Demand: Utility and Consumer's Equilibrium | ISC Class 12 Economics Notes

This note covers utility, total and marginal utility, diminishing marginal utility, consumer's equilibrium through cardinal and ordinal approaches, equimarginal utility, indifference curves, the budget line, demand and its determinants, demand curves, movements and shifts, market demand and Giffen goods.

What is utility, and how do consumers compare satisfaction?

Utility is the want-satisfying capacity of a commodity. A commodity is a good or service that a consumer may use. A consumer usually decides demand on the basis of the satisfaction derived from it. Greater need or a stronger desire gives the commodity greater utility.

Utility is subjective: it depends on the individual. Someone fond of chocolates obtains more satisfaction from a chocolate than someone who is less fond of them. The same commodity need not provide equal satisfaction to different people.

Utility can also change with place and time. The satisfaction from a room heater depends on whether the person is in Ladakh or Chennai, and whether it is summer or winter. Utility therefore describes a relationship between a consumer and a commodity in particular circumstances.

How do cardinal and ordinal approaches differ?

Cardinal utility analysis assumes that satisfaction can be expressed numerically. Ordinal utility analysis instead ranks alternative combinations according to preference. Preferences are the consumer's likes and dislikes. Ranking tells us which combination is preferred without requiring a numerical measure of satisfaction.

A consumption bundle is a combination of quantities of goods. For example, a bundle containing five bananas and ten mangoes differs from one containing ten bananas and five mangoes. Choosing between bundles involves both preferences and what the consumer can afford.

How are total utility and marginal utility related?

Total utility (TU) is the total satisfaction from consuming a given quantity of a commodity. Marginal utility (MU) is the change in total utility caused by consuming one additional unit. Total utility measures satisfaction from the whole quantity; marginal utility measures the additional contribution.

Let n denote the number of units consumed. TUₙ denotes total utility from n units, TUₙ₋₁ total utility from one unit fewer, and MUₙ the marginal utility of the nth unit. The subscript identifies the relevant quantity or unit.

MUₙ = TUₙ − TUₙ₋₁

Total utility can also be obtained by adding successive marginal utilities. Here MU₁ means marginal utility of the first unit, MU₂ of the second, and the dots indicate continuation through the nth unit.

TUₙ = MU₁ + MU₂ + … + MUₙ

How should a utility schedule be read?

From the first through the fourth unit, total utility rises while marginal utility falls. Thus, falling marginal utility does not mean falling total utility. Positive additions still raise the total, but progressively smaller additions make it rise at a diminishing rate.

At the fifth unit, total utility remains 24 and marginal utility is zero. At the sixth unit, total utility falls to 22 and marginal utility is negative. These are distinct situations: a smaller positive addition, no addition, and a negative addition.

Worked example 1. Four bananas give total utility of 28 units and five bananas give total utility of 30 units. Calculate the marginal utility of the fifth banana.

Answer: MU₅ = TU₅ − TU₄ = 30 − 28 = 2 utility units. This is the extra satisfaction from the fifth banana, not total satisfaction from all five.

Quantity is on the horizontal axis and utility on the vertical axis. The blue TU line rises, is level between four and five units, then falls. The dotted MU line falls through zero at five units and becomes negative.

See Fig. 2.1 in your NCERT textbook

What does the law of diminishing marginal utility explain?

Definition: The law of diminishing marginal utility states that marginal utility from each additional unit declines as consumption of that commodity increases, while consumption of other commodities is kept constant.

Usually, marginal utility diminishes as consumption increases. Having obtained some quantity, the consumer's desire for still more becomes weaker. Each successive unit therefore adds less satisfaction. The law concerns additional satisfaction, rather than a claim that all satisfaction immediately begins to fall.

What assumptions support the comparison?

• The units being compared are homogeneous, meaning similar in quality and size.
• Consumption takes place within a suitable continuous period, without a break that substantially renews the want.
• The consumer's tastes and relevant circumstances remain unchanged during the comparison.
• The cardinal approach assumes that satisfaction can be measured; consumption of other commodities is held constant.

These conditions make successive units comparable. A change in the commodity's quality or in the consumer's circumstances would introduce a separate explanation for a change in satisfaction. The comparison is intended to isolate the effect of consuming more of the same commodity.

