Introduction to Consumer Behaviour

This chapter explores the behaviour of an individual consumer. A central theme is the problem of choice, where a consumer must decide how to spend their limited income on various goods and services to achieve the greatest possible satisfaction.

The 'best' or optimal combination of goods for any consumer depends on two main factors:

1. Consumer's Preferences: This refers to the consumer's likes and dislikes, which determine the satisfaction or utility they get from different combinations of goods.
2. Consumer's Budget: This refers to what the consumer can afford to buy, which is determined by the prices of the goods and the consumer's income.

We will examine two primary approaches to understanding consumer behaviour:

• Cardinal Utility Analysis: Assumes that satisfaction (utility) can be measured in numerical units.
• Ordinal Utility Analysis: Assumes that a consumer can only rank their preferences for different combinations of goods, without assigning specific numerical values to their satisfaction.

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Preliminary Notations and Assumptions

For the sake of simplicity, our analysis will focus on a situation where the consumer chooses between only two goods: bananas and mangoes.

• A combination of the two goods is called a consumption bundle.
• We use $x_1$ to denote the quantity of bananas and $x_2$ to denote the quantity of mangoes.
• A bundle is represented as $(x_1, x_2)$. For example, the bundle (5, 10) consists of 5 bananas and 10 mangoes.

Utility

A consumer's demand for a commodity is based on the utility it provides.

Utility is defined as the want-satisfying capacity of a commodity. The more intense the desire or need for a commodity, the greater the utility derived from it.

Utility is a subjective concept:

• Different people can get different levels of utility from the same good. A chocolate lover gets more utility from a chocolate bar than someone who dislikes it.
• Utility can change with time and place. A room heater provides more utility in Ladakh during winter than in Chennai during summer.

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Cardinal Utility Analysis

This approach, primarily associated with neoclassical economists like Alfred Marshall, is built on the fundamental assumption that utility is cardinal, meaning it is quantifiable and can be measured in objective, numerical units. These hypothetical units of satisfaction are called 'utils'. For example, a consumer might say they get 10 utils of satisfaction from the first apple and 8 utils from the second.

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Measures of Utility

There are two important measures of utility that form the basis of this analysis:

1. Total Utility (TU): This refers to the aggregate or total satisfaction a consumer derives from consuming all the units of a specific commodity. It is the sum of the marginal utilities of all the units consumed. As the quantity consumed increases, total utility generally increases, up to a certain point.

   Formula: $ TU_n = \sum_{i=1}^{n} MU_i $

2. Marginal Utility (MU): This is the additional utility gained from the consumption of one more (or one successive) unit of a commodity. It is the change in total utility when one more unit is consumed.

   Formulas:

   $ MU_n = TU_n - TU_{n-1} $

   Or, more generally, $ MU = \frac{\Delta TU}{\Delta Q} $, where $\Delta TU$ is the change in total utility and $\Delta Q$ is the change in quantity consumed.

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Law of Diminishing Marginal Utility (DMU)

A fundamental principle of cardinal analysis is the Law of Diminishing Marginal Utility. It was formulated by H.H. Gossen and later popularized by Alfred Marshall. The law states that as a consumer consumes more and more units of a commodity, the marginal utility derived from each successive unit goes on diminishing, assuming the consumption of other commodities remains constant.

The reason behind this law is rooted in human psychology. As we acquire more of a commodity, the intensity of our want for that commodity decreases. For instance, the first glass of water to a thirsty person provides immense satisfaction (high MU), the second provides less, and the third even less, until a point where another glass might provide no satisfaction at all (zero MU) or even discomfort (negative MU).

Assumptions of the Law of DMU

• Cardinal Measurement: Utility can be measured in numerical units (utils).
• Continuous Consumption: The units of the commodity are consumed in quick succession without a significant time gap.
• Standard Units: The units consumed are of a standard size and quality (e.g., a full cup of tea, not a spoonful).
• Rational Consumer: The consumer is rational and aims to maximize their total utility.
• Constant Marginal Utility of Money: The utility derived from each unit of money (e.g., one rupee) remains constant for the consumer. This is a crucial and often criticized assumption.

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Relationship between Total Utility and Marginal Utility

The relationship between TU and MU can be clearly seen from the table and the corresponding graph.

Units	Total Utility (TU)	Marginal Utility (MU)
1	12	12
2	18	6
3	22	4
4	24	2
5	24	0
6	22	-2

We can observe three distinct phases in the relationship:

1. Phase 1: As long as MU is positive and falling (from unit 1 to 4), TU increases, but at a diminishing rate. Each additional unit adds to the total, but it adds less than the previous unit.
2. Phase 2: When TU reaches its maximum (at 5 units), MU becomes zero. This is known as the point of satiety or saturation. The consumer derives no additional satisfaction from this unit.
3. Phase 3: When TU starts to fall (at 6 units), MU becomes negative. Consuming this additional unit actually reduces the total satisfaction, leading to disutility.

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Derivation of the Demand Curve from DMU

The Law of Diminishing Marginal Utility is the foundation for the Law of Demand within the cardinal approach. To understand this, we first need to define a consumer's equilibrium for a single commodity.

A rational consumer will purchase a good up to the point where the marginal utility they receive from the last unit is equal to the price they pay for it. To be precise, the marginal utility of the good ($MU_x$) should equal the marginal utility of the money ($MU_m$) they give up, which is represented by the price ($P_x$).

