NCERT Solutions for Class 11 Micro Economics Chapter 2: Theory of Consumer Behaviour

The budget set of a consumer refers to the collection of all possible combinations (or bundles) of two goods that the consumer can afford to purchase with their given income and the prevailing market prices.

1. Key Idea: It includes all bundles for which the total expenditure is less than or equal to the consumer's income (M).
2. Formula: The condition for a bundle (x₁, x₂) to be in the budget set is: $$P_1x_1 + P_2x_2 \le M$$ Where:
   • \(P_1\) = Price of Good 1
   • \(x_1\) = Quantity of Good 1
   • \(P_2\) = Price of Good 2
   • \(x_2\) = Quantity of Good 2
   • \(M\) = Consumer's Income
3. Example: If you have ₹50, and a pen costs ₹10 and a notebook costs ₹20, your budget set includes buying 1 pen and 1 notebook (costing ₹30), or 2 pens (costing ₹20), etc.

A budget line (also known as the price line) is a graphical representation of all possible combinations of two goods that a consumer can purchase by spending their entire income, given the prices of the goods.

• Key Difference from Budget Set: The budget line represents combinations where expenditure is exactly equal to income, whereas the budget set includes combinations where expenditure is less than or equal to income.
• Equation: The equation of the budget line is: $$P_1x_1 + P_2x_2 = M$$

The budget line forms the boundary of the budget set.

The budget line is downward sloping because to increase the consumption of one good, a consumer must decrease the consumption of the other good, given that their income is fixed.

1. A budget line represents the maximum amount a consumer can spend.
2. If a consumer wants to buy more of Good 1 (say, more chocolates), they have to spend more money on it.
3. Since their total income is constant, this extra expenditure must be compensated by reducing expenditure on Good 2 (say, fewer packets of chips).
4. This inverse relationship—increasing one good means decreasing the other—results in a negatively sloped or downward-sloping line from left to right.

Given: Price of Good 1 (P₁) = Rs 4, Price of Good 2 (P₂) = Rs 5, Consumer's Income (M) = Rs 20.

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

The equation is \(P_1x_1 + P_2x_2 = M\). Substituting the values, we get: $$4x_1 + 5x_2 = 20$$

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

Set \(x_2 = 0\): \(4x_1 + 5(0) = 20 \Rightarrow 4x_1 = 20 \Rightarrow x_1 = 20 / 4\).
Answer: 5 units.

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

Set \(x_1 = 0\): \(4(0) + 5x_2 = 20 \Rightarrow 5x_2 = 20 \Rightarrow x_2 = 20 / 5\).
Answer: 4 units.

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

The slope is given by \(-\frac{P_1}{P_2}\).
Slope = -4 / 5.
Answer: -0.8.

If income increases to Rs 40 (P₁=4, P₂=5), the consumer can buy more of both goods.

1. New Budget Line Equation: The new equation becomes $$4x_1 + 5x_2 = 40$$
2. Effect on Graph: The budget line will shift outward to the right. This shift is parallel because the slope (\(-\frac{P_1}{P_2}\)) remains unchanged.
3. New Intercepts:
   • Maximum Good 1 = 40 / 4 = 10 units.
   • Maximum Good 2 = 40 / 5 = 8 units.

Original: P₁=Rs 4, P₂=Rs 5, M=Rs 20.
New: P₁=Rs 4, New P₂'=Rs 4, M=Rs 20.

1. Effect on Slope: The slope (\(-\frac{P_1}{P_2}\)) changes from -4/5 to -4/4 = -1. The new budget line will be steeper.
2. Effect on Intercepts:
   • X-intercept (max Good 1): Unchanged. Max Good 1 = 20 / 4 = 5 units.
   • Y-intercept (max Good 2): Changes. New max Good 2 = 20 / 4 = 5 units (was 4).
3. Conclusion: The budget line will pivot or rotate outwards from the x-axis intercept.

Let the initial budget line be: \(P_1x_1 + P_2x_2 = M\).

After doubling prices and income, the new equation is: \((2P_1)x_1 + (2P_2)x_2 = 2M\).

Dividing the new equation by 2, we get back the original equation: \(P_1x_1 + P_2x_2 = M\).

Conclusion: There will be no change in the budget line or the budget set. The consumer's purchasing power remains exactly the same.

Given: x₁=6, x₂=8, P₁=Rs 6, P₂=Rs 8.

The consumer is on her budget line, so \(M = P_1x_1 + P_2x_2\).

M = (6 × 6) + (8 × 8)

M = 36 + 64

M = Rs 100. The consumer's income is Rs 100.

Monotonic preferences mean that a rational consumer always prefers a bundle that has more of at least one good and no less of the other good. In simple terms, "more is always better."

Example: Given Bundle A = (10 apples, 5 bananas) and Bundle B = (10 apples, 6 bananas), a consumer with monotonic preferences will always prefer bundle B to bundle A.

Yes, a consumer with monotonic preferences can be indifferent between the bundles (10, 8) and (8, 6).

