Theory of Consumer Behaviour

This page contains the NCERT Economics class 12 chapter 2 Theory of Consumer Behaviour from Book I Introductory Microeconomics. You can find the solutions for the chapter 2 of NCERT class 12 Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 12 Economics related topic Theory of Consumer Behaviour question and answers.

Buy Class 12 Economics Books NOW!

Exercises

1. What do you mean by the budget set of a consumer?

The budget set of a consumer is defined based on the consumer’s income, the prices of the goods they want to purchase, and the quantities of those goods. If a consumer has an income of

{M}

, and the prices of two goods (for example, bananas and mangoes) are

{p_1}

and

{p_2}

respectively, the consumer can choose to buy any combination of these goods as long as the total cost does not exceed their income.

Mathematically, this can be represented as

{p_1x_1 + p_2x_2 \leq M}

, where

{x_1}

and

{x_2}

are the quantities of bananas and mangoes, respectively. This inequality represents the consumer’s budget constraint.

The budget set, therefore, is the collection of all such bundles of goods that the consumer can afford to buy with their income at the prevailing market prices. It includes all the combinations of bananas and mangoes that satisfy the budget constraint.

In summary the budget set of a consumer includes all the possible combinations of goods that a consumer can afford to purchase given their income and the prices of the goods.

2. What is budget line?

A budget line represents all the possible combinations of two goods that a consumer can purchase given their income and the prices of the goods. It is derived from the budget constraint equation

{p_1x_1 + p_2x_2 = M}

, where

{p_1}

and

{p_2}

are the prices of the two goods,

{x_1}

and

{x_2}

are the quantities of those goods, and

{M}

is the consumer’s income.

The budget line can be expressed as

{x_2 = \dfrac{M}{p_2} - \dfrac{p_1}{p_2} \times x_1}

. This equation shows that the budget line is a straight line with a negative slope. It intersects the axes at

{\dfrac{M}{p_1}}

and

{\dfrac{M}{p_2}}

, representing the maximum quantities of the two goods that the consumer can buy if they spend all their income on one good.

In summary, the budget line is a graphical representation of all the combinations of two goods that a consumer can afford to purchase with their entire budget, given the prices of the goods. It is a straight line with a negative slope, intersecting the axes at points that represent the maximum quantities of the goods that can be purchased.

3. Explain why the budget line is downward sloping.

The budget line is downward sloping because it represents the trade-off between the two goods that a consumer can purchase given their income and the prices of the goods. When a consumer decides to purchase more of one good, they have to give up some amount of the other good to stay within their budget. This trade-off results in a negative relationship between the quantities of the two goods, making the budget line downward sloping.

The slope of the budget line is determined by the ratio of the prices of the two goods. Mathematically, the slope is given by

{-\dfrac{p_1}{p_2}}

, where

{p_1}

and

{p_2}

are the prices of the two goods. This means that for every additional unit of the first good that the consumer decides to purchase, they must give up

{\dfrac{p_1}{p_2}}

units of the second good to stay within their budget. This rate at which the consumer can substitute one good for another in the market is also known as the price ratio.

In summary, the budget line is downward sloping because it represents the trade-off between the quantities of two goods that a consumer can purchase given their budget constraints. The slope of the budget line is determined by the negative ratio of the prices of the two goods, reflecting the rate at which the consumer can substitute one good for another in the market.

4. A consumer wants to consume two goods. The prices of the two goods are ₹ 4 and ₹ 5 respectively. The consumer’s income is ₹ 20.

(i)

Write down the equation of the budget line.

(ii)

How much of good 1 can the consumer consume if she spends her entire income on that good?

(iii)

How much of good 2 can she consume if she spends her entire income on that good?

(iv)

What is the slope of the budget line?

(i) Write down the equation of the budget line.

The equation of the budget line can be represented as

{P_1X_1 + P_2X_2 = M}

, where

{P_1}

and

{P_2}

are the prices of the two goods,

{X_1}

and

{X_2}

are the quantities of the two goods, and

{M}

is the consumer’s income.

Given:

{P_1 = Rs\ 4}

{P_2 = Rs\ 5}

{M = Rs\ 20}

The equation of the budget line is:

{4X_1 + 5X_2 = 20}

(ii) How much of good 1 can the consumer consume if she spends her entire income on that good?

