Theory of Consumer Behaviour Practice Questions — JAMB UTME — Page 3

The table below illustrates the utility schedule of a consumer consuming consecutive units of chocolate bars:

Quantity Consumed ( $Q$ )	Total Utility ( $TU$ ) in Utils	Marginal Utility ( $MU$ ) in Utils
$1$	$15$	$15$
$2$	$27$	$12$
$3$	$36$	$9$
$4$	$42$	$M$
$5$	$45$	$3$

Based on the table, what is the Average Utility ( $AU$ ) of the consumer at $4$ units of consumption?

10.50

utils

6.00

utils

14.00

utils

8.40

utils

Show answer & explanation

Answer: $10.50$ utils

Answer

The Average Utility (

AU

) of the consumer at

4

units of consumption is

10.50

utils.

Average Utility (

AU

) measures satisfaction per unit of commodity consumed and is defined mathematically as

AU = \frac{TU}{Q}

. At

4

units of consumption, the Total Utility (

TU

) is

42

utils. Dividing

42

utils by

4

units yields an Average Utility of

10.50

utils.

Step-by-Step Solution

1

Identify Total Utility (

TU

) at the 4th unit of consumption from the schedule.

TU_4 = 42

utils.

Average Utility requires total satisfaction divided by the total number of units consumed.

2

Apply the Average Utility formula:

AU_n = \frac{TU_n}{n}

.

AU_4 = \frac{42}{4} = 10.50

utils.

Average utility measures the utility per unit of consumption.

Key Concept

Calculation of Average Utility from a Total Utility Schedule

Estimated Time:1m 0s

Question 42Question →

A consumer allocates a fixed monetary budget exclusively between Good $X$ (plotted on the horizontal axis) and Good $Y$ (plotted on the vertical axis). If the market price of Good $X$ decreases while the consumer's income and the price of Good $Y$ remain unchanged, which of the following describes the resulting structural change to the budget line?

The budget line pivots outward along the horizontal axis, becoming flatter.

The budget line shifts parallel to the right away from the origin.

The budget line pivots inward along the vertical axis, becoming steeper.

The slope of the budget line increases because Good

X

is now more expensive relative to Good

Y

.

Show answer & explanation

Answer: The budget line pivots outward along the horizontal axis, becoming flatter.

Answer

The budget line pivots outward along the horizontal axis, becoming flatter.

The horizontal intercept of a budget line is given by

I/P_X

and the vertical intercept by

I/P_Y

. When the price of Good

X

drops while income and the price of Good

Y

remain constant, the maximum quantity of Good

X

affordable increases, pushing the horizontal intercept outward. Since the vertical intercept does not move, the budget line pivots around the vertical intercept and its absolute slope (

P_X/P_Y

) decreases, making the line flatter.

Step-by-Step Solution

1

Identify the equation and intercepts of the budget line

The budget equation is

P_X X + P_Y Y = I

. The horizontal intercept is

I/P_X

, the vertical intercept is

I/P_Y

, and the absolute slope is

P_X/P_Y

.

Intercepts define the maximum quantities affordable of each good when spending all income on that single good.

2

Analyze the impact of a decrease in

P_X

As

P_X

decreases to

P_X'

, the horizontal intercept

I/P_X'

increases (moves further right). The vertical intercept

I/P_Y

remains unchanged.

Income

I

and

P_Y

are constant, so the consumer can purchase more units of Good

X

but the maximum amount of Good

Y

remains fixed.

3

Determine the change in slope

The magnitude of the slope decreases from

P_X/P_Y

to

P_X'/P_Y

, meaning the budget line becomes flatter.

The slope measures the opportunity cost of Good

X

. A cheaper Good

X

requires giving up fewer units of Good

Y

per unit of Good

X

acquired.

Key Concept

Budget Line Rotation and Relative Price Changes

Question 43Question →

Suppose two indifference curves, $IC_1$ and $IC_2$ , intersect at point $A$ on a consumer's indifference map. Which fundamental assumption of ordinal utility theory is logically violated by this intersection?

Transitivity and consistency of consumer preferences

Diminishing marginal rate of substitution between goods

Maximization of total utility when marginal utility reaches zero

Constant marginal rate of substitution across all utility levels

Show answer & explanation

Answer: Transitivity and consistency of consumer preferences

Answer

Transitivity and consistency of consumer preferences

The correct answer is transitivity and consistency of consumer preferences. Indifference curves cannot intersect because if they did, a shared point of intersection would imply that two different levels of utility are equal, contradicting the axiom of transitivity (

If\ A \sim B\ and\ A \sim C,\ then\ B \sim C

).