The equilibrium condition is:

$ \frac{MU_x}{P_x} = MU_m $ or, assuming $MU_m = 1$, the condition simplifies to: $ MU_x = P_x $

Let's use our table to derive a demand schedule:

• Suppose the price of the good is ₹6 per unit. The consumer will buy units as long as $MU_x \ge 6$. From the table, they will buy 2 units (the MU of the 2nd unit is 6). So, at P=₹6, Q=2.
• Now, suppose the price falls to ₹4 per unit. The consumer's condition is now $MU_x \ge 4$. They will buy 3 units (the MU of the 3rd unit is 4). So, at P=₹4, Q=3.
• If the price falls further to ₹2 per unit, the condition becomes $MU_x \ge 2$. They will now buy 4 units. So, at P=₹2, Q=4.

By plotting these price-quantity combinations (P,Q) like (₹6, 2), (₹4, 3), and (₹2, 4), we trace out a downward-sloping demand curve. This demonstrates that because marginal utility diminishes, a consumer is induced to buy more only when the price falls. This inverse relationship is the essence of the Law of Demand.

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Limitations of Cardinal Utility Analysis

• Utility is Subjective: The idea that a psychological concept like satisfaction can be measured in objective, cardinal numbers is highly unrealistic.
• Constant MU of Money: The assumption that the marginal utility of money remains constant is flawed. The utility of a rupee is much higher for a poor person than for a wealthy person.
• Ignores Interdependence of Goods: The analysis typically focuses on one good at a time and does not effectively explain consumer choice when dealing with substitutes and complements.

Due to these limitations, economists developed the more refined and realistic Ordinal Utility Analysis.

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Ordinal Utility Analysis

Ordinal utility analysis, developed by economists like J.R. Hicks and R.G.D. Allen, overcomes a major drawback of the cardinal approach. It is based on a more realistic assumption: consumers do not measure utility in absolute numbers, but they can and do rank different consumption bundles based on the level of satisfaction each provides. A consumer can definitively say they prefer bundle A to bundle B, or are indifferent between them, without needing to specify *how much* more satisfaction A provides.

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Indifference Curve (IC)

An indifference curve is a locus of points representing various consumption bundles, each of which provides the consumer with the same level of total utility or satisfaction. Because all bundles on the curve offer the same satisfaction, the consumer is said to be 'indifferent' about which bundle they consume.

Since it is assumed that more of a good is always better (monotonic preferences), if a consumer gains more of one good (e.g., bananas), they must give up some amount of the other good (mangoes) to be brought back to the same, original level of satisfaction. For this reason, an indifference curve is always downward sloping.

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Marginal Rate of Substitution (MRS)

The Marginal Rate of Substitution (MRS) measures the rate at which a consumer is psychologically willing to substitute one good for another while maintaining the same level of utility. It quantifies the amount of one good (say, mangoes) that a consumer is willing to sacrifice to obtain one additional unit of another good (bananas).

Geometrically, the MRS is the absolute value of the slope of the indifference curve at any given point.

$ MRS_{12} = \left| \frac{\Delta x_2}{\Delta x_1} \right| $ = Amount of Good 2 (mangoes) sacrificed for one additional unit of Good 1 (bananas).

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Law of Diminishing Marginal Rate of Substitution

A key principle of this analysis is the Law of Diminishing Marginal Rate of Substitution. It states that as a consumer increases the consumption of one good ($x_1$), the amount of the other good ($x_2$) they are willing to give up to get one more unit of $x_1$ decreases.

The intuition is simple: As a consumer gets more and more bananas, the marginal utility of an additional banana falls. Simultaneously, as they have fewer mangoes, the marginal utility of each remaining mango rises. Consequently, they are willing to sacrifice fewer mangoes for each extra banana.

Let's illustrate with a schedule:

Combination	Quantity of bananas ($x_1$)	Quantity of Mangoes ($x_2$)	MRS ($ \Delta x_2 / \Delta x_1 $)
A	1	15	-
B	2	12	3 Mangoes for 1 Banana (3:1)
C	3	10	2 Mangoes for 1 Banana (2:1)
D	4	9	1 Mango for 1 Banana (1:1)

As the consumer moves from A to B, they give up 3 mangoes for 1 banana. From B to C, they are only willing to give up 2 mangoes. From C to D, they will only give up 1 mango. The MRS is clearly diminishing.

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Shape of an Indifference Curve

The Law of Diminishing MRS is what gives a standard indifference curve its characteristic shape: convex to the origin. As we move down the curve, it becomes flatter, visually representing the falling MRS.

However, indifference curves can take other shapes for special types of goods:

• Perfect Substitutes: If two goods are perfect substitutes (e.g., a five-rupee coin and a five-rupee note), the consumer is willing to exchange them at a constant rate. The MRS is constant, and the indifference curve is a straight line sloping downwards.
• Perfect Complements: If two goods are perfect complements (e.g., a left shoe and a right shoe), they are consumed in a fixed proportion. Gaining more of one good without the other provides no extra utility. The indifference curves for such goods are L-shaped.

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Monotonic Preferences

This is a standard assumption about a consumer's preferences. Monotonic preferences mean that a consumer will always prefer a bundle that has more of at least one good and no less of the other good. In simple terms, it means "more is better".

For example, a consumer will always prefer the bundle (10 bananas, 8 mangoes) over the bundle (9 bananas, 8 mangoes) because the first bundle contains more bananas with the same number of mangoes.

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Indifference Map and Features of Indifference Curves

An indifference map is a set or family of indifference curves, each representing a different level of satisfaction. It provides a complete picture of a consumer's preferences.

