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

Section II. BASES OF THE THEORY OF MICROECONOMICS

This section is an introductory part necessary for the study of microeconomics. This section provides general concepts that describe behavior in market economy, without which it is impossible to study an advanced course in microeconomics. The section begins with a study of the basic concepts of microeconomics - supply, demand, equilibrium. Further, the concept of elasticity is revealed, which will subsequently be used not only in the course of microeconomics, but also in macroeconomics and the world economy. The section ends with a study of the basics of the behavior of the subjects of a modern market economy.

Chapter 5. DEMAND: SUPPLY AND MARKET EQUILIBRIUM

From the previous chapters it is known that the connection between producers and consumers in the commodity economy is carried out indirectly, indirectly - through the market. A specific form of realization of commodity relations is market mechanism, the main elements of which are supply, demand, price.

The purpose of the analysis of this chapter is the mechanism of interaction between supply and demand, i.e. the supply-demand model, which performs an analytical and descriptive function, is the most useful and important tool in an economist's arsenal.

The supply and demand model on which prices are based has been at the core of economic theory. Despite the fact that under the conditions modern methods regulation of a market economy, equilibrium is achieved not only due to the interaction of market forces, but also with the active economic policy of the state, this model simply and convincingly leads to clear and unambiguous conclusions that can be used to analyze various economic problems. It describes in a simple form some of the forces acting in the economy and thereby displays important aspects real life.1

Demand. Demand functions. Law of demand

Needs in a market economy act in the form of demand. Market demand is an indirect reflection of people's need for a given product or service.

Human needs, as we know, are not limited. Can we talk about unlimited demand? What is the difference between these concepts? The fact is that demand is a form of expression of a need presented on the market and backed by money, i.e. demand is a solvent need. It is not enough to want to buy a product, it is necessary that the consumer has a certain amount of money to realize his desire. The market does not respond to insolvent needs. More precisely, the category of demand can be expressed by the term magnitude or volume of demand.

The value (volume) of demand is the quantity of a good that consumers are willing and able to purchase at a given price from a range of possible prices over a period of time.

It is important to distinguish between the concepts of “volume of demand” and “volume of actual purchase”. The volume (value) of demand is determined only by the buyer, and the volume of the actual purchase is determined by both the buyer and the seller. For example, price restrictions by the state can cause a significant increase in the magnitude of demand. At the same time, the volume of sales (“volume of actual purchase”) is likely to be low as a result of the manufacturer's disinterest in selling at set prices.

What determines the amount of demand? The desires and possibilities of a consumer to purchase a certain amount of goods are influenced by various factors. These include:

the price of goods P (price)

Consumer income I (income)

tastes, fashion T (tastes)

prices for related goods: interchangeable (substitutes) P S or complementary (complements) P ​​C

number of buyers N

expectation of future prices and income W

other factors X

So, in the very general view the demand function is written as follows:

Q d = f (P, I, T, P S , P C , N, X)

Attempts to investigate the nature of the change in the magnitude of demand Q d under the influence of all factors at once will not give a positive result. In this case, to identify the nature of the change in the magnitude of demand Q d , you must first fix the values ​​of all variables except one and study the relationship of Q d with this variable. A similar method means that we examine the dependence of the quantity demanded on each variable other equal conditions.

The quantity demanded for a product primarily depends on the price. If all factors except price are assumed to be constant for a given period, then demand function of price will look:

The inverse relationship between price and quantity demanded is called inverse demand function and looks like:

Ceteris paribus, a decrease in price leads to an increase in the quantity of goods purchased by buyers; an increase in price causes a backlash: the purchase of a product is reduced. Thus, the specified property of demand reflects the inverse relationship between the change in price and the quantity demanded. The inverse relationship between price and demand (other parameters remain unchanged) is universal and reflects the operation of one of the fundamental economic laws - law of demand.

Antoine Augustin Cournot(1801-1877) - creator of the mathematical theory of demand. A. Cournot was primarily a talented mathematician, but he was bored in the world of pure mathematics, and he tried with its help to take a fresh look at the problems of other sciences and find connections between them.

In 1838, Cournot published his most famous book today, An Inquiry into the Mathematical Principles of the Theory of Wealth. In fact, this was the first conscious and consistent attempt to apply a serious mathematical apparatus to the study of economic processes. From this sprout grew a whole branch of science - mathematical economics.

It was A. Cournot who first deeply analyzed the relationship between demand and price in various market situations. This gave him the opportunity to formulate the law of demand and bring economic science to a close understanding of the concept of "elasticity of demand" (A. Marshall picked up the ideas of A. Cournot and brought them to their logical conclusion). Cournot was able to mathematically rigorously prove that the highest sales revenue is most often provided by far from the highest price.

Why does demand behave the way it does? This happens for a number of reasons that argue the law of demand and take into account the following circumstances:

Common sense and life experience directly affect the volume of purchases depending on the price. The lower the price, the more purchases - this is a psychological moment.

Of course, at low prices, the volume of purchases increases, but sooner or later the consumer reaches the limit, when each subsequent unit of the product will bring less and less pleasure, no matter how much the price decreases. After a certain level of saturation of the need, the satisfaction received from a product or service begins to decrease. Economists call this effect the law of diminishing returns. marginal utility. Decreasing marginal utility explains why low prices stimulate demand. Goods sold at a high price are usually not bought for the future or "at random". But if the price is low and affordable, then, most likely, the buyer purchases this product even a little more than he needs.