Step-by-Step Solution

1

Analyze the definition of an indifference curve

Every point on a single indifference curve yields the exact same level of total utility to the consumer.

An indifference curve represents loci of commodity combinations that offer equal satisfaction.

2

Apply logical deductions to intersecting curves

If point

A

lies on both

IC_1

and

IC_2

, then utility at

A

equals utility at point

B

(on

IC_1

) and utility at point

C

(on

IC_2

).

Points on the same curve must yield equal utility.

3

Evaluate the outcome against preference transitivity

By transitivity, if

B = A

and

A = C

, then

B

must equal

C

. However, since

B

and

C

lie on different curves representing different utility levels, this creates a logical contradiction.

Transitivity requires consistent preference ordering (

If\ X \sim Y\ and\ Y \sim Z,\ then\ X \sim Z

). Therefore, indifference curves can never intersect.

Key Concept

Indifference Curve Properties: Non-intersection and Preference Transitivity

Estimated Time:1m 0s

Question 44Question →

Match each fundamental property of a standard indifference curve on the left with its underlying economic principle or theoretical implication on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Downward slope maps to the negative substitution trade-off; Convexity to origin maps to diminishing

MRS_{xy}

; Higher curve placement maps to greater total utility; Inability of curves to intersect maps to preference transitivity.

Each property directly derives from consumer preference axioms. The downward slope stems from commodity trade-offs, convexity stems from diminishing marginal rates of substitution, higher positioning signifies superior satisfaction levels under non-satiation, and non-intersection upholds transitivity in consumer choices.

Step-by-Step Solution

1

Identify the economic rationale for slope

A negative slope indicates that the two commodities are substitutes in consumption.

To remain on the same utility level while gaining more of one commodity, the consumer must sacrifice some of the other commodity.

2

Determine the cause of curvature

Convexity implies that the slope (

MRS_{xy}

) falls continuously as one moves down the curve.

As consumption of Good

X

increases, its marginal utility (

MU_x

) relative to Good

Y

(

MU_y

) decreases.

3

Analyze position and intersection rules

Higher curves contain superior bundles, and crossing curves violate logical preference ordering.

Monotonicity ensures higher curves offer more utility, while transitivity requires that if bundle A equals B and B equals C, then A must equal C.

Key Concept

Properties of indifference curves in ordinal utility theory

Question 45Question →

Suppose two indifference curves, $IC_1$ and $IC_2$ , representing a consumer's preferences for Good $X$ and Good $Y$ , intersect at bundle $P$ . Bundle $Q$ lies solely on $IC_1$ , and bundle $R$ lies solely on $IC_2$ , with bundle $R$ containing strictly more of both goods than bundle $Q$ . Which fundamental economic assumption of ordinal utility theory is violated by this intersection, and what is its logical consequence?

The axiom of transitivity and monotonic preferences; it creates a contradiction where a bundle with more goods yields the same satisfaction as a bundle with fewer goods.

The law of diminishing marginal rate of substitution; it causes the marginal rate of substitution to remain constant along both curves regardless of bundle composition.

The principle of total utility maximization; it forces marginal utility to drop to zero at the point of intersection.

The assumption of diminishing returns; it causes the budget line to become concave relative to the origin.

Show answer & explanation

Answer: The axiom of transitivity and monotonic preferences; it creates a contradiction where a bundle with more goods yields the same satisfaction as a bundle with fewer goods.

Answer

The axiom of transitivity and monotonic preferences; it creates a contradiction where a bundle with more goods yields the same satisfaction as a bundle with fewer goods.

Indifference curves cannot intersect because such an intersection violates the axiom of transitivity and monotonic preferences. If two curves intersect at a common point, transitive logic forces any two distinct bundles on those separate curves to yield equal satisfaction. However, if one bundle contains more of both commodities, monotonic preference requires it to yield strictly higher utility, producing a direct logical contradiction.

Step-by-Step Solution

1

Analyze the preference relations defined by the intersection point

P

Since

P

lies on both

IC_1

and

IC_2

, the consumer is indifferent between

P

and

Q

(

P \sim Q

), and also indifferent between

P

and

R

(

P \sim R

).

By definition, all points on a single indifference curve yield equal total utility.

2

Apply the axiom of transitivity

If

Q \sim P

and

P \sim R

, transitivity requires that

Q \sim R

.

Transitivity dictates consistent ordering of consumer preferences across combinations.

3

Compare the bundles

Q

and

R

using monotonic preferences (non-satiation)

Since bundle

R

contains strictly more of both goods than bundle

Q

, monotonic preference implies

R

must be strictly preferred to

Q

(

R \succ Q

).