Indifference curves have three key properties:

1. Indifference curves slope downwards from left to right. As explained earlier, this reflects the trade-off required to maintain constant utility. If a curve were upward sloping, it would mean a consumer could get more of both goods and be equally satisfied, which violates the assumption that more is better (monotonicity).
2. A higher indifference curve represents a higher level of utility. This is a direct consequence of monotonic preferences. Any bundle on a higher indifference curve (e.g., IC2) must contain more of at least one good than a bundle on a lower curve (e.g., IC1). Since more is preferred, the higher curve must represent a higher level of satisfaction.
3. Two indifference curves never intersect each other. Intersection would lead to a logical contradiction. Suppose two curves, IC1 and IC2, intersect at point A. Let B be another point on IC1 and C be another point on IC2.
   • Since A and B are on IC1, the consumer is indifferent between them (A ~ B).
   • Since A and C are on IC2, the consumer is indifferent between them (A ~ C).
   • By the principle of transitivity, if A ~ B and A ~ C, then B ~ C.
   • However, by looking at the graph, bundle B might have more of one good than C, meaning B should be preferred to C (by monotonicity). This contradicts the conclusion that B ~ C. Therefore, indifference curves cannot intersect.

The Consumer’s Budget

While an indifference map represents what a consumer *wants* to do (their preferences), the consumer's budget represents what they *can* do (their constraints). A consumer's choice is fundamentally constrained by two factors: their fixed income and the market prices of goods. They can only purchase combinations of goods that they can afford.

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Budget Set and Budget Line

To formalize this constraint, let's assume a consumer has a fixed income, denoted by $M$, which they can spend on two goods: bananas (quantity $x_1$) and mangoes (quantity $x_2$). The market price for a unit of bananas is $p_1$, and for mangoes, it is $p_2$.

• The total expenditure on a chosen bundle $(x_1, x_2)$ is calculated by multiplying the quantity of each good by its price and summing the results: $p_1x_1 + p_2x_2$.
• The consumer can afford any bundle as long as the total expenditure does not exceed their income. This fundamental rule is the budget constraint, expressed as an inequality:

  $ p_1x_1 + p_2x_2 \le M $

• The Budget Set is the collection of all possible consumption bundles that the consumer can afford. It includes all bundles that satisfy the budget constraint. Graphically, it is the entire area on and below the budget line.
• The Budget Line represents the specific set of bundles where the consumer spends their entire income. It forms the outer boundary of the budget set. Its equation is:

  $ p_1x_1 + p_2x_2 = M $

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Properties of the Budget Line

Intercepts

The budget line intersects the two axes at points that represent the maximum amount of each good the consumer can buy if they spend their entire income on that good alone.

• Vertical Intercept ($x_2$-axis): This is found by setting $x_1=0$. It gives the maximum quantity of mangoes the consumer can buy: $x_2 = \frac{M}{p_2}$.
• Horizontal Intercept ($x_1$-axis): This is found by setting $x_2=0$. It gives the maximum quantity of bananas the consumer can buy: $x_1 = \frac{M}{p_1}$.

Slope of the Budget Line

The slope of the budget line indicates the rate at which the market allows the consumer to trade one good for another. It is also known as the price ratio.

Derivation of the Slope

We can derive the slope in two ways:

1. By Rearranging the Equation:

We can express the budget line equation in the standard slope-intercept form ($y = mx + c$), where $x_2$ is our 'y' and $x_1$ is our 'x'.

1. Start with the budget line equation: $p_1x_1 + p_2x_2 = M$
2. Isolate the term with $x_2$: $p_2x_2 = M - p_1x_1$
3. Divide by $p_2$ to solve for $x_2$: $x_2 = \frac{M}{p_2} - \frac{p_1}{p_2}x_1$

In this form, the coefficient of $x_1$ is the slope. Therefore, the slope of the budget line is $-\frac{p_1}{p_2}$.

2. Using Calculus (or Deltas):

Consider two points on the budget line, $(x_1, x_2)$ and $(x_1 + \Delta x_1, x_2 + \Delta x_2)$. Both points must satisfy the budget equation.

1. $p_1x_1 + p_2x_2 = M$         ... (i)
2. $p_1(x_1 + \Delta x_1) + p_2(x_2 + \Delta x_2) = M$         ... (ii)
3. Subtracting equation (i) from (ii), we get: $p_1\Delta x_1 + p_2\Delta x_2 = 0$
4. Rearranging to find the slope, which is the ratio of the change in $x_2$ to the change in $x_1$:
5. $p_2\Delta x_2 = -p_1\Delta x_1$
6. $\frac{\Delta x_2}{\Delta x_1} = -\frac{p_1}{p_2}$

The absolute value of the slope, $\frac{p_1}{p_2}$, is the price ratio. It tells us the opportunity cost of consuming one more unit of good 1. To buy one more banana (costing $p_1$), the consumer must give up $p_1/p_2$ units of mangoes.

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Changes in the Budget Set

The budget set is not fixed; it changes when the consumer's income or the prices of the goods change.

• Change in Income:

  When income changes but prices remain constant, the slope of the budget line ($ -p_1/p_2 $) does not change. However, the intercepts ($ M/p_1 $ and $ M/p_2 $) do change. This results in a parallel shift of the budget line.