How does this help explain demand?

As each additional unit yields less satisfaction, the consumer is unwilling to pay as much for it. A lower price makes the purchase of an additional unit worthwhile. This reasoning helps explain why a demand curve, which relates quantity demanded to price, slopes downwards.

The utility schedule also identifies the point at which an additional unit contributes nothing. Beyond that point, a further unit may reduce total satisfaction, as the negative marginal utility in the schedule shows. Neither zero nor negative marginal utility should be confused with zero total utility.

How is consumer's equilibrium reached with one commodity?

Consumer's equilibrium is a position where the consumer obtains maximum satisfaction within the relevant spending constraint, the limit on expenditure, and has no incentive to change the chosen purchase. In the one-commodity cardinal analysis, the satisfaction from an extra unit is compared with the satisfaction sacrificed by paying for it.

Let P be the commodity's price in rupees per unit and MUₘ the marginal utility of money, measured as utility per rupee. Assume MUₘ is positive and constant. Multiplying P by MUₘ expresses the utility cost of buying an extra unit.

MU = P × MUₘ

Equivalently, MU/P = MUₘ. On the left is utility obtained per rupee spent on the commodity; on the right is the utility of a rupee retained. If utility is expressed directly in money terms, the condition is that monetary marginal utility equals price.

How does the consumer adjust purchases?

Diminishing marginal utility supports the adjustment: buying more reduces the additional utility from the commodity, while buying less moves towards units with greater marginal utility. The equality describes an interior choice, where consumption can be adjusted both upwards and downwards. The good must be divisible, meaning available in fractional units as well as whole units, and the purchase must be affordable.

Put quantity on the horizontal axis and utility on the vertical axis. Draw a downward-sloping MU curve and a horizontal line labelled P × MUₘ. Mark their intersection as equilibrium and project it to the quantity axis.

Do not compare utility units directly with rupees. Price must first be converted into utility through MUₘ, or marginal utility must be expressed in money terms. For indivisible goods, an exact equality may be unavailable, so the affordable alternatives must be compared.

How does the law of equimarginal utility guide spending?

The law of equimarginal utility explains how a consumer allocates a fixed expenditure among goods. For an interior optimum, with positive quantities of both goods, maximum satisfaction requires equal marginal utility per rupee spent on each, together with expenditure consistent with the available budget, the money available for spending.

Let MU₁ and MU₂ now denote marginal utilities of goods 1 and 2, rather than successive units of one commodity. Let p₁ and p₂ denote their respective prices per unit. Each ratio below measures satisfaction obtained from an additional rupee of expenditure.

MU₁/p₁ = MU₂/p₂

Where the marginal utility of money is included explicitly, both ratios equal MUₘ. Equal marginal utilities alone are insufficient when prices differ: the consumer must compare what the same expenditure obtains, rather than what one physical unit obtains.

What does an allocation schedule show?

This schedule shows the direction of reallocation for each possible comparison of marginal utility per rupee. With diminishing marginal utility, greater consumption reduces a good's marginal contribution. Reallocation therefore tends to reduce the initial difference in marginal utility per rupee until further transfer cannot improve satisfaction.

The analysis assumes a rational consumer, given prices and income, measurable utilities and sufficiently divisible goods. In this cardinal treatment, satisfaction from each good is considered separately, with the relevant marginal utilities diminishing. A rational consumer chooses according to preferences to obtain the best affordable result.

The spending condition matters as much as the ratio condition. Equality between two marginal ratios does not by itself establish that a proposed bundle is affordable, uses the intended budget, or is the best feasible choice. Both the utility comparison and the expenditure constraint must be checked.

What are indifference curves and the marginal rate of substitution?

An indifference curve joins consumption bundles that provide equal satisfaction. The consumer is indifferent among them, meaning no bundle on that curve is preferred to another. Ordinal analysis therefore compares satisfaction without assigning a numerical quantity of utility to every bundle.

The marginal rate of substitution (MRS) is the amount of one good the consumer is willing to give up for an additional unit of another while keeping satisfaction unchanged. For bananas and mangoes, it measures mangoes sacrificed for an additional banana.

Let Δ, read as delta, mean a change; let X represent bananas and Y mangoes. Vertical bars mean absolute value, so the ratio's magnitude is used rather than its negative sign.