Consumers prefer combinations with larger quantities of goods.

4

Identify the logical contradiction

The deduction

Q \sim R

directly contradicts

R \succ Q

, proving that indifference curves can never intersect under standard rational preference axioms.

Intersecting indifference curves destroy the logical consistency of preference ordering.

Key Concept

Non-intersection of Indifference Curves and Transitivity Axiom

Question 46Question →

If the price of good $X$ falls while the consumer's income and the price of good $Y$ remain unchanged, the budget line rotates outward along the $X$ -axis and becomes less steep.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. A reduction in the price of good

X

increases the horizontal intercept (

\frac{I}{P_x}

) while keeping the vertical intercept (

\frac{I}{P_y}

) fixed, causing the budget line to rotate outward along the

X

-axis and decrease in slope (

\frac{P_x}{P_y}

), which makes it flatter.

A fall in the price of good

X

increases the maximum purchasable quantity of good

X

(

\frac{I}{P_x}

), moving the horizontal axis intercept outward while the vertical axis intercept (

\frac{I}{P_y}

) stays stationary. Since the slope magnitude is the price ratio

\frac{P_x}{P_y}

, a smaller

P_x

yields a smaller slope, making the budget line flatter.

Step-by-Step Solution

1

Identify the formulas for the budget line intercepts and slope.

Horizontal intercept =

\frac{I}{P_x}

, Vertical intercept =

\frac{I}{P_y}

, Absolute slope =

\frac{P_x}{P_y}

.

These equations define how income and prices determine the position and steepness of the budget line.

2

Analyze the impact of a decrease in

P_x

on the intercepts.

The horizontal intercept

\frac{I}{P_x}

increases, while the vertical intercept

\frac{I}{P_y}

remains unchanged.

Because income (

I

) and the price of good

Y

(

P_y

) are constant, only the maximum purchasable amount of good

X

changes.

3

Evaluate the change in the slope of the budget line.

The absolute slope

\frac{P_x}{P_y}

decreases, indicating that the budget line becomes less steep (flatter).

A lower price for good

X

reduces the opportunity cost of good

X

in terms of good

Y

.

Key Concept

Impact of Price Changes on Budget Line Rotation and Slope

Question 47Question →

Match each property of an indifference curve on the left with its correct economic explanation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Downward slope matches giving up one good for another to maintain constant utility; Convexity matches diminishing Marginal Rate of Substitution; Non-intersection matches transitivity and consistency; Higher curve matches higher total satisfaction.

Each property maps directly to its underlying postulate in ordinal utility theory: downward slope represents trade-offs under constant satisfaction, convexity represents diminishing

MRS

, non-intersection guarantees transitivity, and higher curves denote greater total satisfaction.

Step-by-Step Solution

1

Analyze the downward slope property

Downward slope implies a negative relationship between quantities of the two goods, showing substitution to keep total satisfaction constant.

Since utility is constant along a single curve, increasing consumption of Good

X

must be offset by decreasing Good

Y

.

2

Analyze the convexity property

Convexity reflects diminishing

MRS_{xy}

.

As more of Good

X

is consumed, the consumer values additional units of

X

less relative to Good

Y

.

3

Analyze the non-intersection property

Curves cannot cross due to transitivity.

If two curves crossed, a single point of intersection would imply two different levels of satisfaction are equal, violating consistency.

4

Analyze the position of higher curves

Higher curves correspond to greater utility.

Due to monotonicity of preferences, more of a good is preferred to less.

Key Concept

Properties of Indifference Curves and ordinal utility theory assumptions

Question 48Question →

A fundamental property of a standard indifference curve is that it is convex to the origin. Which economic concept directly explains why an indifference curve has this convex shape?

Diminishing marginal rate of substitution

Constant marginal rate of substitution

Increasing marginal rate of substitution

Total utility reaching its maximum when marginal utility is zero

Show answer & explanation

Answer: Diminishing marginal rate of substitution

Answer

Diminishing marginal rate of substitution

The convexity of an indifference curve to the origin is governed by the principle of diminishing marginal rate of substitution (

MRS_{xy}

). As a consumer acquires successive units of one commodity along an indifference curve, their valuation of additional units of that good relative to the other good declines, meaning they sacrifice progressively smaller quantities of the second good.

Step-by-Step Solution

1

Identify the structural property of the indifference curve being evaluated

The curve is convex to the origin

Convexity refers to the inward curvature of the indifference curve toward the origin point on a two-good graph.

2

Analyze the rate at which the consumer substitutes one good for another along the curve

The Marginal Rate of Substitution (

MRS_{xy}

) falls as consumption of Good X increases

To maintain equal satisfaction, equal additional units of Good X require giving up successively smaller quantities of Good Y.

