Class 11 Economics (Mircoeconomics) Chapter 2 Theory of Consumer Behaviour

Key Concept: Law of Demand

c) Demand increases

[Solution Description] The law of demand states that, ceteris paribus (all else being equal), there is an inverse relationship between price and quantity demanded. Thus, when the price of a commodity decreases, the quantity demanded typically increases.

Key Concept: Substitutes and Complements Interaction, Multi-factor Demand Analysis

b) The demand for gasoline will decrease.

[Solution Description] When the price of cars increases, they become more expensive to own, leading to a decrease in their demand. Gasoline, being a complementary good to cars, will also see a decreased demand due to fewer people owning or using cars. Simultaneously, with a tax reduction on public transportation, public transport becomes cheaper, enticing more consumers towards it as opposed to using personal vehicles that require gasoline. Hence, both factors contribute to a decrease in the demand for gasoline.

Key Concept: Elasticity and Expenditure, Real World Application

d) Total revenue decreases by 20\%.

[Solution Description]

With price elasticity of demand $$e_D = -2$$, the demand is elastic, meaning quantity demanded changes at a greater percentage than the price change. A 10\% increase in price results in a 20\% decrease in quantity demanded ($$-2 \times 10\%$$). This significant drop in quantity implies total revenue will decrease because the loss in sales volume outweighs the gain from higher prices.

Key Concept: Demand Curve Shifts

b) The demand curve shifts rightward.

[Solution Description] A normal good is defined by its characteristic that when a consumer’s income increases, the demand for this good also increases. As a result, there is a rightward shift in the demand curve because consumers are willing to purchase more of this good at all price levels due to their increased purchasing power.

Key Concept: Complex MRS Analysis, Advanced Budget Line Changes

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

[Solution Description]

To analyze this problem, we need to understand the relationship between MRS, price ratio, and how changes in income and prices affect the consumer’s budget line.

The assertion states that if a consumer’s MRS is higher than the price ratio across all bundles, it would indicate that they are willing to trade off one good for another at a rate greater than what the market requires, suggesting a non-optimal choice where utility can be increased. This is true because when MRS $$>\frac{P_x}{P_y}$$, the consumer values good X more than its market value compared to good Y, indicating potential to shift towards more of good X to increase utility.

For the reason, when both income ($$I$$) and prices ($$P_x$$ and/or $$P_y$$) change, the budget line may shift due to changes in income and rotate due to changes in relative prices. Specifically:

1. An increase in income $$I$$ shifts the budget line outward parallel.

2. A change in prices alters the slope $$\left(-\frac{P_x}{P_y}\right)$$.

Thus, the Reason provided explains why the set of attainable bundles changes with simultaneous alterations in income and prices but does not directly explain the Assertion about MRS being higher consistently, hence not a direct explanation.

Key Concept: Optimum Bundle Location

d) At the point where the budget line is tangent to an indifference curve.

[Solution Description] For a rational consumer with monotonic preferences, the optimum bundle is found at the point where the budget line is tangent to the highest possible indifference curve. This location represents the maximum satisfaction given the budget constraint.

Key Concept: Indifference Curve Properties

c) Indifference curves never intersect.

[Solution Description] Indifference curves represent different combinations of goods providing the same utility level, and they are downward sloping because a consumer must give up some quantity of one good to gain more of another while maintaining the same utility. They do not intersect because that would imply inconsistent preferences.

Key Concept: Elasticity Calculation

c) -2

[Solution Description]

To find the price elasticity of demand, we use the formula:

$$eD = \frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}$$

Here, the percentage change in quantity demanded is +30\%, and the percentage change in price is -15\%.

Substitute these values into the formula:

$$eD = \frac{+30\%}{-15\%} = -2$$

Therefore, the price elasticity of demand is -2.

Key Concept: Demand Curve Slope

c) Because as price decreases, quantity demanded increases.

[Solution Description] The negative slope of the demand curve is explained by the law of demand, which states that as price decreases, the quantity demanded increases due to consumers being able to afford more and possibly substituting this good for others.

Key Concept: Positive Utility

c) Utility increases

[Solution Description] When the marginal utility of a good is positive, adding more of this good will increase the overall satisfaction or utility derived from it.

Key Concept: MRS and Budget Line

b) MRS is equal to the slope of the budget line.

[Solution Description] At the point of consumer equilibrium, the marginal rate of substitution equals the slope of the budget line. Mathematically, this is expressed as $$MRS = P_X/P_Y$$, where $$P_X$$ and $$P_Y$$ are prices of goods X and Y respectively. This indicates that the consumer is maximizing their utility given their budget constraint.