MRS = |ΔY/ΔX|

How does a substitution schedule work?

Worked example 2. Bundles B and C give equal satisfaction. B contains two bananas and twelve mangoes; C contains three bananas and ten mangoes. Calculate the MRS when moving from B to C.

Answer: The consumer gains 3 − 2 = 1 banana and gives up 12 − 10 = 2 mangoes. MRS = |−2/1| = 2 mangoes per additional banana.

Diminishing marginal rate of substitution (DMRS) means that the amount sacrificed declines as the consumer acquires more of the other good along the same indifference curve. Here the sacrifice falls from three mangoes to two and then one for successive additional bananas.

Bananas are on the horizontal axis and mangoes on the vertical axis. Points A, B, C and D lie on a downward-sloping curve labelled IC, meaning indifference curve. Dotted guides connect the bundles to their quantities on the axes.

See Fig. 2.3 in your NCERT textbook

What properties do indifference curves and indifference maps have?

An indifference map is a family of indifference curves representing a consumer's preferences. Each curve represents equal satisfaction among its own bundles. Different curves represent different satisfaction levels, allowing comparisons across the wider set of consumption possibilities.

Monotonic preferences mean that a consumer prefers a bundle with more of at least one good and no less of the other. This assumption is important when interpreting the position of curves and identifying the best affordable bundle.

How do the main properties follow?

1. Downward slope: to retain equal satisfaction while receiving more bananas, the consumer must give up some mangoes. More bananas with unchanged mangoes would instead be preferred under monotonic preferences.
2. Convexity towards the origin: diminishing MRS makes the curve become flatter as bananas increase. Convexity here means the curve bends towards the point where the two axes meet.
3. Higher curves are preferred: under monotonic preferences, bundles on a higher indifference curve provide greater satisfaction than those on a lower curve.
4. Curves cannot intersect: each intersecting curve would equate its bundles with the shared bundle at the intersection. This implies equal satisfaction from bundles when one has more of one good and no less of the other, contradicting monotonic preferences.

The convex shape is the most common shape, not the only possible one. For perfect substitutes, goods that replace each other while providing exactly the same utility, MRS remains constant and the indifference curve is a straight line.

Five-rupee coins and five-rupee notes illustrate perfect substitution. A consumer indifferent between them exchanges one for one regardless of the number already held. This is different from the diminishing mango sacrifices in the banana-and-mango schedule.

Several downward-sloping blue curves appear between axes labelled Bananas and Mangoes. An arrow points towards higher curves, indicating the direction of preferred bundles.

See Fig. 2.5 in your NCERT textbook

How do the budget set and budget line limit choice?

The budget set contains all bundles affordable at given income and prices. The budget line contains bundles that cost exactly the available income. A preferred bundle outside the budget set cannot be purchased with the consumer's available money.

Let M denote money income available for spending, x₁ the quantity of bananas and x₂ the quantity of mangoes. The previously defined prices p₁ and p₂ now refer to bananas and mangoes. Quantities cannot be negative.

p₁x₁ + p₂x₂ ≤ M is the budget constraint: the symbol ≤ means less than or equal to. The two products on the left are expenditure on bananas and expenditure on mangoes.

p₁x₁ + p₂x₂ = M is the budget-line equation.

What do the intercepts and slope mean?

An intercept is where the line meets an axis. Spending all income on bananas gives the horizontal intercept M/p₁. Spending all income on mangoes gives the vertical intercept M/p₂. With divisible goods, combinations between these endpoints also lie on the line.

Budget-line slope = −p₁/p₂

The slope measures the change in mangoes per unit change in bananas along the line. Its absolute value is the price ratio: the mangoes the consumer must give up to finance an additional banana when the entire budget is already spent.

Worked example 3. A consumer has ₹20. Both goods cost ₹5 per unit and are available only in whole units. Identify the bundles that spend the entire budget, writing bananas first and mangoes second.

Answer: The budget equation is 5x₁ + 5x₂ = 20, so x₁ + x₂ = 4. The complete list is (0, 4), (1, 3), (2, 2), (3, 1) and (4, 0).

In that example, bundles costing less than ₹20 are also affordable and belong to the budget set. They do not belong to the budget line. A bundle such as (3, 3) costs more than the available income and lies outside the budget set.