3

Select the economic principle that matches this behavior

Diminishing marginal rate of substitution

The diminishing rate of substitution directly dictates the convex shape of standard indifference curves.

Key Concept

Diminishing Marginal Rate of Substitution and Indifference Curve Convexity

Question 49Question →

Match each geometric property of indifference curves in Column I with its underlying economic foundation or preference axiom in Column II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Each geometric property maps to its corresponding economic principle: Downward slope relates to the necessary trade-off between goods to keep total utility constant; Convexity towards the origin reflects a diminishing marginal rate of substitution (

MRS_{xy}

); Non-intersection ensures compliance with the axiom of transitivity; Higher curves reflect monotonicity of preferences (non-satiation).

Each geometric property directly corresponds to a fundamental behavioral assumption in ordinal utility theory: downward slope reflects the negative substitution trade-off required for constant utility; convexity reflects diminishing

MRS_{xy}

; non-intersection preserves preference transitivity; and higher curves represent greater satisfaction due to non-satiation.

Step-by-Step Solution

1

Analyze the downward slope property

Downward slope implies a negative marginal rate of substitution (

\frac{dY}{dX} < 0

), requiring substitution of one good for another to maintain equal utility.

Because total utility along an indifference curve is constant (

dU = MU_x dX + MU_y dY = 0

), an increase in

X

must be balanced by a decrease in

Y

.

2

Analyze the convexity property

Convexity implies that the slope (

MRS_{xy}

) diminishes in absolute magnitude as consumption of

X

increases relative to

Y

.

As

X

becomes more abundant, its marginal utility (

MU_x

) falls relative to

MU_y

, reducing the consumer's willingness to sacrifice

Y

for additional units of

X

.

3

Analyze the non-intersection property

Intersecting curves violate preference consistency and transitivity.

If curve

IC_1

and

IC_2

intersect at point

A

, and point

B

lies on

IC_1

while point

C

lies on

IC_2

, transitivity implies

B \sim A

and

A \sim C \implies B \sim C

, contradicting the requirement that distinct curves represent strictly different utility levels.

4

Analyze higher curve position

Curves located further from the origin represent higher utility levels.

Under monotonic preferences (non-satiation), consumption bundles containing more of both goods yield strictly greater satisfaction.

Key Concept

Properties of Indifference Curves and Preference Axioms

Question 50Question →

If a consumer's nominal income increases by $50\%$ while the price of good $X$ increases by $50\%$ and the price of good $Y$ remains constant, the budget line will pivot inward along the vertical axis while keeping its horizontal intercept unchanged.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. The budget line pivots outward along the vertical axis while maintaining a fixed horizontal intercept.

The horizontal intercept

(I / P_X)

remains identical because the

50\%

increase in nominal income is exactly offset by the

50\%

increase in the price of good

X

. However, because the price of good

Y

does not change, the

50\%

increase in income allows the consumer to purchase more of good

Y

, shifting the vertical intercept

(I / P_Y)

outward from the origin. Thus, the pivot is outward, making the statement false.

Step-by-Step Solution

1

Analyze the formula for the horizontal intercept.

The horizontal intercept is given by

\frac{I}{P_X}

. With a

50\%

increase in both

I

and

P_X

, the new intercept is

\frac{1.5 I}{1.5 P_X} = \frac{I}{P_X}

, which remains unchanged.

Proportionate changes in income and the price of a good cancel each other out for that good's axis intercept.

2

Analyze the formula for the vertical intercept.

The vertical intercept is given by

\frac{I}{P_Y}

. With a

50\%

increase in

I

and constant

P_Y

, the new intercept is

\frac{1.5 I}{P_Y} = 1.5 \left(\frac{I}{P_Y}\right)

, which increases by

50\%

.

Higher nominal income with an unchanged price expands the maximum affordable quantity of good

Y

.

3

Determine the direction of the rotational pivot and overall budget line movement.

Since the vertical intercept moves further out from the origin while the horizontal intercept stays fixed, the budget line pivots outward along the Y-axis and becomes steeper.

An inward pivot would require a decrease in maximum purchasable

Y

, which contradicts the

50\%

increase in real purchasing power for good

Y

.

Key Concept

Rotational Pivot of the Budget Line under Non-Proportionate Price and Income Changes

Question 51Question →

In consumer theory, the absolute slope of a budget line representing Good X on the horizontal axis and Good Y on the vertical axis measures which of the following?