  • An increase in income ($M' > M$) causes a parallel outward shift of the budget line, enlarging the budget set. The consumer can now afford more of both goods.
  • A decrease in income ($M' < M$) causes a parallel inward shift of the budget line, shrinking the budget set. The consumer's purchasing power has fallen.
• Change in Price:

  When the price of one good changes while income and the other price remain constant, one intercept stays the same while the other moves. This causes the budget line to pivot or rotate.

  • A decrease in the price of bananas ($p_1' < p_1$) will not change the vertical intercept ($M/p_2$), but it will increase the horizontal intercept ($M/p_1'$). The budget line pivots outwards and becomes flatter.
  • An increase in the price of bananas ($p_1' > p_1$) will not change the vertical intercept, but it will decrease the horizontal intercept. The budget line pivots inwards and becomes steeper.

Optimal Choice of the Consumer

A rational consumer, as assumed in economics, aims to maximize their total satisfaction or utility. This involves making the best possible choice given their limitations. The problem of optimal choice, therefore, is about combining the consumer's preferences (represented by the indifference map) with their constraints (represented by the budget line) to find the single consumption bundle that yields the highest utility.

The consumer's optimal choice, also known as the consumer's equilibrium, must lie on the budget line. We can understand why by considering all possibilities:

• Points above the budget line: These bundles (like any point on IC3 in the diagram below) are more desirable to the consumer as they lie on a higher indifference curve. However, they are unaffordable as they cost more than the consumer's income.
• Points below the budget line: These bundles (like any point on IC1 that is inside the budget set) are affordable, but they are not optimal. The consumer is not spending their entire income. By moving to a point on the budget line, they can get more of one or both goods, and according to the principle of monotonic preferences, reach a higher level of satisfaction.

Therefore, the optimal bundle must be a point on the budget line itself.

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Condition for Consumer Equilibrium

Out of all the affordable bundles on the budget line, the consumer will choose the one that lies on the highest possible indifference curve. This occurs at the point where the budget line is just tangent to an indifference curve.

In the diagram, the budget line touches indifference curve IC2 at point E. This is the consumer's optimum.

• Any other point on the budget line (like F or G) lies on a lower indifference curve (IC1) and therefore provides less satisfaction.
• Point E is the only point on the highest attainable indifference curve (IC2) that is also affordable.

At the point of tangency (E), the slope of the indifference curve is exactly equal to the slope of the budget line. This gives us the mathematical condition for equilibrium:

Slope of Indifference Curve = Slope of Budget Line

$ \left| -MRS \right| = \left| -\frac{p_1}{p_2} \right| $

This simplifies to the fundamental equilibrium condition:

$ MRS = \frac{p_1}{p_2} $

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Equality of the Marginal Rate of Substitution and the Price Ratio

The equilibrium condition $ MRS = p_1/p_2 $ is not just a mathematical result; it has a powerful economic intuition. It represents a state of balance where the consumer has no incentive to change their consumption pattern.

• $MRS$ is the rate at which the consumer is willing to trade good 2 for good 1 (their personal, subjective valuation).
• $p_1/p_2$ (the price ratio) is the rate at which the market allows them to trade good 2 for good 1 (the objective market valuation).

Equilibrium is reached only when the consumer's subjective valuation of the goods is perfectly aligned with the market's objective valuation. To see why, consider situations where they are not equal:

Case 1: $ MRS > \frac{p_1}{p_2} $

Suppose $MRS = 2$ and $p_1/p_2 = 1$.

• Consumer's Willingness: The consumer is willing to give up 2 mangoes to get 1 more banana. This means they value the next banana twice as much as a mango.
• Market's Rate: The market only requires them to give up 1 mango to get 1 banana.

In this situation, the consumer is not at an optimum. They can increase their total satisfaction by buying more bananas and fewer mangoes. The market is offering them a "better deal" on bananas than their own personal valuation. By reallocating their spending towards bananas, they will move down along the budget line and reach a higher indifference curve. This reallocation will continue until their MRS falls and becomes equal to the price ratio.

Case 2: $ MRS < \frac{p_1}{p_2} $

Suppose $MRS = 0.5$ and $p_1/p_2 = 1$.

• Consumer's Willingness: The consumer is only willing to give up 0.5 mangoes to get 1 more banana. This means they value the next banana only half as much as a mango.
• Market's Rate: The market requires them to give up 1 mango to get 1 banana.

Here again, the consumer is not at an optimum. The value they place on an extra banana is less than what the market charges for it (in terms of mangoes). They can increase their satisfaction by buying fewer bananas and more mangoes. By reallocating their spending towards mangoes, they will move up along the budget line, again reaching a higher indifference curve. This will continue until their MRS rises and becomes equal to the price ratio.

Thus, the equilibrium point $MRS = p_1/p_2$ is the only point where the consumer cannot make themselves better off by reallocating their income.

Demand

Demand is an economic principle that refers to a consumer's desire to purchase goods and services and their willingness to pay a specific price for them. A crucial distinction is that demand is not just the desire for a product but desire backed by the necessary purchasing power (ability to pay).

The quantity of a good a consumer chooses, their demand, is the result of their optimal choice process. This choice is influenced by several factors, often called the determinants of demand:

• Price of the good itself ($P_x$): The most direct influence on the quantity demanded.
• Prices of other related goods ($P_r$): This includes substitutes and complements.
• The consumer's income (M): Determines the consumer's purchasing power.
• The consumer's tastes and preferences (T): Subjective factors like habits, fashion, and cultural influences.
• Consumer's expectations (E): Beliefs about future prices, income, or product availability.