A downward-sloping straight line joins the mango intercept M/p₂ to the banana intercept M/p₁. The area below the line is labelled Budget Set. The line itself carries the equation p₁x₁ + p₂x₂ = M.

See Fig. 2.9 in your NCERT textbook

At unchanged prices, higher income shifts the line outwards in parallel and lower income shifts it inwards. A change in the banana price, with income and the mango price fixed, rotates the line around its unchanged mango intercept.

How is equilibrium found through indifference-curve analysis?

It is generally assumed that a consumer has well-defined preferences and behaves rationally. Preferences can usually be represented by an indifference map. The consumer seeks the highest attainable indifference curve, meaning the greatest satisfaction available within the budget set.

With monotonic preferences, a point below the budget line cannot be optimal. There is an affordable point on the line with more of at least one good and no less of the other. Points above the line are unaffordable. The optimum therefore lies on the line.

What is the tangency condition?

In the usual case with a smooth convex curve and both goods consumed, equilibrium occurs where the budget line is tangent to an indifference curve: the line just touches the curve at the optimum. Their slopes have equal absolute values.

MRS = p₁/p₂

MRS expresses the rate at which the consumer is willing to substitute mangoes for an extra banana. The price ratio expresses the rate at which the market permits that substitution. At this interior optimum, willingness to substitute matches the market opportunity.

1. Identify the affordable set using income and both prices.
2. Compare bundles through the consumer's indifference map.
3. Find the highest curve that the budget line can reach.
4. For an interior tangency, check equal slope magnitudes and the full-expenditure condition.

If MRS is two while both goods have the same price, the consumer is willing to sacrifice two mangoes for another banana, but needs to sacrifice only one in the market. Such a position allows an improvement and is not the optimum.

A black budget line touches a black indifference curve. A grey curve lies above the attainable tangency and a blue curve below it. The marked optimal bundle is labelled (x₁*, x₂*), where stars identify the chosen quantities.

See Fig. 2.12 in your NCERT textbook

Note: Tangency is not a universal condition. In other situations, the optimum occurs where the consumer spends the entire income on only one good. Such a choice is called a corner solution.

What are demand, the demand function and the law of demand?

Demand is the quantity of a commodity a consumer is willing to buy and can afford at given prices and income. Willingness and affordability both matter. Preferences help explain what the consumer wants; the budget determines which purchases are feasible.

A demand function expresses how quantity demanded depends on its determinants. Let Q denote quantity demanded, Pᵣ prices of related goods and T tastes and preferences. P and M retain their meanings of own price and money income. The letter f means “a function of”.

Q = f(P, Pᵣ, M, T)

Holding the other determinants constant gives the own-price relationship Q = f(P). A demand schedule presents price and quantity combinations in a table; a demand curve presents the relationship graphically, with price vertically and quantity horizontally.

Why does the ordinary demand curve slope downwards?

Definition: The law of demand states that, other things being equal, quantity demanded falls when a commodity's price rises and rises when its price falls.

The relationship is likely to be negative in general. In cardinal analysis, diminishing marginal utility makes the consumer willing to pay less for additional units. In ordinal analysis, a price change alters the affordable combinations and the consumer's best choice.

The substitution effect is the change towards the relatively cheaper good when satisfaction is held constant. The income effect is the change in consumption caused by altered purchasing power. Purchasing power means how much the consumer's money can buy.

For a normal good, whose demand rises with income, a price fall makes it relatively cheaper and increases purchasing power. Both effects support buying more. The price change does not require an increase in money income: the same money buys more at the lower price.

Price is on the vertical axis and quantity on the horizontal axis. The blue curve slopes downwards from left to right. Guide lines connect selected curve points to the axes, showing lower prices alongside larger quantities.

See Fig. 2.2 in your NCERT textbook

How do demand determinants cause movements and shifts?

A change in the commodity's own price, with other determinants fixed, causes a movement along the demand curve. A change in income, related-good prices or preferences changes demand at given own prices and therefore shifts the curve.

Extension of demand means a rise in quantity demanded following a fall in own price along the same curve. Contraction of demand means a fall in quantity demanded following a rise in own price. These terms distinguish price-induced movements from shifts.

How do income and related goods affect demand?

