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

**Ans. **A budget set is a combination of consumption bundles that are available to the consumer at the existing income levels and at the existing market prices.**Examples:** Suppose income of a consumer is (M).

He wants to buy two commodities (x and y) at given pirce (p_{1} and p_{2}).

**2. What is budget line?**

**Ans. **A budget line shows all the different combination of the two commodities that a consumer can purchase, given his money income and the price of two commodities. Equation of Budget line:

M = P_{x}.

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

**Ans.** The budget line is downward sloping because when more and more of units of one goods are bought, it leads to a fall in demand of the units of other goods at a constant level of income.

Slope of a budget line is P_{x}/P_{y }

**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?**

**Ans.**

- Let us assume than the consumer wants to buy amount of Good 1 and Y amount of Good 2.

Therefore, budget line can be represented using the equation

4X + 5Y = 20. - If the consumer spends the entire income on Good 1, then the value of Good Y will be zero.

4X + 5(0) = 20

x=20/4

X=5

5 units of Good 1 can be bought if she spends her entire income. - If the consumer spends the entire income of Good 2, the value of good X will be zero.

4(0) + 5Y = 20

Y=20/5

Y=4

4 units of Good 2 can be bought if the entire income is spent. - The slope of the budget line can be determined by the unit of good 1 that the consumer is willing to sacirfice for obtaining

equivalent amount of Good 2.

Slope of budget line =p_{1}/p_{2}

=4/5

=0.8

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

**Ans.** When there is an increase in the income of the consumer, the purchasing power of the consumer will also increase. If consumer’s income increases to ₹40 then he can buy more goods. Therefore, there will be a rightward shift in the budget line due to an increase in income.

Hence, AB is the initial budget line and A1B1 is the new budget line.

**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?**

**Ans.** As the price of Good 2 decreases by ₹1 the consumer will be able to purchase more quantity of Good 2 as compared to Good 1 at the given income. Therefore, there will be an upward shift along the vertical axis. (as there is no change in Good 1)

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

**Ans.** If both the prices and the income of the consumer doubles, there will be no change in the budget set.

**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?**

**Ans. **As per the information given:

P_{1} → Price of Good 1

P_{2} → Price of Good 2

x_{1} → Quantity of Good 1

x_{2} → Quantity of Good 2

x_{1} = 6, P_{1} = ₹6

x_{2} = 8, P_{2} = ₹8

M = income

M = P_{1}x_{1} + P_{2}x_{2}

M = (6 × 6) + (8 × 8)

= ₹36 + ₹64

M = ₹100

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.**

**Ans.**

- Given, Income of the consumer = ₹40

Price of both the goods = ₹10

The bundles that are available to the consumer 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). - The bundles that cost her exactly ₹40 are

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

as: (0, 4)

⇒ 0 × 10 + 4 × 10 = ₹40

(1, 3)

⇒ 1 × 10 + 3 × 10 = ₹40

(3, 1)

⇒ 3 × 10 + 1 × 10 = ₹40

(4, 0)

⇒ 4 × 10 + 0 × 10 = ₹40

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

**Ans. **Monotomic preference means that rational consumer will aways prefer more of a commodity without sacrificing the other commodity as it will offer a higher level of satisfaction.

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

**Ans. **As the bundle (10, 8) consists of more quantities of both the products, the consumer has a monotonic preference. Therefore, the consumers will prefer the bundle (10, 8) over (8, 6) and hence, cannot be indifference between the two.

**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)?**

**Ans. **If the preference are monotomic, the bundle (10, 10) will always give higher satisfaction as compared to the other two as the quantities of both the goods is higher in this bundle as compared to the other two.

So, the consumer preferences will be ranked as:

(i) (10, 10)

(ii) (10, 9)

(iii) (9, 9)

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

**Ans. **No, the preference of friend are not monotomic because the bundle (6, 6) will always give her higher satisfaction as compared to the bundle (5, 6).

**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.**

**Ans. **For price more than 15 but less than 20

Market demand = d_{1}(p) + d_{2}(p)

= 20 – p + 0

- 20 – p = d(p) (if 15 < p ≤ 20)

For price more than ₹20

Market demand = d_{1}(p) + d_{2}(p)

= 0 + 0 - 0 = d(p) (if p > 20)

For price less than ₹15.

Market demand = d_{1}(p) + d_{2}(p)

= 20 – p + 30 – 2p - 50 – 3p = d(p) (if p ≤ 15).