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Demand Curve and the Law of Demand

To analyze the effect of price on demand, we invoke the crucial assumption of ceteris paribus, which is Latin for "all other things being equal." This means we hold all other factors that could influence demand—such as a consumer's income, the prices of related goods, and their tastes and preferences—constant, in order to isolate and study the relationship between a good's own price and the quantity demanded.

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The Demand Function, Schedule, and Curve

The relationship between the price of a good and the quantity a consumer optimally chooses can be understood through three related concepts:

1. Demand Function: This is a formal mathematical expression of the relationship between quantity demanded and its various determinants. A complete demand function might look like:

   $ Q_x = f(P_x, P_r, M, T) $

   Where $Q_x$ is the quantity demanded of good X, $P_x$ is its price, $P_r$ is the price of related goods, $M$ is income, and $T$ is tastes. By applying the ceteris paribus assumption, we simplify this to:

   $ Q_x = f(P_x) $

   An algebraic example would be a linear demand function: $ Q_d = 100 - 5P $.

2. Demand Schedule: This is a tabular representation of the demand function, showing the specific quantity of a good that a consumer is willing and able to buy at different possible prices.

   For the function $Q_d = 100 - 5P$, the schedule would be:

   Price ($P$) (in ₹)	Quantity Demanded ($Q_d$) (in units)
   10	$100 - 5(10) = 50$
   12	$100 - 5(12) = 40$
   14	$100 - 5(14) = 30$

3. Demand Curve: This is a graphical representation of the demand schedule. By convention in economics, price (the independent variable) is plotted on the vertical (Y) axis, and quantity demanded (the dependent variable) is plotted on the horizontal (X) axis. The demand curve is a downward-sloping line or curve, visually representing the inverse relationship between price and quantity demanded.

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Deriving a Demand Curve from Indifference Curves and Budget Constraints

The downward slope of the demand curve is not an assumption but a logical consequence of the consumer's optimal choice model. We can derive it by observing how a rational consumer's equilibrium changes when the price of a good changes.

1. Initial Equilibrium: We begin with a consumer in equilibrium at point $E_1$. Here, their budget line, $BL_1$, is tangent to the highest possible indifference curve, $IC_1$. At the initial price $P_1$ for bananas, the consumer optimally chooses to buy quantity $Q_1$. This gives us the first point on their demand curve: $(P_1, Q_1)$.
2. Price Change: Now, assume the price of bananas falls from $P_1$ to $P_2$, while the price of mangoes and the consumer's income remain constant.
3. Effect on Budget Line: This price drop causes the budget line to pivot outwards from the vertical intercept to a new position, $BL_2$. The new line is flatter, reflecting the new, lower price ratio. The consumer's budget set has expanded, meaning their purchasing power (real income) has increased.
4. New Equilibrium: With the expanded budget set, the consumer can now reach a higher level of satisfaction. They find a new equilibrium at point $E_2$, where the new budget line $BL_2$ is tangent to a higher indifference curve, $IC_2$. At this new equilibrium, the consumer optimally chooses to buy quantity $Q_2$, which is greater than $Q_1$. This provides the second point for our demand curve: $(P_2, Q_2)$.

By connecting points like $(P_1, Q_1)$ and $(P_2, Q_2)$ in a separate price-quantity graph, we trace out the individual's downward-sloping demand curve. The total increase in consumption from $Q_1$ to $Q_2$ (the price effect) is composed of two underlying forces:

• Substitution Effect: The good (bananas) has become relatively cheaper compared to mangoes. The consumer has an incentive to substitute the cheaper good for the more expensive one. This effect always leads to an increase in consumption of the good whose price has fallen.
• Income Effect: The price drop increases the consumer's real income. For a normal good, an increase in real income leads to an increase in consumption.

For normal goods, both effects work in the same direction, ensuring that a lower price leads to a higher quantity demanded.

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The Law of Demand and Linear Demand

The Law of Demand is the principle that formalizes the inverse relationship demonstrated above. It states that, ceteris paribus, as the price of a good falls, the quantity demanded for that good increases, and as the price of a good rises, the quantity demanded decreases.

A simple and widely used representation of this law is the linear demand curve. This is a demand curve that is a straight line, implying a constant rate of change between price and quantity. Its functional form is:

$ d(p) = a - bp $

• 'a' is the horizontal intercept. It represents the maximum quantity of the good that would be demanded if the price were zero. It captures the effects of all non-price factors (income, tastes, etc.).
• '-b' represents the slope of the demand curve ($\Delta Q / \Delta P$). The negative sign signifies the inverse relationship. The magnitude of 'b' indicates how sensitive quantity demanded is to price changes; for every one-unit increase in price (e.g., ₹1), the quantity demanded falls by 'b' units.

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Normal and Inferior Goods

This classification is based on how the demand for a good responds to a change in consumer income, holding all prices and other factors constant (ceteris paribus). The change in income leads to a parallel shift of the budget line, allowing the consumer to reach a new equilibrium on a different indifference curve.

• Normal Goods: For most goods, as a consumer's income rises, they can afford to buy more, and their demand for the good also rises. These are called normal goods. There is a positive or direct relationship between income and demand. For example, a person might buy more high-quality groceries, go on more holidays, or purchase better electronic gadgets as their income increases. Graphically, an increase in income shifts the demand curve for a normal good to the right. The income effect for these goods is positive.
• Inferior Goods: For some goods, demand actually decreases as consumer income rises. These are called inferior goods. There is an inverse relationship between income and demand. This happens because these goods are often seen as lower-quality alternatives, and as consumers become wealthier, they substitute away from them towards better-quality goods. For instance, as a family's income rises, they might reduce their consumption of coarse cereals like bajra and switch to basmati rice, or they might travel less by public bus and more by taxi. Graphically, an increase in income shifts the demand curve for an inferior good to the left. The income effect for these goods is negative.