The monetary expenditure required to purchase one unit of Good X

The opportunity cost of Good X in terms of Good Y foregone

The marginal rate of substitution derived from consumer preference curves

The total utility derived from the consumption of both goods

Show answer & explanation

Answer: The opportunity cost of Good X in terms of Good Y foregone

Answer

The opportunity cost of Good X in terms of Good Y foregone

The absolute slope of the budget line is given by the ratio of the prices of the two goods,

\frac{P_x}{P_y}

. This ratio reflects the rate at which the market allows a consumer to trade Good Y for Good X, representing the opportunity cost of acquiring an extra unit of Good X in terms of Good Y foregone.

Step-by-Step Solution

1

Determine the mathematical expression for the slope of the budget line.

The absolute slope of a budget line with Good X on the horizontal axis and Good Y on the vertical axis is given by the relative price ratio

\frac{P_x}{P_y}

.

The ratio of nominal prices indicates the market exchange rate between the two commodities.

2

Relate the price ratio to economic concepts.

The ratio

\frac{P_x}{P_y}

represents the quantity of Good Y that must be given up to obtain one additional unit of Good X.

Opportunity cost is defined as the value of the next best alternative foregone when making a choice.

Key Concept

Budget Line Slope as Relative Price and Opportunity Cost

Question 52Question →

If a consumer exhibits strictly convex preferences for two goods, any consumption bundle formed by taking a strict convex combination (weighted average) of two distinct bundles located on the same indifference curve will yield a strictly higher level of utility than either of the original bundles.

True

False

Show answer & explanation

Answer: True

Answer

The statement is true because strict convexity of preferences dictates that a weighted average (convex combination) of two distinct bundles providing identical utility yields a strictly higher level of utility.

Strict convexity of preferences reflects the principle that consumers prefer balanced combinations of goods over extreme allocations. Geometrically, connecting two distinct bundles on a strictly convex indifference curve creates a line segment whose interior points lie entirely above the curve, placing the consumer on a higher indifference curve with greater utility.

Step-by-Step Solution

1

Define the economic property of strict convexity of preferences.

Strict convexity states that for any two distinct bundles

A = (x_1, y_1)

and

B = (x_2, y_2)

where

A \sim B

, the weighted average bundle

C = \alpha A + (1-\alpha)B

for any

0 < \alpha < 1

satisfies

C \succ A \sim B

.

This formalizes the core theoretical axiom that consumers prefer balanced consumption of both goods rather than extreme specialization.

2

Analyze the geometric relationship between the line segment and the indifference curve.

Drawing a straight line segment between bundle

A

and bundle

B

on indifference curve

IC_1

places all interior points of the line segment in the region strictly above

IC_1

.

Because indifference curves are strictly convex (bowed inward toward the origin), any straight line connecting two points on the curve lies strictly to the northeast of the curve.

3

Relate the geometric position to utility level and Marginal Rate of Substitution (

MRS_{xy}

).

Any point situated strictly above

IC_1

lies on a higher indifference curve

IC_2

, indicating a higher utility level (

U(C) > U(A) = U(B)

).

Strict convexity guarantees a diminishing Marginal Rate of Substitution (

MRS_{xy} = -\frac{dY}{dX} = \frac{MU_x}{MU_y}

), which ensures the curve curves inward away from the chord connecting

A

and

B

.

4

Evaluate the truth value of the given statement.

The statement correctly describes the mathematical and economic implications of strict convexity.

The proposition matches the foundational definition of strictly convex preferences.

Key Concept

Strict Convexity of Preferences and Indifference Curves

Question 53Question →

A consumer's preferences for Good $X$ (on the horizontal axis) and Good $Y$ (on the vertical axis) yield an indifference curve where the consumer is willing to give up $6$ units of $Y$ to acquire $1$ additional unit of $X$ at consumption bundle $A$ . As the consumer moves to bundle $B$ by consuming more $X$ , the rate of substitution drops to $3$ units of $Y$ for $1$ additional unit of $X$ . Which of the following statements correctly explains the economic rationale behind this behavior and its geometric implication for the curve?

The marginal rate of substitution remains constant throughout, causing the indifference curve to be a downward-sloping straight line.

The marginal rate of substitution diminishes because the marginal utility of Good

X

falls relative to Good

Y

, making the indifference curve convex to the origin.

Total utility reaches its maximum at bundle

B

where marginal utility becomes zero, causing the indifference curve to become concave to the origin.

The consumer's total budget constraint shrinks as more of Good

X

is consumed, causing the curve to shift inward toward the origin.

Show answer & explanation

Answer: The marginal rate of substitution diminishes because the marginal utility of Good $X$ falls relative to Good $Y$ , making the indifference curve convex to the origin.

