Chapter 2 Theory of Consumer Behaviour

Q1 What do you mean by the budget set of a consumer?

The budget set refers to the collection of all bundles of goods that a consumer can purchase with their available income at prevailing market prices. It represents the set of all consumption bundles $(x_1, x_2)$ such that:

$$p_1x_1 + p_2x_2 \leq M$$

Where $p_1, p_2$ are prices and $M$ is income.

Q2 What is a budget line?

The budget line is a graphical representation of all possible combinations of two goods that cost exactly equal to the consumer’s income.

$$p_1x_1 + p_2x_2 = M$$

Q3 Explain why the budget line is downward sloping.

The budget line is downward sloping because, with a fixed income, a consumer can only buy more of one good by reducing the consumption of the other good. There is a trade-off or opportunity cost involved, represented by the negative slope.

Q4 Calculations for Budget Line (Income=20, P1=4, P2=5).

Given: $p_1 = 4$, $p_2 = 5$, $M = 20$.

Equation: $4x_1 + 5x_2 = 20$
Max Good 1 ($x_2=0$): $4x_1 = 20 \Rightarrow x_1 = 5$ units.
Max Good 2 ($x_1=0$): $5x_2 = 20 \Rightarrow x_2 = 4$ units.
Slope: Slope $= -\frac{p_1}{p_2} = -\frac{4}{5} = -0.8$.

Q5 How does the budget line change if income increases to Rs 40?

If income increases to Rs 40 (doubles), while prices remain unchanged, the consumer’s purchasing power increases. The budget line will shift parallelly outwards (to the right). The new intercepts will be double the previous ones ($x_1=10, x_2=8$).

Q6 How does the budget line change if the price of good 2 decreases by Re 1?

New Price $p_2′ = 5 – 1 = 4$. Income and $p_1$ remain same.
The vertical intercept (Good 2 axis) increases from $20/5 = 4$ to $20/4 = 5$. The horizontal intercept remains unchanged at 5. The budget line swivels/rotates outwards along the vertical axis, becoming flatter.

Q7 What happens to the budget set if both prices and income double?

The budget set remains unchanged.

Old: $p_1x_1 + p_2x_2 \leq M$
New: $(2p_1)x_1 + (2p_2)x_2 \leq 2M$
Dividing by 2: $p_1x_1 + p_2x_2 \leq M$

Since the purchasing power remains exactly the same, the budget line does not shift.

Q8 Calculate Income given intercepts (6, 8) and prices (Rs 6, Rs 8).

We are given two separate scenarios for spending entire income:

Scenario A: Buy 6 units of Good 1 only. $M = 6 \times 6 = 36$.
Scenario B: Buy 8 units of Good 2 only. $M = 8 \times 8 = 64$.

Note: The question wording implies the consumer can afford 6 units of Good 1 OR 8 units of Good 2. However, the calculation $6 \times 6 = 36$ and $8 \times 8 = 64$ gives conflicting income values. Let’s re-read carefully: “Suppose a consumer can afford to buy 6 units of good 1 and 8 units of good 2 if she spends her entire income.”

This likely means the bundle $(6, 8)$ costs the entire income.
$M = (p_1 \times 6) + (p_2 \times 8)$
$M = (6 \times 6) + (8 \times 8) = 36 + 64 = 100$.

Consumer’s Income = Rs 100

Q9 Integer Bundles (P1=10, P2=10, Income=40).

(i) Available Bundles ($10x_1 + 10x_2 \leq 40 \Rightarrow x_1 + x_2 \leq 4$):
(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) Cost exactly Rs 40 ($x_1 + x_2 = 4$):
(0,4), (1,3), (2,2), (3,1), (4,0)

Q10 What do you mean by ‘monotonic preferences’?

Monotonic preferences imply that a consumer always prefers more of a good to less. Specifically, if bundle A has more of at least one good and no less of the other good compared to bundle B, the consumer strictly prefers A over B.

Q11 Monotonic preferences: Indifferent between (10, 8) and (8, 6)?

No.
Bundle (10, 8) contains more of both goods compared to bundle (8, 6). If preferences are monotonic, the consumer must strictly prefer (10, 8) over (8, 6). She cannot be indifferent.

