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.

Decision:

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.

Decision:

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.

Decision:

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.

Thus, the new demand function 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.

Decision:

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.

Decision:

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.

Decision:

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.

Decision:

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.

Decision:

Let us determine the income elasticity of demand using the 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).

Decision:

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.

Decision:

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.

Decision:

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.

Decision:

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

this work Demand function: Qd=-4+3P, supply function: Qs=20-P. Demand for products increased by 20 (Control) in the subject (Macroeconomics and public administration), was custom-made by the specialists of our company and passed its successful defense. Work - Demand function: Qd=-4+3P, supply function: Qs=20-P. The demand for products increased by 20 in the subject of Macroeconomics and public administration reflects its theme and the logical component of its disclosure, the essence of the issue under study is revealed, the main provisions and leading ideas of this topic are highlighted.
Work - Demand function: Qd=-4+3P, supply function: Qs=20-P. The demand for products increased by 20, contains: tables, drawings, the latest literary sources, the year of delivery and defense of the work - 2017. In work Demand function: Qd=-4+3P, supply function: Qs=20-P. The demand for products increased by 20 (Macroeconomics and public administration), the relevance of the research topic is revealed, the degree of development of the problem is reflected, based on an in-depth assessment and analysis of scientific and methodological literature, in the work on the subject of Macroeconomics and public administration, the object of analysis and its issues are considered comprehensively, as from the theoretical and practical side, the purpose and specific tasks of the topic under consideration are formulated, there is a logic of presentation of the material and its sequence.

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:

1. Balance parameters this market(determination of equilibrium price and equilibrium volume);
2. Coefficients of direct elasticity of supply and demand at the equilibrium point;
3. Consumer and seller surplus, net social gain;
4. The government introduced a commodity subsidy from each sold unit of goods in the amount of N rubles;
5. The amount of the subsidy directed from the state budget;
6. The government introduced a commodity tax on each sold unit of goods in the amount of N rubles;
7. 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 .

1. Determine the equilibrium price and equilibrium sales volume.
2. 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.
3. Analyze the results. How will this affect the behavior of consumers and producers? Present the solution graphically and analytically.

Decision.
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).

GUIDELINES

Example 1 There are three demand functions and their corresponding supply functions:
a) QD \u003d 12 - P, Qs \u003d - 2 + P;
b) QD \u003d 12 - 2P, Qs \u003d - 3 + P;
c) QD \u003d 12 - 2P, Qs \u003d - 24 + 6P.
The state introduces a subsidy to producers in the amount of 3 den. units for every piece. In which case will consumers receive most of the subsidy? Why?
Decision:
Let us determine the equilibrium price and the volume of sales in each case. To do this, we equate the function of supply and demand:
a) 12 - P = -2 + P => P = 7, Q = 5;
b) 12 - 2P = -3 + P => P = 5, Q = 2;
c) 12 - 2P = -24 + 6P => P = 4.5, Q = 3.
If a subsidy to producers is introduced, sellers will be able to reduce the offer price by the amount of the subsidy. We express the offer price taking into account the subsidy:
a) Ps = Qs + 2 - 3 = Qs - 1;
b) Ps = QS + 3 -3 = Qs;
c) Ps = QS / 6 + 4 - 3 = Qs / 6 + 1.
Hence the new suggestion function:
a) Qs = 1 + P;
b) Qs = P;
c) Qs \u003d - 6 + 6P.
We find a new state of equilibrium:
a) 12 - P = 1 + P => P = 5.5; Q=6.5;
b) 12 - 2P = P => P = 4, Q = 4;
c) 12 - 2P = -6 + 6P => P = 2.25, Q = 7.5.
Answer: Thus, consumers will receive most of the subsidy in option c) of supply and demand functions: the price will decrease by 2.25 den. units, i.e. by 50% of the original value, while the sales volume will increase by 2.5 times.
Example 2 The equilibrium price of grain on the world market is P=$1.5 per pound. Q = 720 million pounds of grain is sold annually. Price elasticity demand for grain is equal to ЕP(D) = -0.8. Determine the linear function of demand for grain.
Decision:
It should be noted that the price elasticity of demand is the tangent of the slope of the demand curve to the x-axis. Considering the above, we will compose a linear equation for the dependence of demand on price. The linear dependency model looks like this:
QD = a + EP(D)×P,
where QD - demand, P - price, EP(D) - linear price elasticity of demand.
Knowing that P \u003d 1.5 dollars per pound, q \u003d 720 units. (million pounds), EP(D)= -0.8, we find the unknown parameter in this model:
720 = a - 0.8×1.5; a = 721.2.
Thus, the model of dependence of demand on price looks like this: QD = 721.2 - 0.8P.
Example 3 The cross elasticity between the demand for kvass and the price of lemonade is 0.75. What goods are we talking about? If the price of lemonade increases by 20%, how will the demand for kvass change?
Decision:
Kvass and lemonade are interchangeable goods, since the coefficient of cross elasticity of demand EA,B has a positive value (0.75).
Using the formula for the cross elasticity coefficient EA,B, we determine how the demand for kvass will change with an increase in the price of lemonade by 20%.
If we take the change in demand for kvass as x, and the change in the price of lemonade as y, then we can write the equation EA,B = x/y; whence x = EA, B × y or
x \u003d 0.75y \u003d 0.75 × 20% \u003d 15%.
Thus, with an increase in the price of lemonade by 20%, the demand for kvass will increase by 15%.
Example 4 Given the functions of supply and demand for goods:
QD \u003d 150 - 3P, QS \u003d - 70 + 2P.
The state introduced a tax on goods in the amount of 7.5 USD. from each unit sold. Determine the equilibrium price and equilibrium quantity before and after the introduction of the tax. What part of the tax will be paid by the manufacturer and the buyer?
Decision:
The initial market equilibrium will be in t. E (Pe, Qe), where QD=QS. 150 - 3P = -70 + 2P; 220 = 5p; Pe = 44 c.u.
Let's substitute the equilibrium price (Pе) into the supply or demand function and find the equilibrium sales volume Qe= -70 + 2×44 = 18 units.
After the introduction of the tax, the market equilibrium will move to point E1 (the intersection point of the old demand function Qd = 150 - 3P and new feature sentences QS1 = - 70 + 2(P - t) = -70 + 2P - 15 = -85 + 2P.
Thus, the new equilibrium is calculated as follows:
QD = QS1: 150 - 3P = -85 + 2P; 235 = 5p; Pe1 = 47 c.u.
The new equilibrium sales volume is Qe1 = 150 - 3×47 = 9 units.
The amount of tax paid by the buyer:
tD = Pe1 - Pe = 47 - 44 = 3 c.u.
The amount of tax paid by the seller:
tS \u003d Pe - (Pe1- t) \u003d 44 - (47 - 7.5) \u003d 4.5 c.u.
Since demand is more elastic than supply, in this case the tax burden will fall more on the shoulders of the seller than the buyer.

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).

Decision

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) = 40-8P 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?

Decision

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 draw 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?

Decision

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%.

Decision

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.

Define: Parameters market equilibrium, as well as the volume of the transaction of each trade participant at the equilibrium price.

Present a graphical and analytical solution.