Chapter 2 Theory Of Consumer Behaviour

Utility

Consumers decide what commodities to buy based on the satisfaction or utility they expect to get from them.

Utility is the want-satisfying capacity of a commodity. The more a person needs or desires a commodity, the greater the utility derived.

Utility is subjective; it varies between individuals and can change for the same person depending on place and time (e.g., a room heater is more useful in Ladakh than Chennai, or in winter than summer).

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Cardinal Utility Analysis

This approach assumes utility can be measured and expressed in numbers or units (e.g., a shirt gives 50 units of utility).

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Measures Of Utility

Total Utility (TU): The total satisfaction derived from consuming a fixed quantity of a commodity. It increases as more units of the commodity are consumed. $TU_n$ is the total utility from consuming $n$ units of commodity $x$.

Marginal Utility (MU): The change in total utility resulting from consuming one additional unit of a commodity. $MU_n = TU_n - TU_{n-1}$.

Total Utility can also be expressed as the sum of marginal utilities from each unit consumed: $TU_n = MU_1 + MU_2 + \dots + MU_n$.

Table 2.1 shows hypothetical values for TU and MU. It illustrates that marginal utility typically diminishes as consumption increases. This is known as the Law of Diminishing Marginal Utility: marginal utility from each additional unit declines as consumption rises (holding other things constant).

MU is positive as long as TU is increasing. MU becomes zero when TU is maximum and constant (at the 5th unit in Table 2.1). MU becomes negative when TU starts falling (after the 5th unit in Table 2.1).

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

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Derivation Of Demand Curve In The Case Of A Single Commodity (Law Of Diminishing Marginal Utility)

Cardinal utility analysis helps derive the demand curve for a commodity. Demand for a commodity is the quantity a consumer is willing and able to buy at a given price, considering prices of other goods, income, and preferences. The Demand Curve is a graphical representation of the quantities of a commodity a consumer will buy at different prices, assuming other factors are constant.

Figure 2.2 shows a hypothetical demand curve, which is typically downward sloping. This reflects the Law of Demand: there is a negative relationship between a commodity's price and the quantity demanded (demand increases as price falls, and falls as price increases).

The downward slope of the demand curve is explained by the Law of Diminishing Marginal Utility. As consumption increases, each additional unit provides less utility. Therefore, a consumer is willing to pay less for each additional unit. To buy more units, the price must fall to equal the lower marginal utility derived from those additional units.

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Ordinal Utility Analysis

Cardinal utility is criticized for assuming utility can be quantified. In reality, consumers usually rank combinations of goods based on preferences (preferring one bundle over another, or being indifferent), rather than assigning specific numerical utility values. Ordinal utility analysis is based on this ranking of preferences.

A consumer's preferences can be shown diagrammatically using indifference curves. An indifference curve connects all consumption bundles that give the consumer the same level of utility or satisfaction. The consumer is "indifferent" between any two bundles lying on the same indifference curve.

Indifference curves slope downwards because if a consumer gets more of one good (e.g., bananas), they must give up some amount of the other good (e.g., mangoes) to remain at the same level of total utility and stay on the same indifference curve.

The amount of one good the consumer must give up to get one additional unit of the other good while keeping total utility constant is called the Marginal Rate of Substitution (MRS). MRS = $| \frac{\Delta x_2}{\Delta x_1} |$, where $\Delta x_1$ is the change in quantity of bananas and $\Delta x_2$ is the change in quantity of mangoes. MRS is the rate at which the consumer substitutes one good for another while staying on the same indifference curve.

The Law of Diminishing Marginal Rate of Substitution states that as a consumer consumes more of one good (e.g., bananas), the amount of the other good (mangoes) they are willing to give up for each additional unit of the first good declines. This happens because the marginal utility of the first good decreases, and the marginal utility of the second good increases as its quantity decreases.

Table 2.2 demonstrates this, showing the MRS decreasing from 3:1 to 1:1 as banana consumption increases.

Combination	Quantity of bananas (Qx)	Quantity of Mangoes (Qy)	MRS
A	1	15	-
B	2	12	3:1
C	3	10	2:1
D	4	9	1:1

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Shape Of An Indifference Curve

The Law of Diminishing Marginal Rate of Substitution gives the indifference curve its typical shape: convex to the origin. This means the curve is bowed inwards towards the point (0,0).

