Theory of Consumer BehaviourClass 12 Introductory Microeconomics NCERT Solutions

The budget set of a consumer refers to the collection of all consumption bundles (combinations of two goods) that the consumer can afford to buy with her given income at the prevailing market prices. It includes all bundles where the total expenditure is less than or equal to the consumer's income.

Mathematically, if a consumer has an income M, and the prices of two goods (say, bananas and mangoes) are p₁ and p₂ respectively, the budget set consists of all bundles (x₁, x₂) such that: p₁x₁ + p₂x₂ ≤ M

Here, x₁ and x₂ represent the quantities of the two goods, which must be greater than or equal to zero.

The budget line represents all the consumption bundles (combinations of two goods) that a consumer can purchase by spending her entire income. It is a graphical representation of all bundles that cost exactly equal to the consumer's income (M). The budget line forms the boundary of the budget set.

The equation of the budget line is: p₁x₁ + p₂x₂ = M

Where:

Points on the budget line represent bundles that exhaust the consumer's income, while points below it are affordable but do not use the entire income.

The budget line is downward sloping because a consumer has a fixed income. To purchase more of one good, the consumer must purchase less of the other good. This inverse relationship between the quantities of the two goods gives the budget line its negative slope.

If a consumer decides to increase the consumption of good 1 (say, bananas), she has to spend more on it. Since her income is constant, she must reduce her expenditure on good 2 (mangoes) to stay within her budget. This trade-off is dictated by the market prices of the two goods.

The slope of the budget line is given by the price ratio, -p₁/p₂. The negative sign indicates that the line slopes downwards from left to right, signifying that an increase in the quantity of one good is only possible with a decrease in the quantity of the other.

Given:

(i) Equation of the budget line: The equation of the budget line is p₁x₁ + p₂x₂ = M. Substituting the given values: 4x₁ + 5x₂ = 20

(ii) Consumption of good 1 with entire income: If the consumer spends her entire income on good 1, the quantity of good 2 consumed (x₂) will be 0. Quantity of good 1 = M / p₁ = 20 / 4 = 5 units.

(iii) Consumption of good 2 with entire income: If the consumer spends her entire income on good 2, the quantity of good 1 consumed (x₁) will be 0. Quantity of good 2 = M / p₂ = 20 / 5 = 4 units.

(iv) Slope of the budget line: The slope of the budget line is given by the formula -p₁ / p₂. Slope = -4 / 5 = -0.8.

If the consumer's income increases from Rs 20 to Rs 40 while the prices of the goods remain unchanged (p₁ = Rs 4, p₂ = Rs 5), the consumer can now afford to buy more of both goods. This results in a parallel outward shift of the budget line.

Given:

When the price of good 2 decreases, the budget line will pivot outwards around the horizontal intercept.

Therefore, the budget line pivots outwards from the vertical axis, becoming flatter, while the horizontal intercept stays fixed.

If both the prices and the consumer's income double, the budget set and the budget line will remain unchanged.

Let the original prices be p₁ and p₂ and the income be M. The original budget line equation is: p₁x₁ + p₂x₂ = M

Now, let the new prices be p'₁ = 2p₁ and p'₂ = 2p₂, and the new income be M' = 2M. The new budget line equation is: 2p₁x₁ + 2p₂x₂ = 2M

If we divide the entire new equation by 2, we get: p₁x₁ + p₂x₂ = M

This is identical to the original budget line equation. The horizontal intercept (M'/p'₁ = 2M/2p₁ = M/p₁), the vertical intercept (M'/p'₂ = 2M/2p₂ = M/p₂), and the slope (-p'₁/p'₂ = -2p₁/2p₂ = -p₁/p₂) all remain exactly the same. Since the budget line has not changed, the set of affordable bundles (the budget set) also remains unchanged.

When a consumer spends her entire income on a bundle of goods, that bundle lies on her budget line. The total expenditure on the bundle is equal to her income (M).

Given:

The consumer's income (M) can be calculated using the budget line equation: M = p₁x₁ + p₂x₂ M = (6 × 6) + (8 × 8) M = 36 + 64 M = 100

Therefore, the consumer's income is Rs 100.

Given:

The budget constraint is 10x₁ + 10x₂ ≤ 40, which simplifies to x₁ + x₂ ≤ 4. Since goods are available only in integer units, x₁ and x₂ must be non-negative integers.

(i) All available bundles (the budget set): We need to find all pairs of non-negative integers (x₁, x₂) such that their sum is less than or equal to 4.

Total available 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 that cost exactly Rs 40: These are the bundles that lie on the budget line, where 10x₁ + 10x₂ = 40, or x₁ + x₂ = 4. These bundles are:

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

Specifically, a consumer's preferences are monotonic if, for any two bundles (x₁, x₂) and (y₁, y₂):

For example, a consumer with monotonic preferences will always prefer the bundle (10 bananas, 10 mangoes) over the bundle (9 bananas, 10 mangoes) because the first bundle contains more of one good and the same amount of the other.

No, a consumer with monotonic preferences cannot be indifferent between the bundles (10, 8) and (8, 6).

According to the principle of monotonic preferences, a consumer always prefers a bundle that contains more of at least one good and no less of the other.

Let us compare the two bundles:

Bundle (10, 8) contains more of both good 1 (10 > 8) and good 2 (8 > 6) compared to bundle (8, 6). Therefore, a consumer with monotonic preferences must strictly prefer the bundle (10, 8) to the bundle (8, 6). She cannot be indifferent between them.

If a consumer's preferences are monotonic, we can establish a clear preference ranking among the bundles (10, 10), (10, 9), and (9, 9) based on the 'more is better' principle.

Based on these comparisons, the consumer's preference ranking will be: (10, 10) is preferred to (10, 9), which is preferred to (9, 9).