For most goods, demand moves in the same direction as income; these are normal goods. Demand for an inferior good moves in the opposite direction. Coarse cereals are an example of low-quality food items that can be inferior goods.

A good can be normal at some income levels and inferior at others. At very low incomes, demand for low-quality cereals can increase with income. Beyond a level, further income is likely to reduce their consumption as the consumer switches to better-quality cereals.

Substitutes can be used in place of one another, such as tea and coffee. Demand for a good usually moves in the direction of its substitute's price. A rise in coffee's price is likely to increase tea consumption.

Complements are consumed together, such as tea and sugar. In general, demand moves opposite to the complementary good's price. An increase in sugar's price is likely to decrease demand for tea.

How are increases and decreases in demand identified?

An increase in demand is a rightward shift: more is demanded at each own price. A decrease in demand is a leftward shift: less is demanded at each own price. First identify which determinant changed, then decide whether to move along or shift the curve.

Panel (a) shows an arrow upwards and leftwards along one downward-sloping curve. Panel (b) shows a horizontal rightward arrow between two downward-sloping curves. Both panels label Price vertically and Quantity horizontally.

See Fig. 2.17 in your NCERT textbook

How is market demand derived, and when can the law of demand fail?

Individual demand is the demand of one consumer. Market demand is the sum of all consumers' quantities demanded at a particular price. The individual quantities must be added at the same price, rather than adding the prices paid by different consumers.

Graphically this is horizontal summation: quantities are measured on the horizontal axis and added while price is held fixed. Repeating this at different prices produces the market demand curve from the individual demand curves.

How are individual demand functions added?

Worked example 4. A market has two consumers. Let p be price, d₁(p) the first consumer's demand and d₂(p) the second consumer's demand. Their demands are 10 − p and 15 − p respectively, with each set to zero when its formula becomes negative. Derive market demand.

Answer: For prices from 0 to 10 inclusive, market demand is (10 − p) + (15 − p) = 25 − 2p. Above 10 and up to 15 inclusive, the first consumer's demand is zero, so market demand equals the second consumer's demand, 15 − p, which is zero at p = 15. Above 15, market demand is zero.

The following demand schedule evaluates these functions at their stated price boundaries. Each market quantity is obtained by adding the two individual quantities in its row.

Plot price vertically and the corresponding market quantity horizontally to obtain points on the market demand curve. Join the points consistently with the separate linear relationships for the price ranges. This derives the curve directly from the schedule.

The separate price ranges matter because demand cannot be negative. Once the first consumer stops buying, continuing to add the expression 10 − p would incorrectly subtract quantity from the second consumer's demand. Market demand must instead add the actual non-negative quantities.

What makes a Giffen good an exception?

For an inferior good, the income and substitution effects work in opposite directions. If the substitution effect is stronger, demand and own price remain inversely related. Inferiority alone therefore does not establish an exception to the law of demand.

A Giffen good has an opposing income effect stronger than its substitution effect. Its quantity demanded moves in the same direction as its own price. A fall in price can therefore reduce its consumption, despite making it relatively cheaper.

This is an exception involving the own-price relationship. A rise in demand caused by higher income or changing preferences is instead a shift of the demand curve. It does not test the law's condition that other relevant factors remain unchanged.

Glossary

• Utility — The want-satisfying capacity of a commodity for a particular consumer in particular circumstances.
• Total utility — The total satisfaction obtained from consuming a given quantity of a commodity.
• Marginal utility — The change in total utility caused by consuming one additional unit of a commodity.
• Cardinal utility — An approach that assumes satisfaction can be measured and expressed in numerical units.
• Ordinal utility — An approach that ranks consumption bundles by preference without requiring numerical measurement of satisfaction.
• Consumer's equilibrium — A position providing maximum satisfaction within the relevant budget, without an incentive to change purchases.
• Equimarginal utility — The allocation principle equating marginal utility per rupee across purchased goods at an interior optimum.
• Indifference curve — A curve joining consumption bundles that provide the consumer with the same level of satisfaction.
• Marginal rate of substitution — The amount of one good sacrificed for an additional unit of another while satisfaction remains unchanged.
• Budget line — The set of bundles whose total cost exactly equals the consumer's available income.
• Demand — The quantity a consumer is willing to buy and can afford under given conditions.
• Normal good — A good whose quantity demanded moves in the same direction as the consumer's income.
• Inferior good — A good whose quantity demanded moves in the opposite direction to the consumer's income.
• Giffen good — A good whose opposing income effect outweighs substitution, producing a positive own-price relationship.
• Market demand — The sum of quantities demanded by all consumers at the same price of a good.