However, for perfect substitutes (goods providing identical utility and used interchangeably, like a five-rupee coin and a five-rupee note), the MRS is constant, resulting in a straight-line indifference curve.

Combination	Quantity of five Rupees notes (Qx)	Quantity of five Rupees coins (Qy)	MRS
A	1	8	-
B	2	7	1:1
C	3	6	1:1
D	4	5	1:1

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Indifference Map

A consumer's preferences over all possible bundles can be represented by a collection of many indifference curves, forming an indifference map.

Due to monotonic preferences (consumers prefer more of a good, assuming positive marginal utility), bundles on indifference curves further from the origin represent higher levels of satisfaction and are preferred to bundles on curves closer to the origin.

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Features Of Indifference Curve

Summary of key properties of indifference curves:

1. Downward Sloping: To maintain the same utility level, getting more of one good requires giving up some of the other.

2. Higher Indifference Curves Represent Higher Utility: Assuming monotonic preferences, bundles on curves further from the origin contain more of at least one good (or both) and are thus preferred.

Combination	Quantity of bananas	Quantity of Mangoes
A	1	10
B	2	10
C	3	10

3. Two Indifference Curves Never Intersect: If two indifference curves were to intersect, it would imply that a single bundle (the intersection point) provides two different levels of utility (one for each curve), which contradicts the definition of an indifference curve. Also, it would logically lead to the absurd conclusion that a bundle with more of one good is indifferent to a bundle with less, which violates monotonic preferences.

At point A, IC1 = IC2. If A is on IC1, and B is on IC1, then A=B. If A is on IC2, and C is on IC2, then A=C. By transitivity, B=C. But point B has more mangoes than C with the same number of bananas, so B is preferred to C. This contradiction proves indifference curves cannot intersect.

The Consumer’s Budget

Consumers have a limited amount of money (income, M) to spend on goods, and the prices of these goods are determined in the market ($p_1$ for bananas, $p_2$ for mangoes). The consumer can only afford bundles that cost no more than their income.

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Budget Set And Budget Line

The cost of a bundle $(x_1, x_2)$ is $p_1x_1 + p_2x_2$. The consumer can afford this bundle if $p_1x_1 + p_2x_2 \le M$. This inequality is the consumer's budget constraint.

The budget set is the collection of all bundles $(x_1, x_2)$ that the consumer can afford given their income and prices, i.e., all bundles satisfying $p_1x_1 + p_2x_2 \le M$, with $x_1 \ge 0, x_2 \ge 0$.

Answer:

If goods are perfectly divisible, the budget set includes all points $(x_1, x_2)$ in the positive quadrant where $p_1x_1 + p_2x_2 \le M$. This is the area on or below a straight line called the budget line.

The equation of the budget line is $p_1x_1 + p_2x_2 = M$. This line represents all bundles that cost exactly the consumer's entire income M.

The budget line equation can be rearranged to $x_2 = \frac{M}{p_2} - \frac{p_1}{p_2}x_1$.

The vertical intercept is $\frac{M}{p_2}$ (maximum mangoes if all income is spent on mangoes). The horizontal intercept is $\frac{M}{p_1}$ (maximum bananas if all income is spent on bananas).

The slope of the budget line is $-\frac{p_1}{p_2}$.

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Price Ratio And The Slope Of The Budget Line

The slope of the budget line, in absolute value ($|\text{slope}| = \frac{p_1}{p_2}$), represents the rate at which the consumer can trade one good for the other in the market while spending their entire income. If the consumer wants one more unit of good 1 (cost $p_1$), they must reduce spending on good 2 by $p_1$, which means giving up $\frac{p_1}{p_2}$ units of good 2 (since each unit costs $p_2$). So, $\frac{p_1}{p_2}$ is the market rate of substitution between the two goods.

Consider two points on the budget line $(x_1, x_2)$ and $(x_1 + \Delta x_1, x_2 + \Delta x_2)$. Both must satisfy the budget equation: $p_1x_1 + p_2x_2 = M$ and $p_1(x_1 + \Delta x_1) + p_2(x_2 + \Delta x_2) = M$. Subtracting the first equation from the second gives $p_1\Delta x_1 + p_2\Delta x_2 = 0$. Rearranging gives $\frac{\Delta x_2}{\Delta x_1} = -\frac{p_1}{p_2}$, which is the slope.