If the consumer spends her entire income on good 1, we have to find

{X_1}

and

{X_2 = 0}

Apply the values of

{X_1}

and

{X_2}

into the equation

{4X_1 + 5X_2 = 20}

, we have

{4X_1 + 5 × 0 = 20}

{⇒ 4X_1 = 20}

{⇒ X_1 = \dfrac{20}{4} = 5}

∴ She can consume 5 units of good 1.

(iii) How much of good 2 can she consume if she spends her entire income on that good?

If the consumer spends her entire income on good 2, we have to find

{X_2}

and

{X_1 = 0}

Apply the values of

{X_1}

and

{X_2}

into the equation

{4X_1 + 5X_2 = 20}

, we have

{4 × 0 + 5X_2 = 20}

{⇒ 5X_2 = 20}

{⇒ X_2 = \dfrac{20}{5} = 4}

∴ She can consume 4 units of good 2.

(iv) What is the slope of the budget line?

The slope of the budget line is given by

{-\dfrac{P_1}{P_2}}

So, the slope is

{-\dfrac{4}{5}}

Questions 5, 6 and 7 are related to question 4.

5. How does the budget line change if the consumer’s income increases to ₹ 40 but the prices remain unchanged?

If the consumer’s income increases to ₹ 40 while the prices of the goods remain unchanged, the new budget equation will be

{4X_1 + 5X_2 = 40}

. This will result in a parallel outward shift of the budget line, allowing the consumer to afford more of both goods.

Parallel Outward Shift of Budget Line (When the Income is increased)

6. How does the budget line change if the price of good 2 decreases by a rupee but the price of good 1 and the consumer’s income remain unchanged?

If the price of good 2 decreases by a rupee (making it ₹ 4) while the price of good 1 and the consumer’s income remain unchanged, the new budget equation will be

{4X_1 + 4X_2 = 20}

. This will make the budget line less steep, reflecting the fact that good 2 has become relatively cheaper compared to good 1.

Budget Line Becomes Steeper (When Price of Good 2 is decreased)

7. What happens to the budget set if both the prices as well as the income double?

If both the prices of the goods and the consumer’s income double, the new budget equation will be

{8X_1 + 10X_2 = 40}

. Upon simplification, this will still be equal to

{4X_1 + 5X_2 = 20}

. So, the slope of the budget line remains the same. Also, there won’t be any change in the quantities of good 1 or good 2 purchased..

8. Suppose a consumer can afford to buy 6 units of good 1 and 8 units of good 2 if she spends her entire income. The prices of the two goods are ₹ 6 and ₹ 8 respectively. How much is the consumer’s income?

To find the consumer’s income, you can use the formula:

{P_1X_1 + P_2X_2 = M}

where:

–

{P_1}

and

{P_2}

are the prices of goods 1 and 2, respectively.

–

{X_1}

and

{X_2}

are the quantities of goods 1 and 2 that the consumer can afford, respectively.

Given that:

{P_1}

= ₹ 6

{X_1}

= 6 units

{P_2}

= ₹ 8

{X_2}

= 8 units

Substitute the given values into the formula:

{= (6 \times 6) + (8 \times 8)}

= 36 + 34

= ₹ 100

So, the consumer’s income is ₹ 100.

9. Suppose a consumer wants to consume two goods which are available only in integer units. The two goods are equally priced at ₹ 10 and the consumer’s income is ₹ 40.

(i)

Write down all the bundles that are available to the consumer.

(ii)

Among the bundles that are available to the consumer, identify those which cost her exactly ₹ 40.

Given that both goods are priced at ₹ 10 each and the consumer has an income of ₹ 40, we can find the available bundles and those that cost exactly ₹ 40.