Q12 Preference ranking: (10, 10), (10, 9), (9, 9).

Based on monotonic preferences (more is better):

(10, 10) has more than (10, 9). So, $(10, 10) \succ (10, 9)$.
(10, 9) has more than (9, 9). So, $(10, 9) \succ (9, 9)$.

Ranking: $(10, 10) \succ (10, 9) \succ (9, 9)$.

Q13 Friend indifferent between (5, 6) and (6, 6). Monotonic?

No.
Bundle (6, 6) has more of good 1 than bundle (5, 6) while good 2 is equal. A monotonic consumer would prefer (6, 6). Being indifferent implies preferences are not monotonic.

Q14 Calculate Market Demand Function (2 consumers).

Given: $d_1(p) = 20 – p$ (for $p \le 20$) and $d_2(p) = 30 – 2p$ (for $p \le 15$).

Market Demand $D_m(p) = d_1(p) + d_2(p)$

For $p > 20$: Both demands are 0. $D_m(p) = 0$.
For $15 < p \le 20$: Only consumer 1 buys. $D_m(p) = 20 – p$.
For $p \le 15$: Both buy. $D_m(p) = (20 – p) + (30 – 2p) = 50 – 3p$.

Q15 Market Demand Function (20 identical consumers).

Given: $d(p) = 10 – 3p$. Number of consumers $N = 20$.

Market Demand $D_m(p) = N \times d(p)$

$D_m(p) = 20(10 – 3p) = 200 – 60p$ (for $p \le 10/3$).

Q16 Calculate Market Demand from Table.

Price (p)	d1	d2	Market Demand (d1 + d2)
1	9	24	33
2	8	20	28
3	7	18	25
4	6	16	22
5	5	14	19
6	4	12	16

Q17-18 Normal Good vs Inferior Good.

Good Type	Definition	Example
Normal Good	A good whose demand increases with an increase in the consumer’s income.	Clothing, Electronics.
Inferior Good	A good whose demand decreases with an increase in the consumer’s income.	Coarse grains (Bajra), Low-quality rice.

Q19-20 Substitutes vs Complements.

Type	Definition	Example
Substitutes	Goods that can be used in place of one another. Price of one and demand for the other move in the same direction.	Tea and Coffee; Coke and Pepsi.
Complements	Goods that are consumed together. Price of one and demand for the other move in opposite directions.	Car and Petrol; Ink and Pen.

Q21 Explain price elasticity of demand.

Price elasticity of demand ($e_d$) measures the responsiveness of the demand for a good to changes in its price. It is defined as the percentage change in demand divided by the percentage change in price.

$$e_d = \frac{\% \Delta Q}{\% \Delta P} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$

Q22 Calculate Elasticity (P: 4->5, Q: 25->20).

$P = 4, \Delta P = 1$. $Q = 25, \Delta Q = -5$.

$$e_d = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$ $$e_d = \frac{-5}{1} \times \frac{4}{25} = -5 \times 0.16 = -0.8$$

Elasticity = -0.8

Q23 Elasticity for D(p) = 10 – 3p at price p = 5/3.

Given linear demand $q = a – bp$, where $b = 3$.
At $p = 5/3$, $q = 10 – 3(5/3) = 10 – 5 = 5$.

$$e_d = -b \frac{p}{q}$$ $$e_d = -3 \times \frac{5/3}{5} = -3 \times \frac{5}{15} = -1$$

Elasticity = -1 (Unit Elastic)

Q24 Elasticity = -0.2. Price increases by 5%. Change in Demand?

$\%\Delta Q = e_d \times \%\Delta P$

$\%\Delta Q = -0.2 \times 5\% = -1\%$

Demand goes down by 1%.

Q25 Elasticity = -0.2. Price increases by 10%. Effect on Expenditure?

Demand is inelastic ($|e_d| < 1$).
When demand is inelastic, Price and Total Expenditure move in the same direction.
Since price increases by 10%, Total Expenditure will increase.

Q27 Price decreases 4%, Expenditure increases 2%. Elasticity?

Price decreases $\downarrow$ and Expenditure increases $\uparrow$.
Since Price and Expenditure move in opposite directions, the demand is elastic ($|e_d| > 1$).