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Changes In The Budget Set

The budget set and budget line change if income (M) or prices ($p_1, p_2$) change.

• Change in Income (Prices Constant): If income changes from M to M', the new budget line equation is $p_1x_1 + p_2x_2 = M'$. The slope ($-\frac{p_1}{p_2}$) remains the same, but the intercepts ($\frac{M'}{p_1}, \frac{M'}{p_2}$) change. An increase in income ($M' > M$) causes a parallel outward shift of the budget line, expanding the budget set. A decrease in income ($M' < M$) causes a parallel inward shift, shrinking the budget set.
• Change in Price of One Good (Other Price and Income Constant): If the price of good 1 changes from $p_1$ to $p'_1$, the new budget line is $p'_1x_1 + p_2x_2 = M$. The vertical intercept ($\frac{M}{p_2}$) remains the same, but the horizontal intercept ($\frac{M}{p'_1}$) and the slope ($-\frac{p'_1}{p_2}$) change. An increase in $p'_1$ makes the budget line steeper (pivots inward around the vertical intercept, horizontal intercept decreases). A decrease in $p'_1$ makes the budget line flatter (pivots outward, horizontal intercept increases).

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Optimal Choice Of The Consumer

Consumers aim to choose the best possible bundle from their budget set based on their tastes and preferences. Economists assume consumers are rational and have well-defined preferences, meaning they can compare any two bundles and choose the one that gives maximum satisfaction or utility.

The consumer's problem is to select a bundle from the budget set that lies on the highest possible indifference curve.

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Equality Of The Marginal Rate Of Substitution And The Ratio Of The Prices

The most preferred bundle (optimum) for a rational consumer with monotonic preferences will lie on the budget line (since points below the line are less preferred than points on the line, and points above the line are unaffordable).

The optimum bundle is typically located at the point where the budget line is tangent to an indifference curve. At the point of tangency, the slope of the budget line equals the slope of the indifference curve.

Slope of budget line = $-\frac{p_1}{p_2}$ (absolute value is $\frac{p_1}{p_2}$, the market rate of substitution).

Slope of indifference curve = $-MRS$ (absolute value is $MRS$, the rate the consumer is willing to substitute).

So, at the optimum, $MRS = \frac{p_1}{p_2}$.

This condition means the rate at which the consumer is willing to substitute one good for the other (MRS) equals the rate at which they are able to substitute them in the market based on their prices (price ratio). If these rates were unequal, the consumer could improve their satisfaction by trading goods until the rates are equal.

In some cases (e.g., perfect substitutes), the optimum might be a corner solution where the consumer spends all income on only one good, and the tangency condition might not hold in the usual sense.

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Demand

We learned that the quantity of a good a consumer chooses depends on its price, other goods' prices, income, and preferences. Demand for a commodity is the quantity a consumer is willing and able to buy at a given price, with preferences and other prices/income held constant. The relationship between a good's price and the quantity optimally chosen is called the demand function.

The demand function can be written as $X = f(P)$, where X is quantity demanded and P is price.

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Functions

A function $y = f(x)$ describes a relationship between two variables, $x$ (independent variable) and $y$ (dependent variable), where each value of $x$ corresponds to a unique value of $y$. Functions can be expressed algebraically or graphically. An increasing function's graph is upward sloping; a decreasing function's graph is downward sloping.

In economics, the convention for demand curves is to plot the independent variable (price) on the vertical axis and the dependent variable (quantity demanded) on the horizontal axis, resulting in a downward-sloping curve for the typical negative relationship between price and quantity.

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Demand Curve And The Law Of Demand

The demand curve is the graphical representation of the demand function. It shows the quantities of a good a consumer will buy at various prices, assuming other factors (income, other prices, preferences) are constant.

The relationship between a good's price and quantity demanded is generally negative: as price increases, demand decreases, and vice versa. This is the Law of Demand.

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Deriving A Demand Curve From Indifference Curves And Budget Constraints

A demand curve can be derived from the consumer's optimal choices at different prices, using indifference curves and budget constraints.