(i) Available Bundles:

Since the goods are available only in integer units and each unit costs ₹ 10, the consumer can buy up to 4 units of a single good with her income of ₹ 40. The available bundles of the two goods (Good 1 and Good 2) can be listed as follows (in the format (units of Good 1, units of Good 2)):

Option

Pairs

Remarks

Option I

(0, 0), (0, 1), (0, 2), (0, 3), (0, 4)

0 quantity of good 1 and upto (≤ 4) quantity of good 2

Option II

(1, 0), (1, 1), (1, 2), (1, 3)

exactly 1 quantity of good 1 and upto 3 (≤ 3) quantity of good 2

Option III

(2, 0), (2, 1), (2, 2)

exactly 2 quantity of good 1 and upto 2 (≤ 2) quantity of good 2

Option IV

(3, 0), (3, 1)

exactly 3 quantity of good 1 and upto 1 (≤ 1) quantity of good 2

Option V

(4, 0)

exactly 4 quantity of good 1 and 0 quantity of good 2

(ii) Bundles Costing Exactly ₹ 40:

To find the bundles that cost exactly ₹ 40, we can use the formula:

{\text{Cost} = P_1X_1 + P_2X_2}

where

{P_1 = P_2 = ₹~10}

. We need to find the bundles where the cost is ₹ 40.

S.No.

Pair

Total Cost

(4, 0)

{(10 \times 4) + (10 \times 0) = ₹~40}

(0, 4)

{(10 \times 0) + (10 \times 4) = ₹~40}

(2, 2)

{(10 \times 2) + (10 \times 2) = ₹~40}

So, the bundles that cost exactly ₹ 40 are (4, 0), (0, 4), and (2, 2).

10. What do you mean by ‘monotonic preferences’?

Monotonic preferences refer to a type of consumer preference where a bundle of goods is preferred over another if it has more of at least one of the goods and no less of the other goods compared to the other bundle. In other words, a consumer with monotonic preferences will always prefer having more of a good, all else being equal.

This concept is based on the assumption that more of a good is better than less, which is a common assumption in consumer theory. Monotonic preferences imply that the consumer prefers bundles that are at least as good in all aspects and strictly better in some aspects compared to other bundles.

In summary, monotonic preferences refer to the consumer’s tendency to prefer more of a good, all else being equal, and to prefer bundles that are strictly better in some aspects and at least as good in all aspects compared to other bundles.

11. If a consumer has monotonic preferences, can she be indifferent between the bundles (10, 8) and (8, 6)?

No. Given the definition of monotonic preferences, a consumer with monotonic preferences prefers more of any good, all else being equal.

In the case of the bundles (10, 8) and (8, 6), the first bundle has more of both goods compared to the second bundle. Therefore, according to the principle of monotonic preferences, the consumer would prefer the bundle (10, 8) over the bundle (8, 6) and would not be indifferent between them.

So, if a consumer has monotonic preferences, she would not be indifferent between the bundles (10, 8) and (8, 6); she would prefer the bundle (10, 8).

12. Suppose a consumer’s preferences are monotonic. What can you say about her preference ranking over the bundles (10, 10), (10, 9) and (9, 9)?

Given that the consumer’s preferences are monotonic, we can analyze her preference ranking over the bundles (10, 10), (10, 9), and (9, 9) based on the principle that more of any good is preferred to less, all else being equal.

Bundle (10, 10) vs. Bundle (10, 9):

–

Bundle (10, 10) has more of the second good compared to Bundle (10, 9) while the quantity of the first good is the same in both bundles.

–

According to monotonic preferences, the consumer would prefer Bundle (10, 10) over Bundle (10, 9).

Bundle (10, 10) vs. Bundle (9, 9):

–

Bundle (10, 10) has more of both goods compared to Bundle (9, 9).

–

According to monotonic preferences, the consumer would prefer Bundle (10, 10) over Bundle (9, 9).

Bundle (10, 9) vs. Bundle (9, 9):

–

Bundle (10, 9) has more of the first good compared to Bundle (9, 9) while the quantity of the second good is the same in both bundles.

–

According to monotonic preferences, the consumer would prefer Bundle (10, 9) over Bundle (9, 9).

In summary, if a consumer’s preferences are monotonic, her preference ranking over the bundles (10, 10), (10, 9), and (9, 9) would be as follows:

S.No.

Bundle

Preference

Bundle (10, 10)

(most preferred)

Bundle (10, 9)

Bundle (9, 9)

(least preferred)

13. Suppose your friend is indifferent to the bundles (5, 6) and (6, 6). Are the preferences of your friend monotonic?

No. Her preference is not monotonic.

If my friend is indifferent between the bundles (5, 6) and (6, 6), it implies that she values both bundles equally, despite the fact that the second bundle has more of the first good compared to the first bundle.