Answer

The marginal rate of substitution diminishes because the marginal utility of Good X falls relative to Good Y, making the indifference curve convex to the origin.

As a consumer moves down an indifference curve by consuming more of Good X in place of Good Y, the marginal utility of Good X decreases while that of Good Y increases. Since the Marginal Rate of Substitution (

MRS_{xy}

) equals the ratio of marginal utilities (

\frac{MU_x}{MU_y}

),

MRS_{xy}

decreases along the curve. Geometrically, this diminishing rate causes the slope of the curve to become flatter from left to right, making the indifference curve convex to the origin.

Step-by-Step Solution

1

Analyze the change in substitution rates between bundle A and bundle B

The consumer sacrifices fewer units of Good Y (decreasing from 6 to 3) for each extra unit of Good X.

This reduction demonstrates a diminishing Marginal Rate of Substitution (

MRS_{xy}

) along the curve.

2

Relate the Marginal Rate of Substitution to Marginal Utility ratios

The Marginal Rate of Substitution is expressed as

MRS_{xy} = \frac{MU_x}{MU_y}

. As more of Good X is consumed,

MU_x

declines relative to

MU_y

.

The principle of diminishing marginal utility dictates that acquiring more units of a specific commodity reduces its relative additional satisfaction.

3

Deduce the geometric shape of the curve

A progressively decreasing absolute slope (

MRS_{xy}

) from left to right establishes that the curve bends inward.

Diminishing marginal rate of substitution is the exact theoretical foundation for the convexity of an indifference curve to the origin.

Key Concept

Diminishing Marginal Rate of Substitution and Convexity of Indifference Curves

Estimated Time:1m 30s

Question 54Question →

An increase in a consumer's money income, holding the prices of all goods constant, causes the slope of the budget line to become steeper.

True

False

Show answer & explanation

Answer: False

Answer

False. An increase in income while holding prices constant causes a parallel outward shift of the budget line, leaving its slope unchanged.

The correct answer is False. The slope of the budget line is determined strictly by the ratio of the prices of the two goods (

-\frac{P_X}{P_Y}

). An increase in consumer income with prices held constant shifts both intercepts outward by the same proportion, producing a parallel shift of the budget line without altering its steepness.

Step-by-Step Solution

1

Recall the formula for the slope of a budget line.

The slope of the budget line is given by

-\frac{P_X}{P_Y}

, where

P_X

is the price of Good X on the horizontal axis and

P_Y

is the price of Good Y on the vertical axis.

The slope represents the market rate of substitution, determined entirely by relative prices.

2

Analyze the impact of an increase in nominal income (

I

) when

P_X

and

P_Y

remain constant.

Both the horizontal intercept (

\frac{I}{P_X}

) and vertical intercept (

\frac{I}{P_Y}

) increase proportionally.

Higher nominal income increases the maximum achievable quantities of both goods.

3

Determine if the slope changes.

Since neither

P_X

nor

P_Y

changes, the price ratio

-\frac{P_X}{P_Y}

remains identical, causing a parallel shift rather than a change in steepness.

A change in slope requires a change in the relative price ratio (

P_X / P_Y

).

Key Concept

Parallel Shifts vs. Rotations of the Budget Line

Question 55Question →

A consumer allocates a total income of ₦ $15,000$ exclusively to buy Good $X$ and Good $Y$ . The price of Good $X$ ( $P_X$ ) is ₦ $1,500$ per unit, and the price of Good $Y$ ( $P_Y$ ) is ₦ $1,000$ per unit. If the consumer buys $6$ units of Good $X$ , what is the maximum number of units of Good $Y$ that can be purchased?

Show answer & explanation

Answer: 6

Answer

The maximum number of units of Good

Y

the consumer can purchase is

6

units.

Using the budget equation

I = P_X Q_X + P_Y Q_Y

, substituting the given values yields

15,000 = (1,500 \times 6) + (1,000 \times Q_Y)

. Simplifying gives

15,000 = 9,000 + 1,000 Q_Y

, so

1,000 Q_Y = 6,000

, resulting in

Q_Y = 6

units.

Step-by-Step Solution

1

Calculate expenditure on Good

X

Expenditure on

X = 6 \times 1,500 = 9,000

Total spending on Good

X

is quantity multiplied by unit price.

2

Determine remaining budget for Good

Y

Remaining budget =

15,000 - 9,000 = 6,000

Subtracting expenditure on Good

X

from total income leaves the available budget for Good

Y

.

3

Calculate maximum quantity of Good

Y

Quantity of Good

Y = 6,000 / 1,000 = 6

Dividing the remaining budget by the unit price of Good

Y

yields the maximum affordable quantity of Good

Y

.