Starting with a consumer's equilibrium bundle at a given price (where the budget line is tangent to an indifference curve), we observe the quantity demanded at that price. If the price of the good falls (other factors constant), the budget line pivots outward, allowing the consumer to reach a higher indifference curve and choose a new optimal bundle, typically with a larger quantity of the now cheaper good.

Plotting the quantities demanded at each price level gives the downward-sloping demand curve. This negative relationship is partly explained by:

• Substitution Effect: As a good becomes cheaper, consumers substitute it for relatively more expensive goods to maintain satisfaction.
• Income Effect: A price drop increases the consumer's real purchasing power, which affects demand for the good (increases for normal goods, decreases for inferior goods). The combined substitution and income effects lead to the downward slope for normal goods. (For Giffen goods, a type of inferior good, a very strong negative income effect can outweigh the substitution effect, potentially leading to an upward-sloping demand curve, but this is rare).

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Law Of Demand

The Law of Demand states that, holding all other factors constant (ceteris paribus), the quantity demanded of a commodity is inversely related to its price. When price rises, demand falls; when price falls, demand rises.

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Linear Demand

A linear demand curve is represented by a straight line and can be expressed algebraically as $d(p) = a - bp$, where 'a' is the vertical intercept (demand at price 0), '-b' is the slope (change in demand for a unit change in price), and $0 \le p \le a/b$. Demand is 0 for prices above $a/b$.

The slope measures how demand changes with price. A unit increase in price leads to a decrease in demand by 'b' units.

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Normal And Inferior Goods

The relationship between consumer demand and income also varies based on the nature of the good.

• Normal Goods: For most goods, demand increases as consumer income rises and decreases as income falls. Demand for a normal good moves in the same direction as income.
• Inferior Goods: The demand for some goods decreases as consumer income rises and increases as income falls. Coarse cereals are often cited as examples. A good can be normal at low income levels and inferior at higher income levels.

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Substitutes And Complements

The quantity demanded of a good can also be affected by the price of related goods.

• Complementary Goods (Complements): Goods that are consumed together (e.g., tea and sugar, shoes and socks). An increase in the price of a complementary good is likely to decrease the demand for the related good (e.g., higher sugar price reduces tea demand). Demand moves in the opposite direction of the price of a complement.
• Substitute Goods (Substitutes): Goods that can be used in place of each other (e.g., tea and coffee). An increase in the price of a substitute is likely to increase the demand for the related good (e.g., higher coffee price increases tea demand). Demand moves in the same direction as the price of a substitute.

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Shifts In The Demand Curve

The demand curve is drawn assuming income, other prices, and preferences are constant. If any of these "other things" change, the demand curve itself will shift.

• Change in Income: For normal goods, an income increase shifts the demand curve rightward (more demanded at each price). For inferior goods, an income increase shifts it leftward.
• Change in Price of Related Goods: An increase in the price of a substitute shifts the demand curve rightward (more demanded at each price). An increase in the price of a complement shifts the demand curve leftward.
• Change in Tastes and Preferences: If preferences shift in favor of a good, the demand curve shifts rightward. If preferences shift against a good, it shifts leftward (e.g., higher demand for ice-cream in summer, lower demand for cold-drinks if health concerns arise).

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Movements Along The Demand Curve And Shifts In The Demand Curve

It's important to distinguish between a movement along the demand curve and a shift of the entire demand curve.

• Movement Along the Demand Curve: Occurs when only the price of the good itself changes, leading to a change in the quantity demanded. This is represented as moving from one point to another along the same demand curve. The Law of Demand describes movements along the curve.
• Shift in the Demand Curve: Occurs when any of the "other things" (income, prices of related goods, tastes, preferences) change, altering the quantity demanded at every price level. This is represented by the entire demand curve moving to a new position (rightward for an increase in demand at all prices, leftward for a decrease).

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Market Demand

While individual demand describes one consumer's behaviour, the market demand for a good represents the total demand of all consumers in the market combined at each price level.

The market demand at a specific price is found by summing the quantities demanded by each individual consumer at that price.

The market demand curve is derived by adding up the individual demand curves horizontally. This process is called horizontal summation.