Monotonic preferences imply that a consumer always prefers more of any good, all else being equal. In this case, since the second bundle (6, 6) has more of the first good while the amount of the second good remains the same, a consumer with monotonic preferences should prefer the second bundle (6, 6) over the first bundle (5, 6).

However, since my friend is indifferent between these two bundles, it indicates that her preferences are not monotonic. She does not necessarily prefer more of a good, all else being equal, which is a violation of the principle of monotonic preferences.

14. Suppose there are two consumers in the market for a good and their demand functions are as follows:

d~1~(p) = 20 – p for any price less than or equal to 20, and d~1~(p) = 0 at any price greater than 20.

d~2~(p) = 30 – 2p for any price less than or equal to 15 and d~1~(p) = 0 at any price greater than 15.

Find out the market demand function.

The market demand function can be found by adding the individual demand functions of all consumers in the market. Given the demand functions for the two consumers:

{d_1(p) = 20 - p}

for

{p \leq 20}

and

{d_1(p) = 0}

for

{p > 20}

{d_2(p) = 30 - 2p}

for

{p \leq 15}

and

{d_2(p) = 0}

for

{p > 15}

We can find the market demand function by considering different price ranges:

For

{p > 20}

Both

{d_1(p)}

and

{d_2(p)}

are 0.

Market demand

{= d_1(p) + d_2(p)}

= 0 + 0

= 0

For

{15 < p \leq 20}[/katex]:</div> <div>[katex]{d_1(p) = 20 - p}

{d_2(p) = 0}

(since

{p > 15}

)

Market demand

{= d_1(p) + d_2(p)}

{= (20 - p) + 0}

{= 20 - p}

For

{p \leq 15}

{d_1(p) = 20 - p}

{d_2(p) = 30 - 2p}

Market demand

{= d_1(p) + d_2(p)}

{ = (20 - p) + (30 - 2p)}

{= 50 - 3p}

So, the market demand function is:

{D(p) = \begin{cases} 50 - 3p & \text{if } p ≤ 15 \\ 20 - p & \text{if } 15 < p ≤ 20 \\ 0 & \text{if } p > 20 \end{cases}}

15. Suppose there are 20 consumers for a good and they have identical demand functions:

{d(p) = 10 - 3p}

for any price less than or equal to

{\dfrac{10}{3}}

and

{d_1(p) = 0}

at any price greater than

{\dfrac{10}{3}}

What is the market demand function?

Given that there are 20 consumers with identical demand functions:

{d(p) = \begin{cases} 10 - 3p & \text{if } p ≤ \dfrac{10}{3} \\ 0 & \text{if } p > \dfrac{10}{3} \end{cases}}

To find the market demand function, we need to sum the individual demand functions of all the consumers. Since all consumers have identical demand functions, we can multiply a single consumer's demand function by the number of consumers (20 in this case).

D(p)

{= 20 \times d(p)}

{= \begin{cases} 20(10 - 3p) & \text{if } p ≤ \dfrac{10}{3} \\ 20(0) & \text{if } p > \dfrac{10}{3} \end{cases}}

Now, simplifying the expression:

{D(p) = \begin{cases} 200 - 60p & \text{if } p \leq \dfrac{10}{3} \\ 0 & \text{if } p > \dfrac{10}{3} \end{cases}}

So, the market demand function is:

{D(p) = \begin{cases} 200 - 60p & \text{if } p \leq \dfrac{10}{3} \\ 0 & \text{if } p > \dfrac{10}{3} \end{cases}}

16. Consider a market where there are just two consumers and suppose their demands for the good are given as follows:

{d_1}

{d_2}

Calculate the market demand for the good.

The market demand for a good is calculated by summing up the individual demands of all consumers at each price level. Given the demands of the two consumers (d₁ and d₂) at different price levels (p), we can calculate the market demand (D) as follows:

d₁

d₂

D (Market Demand) (d₁ + d₂)

9 + 24 = 33

8 + 20 = 28

7 + 18 = 25

6 + 16 = 22

5 + 14 = 19

4 + 12 = 16

So, the market demand for the good at different price levels is as follows:

●

At p = 1, D = 33

●

At p = 2, D = 28

●

At p = 3, D = 25

●

At p = 4, D = 22

●

At p = 5, D = 19

●

At p = 6, D = 16

17. What do you mean by a normal good?

A normal good is defined as a type of good for which the quantity demanded by a consumer increases as the consumer’s income increases, and decreases as the consumer’s income decreases, all other factors being constant. In other words, the demand for a normal good moves in the same direction as the income of the consumer. For most goods, this is the typical relationship observed; as people have more income, they tend to buy more of a particular good, and vice versa.