**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 d _{1}(p) = 0 at any price greater than 10/3What is the market demand function?**

**Ans. **$$\text{For price}<\frac{10}{3}\\\text{Market demand = Total sum of demand of all the consumers in the market}\\\text{Market demand} = 20 \Sigma d(p)\\= 20 × (10 – 3p)\\= 200 – 60p\\\text{For price}>\frac{10}{3}\\Market demand = 20 × d_1(p)\\= 20 × 0 = 0\\\text{Market demand function is}\\= 200 – 60p(\text{if p}\leq\frac{10}{3})\\=0(\text{if p}\geq\frac{10}{3})$$

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

p | d _{1} | d _{2} |

1 | 9 | 24 |

2 | 8 | 20 |

3 | 7 | 18 |

4 | 6 | 16 |

5 | 5 | 14 |

6 | 4 | 12 |

**Calculate the market demand for the good.**

**Ans. **Market demand can be calculated using the formula D = d_{1} + d_{2 }

p | d_{1} | d_{2} | D = d_{1} + d_{2} |

1 | 9 | 24 | 33 = 9 + 24 |

2 | 8 | 20 | 28 = 8 + 20 |

3 | 7 | 18 | 25 = 7 + 18 |

4 | 6 | 16 | 22 = 6 + 16 |

5 | 5 | 14 | 19 = 5 + 14 |

6 | 4 | 12 | 16 = 4 + 12 |

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

**Ans.** A normal good can be defined as a good whose demand increases with the increase in consumer’s income. Therefore, its demand directly proportional to the income

I ↑ D ↑

I ↓ D ↓

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

**Ans.** Inferior good are the goods whose demand decreases with an increase in the consumer’s income. Therefore, its demand is inversely proportional to the income.

I ↑ D ↓

**Examples:** Frozen foods, cheap grocery products.

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

**Ans.** Substitutes are the goods which can be used in place of one another. If the price of one product increases, its demand will decrease because the consumer will shift his preference to the substitute of that product.

Examples: Tea and coffee (can be used in place of one another)

If price of T

ea rises P ↑

Demand of T

ea falls D_{1} ↓

Demand of coffee will rise D_{2} ↑

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

**Ans.** Complements are the goods which are used with one another or consumed together.

Examples: Car and Petrol.

If the price of car rises, then decreases the demand of petrol because of fall in demand of cars. Therefore, we can say, price of one product is inversely proportional to the demand of other product.

Price of car P ↑

Demand of car D_{1} ↓

Demand of petrol falls D_{2} ↓

**21. Explain price elasticity of demand.**

**Ans.** Price elasticity is the degree of responsiveness of change in the price of one commodity response to a change in quantity demanded of commodity at a given price of level.

Price elasticity of demand

$$=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}\\e_p=\frac{\%\Delta in Q_d}{\%\Delta in P} \\Or\space e_p=\frac{\Delta Q}{\Delta P}×\frac{p}{Q}$$

where,

DQ = Q_{2} – Q_{1} (% change in demand for good)

DP = P_{2} – P_{1} (% chnage in price of good)

P = Intial price

Q = Initial quantity

**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 .**

**Ans.** As per the given data:

P_{1} = ₹4 Q_{1} = 25

P_{2} = ₹5 Q_{2} = 20

ΔP = P_{2} – P_{1} ΔQ = Q_{2} – Q_{1}

= 5 – 4

= 20 – 25

= 1 = – 5

ΔP = 1 ΔQ = 5

$$Or\space e_p=\frac{\Delta Q}{\Delta P}×\frac{p}{Q}\\=\frac{5}{1}×\frac{4}{25}=\frac{4}{5}\\e_p = 0·8.$$

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

**Ans.** D(p) = 10 – 3p

$$p=\frac{5}{3}\\D=10-\frac{3×5}{3}=10-5=5\\\frac{\Delta Q}{\Delta P}=-3\\\text{(change in demand per unit change in price)}\\e_p=\frac{\Delta Q}{\Delta P}×\frac{p}{Q}\\e_d=-3×\frac{5}{3}\\=-3×\frac{5}{3}×\frac{1}{5}\\e_d=1\\\text{\ Elasticity of demand at price p}=\frac{5}{3}\text{is unitary elastic.} $$

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

**Ans.** e_{d} = – 0·2

Change in price = 5%

$$e_d=\frac{\text{Percentage change in demand}}{\text{Percentage change in price}}\\0.2=\frac{\text{\% change in demand}}{5}\\\text{\% change in demand} = 1\\\text{The demand for the good will do down by 1\%.}$$

**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?**

**Ans.** Price elasticity e_{d} = – 0·2

% change in price = 10%

$$e_d=\frac{\text{\% change in demand}}{\text{\%change in price}}\\0.2=\frac{\text{\% change in demand}}{10}\\\text{\% change in demand} = 2\%\\\text{Since, the demand becomes inelastic, the expenditure will increase.}$$

**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?**

**Ans. If**$$e_d=\frac{\text{\% change in demand}}{\text{\%change in price}}\\0.2=\frac{4}{2}\\e_d=2$$

Then, the elasticity of demand is more than 1.

Therefore, a small change can lead to bigger change in demand.

Hence, the demand in elastic.

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