#### NCERT Solutions for Class 12th: Ch 2 Theory of Consumer Behaviour Microeconomics

Page No: 34

Exercises

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

The collection of all bundles that the consumer can buy with their income at the prevailing market prices is called budget set of a consumer.

2. What is a budget line?

The budget line represents the different combinations of two goods that a consumer can buy with their given income and prices of commodities.
Let x1 be the amount of good 1.
x2 be the amount of good 2.
P1 be the price of good 1.
P2 be the price of good 2.
P1x1 = Total money spent on good 1
P1x2 = Total money spent on good 2
Then, the budget line will be:
P1x1 + P2x2 = M

3. Explain why the budget line is downward sloping.

The budget line is downward sloping because a consumer can increase the consumption of good 1 only by decreasing the consumption of good 2. The consumer have limited income which she can spend to choose goods between good 1 and good 2.

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 he/she spends his/her entire income on that good?
(iii) How much of good 2 can be consumed if he/she spends his/her entire income on that good?
(iv) What is the slope of the budget line?

(i) P1 = Rs 4
P2 = Rs 5
M = Rs 20
Equation of the budget line = P1x1 + P2x2 = M
4x1 + 5x2=20

(ii) Total income = Rs 20
Price of good 1 per unit = Rs 4
Amount of good 1 consumer can purchase by spending entire income = 20/4 = 5 units.

(iii) Total income = Rs 20
Price of good 2 per unit = Rs 5
Amount of good 1 consumer can purchase by spending entire income = 20/5 = 4 units.

(iv) Slope of the budget lines = -P1/P2
= -Price of good 1/Price of good 2 = -4/5 = -0.8

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

After income increase,
P1 = Rs 4
P2 = Rs 5
M = Rs 40
x1 = 40/P= 40/4 = 10 Units
x2 = 40/P2 = 40/5 = 8 Units
New Budget line is shown in the given figure
The new budget line R1S1 will show a parallel rightward shift from initial budget line RS. When the income increases then consumer can buy more goods at the prevailing market prices therefore intercept increases however slope of the line remains same as prices do not change.

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?

After price of good 2 decreases by a rupee,
P1 = Rs 4
P2 = Rs 4
M = Rs 20
x1 = 40/P= 20/4 = 5 Units
x2 = 40/P2 = 20/4 = 5 Units
New Budget line is shown in the given figure
The slope of the new budget line will be more as price of good 2 changes. Also, the new budget line will be steeper than the initial budget line.

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

When the prices as well as the income double then there will be no impact on budget set. Original budget set is P1x1 + P2x2 = M. If the prices and income double then the new budget set will be:
2P1x1 + 2P2x2 = 2M
⇒ 2(P1x1 + P2x2) = 2M
⇒ P1x1 + P2x2 = M
So, there is no change in budget set. Also, the new budget line will be same.

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

P1 = Rs 6
P2 = Rs 8
x1 = 6
x2 = 8
Income = P1x1 + P2x2
∴ 6 × 6 + 8 × 8 = 36 + 64 = 100
Therefore, the consumer's income is Rs 100.

9. Suppose a consumer wants to consume two goods that 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 a consumer, identify those that cost will him/her exactly Rs 40.

(i) The bundles that are available to the consumer as they cost Rs 40 or less are:
 (0, 0) (0, 1) (0, 2) (0, 3) (0, 4) (1, 0) (1, 1) (1, 2) (1, 3) (1, 4) (2, 0) (2, 1) (2, 2) (2, 3) (2, 4) (3, 0) (3, 1) (3, 2) (3, 3) (3, 4) (4, 0) (4, 1) (4, 2) (4, 3) (4, 4)

(ii)  The bundles that are available to a consumer that cost him exactly Rs 40 are (0, 4), (1, 3), (2, 2), (3, 1), (4, 0).

10. What do you mean by monotonic preferences?

Monotonic preferences means that the consumer prefers a particular bundle over the other bundle if the former consists of at least more of one good and no less of the other good.

11. If the consumer has monotonic preferences, then can he/she be indifferent towards bundles (10, 8) and (8, 6)?

No, he/she cannot be indifferent between the two bundles because in the second bundle the quantity of both the goods has reduced.

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

If the consumer's preferences are monotonic then the ranking over the bundles will be (10, 10), (10, 9) and (9, 9) because consumer is not indifferent in monotonic preferences and wants more quantity than less.