In summary, a normal good is characterized by an increase in demand when consumer income rises, and a decrease in demand when consumer income falls.

18. What do you mean by an ‘inferior good’? Give some examples.

An "inferior good" refers to a type of good for which the demand decreases as the consumer's income increases, and vice versa. In other words, as people become wealthier, they tend to buy less of these goods. This is in contrast to normal goods, where demand increases with an increase in consumer income.

Examples of inferior goods include low-quality food items like coarse cereals. As a consumer's income increases, they might opt for higher-quality food items and reduce their consumption of these inferior goods.

Few more examples are given below:

Bajra and Jowar: These are types of coarse cereals that people tend to consume less of as their income increases, opting instead for higher-quality cereals like rice or wheat.

Hand-Me-Down Clothes: As income increases, consumers are more likely to purchase new clothing rather than second-hand or hand-me-down clothes.

Public Transportation: Higher-income individuals might prefer to use their own vehicles or hire cabs rather than using crowded public buses or trains.

Unbranded Products: Consumers might switch from unbranded or local products to branded products as their income increases.

Street Food: While street food is popular across all income groups, some individuals might choose to dine in restaurants more frequently as their income rises.

These examples reflect the general trend that as people's incomes increase, they tend to shift towards higher quality or more expensive options, reducing their consumption of goods and services that are considered to be of lower quality.

19. What do you mean by substitutes? Give examples of two goods which are substitutes of each other.

Substitutes are different goods that can satisfy the same need or desire and can be used in place of each other. When the price of one substitute good rises, the demand for the other substitute good tends to increase, and vice versa. This is because consumers shift their preference to the cheaper good when the price of the other good increases.

An example of two goods that are substitutes for each other could be tea and coffee. If the price of tea increases, people might start buying more coffee as a substitute, and vice versa.

Below are few more examples:

Rice and Wheat: These are staple foods in different parts of India. If the price of rice increases, people might consume more wheat-based products like chapatis, and vice versa.

Public Transport and Two-Wheelers: If the cost of using public transportation increases, people might prefer to use two-wheelers for commuting, and vice versa.

Cotton Clothing and Synthetic Clothing: If the price of cotton clothing increases, consumers might opt for cheaper synthetic clothing, and vice versa.

Cooking Gas and Electric Stoves: If the price of cooking gas increases, people might start using electric stoves for cooking, and vice versa.

These examples illustrate how consumers might switch between different goods based on changes in prices, availability, or personal preferences.

20. What do you mean by complements? Give examples of two goods which are complements of each other.

Complements are goods that are typically used together, and the consumption of one good enhances the consumption of the other. When the price of one complement good rises, the demand for the other complement good tends to decrease, and vice versa. This is because the increase in the price of one good makes the combined cost of using both goods together more expensive, leading to a decrease in demand for both goods.

An example of two goods that are complements of each other could be cars and petrol. If the price of petrol increases significantly, people might use their cars less often or might not buy cars at all, leading to a decrease in demand for both cars and petrol. Another example could be printers and ink cartridges; if the price of ink cartridges increases, the demand for printers might decrease as the overall cost of printing increases.

Here are a few more examples of complementary goods:

Mobile Phones and SIM Cards: People buy SIM cards to use in their mobile phones. If the price of SIM cards increases, the demand for mobile phones might decrease, and vice versa.

Tea and Sugar: Many people in India prefer to drink their tea with sugar. If the price of sugar increases, the demand for tea might decrease as the overall cost of making tea increases.

Computers and Software: Computers require software to function. If the price of software increases, the demand for computers might decrease, and vice versa.

Shoes and Socks: These are typically worn together. If the price of socks increases, the demand for shoes might decrease slightly, and vice versa.

Television and Set-Top Boxes: To watch cable or satellite TV in India, you need a set-top box. If the price of set-top boxes increases, the demand for televisions might decrease, and vice versa.