Common errors and misconceptions

• Misconception: Falling marginal utility means total utility must fall. Correct: Total utility rises while marginal utility remains positive, even when successive additions become smaller.
• Misconception: Zero marginal utility means zero total utility. Correct: Zero marginal utility means the additional unit leaves total utility unchanged.
• Misconception: Equilibrium requires equal marginal utilities whatever the prices. Correct: The interior cardinal condition equates marginal utility per rupee, so prices must be included.
• Misconception: All affordable bundles lie on the budget line. Correct: Bundles costing less than income are also affordable; they lie below the line in the budget set.
• Misconception: Every consumer optimum must be a tangency. Correct: Other situations can produce a corner optimum with the entire income spent on one good.
• Misconception: A fall in own price shifts the demand curve rightwards. Correct: With other determinants unchanged, it produces an extension along the existing curve.
• Misconception: Every inferior good is a Giffen good. Correct: The opposing income effect must be stronger than the substitution effect for the own-price relationship to become positive.
• Misconception: Market demand adds quantities chosen at different prices. Correct: Add individual quantities at the same price, then repeat the process for other prices.

Exam-style questions with model answers

Q1. Distinguish total utility from marginal utility. [2 marks]

1. Total utility is the total satisfaction from consuming a given quantity of a commodity.
2. Marginal utility is only the change in that total caused by consuming one additional unit, so it measures the addition and not the whole.

Q2. Total utility from four, five and six units is 24, 24 and 22 utility units respectively. Calculate marginal utility of the fifth and sixth units and explain each result. [4 marks]

1. Marginal utility of the fifth unit equals total utility from five units minus total utility from four units: 24 − 24 = 0 utility units.
2. The fifth unit adds no satisfaction, so total utility remains unchanged at 24 utility units.
3. Marginal utility of the sixth unit equals 22 − 24 = −2 utility units.
4. The sixth unit reduces total satisfaction by two utility units; negative marginal utility therefore accompanies falling total utility.

Q3. Explain the one-commodity cardinal equilibrium condition and the adjustment when it is not satisfied. Assume diminishing marginal utility, divisible consumption, affordability and a positive constant marginal utility of money. [4 marks]

1. Equilibrium requires marginal utility of the commodity to equal price multiplied by marginal utility of money. Both sides then measure utility rather than mixing utility units and rupees.
2. If the commodity's marginal utility exceeds this utility cost, an additional purchase raises satisfaction net of the sacrifice of money.
3. If marginal utility is below the utility cost, the consumer benefits by reducing purchases.
4. Diminishing marginal utility supports adjustment towards equality: buying more lowers marginal utility, while reducing purchases removes units with insufficient marginal benefit.

Q4. Two equally preferred bundles contain respectively two bananas with twelve mangoes and three bananas with ten mangoes. Calculate the marginal rate of substitution for this change and explain what it measures. [2 marks]

1. The consumer gives up two mangoes for one extra banana, so the marginal rate of substitution is two mangoes per banana.
2. It measures the sacrifice the consumer accepts while moving between bundles that provide unchanged satisfaction.

Q5. A consumer has ₹20 and can buy bananas and mangoes only in whole units. Each costs ₹5. Write the budget equation, list all full-expenditure bundles, calculate both intercepts, and distinguish the budget set from the budget line. [5 marks]

1. Let x₁ be bananas and x₂ mangoes. The budget-line equation is 5x₁ + 5x₂ = 20, giving combinations that exactly exhaust the available income.
2. Writing bananas first, the complete list is (0, 4), (1, 3), (2, 2), (3, 1) and (4, 0).
3. The banana intercept is 20/5 = 4 bananas when no mangoes are purchased.
4. The mango intercept is 20/5 = 4 mangoes when no bananas are purchased.
5. The budget set includes all non-negative whole-unit bundles costing no more than ₹20. The budget line includes only those costing exactly ₹20; cheaper bundles belong to the set but not the line.

