Question 1

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

Accepted Answer

The budget set of a consumer is the set of all possible combinations of two goods that the consumer can afford to buy with a given income and prices of the goods. It includes all bundles of goods whose total cost is less than or equal to the consumer's income. — The budget set is derived from the consumer's income and the prices of goods. If the consumer has income M, and prices of goods are p1 and p2, then the budget set includes all combinations (x1, x2) such that p1*x1 + p2*x2 ≤ M.

Question 2

What is budget line?

Accepted Answer

The budget line is a graphical representation of all combinations of two goods that a consumer can buy by spending the entire income. It shows the maximum quantity of one good that can be purchased for any given quantity of the other good, given the prices and income. — The budget line is derived from the budget constraint equation p1*x1 + p2*x2 = M. It is a straight line with intercepts M/p1 and M/p2 on the axes representing quantities of the two goods.

Question 3

Explain why the budget line is downward sloping.

Accepted Answer

The budget line is downward sloping because to consume more of one good, the consumer must give up some quantity of the other good due to limited income. This trade-off causes a negative slope. — From the budget line equation p1*x1 + p2*x2 = M, rearranged as x2 = (M/p2) - (p1/p2)*x1, the slope is -p1/p2, which is negative. This negative slope indicates the rate at which one good must be sacrificed to gain more of the other good.

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 she consume if she spends her entire income on that good?
(iv) What is the slope of the budget line?

Accepted Answer

(i) Let x1 and x2 be quantities of good 1 and good 2 respectively.
Prices: p1 = Rs 4, p2 = Rs 5, Income M = Rs 20.
Budget line equation: 4x1 + 5x2 = 20.

(ii) If entire income is spent on good 1, then x2 = 0.
4x1 = 20 ⇒ x1 = 20/4 = 5 units.

(iii) If entire income is spent on good 2, then x1 = 0.
5x2 = 20 ⇒ x2 = 20/5 = 4 units.

(iv) Slope of budget line = -p1/p2 = -4/5 = -0.8. — Step 1: Write the budget constraint using given prices and income.
Step 2: For maximum consumption of good 1, set good 2 quantity to zero and solve.
Step 3: For maximum consumption of good 2, set good 1 quantity to zero and solve.
Step 4: Calculate slope as negative ratio of prices.

This shows the trade-off between the two goods given the consumer's budget.

Question 5

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

Accepted Answer

When the consumer's income increases to Rs 40 while the prices of goods remain unchanged, the budget line shifts outward parallel to the original budget line. This is because the consumer can now afford more of both goods. The slope of the budget line remains the same since prices are unchanged, but the intercepts on both axes increase proportionally to the increase in income. — The budget line equation is given by p1x1 + p2x2 = m, where m is income. If m increases from original income to Rs 40, the intercepts on the axes (m/p1 and m/p2) increase, shifting the budget line outward parallelly.

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?

Accepted Answer

If the price of good 2 decreases by Rs 1, while the price of good 1 and income remain unchanged, the budget line pivots outward around the intercept on the good 1 axis. The consumer can now afford more units of good 2 for the same income, so the intercept on the good 2 axis increases (m/(p2 - 1)). The slope of the budget line changes because the relative prices have changed. — Original budget line: p1x1 + p2x2 = m. New budget line: p1x1 + (p2 - 1)x2 = m. The intercept on x2 axis increases from m/p2 to m/(p2 - 1), causing the budget line to pivot outward on the x2 axis.

Question 7

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

Accepted Answer

If both prices and income double, the budget set remains unchanged. This is because the budget constraint equation p1x1 + p2x2 = m becomes 2p1x1 + 2p2x2 = 2m, which simplifies to p1x1 + p2x2 = m after dividing both sides by 2. Hence, the consumer's purchasing power and the budget line remain the same. — Doubling prices and income proportionally does not change the budget set since the relative prices and income remain the same. The budget line equation is effectively unchanged.

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?

Accepted Answer

Given: Quantity of good 1 = 6 units, price of good 1 = Rs 6
Quantity of good 2 = 8 units, price of good 2 = Rs 8
Consumer spends entire income on these quantities.
Income = (Price of good 1 × Quantity of good 1) + (Price of good 2 × Quantity of good 2)
= (6 × 6) + (8 × 8) = 36 + 64 = Rs 100
Therefore, the consumer's income is Rs 100. — Income is total expenditure on both goods. Multiplying quantity by price for each good and adding gives total 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 her exactly Rs 40.