Giffen Goods: A Special Case of Inferior Goods

A Giffen good is a rare and extreme type of inferior good for which demand increases as its price increases, thus violating the fundamental Law of Demand. This results in an upward-sloping demand curve.

This paradoxical outcome occurs when two conditions are met:

1. The good must be strongly inferior (i.e., it has a strong negative income effect).
2. The good must constitute a very large portion of the consumer's total budget.

The mechanism works as follows: When the price of the Giffen good (e.g., a very basic staple food for a very poor household) increases, it makes the consumer feel significantly poorer (a powerful negative income effect). This drop in real income is so severe that the consumer can no longer afford more expensive food items (like vegetables or meat). To get enough calories to survive, they are forced to cut back on the expensive items and buy even more of the now higher-priced staple food. In this case, the negative income effect is so strong that it completely overwhelms the normal substitution effect (which would push the consumer to buy less of the good as it becomes relatively more expensive).

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Substitutes and Complements

This classification depends on how the demand for one good ($Q_x$) responds to a change in the price of a related good ($P_y$). This relationship is measured by cross-price elasticity.

• Substitutes: These are goods that can be used in place of each other to satisfy a similar want (e.g., tea and coffee, Ola and Uber, butter and margarine). There is a positive relationship between the price of one good and the demand for its substitute.

  Example: If the price of coffee increases, coffee becomes relatively more expensive than tea. Consumers will substitute away from coffee and towards the cheaper alternative, tea. Consequently, the demand for tea will increase, even though its own price has not changed. This is shown as a rightward shift in the demand curve for tea.

• Complements: These are goods that are consumed together as a pair (e.g., car and petrol, printer and ink cartridges, smartphone and a mobile data plan). There is a negative relationship between the price of one good and the demand for its complement.

  Example: If the price of petrol increases significantly, the total cost of owning and driving a car rises. This makes cars less attractive to potential buyers, so the demand for cars is likely to fall, even though the price of cars has not changed. This is shown as a leftward shift in the demand curve for cars.

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Movements Along vs. Shifts in the Demand Curve

It is crucial to distinguish between a "change in quantity demanded" and a "change in demand," as they have different causes and graphical representations.

• Movement Along the Demand Curve (Change in Quantity Demanded): This is caused exclusively by a change in the price of the good itself, while all other factors (the ceteris paribus conditions) are held constant. It represents the consumer's reaction to a different price on their existing preference map.
  • A decrease in price leads to a downward movement along the curve to a higher quantity demanded. This is often called an 'extension' or 'expansion' of demand.
  • An increase in price leads to an upward movement along the curve to a lower quantity demanded. This is often called a 'contraction' of demand.
• Shift in the Demand Curve (Change in Demand): This is caused by a change in any of the underlying determinants of demand other than the good's own price. The entire demand curve moves to a new position, indicating that at every price, consumers are now willing to buy a different quantity.
  • Rightward Shift (Increase in Demand): Consumers are willing to buy more of the good at each price. This can be caused by:
    • An increase in income (for a normal good).
    • An increase in the price of a substitute good.
    • A decrease in the price of a complementary good.
    • A favourable change in tastes or preferences (e.g., a new health study praises the benefits of the good).
    • Expectation of a future price rise.
  • Leftward Shift (Decrease in Demand): Consumers are willing to buy less of the good at each price. This can be caused by:
    • A decrease in income (for a normal good).
    • A decrease in the price of a substitute good.
    • An increase in the price of a complementary good.
    • An unfavourable change in tastes or preferences.
    • Expectation of a future price fall.

Market Demand

While the analysis of an individual consumer's demand is the foundation, in reality, markets are composed of many consumers. Market demand for a good is the aggregate of the quantities demanded by all individual consumers in the market at a particular price, over a specific period. It represents the total demand for a product from all its potential buyers.

Like individual demand, market demand is also governed by the Law of Demand, meaning it will also have an inverse relationship with price, resulting in a downward-sloping market demand curve.

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Derivation of the Market Demand Curve: Horizontal Summation

The market demand curve is derived by the horizontal summation of all individual demand curves. The term "horizontal" is used because we are summing the quantities (which are on the horizontal axis) for each specific price level (on the vertical axis).

The Process of Horizontal Summation

1. Select a specific price.
2. At that price, find the quantity demanded by Consumer A, Consumer B, Consumer C, and so on, from their individual demand curves.
3. Add these quantities together to get the total market quantity demanded at that price.
4. Plot this total quantity against the selected price. This gives one point on the market demand curve.
5. Repeat this process for all possible prices to trace out the entire market demand curve.

Because we are adding positive quantities together, the market demand curve will be positioned to the right of all individual demand curves and will generally be flatter (more elastic) than the individual curves.

Derivation using a Demand Schedule

This process is easily illustrated with a demand schedule. Suppose the market consists of only two consumers, A and B.

Price (₹)	Consumer A's Demand ($Q_A$)	Consumer B's Demand ($Q_B$)	Market Demand ($Q_M = Q_A + Q_B$)
10	5	8	13
8	9	12	21
6	14	18	32

By plotting the first column (Price) against the last column (Market Demand), we can draw the market demand curve.