Key Concept: Budget Line Shift

c) It shifts outward

[Solution Description] The budget line equation is $$p_1x_1 + p_2x_2 = M$$. Doubling the income to $$2M$$ results in the entire budget line shifting outward, maintaining its slope but allowing more of both goods to be consumed.

Key Concept: Application of Formula

b) 23

[Solution Description]

To find the Total Utility after consuming 3 units, we use the formula for Total Utility:

$$TU_3 = MU_1 + MU_2 + MU_3$$

Substitute the given values:

$$TU_3 = 10 + 8 + 5 = 23$$

Therefore, the Total Utility after consuming 3 units is 23.

Key Concept: Price Ratio Impact

b) It becomes flatter

[Solution Description] The slope of the budget line is defined as $$-p_1/p_2$$. If the price of good $$x_2$$ triples, the new price is $$3p_2$$. Substituting this into the slope gives $$-p_1/(3p_2)$$, which is one-third of the original slope. Hence, the slope becomes flatter.

Key Concept: Income Effect

a) The demand curve shifts rightward because the product is a normal good.

[Solution Description] Since the consumer’s income has increased, the behavior depends on whether the product is a normal or an inferior good. For normal goods, the demand curve shifts rightward from $$D_1$$ to $$D_2$$. Hence, the correct scenario is that it shifts rightward if it’s a normal good.

Key Concept: Indifference Curve Analysis, Complex Bundle Analysis

b) Conflicting preferences

[Solution Description]

If two indifference curves intersect, it violates a fundamental concept in microeconomics: each point on an indifference curve represents combinations of goods that provide the same level of utility to the consumer.

Let’s analyze what happens when two indifference curves intersect at point A:

At point A, the consumer is indifferent between bundles on both curves, implying these offer the same satisfaction or utility.

By definition of indifference curves, any single curve represents different quantities or bundles offering identical satisfaction levels. Thus, intersection suggests equal utility from differing bundles on separate curves, conflicting with consistent preference ordering.

Therefore, it implies inconsistent preferences because differing bundles would give equal utility, suggesting conflicting information.

Correct interpretation: intersecting curves suggest contradictory evidence on consumer preferences.

Key Concept: Rational Consumer Behavior

a) Maximizes utility within budget

[Solution Description] A rational consumer aims to maximize utility subject to their budget constraint. This means choosing a bundle that lies on the highest attainable indifference curve, thus maximizing satisfaction or utility without exceeding the budget limit.

Key Concept: Law of Diminishing MRS

c) It implies that the indifference curve is convex.

[Solution Description] The law of diminishing marginal rate of substitution (MRS) implies that as a consumer substitutes one good for another, the willingness to give up more of one good to gain additional units of the other decreases. This diminishing willingness causes the indifference curve to be convex to the origin.

Key Concept: Elasticity and Expenditure, Real World Application

c) -3

[Solution Description]

When the price decreases, if the expenditure increases, it indicates that the demand is elastic. The relationship is given by:

$$\text{Percentage change in expenditure} = \frac{\Delta Q}{Q} + \frac{\Delta P}{P}$$

Given:

$$\frac{\Delta P}{P} = -10\%$$

Let $$\frac{\Delta Q}{Q} = x$$.

Since the total expenditure increased by 20\%, we have:

$$20\% = x – 10\%$$

Solving for $$x$$:

\begin{align*}

x &= 20\% + 10\%

x &= 30\%

\end{align*}

Thus, the percentage change in quantity demanded is 30\%. The price elasticity of demand $$E_d$$ can be calculated as:

$$E_d = \frac{\Delta Q/Q}{\Delta P/P} = \frac{30\%}{-10\%} = -3$$

Therefore, the price elasticity of demand is -3.

Key Concept: Utility Measurement

c) In numbers

[Solution Description] In cardinal utility analysis, utility is measured in actual numbers, allowing for arithmetic operations like addition and subtraction.

Key Concept: Elasticity Interpretation

b) Demand is inelastic

[Solution Description] Calculate the elasticity using $$e_D = \frac{\text{percentage change in demand}}{\text{percentage change in price}}$$. Here, percentage change in demand is 10\% and percentage change in price is -15\%. Therefore:

$$e_D = \frac{10}{-15} = -\frac{2}{3}.$$

Since $$e_D < 1$$, demand is inelastic.

Key Concept: Income Effect

a) Real income increases; demand increases

[Solution Description] When the price of a normal good decreases, the purchasing power of a consumer’s income effectively increases, meaning they can now afford to buy more with the same amount of money. This increase in real income leads to an increase in demand for the normal good due to the positive income effect.

Key Concept: Income Effect

c) The demand increases

[Solution Description] For a normal good, as consumer income increases, the quantity demanded also tends to increase. This is because normal goods are those for which demand rises with an increase in income.