Key Concept

Budget Constraint and Linear Budget Equation

Question 56Question →

A consumer adjusting their bundle of goods moves along an indifference curve, giving up $4$ units of Good $Y$ to obtain $2$ additional units of Good $X$ without changing their total level of satisfaction. What is the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) over this range?

2.0

0.5

6.0

1.0

Show answer & explanation

Answer: $2.0$

Answer

The Marginal Rate of Substitution (

MRS_{xy}

) is equal to

2.0

.

The Marginal Rate of Substitution of

X

for

Y

(

MRS_{xy}

) measures the units of Good

Y

a consumer must sacrifice to gain one additional unit of Good

X

while keeping total utility constant. Here, sacrificing

4

units of

Y

for

2

units of

X

gives an average rate of

\frac{4}{2} = 2.0

.

Step-by-Step Solution

1

Identify the change in quantity of Good

Y

(

\Delta Y

) and Good

X

(

\Delta X

)

\Delta Y = -4

(reduction of 4 units of

Y

) and

\Delta X = +2

(gain of 2 units of

X

)

The consumer gives up

Y

in exchange for

X

to remain on the same indifference curve.

2

Apply the Marginal Rate of Substitution formula

MRS_{xy} = -\frac{\Delta Y}{\Delta X} = -\left(\frac{-4}{2}\right) = 2.0

The magnitude of the slope of the indifference curve represents the rate at which

Y

is substituted for

X

.

Key Concept

Marginal Rate of Substitution (MRS) along an Indifference Curve

Estimated Time:1m 0s

Question 57Question →

A consumer allocating an income of $\text{₦}1,800$ between Good $X$ and Good $Y$ faces market prices of $P_x = \text{₦}40$ and $P_y = \text{₦}30$ per unit, respectively. The consumer's Marginal Rate of Substitution of Good $X$ for Good $Y$ is given by $MRS_{xy} = \frac{2Y}{X}$ . Assuming the consumer maximizes satisfaction subject to their budget constraint, how many units of Good $X$ will be consumed at equilibrium?

Show answer & explanation

Answer: 30

Answer

At consumer equilibrium under ordinal utility analysis, the optimal quantity of Good

X

consumed is 30 units.

At consumer equilibrium under ordinal utility, the tangency condition requires

MRS_{xy} = \frac{P_x}{P_y}

. Substituting

MRS_{xy} = \frac{2Y}{X}

and prices

P_x = 40

,

P_y = 30

gives

\frac{2Y}{X} = \frac{40}{30}

, which simplifies to

Y = \frac{2}{3}X

. Substituting

Y = \frac{2}{3}X

into the consumer's budget constraint

40X + 30Y = 1800

yields

40X + 30\left(\frac{2}{3}X\right) = 1800 \implies 60X = 1800 \implies X = 30

units.

Step-by-Step Solution

1

Equate the Marginal Rate of Substitution (

MRS_{xy}

) to the price ratio (

P_x / P_y

) to apply the tangency condition for ordinal utility equilibrium.

\frac{2Y}{X} = \frac{40}{30} \implies \frac{2Y}{X} = \frac{4}{3} \implies 6Y = 4X \implies Y = \frac{2}{3}X

Consumer equilibrium under ordinal utility requires that the slope of the indifference curve (

MRS_{xy}

) equals the slope of the budget line (

P_x / P_y

).

2

Substitute the expression for

Y

into the budget constraint equation

P_x X + P_y Y = I

.

40X + 30\left(\frac{2}{3}X\right) = 1800

To achieve maximum utility within income limits, the entire income of

\text{₦}1,800

must be spent on goods

X

and

Y

.

3

Simplify the equation and solve for the value of

X

.

40X + 20X = 1800 \implies 60X = 1800 \implies X = 30

Combining like terms gives a linear equation in

X

, yielding 30 units at equilibrium.

Key Concept

Consumer equilibrium under ordinal utility occurs where the highest attainable indifference curve is tangent to the budget line, satisfying

MRS_{xy} = \frac{P_x}{P_y}

alongside the budget constraint

P_x X + P_y Y = I

.

Question 58Question →

A consumer achieves equilibrium under the ordinal utility framework while purchasing Good $X$ and Good $Y$ . If the market price of Good $X$ is $\text{₦}150$ and the market price of Good $Y$ is $\text{₦}50$ , calculate the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) at the equilibrium point.

Show answer & explanation

Answer: 3

Answer

The Marginal Rate of Substitution of Good

X

for Good

Y

(

MRS_{xy}

) at the consumer's equilibrium point is

3

.