Explanation: Monotonic preference applies when one bundle has more of at least one good and no less of the other. Here, bundle (10, 8) has more of both goods than (8, 6). Therefore, according to monotonic preferences, bundle (10, 8) must be strictly preferred to (8, 6). They cannot lie on the same indifference curve.
Correction from original markdown: Monotonicity implies (10,8) is strictly preferred to (8,6). They cannot be on the same indifference curve. The question asks if they can be indifferent, and the answer is No, they cannot, because (10,8) is unambiguously better than (8,6).
Let's re-evaluate the provided markdown answer, which says "Yes". That is incorrect. Let's use the correct economic logic.
Correct Answer: No. A consumer with monotonic preferences cannot be indifferent. Bundle A=(10,8) has more of both Good 1 and Good 2 than Bundle B=(8,6). Therefore, by the principle of monotonic preferences ("more is better"), Bundle A must be strictly preferred to Bundle B. They cannot give the same level of satisfaction.

Let Bundle A = (10, 10), Bundle B = (10, 9), and Bundle C = (9, 9).

1. Comparing A and B: Bundle A has the same amount of Good 1 but more of Good 2. Therefore, A is preferred to B (A > B).
2. Comparing B and C: Bundle B has the same amount of Good 2 but more of Good 1. Therefore, B is preferred to C (B > C).

Conclusion: The preference ranking is A > B > C, or (10, 10) is preferred to (10, 9), which is preferred to (9, 9).

The Law of Diminishing Marginal Utility (DMU) states that as a consumer consumes more units of a commodity, the additional satisfaction (marginal utility) from each successive unit declines.

Analysis: As more chocolates are consumed, MU decreases from 10 to 0, and then becomes negative. This demonstrates the Law of DMU.

1. When MU is positive and decreasing, TU increases at a decreasing rate.
2. When MU is zero, TU is maximum (point of satiety).
3. When MU is negative, TU starts to fall.
4. TU is the summation of all MUs: \(TU_n = \sum MU\).

Consumer's Equilibrium is a state of maximum satisfaction.

Case 1: Single Commodity

A consumer is in equilibrium when the marginal utility of a good equals its price. Condition: $$MU_x = P_x$$

• If \(MU_x > P_x\): Consumer will buy more.
• If \(MU_x < P_x\): Consumer will buy less.

Case 2: Two or More Commodities

Governed by the Law of Equi-Marginal Utility. Equilibrium is when the ratio of marginal utilities to prices is equal for all goods. Condition: $$\frac{MU_x}{P_x} = \frac{MU_y}{P_y} = MU_m$$ This means the last rupee spent on each good gives the same satisfaction.

A demand curve shows the inverse relationship between price and quantity demanded. It is derived from the consumer's equilibrium condition \(MU_x = P_x\).

1. Start with Equilibrium: Assume at Price P₁, the consumer buys Q₁ units, where \(MU_1 = P_1\).
2. Price Falls: Let price fall to P₂. Now, \(MU_1 > P_2\). The consumer is getting more value than the price.
3. Restoring Equilibrium: To restore equilibrium, the consumer buys more. Due to the Law of DMU, as quantity increases, MU falls.
4. New Equilibrium: The consumer stops buying more when the MU falls to match the new price, i.e., \(MU_2 = P_2\). Let this be at quantity Q₂.
5. Conclusion: Since P₁ > P₂, then MU₁ > MU₂. As MU falls when quantity increases, it implies Q₂ > Q₁. Thus, a lower price (P₂) leads to a higher quantity demanded (Q₂). Plotting these (P, Q) pairs gives a downward-sloping demand curve.

Two indifference curves cannot intersect because each curve represents a different level of satisfaction. Intersection would violate the assumption of transitivity.

Proof by Contradiction:

1. Assume two curves, IC₁ and IC₂, intersect at point A.
2. Let point B be on IC₁ and point C be on IC₂.
3. Since A and B are on IC₁, Satisfaction(A) = Satisfaction(B).
4. Since A and C are on IC₂, Satisfaction(A) = Satisfaction(C).
5. By transitivity, this implies Satisfaction(B) = Satisfaction(C).
6. However, if point C contains more of at least one good than point B, monotonic preferences state C must be preferred to B. This creates a contradiction.
7. Therefore, the initial assumption is wrong. Two ICs can never intersect.

Consumer's equilibrium (Indifference Curve approach) is where a consumer maximizes satisfaction, given their budget constraint.

Conditions for Equilibrium:

1. The budget line must be tangent to the indifference curve. This means the slope of the IC (MRS) must equal the slope of the budget line (Price Ratio): $$\text{MRS}_{xy} = \frac{P_x}{P_y}$$
2. The indifference curve must be convex to the origin at the point of tangency. This is ensured by the law of diminishing MRS.

Explanation: A consumer wants to reach the highest possible indifference curve. The budget line shows what is affordable. The equilibrium point is where the budget line just touches (is tangent to) the highest attainable indifference curve. Any curve higher is unaffordable, and any curve lower gives less satisfaction.

(a) Formulate Priya's budget line equation.
Equation: \(25X + 50Y = 500\)

(b) Can Priya afford 10 Gel Pens and 6 Chocolate Bars?
Cost = (10 × 25) + (6 × 50) = 250 + 300 = ₹550. Since ₹550 > ₹500, she cannot afford this combination.

(c) What is the MRS at her equilibrium point?
At equilibrium, \(\text{MRS}_{xy} = \frac{P_x}{P_y}\).
MRS = 25 / 50 = 0.5. She is willing to give up 0.5 chocolate bars for 1 extra gel pen.