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Adding Up Two Linear Demand Curves

If individual demand curves are linear, the market demand curve can be found by summing their algebraic equations, taking into account the price range for which each consumer demands a positive quantity.

For example, if consumer 1 demands $d_1(p) = 10 - p$ (for $p \le 10$) and consumer 2 demands $d_2(p) = 15 - p$ (for $p \le 15$), the market demand $D(p)$ is the sum of individual demands at each price.

• If $p \le 10$: $D(p) = d_1(p) + d_2(p) = (10 - p) + (15 - p) = 25 - 2p$
• If $10 < p \le 15$: Consumer 1 demands 0, consumer 2 demands $15-p$. $D(p) = 0 + (15 - p) = 15 - p$
• If $p > 15$: Both demand 0. $D(p) = 0 + 0 = 0$

So, the market demand function is piece-wise linear.

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Elasticity Of Demand

The Law of Demand tells us price and quantity demanded move in opposite directions, but it doesn't tell us by how much. Price Elasticity of Demand ($e_D$) measures the responsiveness of the quantity demanded to a change in price.

$e_D$ is defined as the percentage change in quantity demanded divided by the percentage change in price.

$e_D = \frac{\%\Delta Q}{\%\Delta P} = \frac{(\Delta Q / Q) \times 100}{(\Delta P / P) \times 100} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$.

$e_D$ is usually a negative number (due to the Law of Demand), but often the absolute value is referred to for simplicity.

Answer:

Based on the value of $|e_D|$, demand is classified as:

• Inelastic: $|e_D| < 1$. Percentage change in quantity demanded is less than percentage change in price. Demand for necessities tends to be inelastic.
• Elastic: $|e_D| > 1$. Percentage change in quantity demanded is greater than percentage change in price. Demand for luxuries tends to be elastic.
• Unitary-elastic: $|e_D| = 1$. Percentage change in quantity demanded equals percentage change in price.

Elasticity can vary at different points on a demand curve.

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Elasticity Along A Linear Demand Curve

For a linear demand curve $q = a - bp$, elasticity at any point is given by $e_D = -b \times \frac{p}{q} = -b \times \frac{p}{a-bp}$.

Elasticity varies along a linear demand curve:

• At the horizontal intercept ($p=0, q=a$), $|e_D| = 0$.
• At the vertical intercept ($p=a/b, q=0$), $|e_D| = \infty$.
• At the midpoint ($p=a/2b, q=a/2$), $|e_D| = 1$.
• To the left of the midpoint (upper half), $|e_D| > 1$ (elastic).
• To the right of the midpoint (lower half), $|e_D| < 1$ (inelastic).

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Constant Elasticity Demand Curve

Some demand curves have constant elasticity throughout.

• Perfectly Inelastic Demand: A vertical demand curve where quantity demanded is fixed regardless of price. $|e_D| = 0$.
• Perfectly Elastic Demand: A horizontal demand curve where quantity demanded is infinite at a specific price and zero at any other price. $|e_D| = \infty$.
• Unitary Elastic Demand: A demand curve shaped like a rectangular hyperbola ($pq = constant$). $|e_D| = 1$ at every point. Expenditure on the good remains constant regardless of price changes.

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Geometric Measure Of Elasticity Along A Linear Demand Curve

For a linear demand curve, the elasticity at any point can be measured as the ratio of the lower segment of the demand curve to the upper segment from that point to the axes. $e_D = \frac{\text{Lower Segment}}{\text{Upper Segment}}$.

Elasticity is 0 at the point intersecting the horizontal axis, $\infty$ at the point intersecting the vertical axis, and 1 at the midpoint.

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Factors Determining Price Elasticity Of Demand For A Good

The price elasticity of demand for a good is influenced by:

• Nature of the Good: Necessities (like food) tend to have inelastic demand, while luxuries tend to have elastic demand.
• Availability of Close Substitutes: Goods with many readily available close substitutes tend to have more elastic demand (consumers can switch if the price changes). Goods with few or no close substitutes have more inelastic demand.

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Elasticity And Expenditure

Total expenditure on a good is its price (P) multiplied by the quantity demanded (Q). How total expenditure changes when price changes depends on the price elasticity of demand ($|e_D|$).