The operation of the law of demand can be explained on the basis of two interrelated effects − income effect and substitution effect.

Clearly, at a lower price, the buyer can afford to buy more of a given good without forgoing other goods. He feels richer because the price decrease increases his real purchasing power, or real income with a constant amount of his money income. This is income effect.

income effect(as a result of a change in price) - a change in the quantity demanded for a product, due to the fact that a change in its price leads to a change in the real income of the consumer.

The extent of the income effect depends mainly on how much of the income is spent on the purchase of a given product. The more income is spent on a good, the more the effect of price increases on the consumer's real income will be, and the more consumption will be reduced.

On the other hand, the consumer is inclined to replace more expensive goods with cheaper analogues, which leads to an increase in the demand for these goods. This is substitution effect.

substitution effect- the desire of consumers to buy goods in more when its relative price goes down (substituting this good for others) and to consume less of it when its relative price goes up (replacing this good with others). It is this effect that determines the negative slope of the demand curve.

The magnitude of the substitution effect depends mainly on the quantity and availability of substitute goods.

The income effect combined with the substitution effect form the overall Effect price changes.

The functional relationship between the quantity demanded and the price can be expressed different ways:

1. Tabular- in the form of a table or scale of demand (table 5.1):

Table 5.1

The ratio of the price of good X to the quantity X demanded.

2. The rate of economic growth.

3. Simplified description of some aspects or properties of the economic system.

4. Competitiveness.

5. Need for something.

6. The desire of economic entities to maximize benefits under the existing restrictions.

7. Resources spent on production.

8. One of the possible options.

9. One of the properties of economic resources.

Topic: “Theory of supply and demand”

1. How will the position of your demand curve for CDs be affected by the following events (ceteris paribus):

a) increase in income;

b) you are tired of listening to music at home alone - it is better to go to concerts and discos with friends more often;

c) the price of tape cassettes has risen again;

d) prices for CD players have decreased;

e) the price of cassette recorders has increased;

f) your friends think (and you tend to think the same) that due to the oversupply of CDs on the market, their price will gradually decrease;

g) the cost of sound recording has increased.

2. The table presents data on the individual demand volumes of consumers A, B, C.

Define:

a) market demand

b) build graphs of individual and market demand

3. There are three consumers in the market for a certain good: A, B, C. The individual demand curves are shown in the graphs. Draw a market demand curve.

4. Market demand for notebooks is characterized by the following scale of demand: at a price of 10 rubles. the quantity demanded is 700 pieces, at a price of 20 rubles. the quantity demanded decreases to 600 pieces, and at a price of 30 rubles. reduced to 500 pcs. Determine the market demand function for notebooks.

5. The initial price is P1=10, and the quantity demanded is Q1=450. Due to the increase in price to P2=40, the quantity demanded has decreased to Q2=300.

Define:

a) demand function

b) the value of demand at Р= 20

6. The demand function of an individual consumer has the form:

QD1 = 5 - 0.5P

Determine the market demand function (the "Marshallian" form) if there are 5 firms in the market.

7. The individual demand functions are given:

QD1 = 100 - P1

QD3 = 20 - 2P3

Determine the aggregate demand function and represent it graphically.

8. The individual offer function looks like this:

Define a function market supply if the market has 8 identical firms. ("Marshallian" look)

9. What impact will each of the following items have on the demand for product B, on the equilibrium quantity and equilibrium price, given the quantity supplied?

a) product B becomes more fashionable;

b) the price of product C, a substitute for product B, goes down;

c) consumers expect prices to fall and incomes to rise;

d) there is a rapid increase in population.

10. For a given quantity of demand, how will each position affect supply, the equilibrium price and quantity of good B:

a) a decrease in the price of product A, the production of which uses the same technologies and resources that the production of product B requires;

b) the introduction of a tax on the sale of product B;

c) granting a subsidy to the producer of product B;

d) technological progress in the production of product B;

e) reduction in the number of firms producing the product;

f) an increase in the price of inputs to produce product B.

11. Patties replace buns in consumption, and butter complements. What happens in the respective markets if the price of buns goes down?

a) the price of cakes and butter will decrease;

b) the price of patties will rise and butter will fall;

c) the price of cakes will go down, but butter will go up;

d) the price of cakes and butter will rise

12. Demand and supply of players are described by the following equations:

Qd = 300 - 20P, Qs = 20 + 50P.

a) draw supply and demand curves and determine the equilibrium price and quantity;

b) due to a change in fashion, demand changes according to the equation:

Qd = 510 - 20P. What happens to the demand curve? Find a new balance.

13. There are 2 sellers and 2 consumers in the market.

The demand function of buyers, respectively, has the form:

QD1 = 10 - P, QD2 = 15 - 3P

The sellers' supply functions have the form:

QS1 = 2P - 6, QS2 = 4P

Determine the equilibrium price and the volume of the deal for each trader. Provide a graphical solution to the problem.

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16. The demand function has the form: Qd = 20 - 3P. The supply function has the form: Qs = -3 + 6P. Based on the given functions, determine the type of equilibrium. (Stable or unstable)

17. Consumer surplus is 15, producer surplus is 5, demand price (Pd)=10, supply price (Ps)=2

Determine the equilibrium values ​​of price and quantity (PE-? and QE-?)

1) how the equilibrium values ​​of price and volume have changed;

2) consumer and producer surpluses before and after the introduction of the tax;

3) state income from the introduction of the tax;

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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. Define linear function 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.

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.