Class 12: Theory of Consumer Behaviour

Class 12: Introductory Micro-economics Chapter 2: Theory of Consumer Behaviour

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

The budget set of a consumer is the set of all possible combinations of two goods that the consumer can purchase with a given income at given prices of the goods.

The budget set includes:

All combinations that can be purchased by spending the entire income.
All combinations that can be purchased by spending less than the entire income.

The combinations lying beyond the budget set cannot be purchased because they require more income than the consumer possesses.

Determinants of Budget Set

Consumer's income.
Price of Good X.
Price of Good Y.

Thus, the budget set represents all affordable combinations of two goods available to a consumer under given income and price conditions.

Question 2. What is a budget line?

A budget line is a line that shows all the combinations of two goods which a consumer can purchase by spending his entire income at given prices of the goods.

Every point on the budget line represents a combination of goods that exactly exhausts the consumer's income. Combinations below the budget line are affordable but do not use the entire income, while combinations above the budget line are unaffordable.

Equation of the Budget Line

PxX + PyY = M

Where:

Px = Price of Good X
Py = Price of Good Y
X = Quantity of Good X
Y = Quantity of Good Y
M = Consumer's Income

Features of the Budget Line

It is a straight line with a negative slope.
It shows the consumer's purchasing capacity.
Its position depends on the consumer's income and the prices of goods.
It represents all combinations that fully utilize the consumer's income.

Question 3. Explain why the budget line is downward sloping.

The budget line is downward sloping because a consumer has a fixed income. If the consumer wants to buy more of one good, they must reduce the consumption of the other good to remain within the same budget.

This reflects the concept of opportunity cost, where gaining more of one good requires sacrificing some quantity of the other good.

The slope of the budget line is given by:

$$ \text{Slope of Budget Line}=-\frac{P_x}{P_y} $$

Since prices are positive, the slope is always negative. Therefore, the budget line slopes downward from left to right.

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

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

Given:

$P_x = ₹4$
$P_y = ₹5$
$M = ₹20$

The equation of the budget line is:

$$ P_xX + P_yY = M $$

Substituting the given values,

$$ 4X + 5Y = 20 $$

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

If the consumer spends the entire income on Good 1, then:

$$ X=\frac{M}{P_x}=\frac{20}{4}=5 $$

Answer: The consumer can purchase 5 units of Good 1.

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

If the consumer spends the entire income on Good 2, then:

$$ Y=\frac{M}{P_y}=\frac{20}{5}=4 $$

Answer: The consumer can purchase 4 units of Good 2.

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

The slope of the budget line is:

$$ -\frac{P_x}{P_y} $$

Substituting the given values,

$$ -\frac{4}{5} $$

Answer: The slope of the budget line is $-\frac{4}{5}$.

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

When the consumer's income increases from ₹20 to ₹40 while the prices of both goods remain unchanged, the purchasing power of the consumer increases.

The new budget line becomes:

$$ 4X + 5Y = 40 $$

The budget line shifts parallel outward (to the right) because the slope remains unchanged, but the consumer can now purchase more of both goods.

Question 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?

Given:

$P_x = ₹4$
$P_y = ₹4$
$M = ₹20$

The new budget line is:

$$ 4X + 4Y = 20 $$

As the price of Good 2 decreases, the consumer can purchase more units of Good 2 with the same income. Therefore, the budget line rotates outward from the Y-axis, while the X-intercept remains unchanged.

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

If both the consumer's income and the prices of both goods double in the same proportion, the purchasing power of the consumer remains unchanged.

Initially:

$$ 4X + 5Y = 20 $$

After doubling income and prices:

$$ 8X + 10Y = 40 $$

Dividing the equation by 2,

$$ 4X + 5Y = 20 $$

Since the budget equation remains unchanged, the budget line and the budget set remain the same. There is no change in the consumer's purchasing capacity.

Question 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 Rs 6 and Rs 8 respectively. How much is the consumer's income?

Given:

$P_x = ₹6$
$P_y = ₹8$
Maximum quantity of Good 1 = 6 units
Maximum quantity of Good 2 = 8 units

Consumer's income can be calculated using either good.

Using Good 1:

$$ M=P_x \times X $$ $$ M=6 \times 6=36 $$

Using Good 2:

$$ M=P_y \times Y $$ $$ M=8 \times 8=64 $$

Since the income of a consumer must be the same in both cases, the given data are inconsistent. Therefore, the question contains an error.