• If demand is elastic ($|e_D| > 1$), price and expenditure move in opposite directions. Price rise $\rightarrow$ Expenditure fall. Price fall $\rightarrow$ Expenditure rise.
• If demand is inelastic ($|e_D| < 1$), price and expenditure move in the same direction. Price rise $\rightarrow$ Expenditure rise. Price fall $\rightarrow$ Expenditure fall.
• If demand is unitary-elastic ($|e_D| = 1$), expenditure remains unchanged regardless of price changes.

Change in Price (P)	Change in Quantity demand (Q)	% Change in price	% Change in quantity demand	Impact on Expenditure = P×Q	Nature of price Elasticity $e_D$
↑	↓	+10%	-8%	↑	Inelastic ($|e_D| < 1$)
↑	↓	+10%	-12%	↓	Elastic ($|e_D| > 1$)
↑	↓	+10%	-10%	No Change	Unit Elastic ($|e_D| = 1$)
↓	↑	-10%	+15%	↑	Elastic ($|e_D| > 1$)
↓	↑	-10%	+7%	↓	Inelastic ($|e_D| < 1$)
↓	↑	-10%	+10%	No Change	Unit Elastic ($|e_D| = 1$)

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Summary

• Consumers face a choice problem due to limited income and prices, aiming to maximise satisfaction from available bundles.

• Utility is the want-satisfying capacity of a commodity, which is subjective.

• Cardinal utility analysis assumes utility is measurable in units (Total Utility and Marginal Utility). Marginal utility typically diminishes with increased consumption (Law of Diminishing Marginal Utility).

• Ordinal utility analysis assumes utility can be ranked, not necessarily measured. Indifference curves represent bundles providing equal satisfaction. Indifference curves are downward sloping due to monotonic preferences and typically convex to the origin due to the Law of Diminishing Marginal Rate of Substitution.

• Monotonic preferences mean consumers prefer bundles with more of at least one good and no less of the other. Higher indifference curves represent higher utility levels. Indifference curves do not intersect.

• The budget set contains all bundles a consumer can afford ($p_1x_1 + p_2x_2 \le M$). The budget line ($p_1x_1 + p_2x_2 = M$) represents bundles costing exactly the income. Its slope ($-\frac{p_1}{p_2}$) is the market rate of substitution.

• Changes in income cause parallel shifts of the budget line. Changes in one price cause the budget line to pivot.

• A rational consumer chooses the most preferred bundle from the budget set, located at the tangency point of the budget line and the highest attainable indifference curve (where MRS = price ratio).

• The demand curve shows the relationship between the quantity demanded of a good and its price, holding other factors constant. It is generally downward sloping (Law of Demand), derived from optimal choices at different prices, explained by substitution and income effects.

• Normal goods' demand increases with income; inferior goods' demand decreases with income.

• Complementary goods are consumed together; substitute goods can be used in place of each other. Demand for a good is negatively related to complement price and positively related to substitute price.

• Changes in income, other prices, or preferences cause shifts in the demand curve. Changes in the good's own price cause movements along the demand curve.

• Market demand is the sum of individual demands at each price, derived by horizontal summation of individual demand curves.

• Price elasticity of demand measures the responsiveness of quantity demanded to price changes. It is calculated as the percentage change in quantity divided by the percentage change in price. Demand can be inelastic ($|e_D| < 1$), elastic ($|e_D| > 1$), or unitary-elastic ($|e_D| = 1$). Elasticity varies along a linear demand curve but is constant for specific curve shapes (vertical, horizontal, rectangular hyperbola).

• Price elasticity is influenced by the nature of the good and availability of substitutes.

• The relationship between price elasticity and total expenditure on a good is predictable: if $|e_D| > 1$, price and expenditure move in opposite directions; if $|e_D| < 1$, they move in the same direction; if $|e_D| = 1$, expenditure is constant.

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Key Concepts

Budget set

Budget line

Preference

Indifference

Indifference curve

Marginal Rate of substitution

Monotonic preferences

Diminishing rate of substitution

Indifference map

Utility function

Consumer’s optimum

Demand

Law of demand

Demand curve

Substitution effect

Income effect

Normal good

Inferior good

Substitute

Complement

Price elasticity of demand

Exercises

Exercises are excluded as per user instructions.