In ordinal utility theory, consumer equilibrium occurs where the budget line is tangent to the highest attainable indifference curve. At this tangency point, the slope of the indifference curve—known as the Marginal Rate of Substitution (

MRS_{xy}

)—equals the ratio of the prices of the two goods (

\frac{P_x}{P_y}

). Given

P_x = \text{₦}150

and

P_y = \text{₦}50

,

MRS_{xy} = \frac{150}{50} = 3

.

Step-by-Step Solution

1

State the consumer equilibrium condition under ordinal utility analysis.

MRS_{xy} = \frac{P_x}{P_y}

At the point of consumer equilibrium, the indifference curve is tangent to the budget line, meaning their slopes are equal.

2

Substitute the prices of Good

X

and Good

Y

to find the ratio.

MRS_{xy} = \frac{150}{50} = 3

Dividing the price of Good

X

(₦150) by the price of Good

Y

(₦50) yields the slope of the budget line.

Key Concept

Consumer Equilibrium Tangency Condition

Question 59Question →

A consumer allocates a monthly income of $\text{₦}12,000$ between Good $X$ and Good $Y$ . The market price of Good $Y$ is $\text{₦}400$ per unit. At consumer equilibrium under ordinal utility analysis, the consumer purchases $15$ units of Good $Y$ . If the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) at this equilibrium point is $1.5$ , how many units of Good $X$ does the consumer purchase?

Show answer & explanation

Answer: 10

Answer

10 units

Under ordinal utility theory, consumer equilibrium occurs at the point of tangency between the highest attainable indifference curve and the budget line, satisfying

MRS_{xy} = \frac{P_x}{P_y}

. Given

MRS_{xy} = 1.5

and

P_y = \text{₦}400

, the price of Good

X

is

P_x = 1.5 \times 400 = \text{₦}600

. Spending

15

units of

Y

at

\text{₦}400

consumes

\text{₦}6,000

of the total

\text{₦}12,000

budget, leaving

\text{₦}6,000

for Good

X

. Dividing

\text{₦}6,000

by

P_x = \text{₦}600

yields exactly

10

units of Good

X

.

Step-by-Step Solution

1

Calculate the total expenditure on Good Y

₦6,000

Multiply the equilibrium quantity of Y (15 units) by the unit price of Y (₦400).

2

Determine the remaining budget allocated to Good X

₦6,000

Subtract total expenditure on Y from the overall income (₦12,000 - ₦6,000).

3

Calculate the unit price of Good X using the ordinal equilibrium condition

₦600

At consumer equilibrium under ordinal utility, the slope of the indifference curve equals the slope of the budget line (

MRS_{xy} = \frac{P_x}{P_y}

). Thus,

1.5 = \frac{P_x}{400} \Rightarrow P_x = 600

.

4

Calculate the quantity of Good X purchased

10 units

Divide the expenditure on Good X (₦6,000) by the price of Good X (₦600).

Key Concept

Consumer Equilibrium under Ordinal Utility

Question 60Question →

A consumer allocates a total monetary budget of ₦18,000 to purchase Good $X$ (plotted on the horizontal axis) and Good $Y$ (plotted on the vertical axis). At current market prices, the consumer can afford a maximum of 60 units of Good $X$ or 45 units of Good $Y$ . If the price of Good $X$ decreases by $25\%$ while the price of Good $Y$ and total money income remain constant, what is the absolute value of the slope of the new budget line?

0.5625

0.7500

1.7778

0.4219

Show answer & explanation

Answer: 0.5625

Answer

The absolute value of the slope of the new budget line is 0.5625.

The initial unit prices derived from maximum affordable quantities are Px = ₦300 and Py = ₦400. Decreasing Px by 25% gives a new price Px' = ₦225. Because the slope of the budget line on a standard coordinate system (Good X on the horizontal axis) equals -Px / Py, its magnitude is 225 / 400 = 0.5625.

Step-by-Step Solution

1

Calculate initial unit prices of Good X and Good Y from budget intercepts

Px = ₦18,000 / 60 = ₦300; Py = ₦18,000 / 45 = ₦400

The maximum quantity of each good attainable with full budget equals Income divided by unit price.

2

Determine the updated price of Good X after a 25% price decrease

Px' = ₦300 × (1 - 0.25) = ₦225

A 25% price fall reduces the nominal price per unit of Good X by ₦75.

3

Compute the slope of the new budget line

Absolute slope = Px' / Py = 225 / 400 = 0.5625

The absolute slope of a budget line with Good X on the horizontal axis represents relative prices (Px / Py).

Key Concept

Budget Line Slope and Price Changes

Estimated Time:2m 0s

Theory of Consumer Behaviour

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept