 2 = 20 - 6P + 0.2 (20 - 6P) = 24 - 4.8P.
4. Demand and supply for a product are described by the equations: Q d \u003d 92 - 2P, Q s \u003d -20 + 2P, where Q is the quantity of this product, P is its price. Calculate the equilibrium price and quantity of goods sold. Describe the consequences of setting a price of 25 monetary units.
Solution:
At the point of equilibrium Q d = Q s . Accordingly, 92 - 2P = -20 + 2P. Let's make calculations and determine the equilibrium price and equilibrium quantity: P e = 28; Q e = 36.
When the price is set at 25 monetary units, there is a shortage in the market.
Let's determine the size of the deficit. With P const = 25 monetary units, Q d = 92 - 2 25 = 42 units. Q s \u003d -20 + 2 25 \u003d 30 units.
Therefore, if the price is set at 25 monetary units, the deficit in the market for this product will be Q s - Q d = 30 - 42 = 12 units.
5. Given the supply and demand functions:
Q d (P) = 400 - 2P;
Q s (P) \u003d 50 + 3P.
The government introduced a fixed price for goods at the level of 50 thousand rubles. for a unit. Calculate the amount of deficit in the market.
Solution:
The equilibrium price is set under the condition Q d = Q s . According to the condition of the problem, P const = 50 thousand rubles.
Let us determine the volume of supply and demand at P = 50 thousand rubles. for a unit. Accordingly, Q d (50) = 400 - 2 50 = 300; Q s (50) = 50 + 2 50 = 150.
Thus, when the government sets a fixed price for goods at the level of 50 thousand rubles. per unit, the amount of deficit in the market will be: Q d - Q s = 300 - 150 = 250 units.
6. The demand for a product is represented by the equation P = 41 - 2Q d , and the supply P = 10 + 3Q s . Determine the equilibrium price (P e) and the equilibrium quantity (Q e) of the good on the market.
Solution:
Market equilibrium condition: Q d = Q s . Let's equate the supply and demand functions: 41 - 2 Q d = 10 + 3Q s . Let's produce necessary calculations and determine the equilibrium quantity of goods on the market: Q e = 6.2. Let's determine the equilibrium price of goods on the market by substituting the obtained equilibrium quantity of goods into the supply equation: P = 10 + 3Q s = 28.6.
Let us substitute (for verification) the resulting equilibrium quantity of goods into the demand equation P = 41 - 2 6.2 = 28.6.
Thus, in the market for this product, the equilibrium price (P e) will be 28.6 monetary units, and 6.2 units of the product (Q e) will be sold at this price.
7. The demand function has the form: Q d \u003d 700 - 35Р. Determine the elasticity of demand at a price of 10 monetary units.
Solution:
The elasticity of demand at the equilibrium point is determined by the formula of point price elasticity and is equal to: E d p \u003d - (P 1 /Q 1) · (ΔQ d p / ΔP), where ΔQ d p / ΔP is the derivative of the demand function.
Let's make calculations: ΔQ d p / ΔP = (Q d) / ? = 35. Determine the elasticity of demand at a price equal to 10 monetary units: E d p = 10/(700-35 10) 35 = 1.
Therefore, the demand for this product at a price equal to 10 monetary units is elastic, so 1< Е d p < ∞ .
8. Calculate the income elasticity of demand for a product if, with an increase in income from 4,500 rubles to 5,000 rubles per month, the volume of purchases of goods decreases from 50 to 35 units. Round your answer to the third decimal place.
Solution:
Determine the income elasticity of demand for following formula: E d I = (I/Q) × (ΔQ/ΔI) = (4500/50) × (15/500) = 2.7.
Consequently, this product for these buyers has the status of a normal or quality product: the income elasticity of demand for the product (E d I) has a positive sign.
9. The demand equation is: Q d = 900 - 50P. Determine the maximum demand (market capacity).
Solution:
The maximum market capacity can be defined as the volume of the market for a given product (Q d) with the value of the price for this product equal to zero (P = 0). The free term in the linear demand equation characterizes the value of the maximum demand (market capacity): Q d = 900.
10. Market demand function Q d = 10 - 4Р. The increase in household income has led to an increase in demand by 20% at each price. Define a new demand function.
Solution:
Based on the condition of the problem: Q d 1 = 10 - 4P; Q d 2 \u003d Q d 1 + ΔQ; ΔQ \u003d 0.2Q d 1.
Therefore, the new demand function Q d 2 = 10 - 4P + 0.2(10-4P) = 12 - 4.8P.
11 . The price of the goods changes as follows: P 1 = 3 dollars; P 2 = 2.6 dollars. The range of changes in the volume of purchases in this case is: Q 1 = 1600 units; Q 2 \u003d 2000 units.
Determine E d p (price elasticity of demand) at the equilibrium point.
Solution:
To calculate the price elasticity of demand, we use the formula: E d P = (P/Q) · (ΔQ/ΔP). Accordingly: (3/1600) (400/0.4) = 1.88.
The demand for this product is elastic, since E d p (price elasticity of demand) at the equilibrium point is greater than one.
12. Refusing to work as a carpenter with a salary of 12,000 den. units per year or work as a referent with a salary of 10,000 den. units per year, Pavel entered college with an annual tuition fee of 6,000 den. units
Determine the opportunity cost of his decision in the first year of study if Pavel has the opportunity to work in a store for 4,000 denier in his spare time. units in year.
Solution:
The opportunity cost of Paul's education is equal to the cost of a year's college tuition and the cost of missed opportunities. It should be borne in mind that if there are several alternative options, then the maximum cost is taken into account.
Therefore: 6,000 den. units + 12 000 den. units = 18,000 den. units in year.
Since Pavel receives additional income that he could not receive if he worked, then this income must be deducted from the opportunity cost of his decision.
Therefore: 18,000 den. units - 4 000 den. units = 14,000 den. units in year.
Thus, the opportunity cost of Paul's decision in the first year of study is 14,000 den. units