These examples illustrate how the demand for one good is closely linked to the demand for its complement, and changes in the price of one can affect the demand for the other.

21. Explain price elasticity of demand.

Price elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. The formula for price elasticity of demand

{e_D}

is given by:

{e_D}

{= \dfrac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}}

{= \dfrac{\dfrac{ΔQ}{Q} × 100}{\dfrac{ΔP}{P} × 100}}

{= \dfrac{ΔQ}{ΔP} × \dfrac{P}{Q}}

Where

{ΔP}

is the change in price,

{ΔQ}

is the change in quantity demanded,

{P}

is the initial price, and

{Q}

is the initial quantity demanded.

The price elasticity of demand can be classified into different types based on its value:

Elastic Demand

{(|e_D| > 1)}

: The quantity demanded is highly responsive to changes in price. A small change in price leads to a larger change in quantity demanded.

Inelastic Demand

{(|e_D| \lt 1)}

: The quantity demanded is not very responsive to changes in price. A change in price leads to a proportionally smaller change in quantity demanded.

Unitary Elastic Demand

{(|e_D| = 1)}

: The percentage change in quantity demanded is exactly equal to the percentage change in price.

Perfectly Elastic Demand

{(|e_D| = ∞)}

: The quantity demanded is extremely sensitive to changes in price. Even a very small change in price leads to an infinite change in quantity demanded.

Perfectly Inelastic Demand

{(|e_D| = 0)}

: The quantity demanded does not change at all in response to changes in price.

The price elasticity of demand depends on various factors including the availability of substitutes, the nature of the good (whether it is a necessity or a luxury), and the proportion of income spent on the good. For example, demand for essential goods like food is generally inelastic, while demand for luxury goods is more elastic.

In summary, price elasticity of demand is a crucial concept in economics that measures how responsive the quantity demanded of a good is to a change in its price.

22. Consider the demand for a good. At price ₹ 4, the demand for the good is 25 units. Suppose price of the good increases to ₹ 5, and as a result, the demand for the good falls to 20 units. Calculate the price elasticity.

To calculate the price elasticity of demand, we can use the formula:

{e_D = \dfrac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}}

Given that:

Initial price

{(P_1)}

= ₹ 4

New price

{(P_2)}

= ₹ 5

Initial quantity demanded

{(Q_1)}

= 25 units

New quantity demanded

{(Q_2)}

= 20 units

Let's first calculate the percentage change in quantity demanded:

Percentage change in quantity demanded

{= \dfrac{(Q_2 - Q_1)}{Q_1} \times 100}

{= \dfrac{(20 - 25)}{25} × 100}

{= \dfrac{-5}{25} × 100}

= -20%

Let's now calculate the percentage change in price:

Percentage change in price

{= \dfrac{(P_2 - P_1)}{P_1} × 100}

{= \dfrac{(5 - 4)}{4} × 100}

{= \dfrac{1}{4} × 100}

= 25%

Now, plug these values into the formula for price elasticity of demand:

{e_D}

{= \dfrac{-20\%}{25\%}}

= -0.8

The negative sign indicates that the relationship between price and quantity demanded is inverse, which is a typical behavior according to the law of demand. However, when discussing price elasticity, we often refer to the absolute value. So, the price elasticity of demand in this case is 0.8, which indicates that the demand is inelastic since the value is less than 1.

23. Consider the demand curve

{D(p) = 10 - 3p}

. What is the elasticity at price

{\dfrac{5}{3}}

Given that

Demand Curve

{D(p)}

{= 10 - 3p}

Price

{p}

{= \dfrac{5}{3}}

To find the price elasticity of demand at a specific price, we can use the formula:

{e_D = \dfrac{dD}{dp} × \dfrac{p}{D(p)}}

First, find the derivative of the demand curve with respect to price (after differentiating the given demand curve equation):

{\dfrac{dD}{dp} = -3}

Now, substituting in the value of

{p}

into the demand curve to find

{D(p)}

{D\left(\dfrac{5}{3}\right)}

{= 10 - 3\left(\dfrac{5}{3}\right)}

= 10 - 5

= 5

Now, substituting these values into the elasticity formula:

{e_D}

{= \dfrac{dD}{dp} × \dfrac{p}{D(p)}}

{= -3 × \dfrac{\dfrac{5}{3}}{5}}

{= -3 × \dfrac{1}{3}}

= -1

The price elasticity of demand at the price

{\dfrac{5}{3}}

is -1, which indicates that the demand is unitary elastic at this price level.