Q6. Explain consumer's equilibrium using indifference curves and a budget line. Assume monotonic preferences and the usual smooth convex curves with an interior optimum. Include the limitation of the tangency rule. [6 marks]

1. The consumer seeks the highest attainable indifference curve, representing maximum satisfaction among affordable consumption bundles.
2. A point below the budget line cannot be optimal under monotonic preferences because an affordable bundle on the line offers more of at least one good and no less of the other.
3. Bundles above the budget line cost more than available income, so the consumer cannot choose them.
4. At the interior optimum, the budget line is tangent to the highest reachable indifference curve, while less preferred affordable bundles lie on lower curves.
5. The marginal rate of substitution equals the price ratio: willingness to exchange the goods equals the exchange rate permitted by their market prices.
6. Tangency is not universal. In other situations, a corner optimum can arise with all income spent on only one good.

Q7. Tea and coffee are substitutes; tea and sugar are complements. Explain the effect on tea demand of each of the following separately: a fall in tea's own price, a rise in coffee's price and a rise in sugar's price. Assume tea obeys the ordinary law of demand. Hold all other determinants constant in each case. [3 marks]

1. A fall in tea's own price produces an extension of quantity demanded along the same demand curve, under the ordinary law of demand.
2. A rise in coffee's price is likely to increase demand for tea because consumers can substitute tea for coffee. Tea's demand curve shifts rightwards.
3. A rise in sugar's price is likely to reduce demand for tea because they are consumed together. Tea's demand curve shifts leftwards.

Q8. A market has two consumers. With p denoting price, their quantities demanded are 10 − p and 15 − p respectively, each replaced by zero when negative. Derive market demand for every non-negative price range and explain the method. [4 marks]

1. Market demand adds the two consumers' quantities at the same price. Graphically, this is horizontal summation because quantity is measured on the horizontal axis.
2. For prices from zero to ten inclusive, both formulas are non-negative, giving market demand 25 − 2p.
3. Above ten and up to fifteen inclusive, the first consumer demands zero, so market demand is 15 − p.
4. Above fifteen, neither consumer buys the good and market demand is zero. Negative formula values must not be counted as negative purchases.

Key takeaways

• Utility is subjective: satisfaction from the same commodity can differ between individuals and change with place or time.
• Total utility rises with positive marginal utility, remains unchanged with zero marginal utility and falls with negative marginal utility.
• Cardinal equilibrium compares marginal utility per rupee, together with affordability and the relevant spending constraint.
• An indifference curve joins equally satisfying bundles; the diminishing marginal rate of substitution explains its most common convex shape.
• The budget line shows full expenditure, while the budget set includes every affordable bundle on or below it.
• At a usual interior ordinal optimum, the marginal rate of substitution equals the price ratio; corner solutions require separate treatment.
• Own-price changes cause movements along demand curves; income, preferences and related-good prices can shift the curves.
• Market demand adds quantities at the same price; a Giffen good has an opposing income effect stronger than substitution.

Test yourself

Can total utility rise while marginal utility falls?

Yes. As long as marginal utility remains positive, total utility rises, but progressively smaller additions make it rise at a diminishing rate.

Why compare marginal utility per rupee rather than marginal utility alone?

Goods can have different prices. Comparing utility per rupee identifies the satisfaction obtained from the same amount of expenditure on each good.

What does diminishing marginal rate of substitution mean?

As more of one good is obtained along an indifference curve, the consumer gives up progressively smaller amounts of the other while maintaining satisfaction.

What happens to the budget line when income increases and both prices remain fixed?

Both intercepts increase and the budget line shifts outwards in parallel. Its slope remains unchanged because the price ratio has not changed.

Why is an affordable point below the budget line not optimal under monotonic preferences?

An affordable bundle on the line can provide more of at least one good without reducing the other, so the consumer prefers it.

Does a rise in an inferior good's demand after income falls contradict the law of demand?

No. Income has changed, so the demand curve shifts. The law of demand concerns own-price changes with other determinants held constant.

Why is every inferior good not necessarily a Giffen good?

An inferior good becomes Giffen only when its opposing income effect outweighs its substitution effect. Otherwise, demand and own price remain inversely related.

At what prices should individual quantities be added to obtain market demand?

Add every consumer's quantity at the same price, then repeat at other prices to construct the market demand relationship.