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

No, friend is not monotonic because he is indifferent to the bundles. If preferences of friend is monotonic then he must prefer second bundle as it contains more of both the goods.

14. Suppose there are two consumers in the market for a good and their demand functions are as follows:
d1(p) = 20 - p for any price less than or equal to 20 and d1(p) = 0 at any price greater than 20.
d2(p) = 30 - 2p for any price less than or equal to 15 and d1(p) = 0 at any price greater than 15.
Find out the market demand function.

d1(p) = 20 - p         p ≤ 20
d1(p) = 0                p > 20      ...(i)
d2(p) = 30 - 2p      p ≤ 15
d1(p) = 0               p > 2015      ...(ii)
Adding equation (i) and (ii) to market demand function (dm), we get
dm(p) = 50 - 3p for p ≤ 50/3
dm(p) = 20 - p   for p < 50/3 ≤ 20
dm(p) = 0          for p > 20

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 10/3 and d1(p) = 0 at any price greater than 10/3.
What is the market demand function?

d1(p) = 10 - 3p for p ≤ 10/3
d1(p) = 0           for p ≤ 10/3
Number of consumers = 20
Market demand function dm(p) is obtained by multiplying individual demand function by 20.
Therefore, dm(p) = (10 - 3p) (20) for p ≤ 10/3
dm(p) = 0                     for p ≤ 10/3

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 goods.

 p d1 d2 1 2 3 4 5 6 9 8 7 6 5 4 24 20 18 16 14 12
 p d1 d2 Market demand = D = d1 + d2 1 2 3 4 5 6 9 8 7 6 5 4 24 20 18 16 14 12 9 + 24 = 33 8 + 20 = 28 7 + 18 = 25 6 + 16 = 22 5 + 14 = 19 4 + 12 = 16

17. What do you mean by a normal good?

A good whose demand increases with the increase in income of the consumers and demand decreases with the decrease in income of the consumers is known as normal good. There is a direct relationship between income and demand.

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

A good whose demands move in the opposite direction of the income of the consumer is known as an inferior good. For example: low quality food items like coarse cereals.

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

Those goods that can be consumed in place of other goods are called substitute goods. For example: Tea and coffee are goods that can be substitutes for each other. If the price of coffee increases, the consumers can shift to tea, and hence, the consumption of tea is likely to go up.

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

Those goods that are consumed together are called complementary goods. For example: Tea and sugar. An increase in the price of sugar is likely to decrease the demand for tea and a decrease in the price of sugar is likely to increase the demand for tea.

21. Explain price elasticity of demand.

Price-elasticity of demand is a measure of the responsiveness of the demand for a good to changes in its price. It is defined as the percentage change in demand for the good divided by the percentage change in its price.
eD = Percentage change in demand for the good/Percentage change in the price of the good
eD = Î”P/Î”Q × P/Q
where,
Î”Q = Q2 - Q1, change in demand
Î”P = P2 - P1, change in demand
P = Initial price
Q = Initial quantity

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

P1 = 4                 Q1 = 25
P2 = 5                 Q2 = 20
Î”P = P2 - P1         Î”Q = Q2 - Q1
= 5 - 4                 = 20 - 25
= 1                      = -5
eD = Î”P/Î”Q × P/Q
= -5/1 × 4/25
= -4/5
eD = -0.8

23. Consider the demand curve D(p) = 10 – 3p. What is the elasticity at price 5/3?

Elasticity of demand of demand (eD) alognwith linear demand curve q = a - bp

i.e., the elasticity of demand at price 5/3 is unitary elastic.

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, then by what percentage will the demand for the good go down?

Price elasticity of demand = -0.2
Percentage change in price = 5%
Price elasticity of demand = Percentage change in demand/Percentage change in the price
-0.2 = Percentage change in demand/5
Percentage change in demand = -1
The demand for 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 its price?

Price elasticity of demand = -0.2
Percentage increase in price = 10%
Price elasticity of demand = Percentage change in demand/Percentage change in the price
-0.2 = Percentage change in demand/10
Percentage change in demand = -2
Thus, percentage decrease in demand is less than the percentage increase in price. This means that when price increases and e< 1, the demand is inelastic and hence, the expenditure will increase.

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?