24. Suppose the price elasticity of demand for a good is -0.2. If there is a 5% increase in the price of the good, by what percentage will the demand for the good go down?

The price elasticity of demand

{(e_D)}

is given by the formula:

{e_D = \dfrac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}}

Given that the price elasticity of demand

{(e_D)}

is -0.2 and there is a 5% increase in the price of the good, we can rearrange the formula to find the percentage change in quantity demanded:

percentage change in quantity demanded

{= e_D × \text{percentage change in price}}

{= -0.2 \times 5\%}

{= -1\%}

So, if there is a 5% increase in the price of the good, the demand for the good will go down by 1%.

25. Suppose the price elasticity of demand for a good is -0.2. How will the expenditure on the good be affected if there is a 10 % increase in the price of the good?

The price elasticity of demand

{(e_D)}

measures the responsiveness of quantity demanded to a change in price. Given that the price elasticity of demand

{(e_D)}

for a good is -0.2, we can use this information to determine how the expenditure on the good will be affected by a 10% increase in its price.

Expenditure (or total revenue) is given by the product of price

{(P)}

and quantity demanded

{(Q)}

Expenditure =

{= P \times Q}

When the price of a good increases by 10% and the price elasticity of demand is -0.2, the percentage change in quantity demanded is:

percentage change in quantity demanded

{= e_D}

× percentage change in price

= -0.2 × 10%

= -2%

This means that the quantity demanded will decrease by 2% in response to a 10% increase in price.

To determine the effect on expenditure:

The price increases by 10% i.e., new price is

{(1 + 0.10)P = 1.10P}

The quantity demanded decreases by 2% i.e., new quantity is

{(1 - 0.02)Q = 0.98Q}

The new expenditure, relative to the original, is:

New Expenditure

{= (1 + 0.10)P \times (1 - 0.02)Q}

{= 1.10P \times 0.98Q}

{= 1.078PQ}

This represents a 7.8% increase in expenditure compared to the original expenditure

{(PQ)}

Therefore, with a 10% increase in the price of the good and a price elasticity of demand of -0.2, the expenditure on the good will increase by 7.8%.

27. Suppose there was a 4% decrease in the price of a good, and as a result, the expenditure on the good increased by 2%. What can you say about the elasticity of demand?

To analyze the elasticity of demand based on the given scenario, we can use the concept of price elasticity of demand. The price elasticity of demand

{(e_D)}

is calculated using the formula:

We know that

{ΔE = Δp × [q(1 + e_D)]}

where

{ΔE}

is the change in expenditure,

{Δp}

is the change in price,

{q}

is the quantity, and

{e_D}

is the price elasticity of demand.

It is given in the problem that

{ΔE}

= 2%

= 0.02

{ΔP}

= -2%

= -0.04

Substituting, we get

{Δp × [q(1 + e_D)] = ΔE}

{⇒ -0.04 × [q(1 + e_D)] = 0.02}

{⇒ [q(1 + e_D)] = \dfrac{0.02}{-0.04}}

{⇒ [q(1 + e_D)] = \dfrac{-1}{2}}

{⇒ q(1 + e_D) \lt 0}

We know that the quantity

{q}

is always greater than 1. So, we can say that

{(1 + e_D) \lt 0}

{⇒ e_D \lt -1}

Now, let's analyze the elasticity:

If the good is elastic

{(|e_D| > 1)}

: A percentage decrease in price leads to a greater percentage increase in quantity demanded, resulting in an increase in total expenditure. This seems to align with the given scenario.

If the good is inelastic

{(|e_D| \lt 1)}

: A percentage decrease in price leads to a smaller percentage increase in quantity demanded, which would typically result in a decrease in total expenditure. This does not align with the given scenario.

If the good has unitary elasticity

{(|e_D| = 1)}

: A percentage decrease in price is exactly offset by a percentage increase in quantity demanded, resulting in no change in total expenditure. This also does not align with the given scenario.

Based on the information provided, we can infer that the demand for the good is likely elastic

{(|e_D| > 1)}

since the expenditure on the good increased when the price decreased.