No, the preferences of my friend are not monotonic.

Monotonic preferences imply that a consumer will always prefer a bundle that has more of at least one good and no less of the other. Let us compare the two bundles:

Bundle (6, 6) has more of good 1 (6 > 5) and the same amount of good 2 as bundle (5, 6). According to the assumption of monotonic preferences, the friend should strictly prefer the bundle (6, 6) to the bundle (5, 6).

Since the friend is indifferent between the two bundles, their preferences violate the principle of monotonicity.

To find the market demand function, we perform a horizontal summation of the individual demand functions, D(p) = d₁(p) + d₂(p). We must consider different price ranges.

The complete market demand function is:

The market demand is the sum of the individual demands of all consumers. Since there are 20 consumers with identical demand functions, we can find the market demand by multiplying the individual demand function by 20.

Individual demand function: d(p) = 10 - 3p Number of consumers = 20

Market demand D(p) = 20 × d(p) D(p) = 20 × (10 - 3p) D(p) = 200 - 60p

This is valid for the price range where individual demand is positive, i.e., p ≤ 10/3. For any price greater than 10/3, the individual demand is 0, so the market demand will also be 0.

Therefore, the market demand function is:

To calculate the market demand for the good, we add the quantities demanded by each consumer (d₁ and d₂) at each price level (p). The market demand (Dm) is the horizontal summation of individual demands.

Dm = d₁ + d₂

We can calculate this for each price given in the table:

The market demand schedule is as follows:

A normal good is a good for which the demand increases as the consumer's income increases, and decreases as the consumer's income decreases, holding other factors like price constant. There is a positive relationship between a consumer's income and the quantity demanded of a normal good.

For example, if a consumer's income rises, they might choose to buy more full-cream milk or better quality clothing. These would be considered normal goods for that consumer. Most goods fall into this category.

An inferior good is a good for which the demand decreases as the consumer's income increases, and increases as the consumer's income decreases. There is an inverse relationship between a consumer's income and the quantity demanded of an inferior good.

This happens because as consumers become wealthier, they switch from consuming these lower-quality goods to consuming better-quality substitutes.

Substitutes are goods that can be used in place of each other to satisfy a particular want. The demand for a good usually moves in the same direction as the price of its substitutes. If the price of one substitute good increases, the demand for the other substitute good will rise as consumers switch to the relatively cheaper option.

Complements, or complementary goods, are goods that are consumed together. The demand for a good moves in the opposite direction of the price of its complementary good. If the price of one complementary good increases, the demand for the other good will fall because the overall cost of using them together has risen.

Price elasticity of demand (eD) is a measure of the degree of responsiveness of the quantity demanded of a good to a change in its price. It quantifies how much the demand for a good changes when its price changes. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

The formula is: eD = (Percentage change in quantity demanded) / (Percentage change in the price of the good)

Given:

First, we calculate the percentage change in quantity demanded: Percentage change in quantity = [(Q₂ - Q₁) / Q₁] × 100 = [(20 - 25) / 25] × 100 = [-5 / 25] × 100 = -20%

Next, we calculate the percentage change in price: Percentage change in price = [(P₂ - P₁) / P₁] × 100 = [(5 - 4) / 4] × 100 = [1 / 4] × 100 = 25%

Now, we calculate the price elasticity of demand (eD): eD = (Percentage change in quantity demanded) / (Percentage change in price) eD = -20% / 25% eD = -0.8

The price elasticity of demand is -0.8. Since the absolute value (0.8) is less than 1, the demand for the good is inelastic.

Given the linear demand curve: D(p) = q = 10 - 3p

The formula for price elasticity of demand for a linear curve is: eD = (-b) × (p/q) Where 'b' is the slope coefficient of price in the demand function.

From the equation, we can see that b = 3.

Step 1: Find the quantity (q) at the given price (p = 5/3). q = 10 - 3p q = 10 - 3(5/3) q = 10 - 5 q = 5

Step 2: Calculate the elasticity using the formula. eD = (-b) × (p/q) eD = (-3) × ( (5/3) / 5 ) eD = (-3) × (5 / 15) eD = (-3) × (1 / 3) eD = -1

Therefore, the elasticity of demand at the price of 5/3 is -1, which means the demand is unitary elastic at that point.

Given:

We use the formula for price elasticity of demand: eD = (Percentage change in quantity demanded) / (Percentage change in price)

-0.2 = (Percentage change in quantity demanded) / 5%

To find the percentage change in quantity demanded, we rearrange the formula: Percentage change in quantity demanded = eD × Percentage change in price Percentage change in quantity demanded = -0.2 × 5% Percentage change in quantity demanded = -1%

The negative sign indicates a decrease. Therefore, the demand for the good will go down by 1%.

Given:

The relationship between price elasticity and total expenditure is as follows: When demand is price inelastic (i.e., the absolute value of elasticity is less than 1), total expenditure moves in the same direction as the price change.

In this case, the absolute value of the elasticity is |eD| = |-0.2| = 0.2, which is less than 1. This means the demand for the good is inelastic.

Since the price of the good increases by 10%, and the demand is inelastic, the total expenditure on the good will increase.

Explanation: A 10% increase in price will lead to a smaller percentage decrease in quantity demanded (specifically, -0.2 × 10% = -2%). Because the price rises more than the quantity falls, the total expenditure (Price × Quantity) will rise.

The relationship between a price change, the change in expenditure, and the price elasticity of demand helps us answer this question.

Given:

We observe that the price and the total expenditure moved in opposite directions (price went down, expenditure went up).

According to the rules of elasticity and expenditure:

This means that the percentage increase in quantity demanded was greater than the percentage decrease in price. Therefore, we can conclude that the absolute value of the price elasticity of demand is greater than 1 (|eD| > 1).