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Adding up Two Linear Demand Curves

When deriving market demand from linear demand functions, we must be careful because consumers may enter the market at different price points. This can create a "kink" in the market demand curve.

Let's use the example from the text where the market has two consumers with the following demand functions:

• Consumer 1: $ d_1(p) = 10 - p $ (This consumer buys only if the price is ₹10 or less).
• Consumer 2: $ d_2(p) = 15 - p $ (This consumer buys only if the price is ₹15 or less).

To find the market demand ($D_M$), we must consider three different price ranges:

Case 1: Price is greater than ₹15 ($p > 15$)

In this range, the price is too high for both consumers. Therefore, the quantity demanded by both is zero.

$ D_M = d_1(p) + d_2(p) = 0 + 0 = 0 $

Case 2: Price is between ₹10 and ₹15 ($10 < p \le 15$)

In this range, the price is low enough for Consumer 2 to buy, but still too high for Consumer 1. So, only Consumer 2 is in the market.

$ D_M = d_1(p) + d_2(p) = 0 + (15 - p) = 15 - p $

Case 3: Price is ₹10 or less ($p \le 10$)

In this low price range, both consumers are willing to buy the good. We find the market demand by adding both their demand functions.

$ D_M = d_1(p) + d_2(p) = (10 - p) + (15 - p) = 25 - 2p $

The Complete Market Demand Function

The market demand is a piecewise function composed of these segments:

$ D_M(p) = \begin{cases} 0 & \text{if } p > 15 \\ 15 - p & \text{if } 10 < p \le 15 \\ 25 - 2p & \text{if } 0 \le p \le 10 \end{cases} $

Graphically, this results in a demand curve that is kinked at the price of ₹10, which is the price at which Consumer 1 enters the market. The slope becomes steeper below this price because both consumers are now responsive to price changes.

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Factors Affecting Market Demand

The market demand curve shifts due to factors that affect individual demands, as well as factors unique to the market as a whole.

1. All factors affecting individual demand: Changes in consumer tastes, income, and the prices of related goods will shift individual demand curves and therefore also shift the market demand curve.
2. Number of Consumers in the Market: This is a key determinant of market demand.
   • An increase in the number of consumers (e.g., due to population growth or new market entry) will shift the market demand curve to the right.
   • A decrease in the number of consumers will shift it to the left.
3. Distribution of Income: How income is distributed among the population can affect market demand. For example, if income is redistributed from the wealthy to the poor, the market demand for inferior goods might increase, while the demand for luxury goods might decrease, even if the total income in the economy remains the same.
4. Demographics: Changes in the age, gender, or ethnic composition of the population can influence market demand for specific goods. For example, an aging population will increase the market demand for healthcare services and retirement homes.

Elasticity of Demand

The Law of Demand provides the direction of the relationship between price and quantity demanded (inverse), but it doesn't quantify the extent of this relationship. Price elasticity of demand ($e_D$) is a crucial economic measure that quantifies the responsiveness or sensitivity of the quantity demanded of a good to a change in its own price. It answers the question: "By how much does quantity demanded change when the price changes?"

It is defined as the ratio of the percentage change in quantity demanded to the percentage change in price. Using percentages allows for a unit-free measure, making it possible to compare the elasticity of different goods.

$ e_D = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} = \frac{\% \Delta Q}{\% \Delta P} $

The more detailed formula for calculation is:

$ e_D = \frac{\frac{Q_2 - Q_1}{(Q_1+Q_2)/2}}{\frac{P_2 - P_1}{(P_1+P_2)/2}} $ (Midpoint Formula) or, for a specific point, $ e_D = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} $ (Point Elasticity Formula)

Due to the Law of Demand, the relationship between price and quantity is inverse, making the calculated $e_D$ a negative number. However, for simplicity and ease of comparison, economists usually refer to its absolute value, $|e_D|$.

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Types (or Degrees) of Price Elasticity

The value of elasticity indicates how responsive demand is. We can categorize it into five types:

• Elastic Demand ($|e_D| > 1$): The percentage change in quantity demanded is greater than the percentage change in price. This indicates a high degree of responsiveness. It is typical for luxury goods, goods with many substitutes, or goods that take up a large portion of a consumer's income (e.g., foreign holidays, cars). The demand curve is relatively flat.
• Inelastic Demand ($|e_D| < 1$): The percentage change in quantity demanded is less than the percentage change in price. This indicates a low degree of responsiveness. It is common for necessities, goods with no close substitutes, or goods that are inexpensive (e.g., salt, medicine, petrol for a car owner). The demand curve is relatively steep.
• Unitary Elastic Demand ($|e_D| = 1$): The percentage change in quantity demanded is exactly equal to the percentage change in price.
• Perfectly Inelastic Demand ($|e_D| = 0$): Quantity demanded does not change at all, regardless of the price. The demand curve is a vertical line. This is a theoretical extreme, but life-saving medicines can be a close real-world example.
• Perfectly Elastic Demand ($|e_D| = \infty$): Consumers are willing to buy an infinite amount at a specific price, but the quantity demanded drops to zero if the price increases even slightly. The demand curve is a horizontal line. This is characteristic of an individual firm in a perfectly competitive market.

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Elasticity along a Linear Demand Curve

A common misconception is that a straight-line (linear) demand curve has a constant elasticity. This is incorrect. The elasticity actually varies at every point along a linear demand curve.