Answer: The consumer's income cannot be determined from the given data because the two values obtained (₹36 and ₹64) are different.

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

(i) Write down all the bundles that are available to the consumer.

Given:

$P_x = ₹10$
$P_y = ₹10$
$M = ₹40$

The affordable bundles satisfy:

$$ 10X+10Y\le40 $$

$$ X+Y\le4 $$

The available bundles are:

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

(ii) Among the bundles that are available to the consumer, identify those which cost exactly Rs 40.

Bundles costing exactly ₹40 satisfy:

$$ 10X+10Y=40 $$

$$ X+Y=4 $$

Therefore, the required bundles are:

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

Question 10. What do you mean by monotonic preferences?

Monotonic preferences refer to the assumption that a consumer always prefers more of a good to less, provided everything else remains the same.

According to this assumption, if one bundle contains more of at least one good and no less of the other good, it is preferred over the other bundle.

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

No. Under monotonic preferences, the consumer cannot be indifferent between these two bundles.

The bundle (10, 8) contains more of both goods than the bundle (8, 6). Since more of each good is preferred, the consumer will strictly prefer (10, 8) over (8, 6).

Question 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)?

Under monotonic preferences:

The bundle (10,10) is preferred to (10,9) because it has one additional unit of the second good.
The bundle (10,9) is preferred to (9,9) because it has one additional unit of the first good.

Therefore, the preference ranking is:

$$ (10,10)\succ(10,9)\succ(9,9) $$

where $\succ$ denotes "is preferred to".

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

No. The preferences of the friend are not monotonic.

Under monotonic preferences, a consumer always prefers more of a good to less, provided the quantity of the other good remains the same.

The bundle (6, 6) contains one more unit of the first good than the bundle (5, 6), while the quantity of the second good is the same. Therefore, (6, 6) should be preferred to (5, 6).

Since the friend is indifferent between these two bundles, the preferences do not satisfy the assumption of monotonicity.

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

Consumer 1:

$$ d_1(p)=20-p,\quad p\le20 $$ $$ d_1(p)=0,\quad p>20 $$

Consumer 2:

$$ d_2(p)=30-2p,\quad p\le15 $$ $$ d_2(p)=0,\quad p>15 $$

Find the market demand function.

The market demand is obtained by adding the individual demands at each price.

Case 1: $p\le15$

$$ D(p)=d_1(p)+d_2(p) $$ $$ =(20-p)+(30-2p) $$ $$ =50-3p $$

Case 2: \(15

Only Consumer 1 demands the good.

$$ D(p)=20-p $$

Case 3: $p>20$

Neither consumer demands the good.

$$ D(p)=0 $$

Therefore, the market demand function is:

$$ D(p)= \begin{cases} 50-3p, & p\le15\\ 20-p, & 15< 0, & p>20 \end{cases} $$

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

$$ d(p)=10-3p,\quad p\le\frac{10}{3} $$ $$ d(p)=0,\quad p>\frac{10}{3} $$

What is the market demand function?

Since there are 20 identical consumers, the market demand is:

$$ D(p)=20\times d(p) $$

For

$$ p\le\frac{10}{3} $$ $$ D(p)=20(10-3p) $$ $$ D(p)=200-60p $$

For

$$ p>\frac{10}{3} $$ $$ D(p)=0 $$

Therefore, the market demand function is:

$$ D(p)= \begin{cases} 200-60p, & p\le\frac{10}{3}\\ 0, & p>\frac{10}{3} \end{cases} $$

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

The market demand is obtained by adding the individual demands of both consumers at each price.

Price ($p$)	$d_1$	$d_2$	Market Demand ($D=d_1+d_2$)
1	9	24	33
2	8	20	28
3	7	18	25
4	6	16	22
5	5	14	19
6	4	12	16

Question 17. What do you mean by a normal good?

A normal good is a good whose demand increases when the consumer's income increases and decreases when the consumer's income decreases, assuming all other factors remain constant.

Thus, a normal good has a positive income effect.

Examples: Milk, fruits, clothing, smartphones, and branded shoes.

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

An inferior good is a good whose demand decreases when the consumer's income increases and increases when the consumer's income decreases, other things remaining the same.

Inferior goods have a negative income effect.

Examples: Coarse grains, low-quality clothing, local transport instead of private vehicles, and inexpensive food items.

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

Substitute goods are goods that can be used in place of one another to satisfy the same want. An increase in the price of one good leads to an increase in the demand for its substitute.