Accepted Answer

(i) Since both goods cost Rs 10 each and income is Rs 40, the consumer can buy bundles (x1, x2) such that 10x1 + 10x2 ≤ 40, with x1 and x2 integers ≥ 0.
Possible 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) Bundles costing exactly Rs 40 satisfy 10x1 + 10x2 = 40 ⇒ x1 + x2 = 4.
These bundles are:
(0,4), (1,3), (2,2), (3,1), (4,0). — Income constraint: 10x1 + 10x2 ≤ 40 ⇒ x1 + x2 ≤ 4.
Since x1, x2 are integers, list all integer pairs with sum ≤ 4 for (i) and sum = 4 for (ii).

Question 10

What do you mean by 'monotonic preferences'?

Accepted Answer

Monotonic preferences mean that a consumer always prefers more of at least one good without having less of any other good. In other words, if a bundle A has at least as much of every good as bundle B and more of at least one good, then the consumer strictly prefers A to B. — Monotonicity implies 'more is better' or 'more is at least not worse' for the consumer's preferences.

Question 11

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

Accepted Answer

No, if the consumer has monotonic preferences, she cannot be indifferent between (10, 8) and (8, 6) because (10, 8) has more of both goods compared to (8, 6). Monotonic preferences imply that more of any good is strictly preferred, so (10, 8) is strictly preferred to (8, 6). — Since (10, 8) ≥ (8, 6) in both goods and strictly greater in both, monotonicity implies strict preference, not indifference.

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)?

Accepted Answer

With monotonic preferences:
- (10, 10) is strictly preferred to (10, 9) because it has more of good 2.
- (10, 9) is strictly preferred to (9, 9) because it has more of good 1.
Therefore, the preference ranking is (10, 10) > (10, 9) > (9, 9). — Monotonicity implies that more of any good is preferred. Comparing bundles pairwise, the one with more quantity of at least one good and no less of the other is preferred.

Question 13

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

Accepted Answer

No, if your friend is indifferent between (5, 6) and (6, 6), then her preferences are not monotonic. Because (6, 6) has more of good 1 and the same amount of good 2 compared to (5, 6), monotonic preferences would imply that (6, 6) is strictly preferred to (5, 6), not indifferent. — Monotonic preferences require strict preference for bundles with more of at least one good and no less of others. Indifference here contradicts monotonicity.

Question 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.

Accepted Answer

The market demand function is the sum of individual demands where both are positive. For prices p ≤ 15: d₁(p) = 20 - p d₂(p) = 30 - 2p Market demand D(p) = d₁(p) + d₂(p) = (20 - p) + (30 - 2p) = 50 - 3p For 15 < p ≤ 20: d₁(p) = 20 - p d₂(p) = 0 (since p > 15) Market demand D(p) = 20 - p For p > 20: d₁(p) = 0 d₂(p) = 0 Market demand D(p) = 0 Therefore, D(p) = 50 - 3p, for p ≤ 15 20 - p, for 15 < p ≤ 20 0, for p > 20 — Market demand is sum of individual demands where positive. For p ≤ 15, both demand positive; for 15 < p ≤ 20, only first consumer demands; above 20, no demand.

Question 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?

Accepted Answer

Individual demand: d(p) = 10 - 3p for p ≤ 10/3, else 0.
Number of consumers = 20.
Market demand D(p) = 20 × d(p) = 20 × (10 - 3p) = 200 - 60p for p ≤ 10/3.
For p > 10/3, D(p) = 0.

Therefore,
D(p) =
 200 - 60p, for p ≤ 10/3
 0, for p > 10/3 — Market demand is sum of identical individual demands multiplied by number of consumers.

Theory of Consumer Behaviour

Theory of Consumer Behaviour — Study Notes

Introduction to Theory of Consumer Behaviour

2.1 UTILITY

Derivation of Demand Curve in the Case of a Single Commodity (Law of Diminishing Marginal Utility)

Practice Questions — Theory of Consumer Behaviour

All 5 Chapters in Introductory Microeconomics