Given a linear demand curve $q = a - bp$, we use the point elasticity formula: $e_D = \frac{\Delta q}{\Delta p} \times \frac{p}{q}$. For a linear curve, the slope term ($\Delta q / \Delta p$) is constant and equals $-b$. Thus, the formula becomes:

$ e_D = -b \times \frac{p}{q} = -b \frac{p}{a - bp} $

As we move along the curve, the ratio $p/q$ changes continuously, causing the elasticity to change:

• At the top of the curve (vertical intercept), $q=0$ and $p$ is at its maximum. Here, $|e_D| = \infty$ (Perfectly Elastic).
• In the upper half of the curve, demand is elastic ($|e_D| > 1$).
• At the exact midpoint of the curve, demand is unitary elastic ($|e_D| = 1$).
• In the lower half of the curve, demand is inelastic ($|e_D| < 1$).
• At the bottom of the curve (horizontal intercept), $p=0$. Here, $|e_D| = 0$ (Perfectly Inelastic).

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Geometric Measure of Elasticity along a Linear Demand Curve

A simple geometric method can be used to measure elasticity at any point on a linear demand curve. The elasticity at a given point is the ratio of the length of the lower segment of the demand curve to the length of the upper segment.

$ |e_D| = \frac{\text{Length of the Lower Segment}}{\text{Length of the Upper Segment}} $

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Constant Elasticity Demand Curves

While a linear curve has varying elasticity, some non-linear curves have constant elasticity throughout:

• Perfectly Inelastic Curve ($|e_D|=0$): A vertical line where quantity is fixed.
• Perfectly Elastic Curve ($|e_D|=\infty$): A horizontal line where price is fixed.
• Unitary Elastic Curve ($|e_D|=1$): A curve shaped as a rectangular hyperbola.

Rectangular Hyperbola

A rectangular hyperbola is a curve where the area of all rectangles formed by a point on the curve and the axes is constant. For a demand curve, this means that for any point on the curve, the product of Price and Quantity ($P \times Q$) is a constant. Since total expenditure ($P \times Q$) is constant, any percentage change in price must be exactly offset by an equal percentage change in quantity, which is the definition of unitary elasticity.

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Factors Determining Price Elasticity of Demand for a Good

1. Availability of Close Substitutes: The most important factor. If a good has many close substitutes (e.g., different brands of soft drinks), its demand is highly elastic. If it has no close substitutes (e.g., salt), its demand is highly inelastic.
2. Nature of the Commodity: Necessities (food, medicine) tend to have inelastic demand, while luxuries (sports cars, designer watches) have elastic demand.
3. Proportion of Income Spent: Goods that constitute a very small fraction of a consumer's income (e.g., a matchbox) tend to have inelastic demand. Goods that take up a large part of the budget (e.g., rent, a car) have more elastic demand.
4. Time Horizon: Demand is generally more elastic over a longer period. In the short run, consumers may not be able to change their habits, but in the long run, they can find substitutes (e.g., if petrol prices rise, a person might buy a more fuel-efficient car in the long run).
5. Number of Uses: A good with multiple uses (e.g., milk) tends to have a more elastic demand than a good with only one use.

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Elasticity and Total Expenditure (Total Revenue Test)

Total expenditure by consumers on a good is calculated as Price × Quantity ($TE = P \times Q$). Understanding elasticity is crucial for a firm to predict how its total revenue (which is the same as total consumer expenditure) will change when it changes its price.

If Demand is...	And Price...	Then Total Expenditure...	Reason
Elastic ($|e_D| > 1$)	Increases ($ \uparrow $)	Decreases ($ \downarrow $)	Quantity changes by a larger percentage than price.
	Decreases ($ \downarrow $)	Increases ($ \uparrow $)
Inelastic ($|e_D| < 1$)	Increases ($ \uparrow $)	Increases ($ \uparrow $)	Price changes by a larger percentage than quantity.
	Decreases ($ \downarrow $)	Decreases ($ \downarrow $)
Unitary Elastic ($|e_D| = 1$)	Increases ($ \uparrow $)	Remains Constant	Percentage changes are equal and opposite.
	Decreases ($ \downarrow $)	Remains Constant

Relationship between Elasticity and change in Expenditure on a Good

We can formalize the relationship. The change in expenditure ($\Delta E$) for a small change in price ($\Delta p$) is approximately:

$ \Delta E \approx q\Delta p + p\Delta q $

Factoring out terms, we get:

$ \Delta E \approx \Delta p \left[ q + p \left(\frac{\Delta q}{\Delta p}\right) \right] = \Delta p \left[ q \left(1 + \frac{p}{q} \frac{\Delta q}{\Delta p}\right) \right] $

Since the price elasticity of demand, $e_D$, is defined as $\frac{p}{q} \frac{\Delta q}{\Delta p}$ (and is a negative number), the equation becomes:

$ \Delta E \approx \Delta p [q(1 + e_D)] $

This equation confirms the relationship in the table:

• If demand is elastic ($e_D < -1$), then $(1+e_D)$ is negative. Thus, $\Delta E$ will have the opposite sign of $\Delta p$. (Price up, Expenditure down).
• If demand is inelastic ($-1 < e_D < 0$), then $(1+e_D)$ is positive. Thus, $\Delta E$ will have the same sign as $\Delta p$. (Price up, Expenditure up).
• If demand is unitary elastic ($e_D = -1$), then $(1+e_D)$ is zero. Thus, $\Delta E = 0$. (Expenditure is constant).

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