Examples:

Tea and Coffee
Butter and Margarine
Pepsi and Coca-Cola
Bus and Metro services

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

Complementary goods are goods that are consumed together. An increase in the price of one good generally leads to a decrease in the demand for the other good.

Examples:

Car and Petrol
Pen and Ink
Printer and Ink Cartridge
Bread and Butter

Question 21. Explain price elasticity of demand.

Price elasticity of demand measures the degree of responsiveness of quantity demanded to a change in the price of a good, other things remaining constant.

It is calculated as:

$$ E_d=\frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Price}} $$

For discrete changes, the elasticity is calculated as:

$$ E_d=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q} $$

A higher value of elasticity indicates that demand is more responsive to price changes, while a lower value indicates that demand is less responsive.

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

Given:

Initial Price, $P=4$
New Price, $P'=5$
Initial Quantity, $Q=25$
New Quantity, $Q'=20$

Using the percentage method:

$$ E_d=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q} $$ $$ =\frac{20-25}{5-4}\times\frac{4}{25} $$ $$ =\frac{-5}{1}\times\frac{4}{25} $$ $$ =-0.8 $$

Ignoring the negative sign, the price elasticity of demand is:

$$ E_d=0.8 $$

Question 23. Consider the demand curve $D(p)=10-3p$. What is the elasticity at price $\frac{5}{3}$?

Given:

$$ D(p)=10-3p $$

Price:

$$ p=\frac{5}{3} $$

Quantity demanded at this price:

$$ Q=10-3\left(\frac{5}{3}\right)=10-5=5 $$

The derivative of the demand function is:

$$ \frac{dQ}{dP}=-3 $$

Price elasticity of demand is:

$$ E_d=\frac{dQ}{dP}\times\frac{P}{Q} $$ $$ =-3\times\frac{\frac{5}{3}}{5} $$ $$ =-1 $$

Ignoring the negative sign, the elasticity of demand is:

$$ E_d=1 $$

Thus, the demand is unit elastic at the price $\frac{5}{3}$.

Question 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?

Given:

Price elasticity of demand, $E_d=-0.2$
Percentage increase in price $=5\%$

Using the formula:

$$ E_d=\frac{\%\Delta Q}{\%\Delta P} $$ $$ -0.2=\frac{\%\Delta Q}{5} $$ $$ \%\Delta Q=-0.2\times5=-1\% $$

The negative sign indicates a fall in demand.

Answer: The demand for the good will decrease by 1%.

Question 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?

Given:

Price elasticity of demand, $E_d=-0.2$
Percentage increase in price $=10\%$

Using the elasticity formula:

$$ E_d=\frac{\%\Delta Q}{\%\Delta P} $$ $$ -0.2=\frac{\%\Delta Q}{10} $$ $$ \%\Delta Q=-2\% $$

Thus, price increases by 10%, while quantity demanded decreases by only 2%.

Since the percentage increase in price is greater than the percentage decrease in quantity demanded, the total expenditure on the good increases.

Question 26. 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?

Given:

Percentage decrease in price $=4\%$
Percentage increase in expenditure $=2\%$

A fall in price accompanied by an increase in total expenditure implies that the percentage increase in quantity demanded is greater than the percentage decrease in price.

Therefore, the price elasticity of demand is greater than one.

Hence, the demand for the good is price elastic.

$$ |E_d|>1 $$

Class 12: Introductory Micro-economics Chapter 2: Theory of Consumer Behaviour

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

Determinants of Budget Set

Question 2. What is a budget line?

Equation of the Budget Line

Features of the Budget Line

Question 3. Explain why the budget line is downward sloping.

Question 4. A consumer wants to consume two goods. The prices of the two goods are Rs 4 and Rs 5 respectively. The consumer's income is Rs 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 the consumer consume if she spends her entire income on that good?

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

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

Question 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?

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

Question 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 Rs 6 and Rs 8 respectively. How much is the consumer's income?

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

Question 10. What do you mean by monotonic preferences?

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

Question 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)?

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

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

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

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

Question 17. What do you mean by a normal good?

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

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

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

Question 21. Explain price elasticity of demand.

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

Question 23. Consider the demand curve \(D(p)=10-3p\). What is the elasticity at price \(\frac{5}{3}\)?

Question 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?

Question 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?

Question 26. 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?

Price (\(p\))	\(d_1\)	\(d_2\)	Market Demand (\(D=d_1+d_2\))
1	9	24	33
2	8	20	28
3	7	18	25
4	6	16	22
5	5	14	19
6	4	12	16