Key Concept: Concept Identification

c) Expenditure remains unchanged

[Solution Description] Since $$eD = -1$$, it indicates unit elasticity. In this scenario, a change in price does not change the expenditure on the good because the percentage change in quantity demanded is equal and opposite to the percentage change in price.

Key Concept: Basic Concept

c) At the midpoint of the demand curve

[Solution Description] The elasticity of a linear demand curve is equal to 1 at its midpoint.

Key Concept: Zero and Negative Marginal Utility

c) Total utility decreases

[Solution Description] When marginal utility becomes negative, it indicates that consuming an additional unit of a commodity causes the total utility to decrease. This reflects a situation where further consumption leads to dissatisfaction or disutility.

Key Concept: Convexity Reason

c) Diminishing MRS

[Solution Description] Indifference curves are typically convex to the origin due to the law of diminishing marginal rate of substitution (MRS). As a consumer moves along an indifference curve, sacrificing more of one good for additional units of another, the willingness to trade diminishes because each extra unit of a good yields less additional satisfaction, maintaining the balance between goods.

Key Concept: Slope Implication

c) Consumers must trade off one good for another

[Solution Description] The downward slope of an indifference curve indicates that to maintain the same level of utility, a consumer must trade off one good for another. This reflects the concept of monotonic preferences, where more of one good results in less of another while keeping utility constant.

Key Concept: Optimum Bundle Location, Indifference Curve Tangency

a) $$(x_1, x_2) = (5, 2.5)$$

[Solution Description] To find the optimum bundle where an indifference curve is tangent to the budget line, we set the marginal rate of substitution (MRS) equal to the price ratio $$\frac{p_1}{p_2}$$. For the utility function $$U(x_1, x_2) = x_1^{0.5} \cdot x_2^{0.5}$$, the MRS is calculated as:

$$\text{MRS} = \frac{\partial U/\partial x_1}{\partial U/\partial x_2} = \frac{0.5x_1^{-0.5}x_2^{0.5}}{0.5x_1^{0.5}x_2^{-0.5}} = \frac{x_2}{x_1}$$

Setting the MRS equal to the price ratio:

$$\frac{x_2}{x_1} = \frac{p_1}{p_2} = \frac{5}{10} = 0.5$$

Solving this gives $$x_2 = 0.5x_1$$. Substituting into the budget constraint:

$$5x_1 + 10(0.5x_1) = 50

5x_1 + 5x_1 = 50

10x_1 = 50

x_1 = 5$$

Plugging back $$x_1 = 5$$ into $$x_2 = 0.5x_1$$, we get $$x_2 = 0.5 \times 5 = 2.5$$. Thus, the optimum bundle is $$(x_1, x_2) = (5, 2.5)$$.

Key Concept: MRS Calculation

c) 3 pens per book

[Solution Description] To calculate the MRS, use the formula $$MRS_{Y/X} = |\Delta Y / \Delta X|$$, where $$\Delta Y$$ and $$\Delta X$$ represent the change in quantities of the two goods. Moving from C to D, $$\Delta$$ Books = 3 – 2 = 1, and $$\Delta$$ Pens = 5 – 8 = -3. Therefore, $$MRS = |(-3)/1| = 3$$. This means the consumer is willing to give up 3 pens for each additional book.

Key Concept: Price Change Impact

b) It pivots outward around the vertical intercept

[Solution Description]

Halving the price of good 1 decreases its per-unit cost, effectively increasing the maximum amount of good 1 that can be bought with the same income, which pivots the budget line outward around the vertical intercept. The new horizontal intercept will be at $$2M/p1$$, changing from the original $$M/p1$$.

Key Concept: Utility Variation

d) Total utility increases at a decreasing rate.

[Solution Description] According to the Law of Diminishing Marginal Utility, as more units of a commodity are consumed, the additional satisfaction (marginal utility) derived from each subsequent unit decreases. This means that although total utility increases with consumption, its rate of increase diminishes.

Key Concept: Basic Concept

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

[Solution Description]

The assertion states that the demand curve results from the inverse relation between price and quantity demanded, which is correct. This relationship is depicted by a downward sloping demand curve. The reason correctly identifies the mechanisms through which this occurs: when prices fall, consumers substitute toward the cheaper good (substitution effect), and their real income effectively increases allowing them to purchase more (income effect). Both are true statements and the reasoning provided directly explains why there is an inverse relationship.

Key Concept: Mathematical Representation, Real-world Implications

a) Provides clarity in market demand prediction.

[Solution Description] Non-intersecting indifference curves ensure clear hierarchical preferences, implying consistent utility rankings. In markets, this translates into predictable demand patterns and stable pricing mechanisms, facilitating optimal allocation of resources without contradictions in consumer behavior.