Theory of Consumer Behaviour Practice Questions — JAMB UTME — Page 2

Question 21Question →

The table below presents a consumer's indifference schedule showing various combinations of Good $X$ and Good $Y$ that yield the same level of satisfaction:

Combination	Good $X$ (units)	Good $Y$ (units)
I	1	18
II	2	12
III	3	7
IV	4	3
V	5	1

What is the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) as the consumer transitions from combination II to combination III, and which property of indifference curves is confirmed by the overall progression across all combinations?

MRS_{xy} = 5

; it confirms that indifference curves are convex to the origin due to a diminishing marginal rate of substitution.

MRS_{xy} = 5

; it confirms that indifference curves are concave to the origin due to an increasing marginal rate of substitution.

MRS_{xy} = 7

; it confirms that indifference curves slope downward with a constant marginal rate of substitution.

MRS_{xy} = 12

; it confirms that higher indifference curves represent higher levels of total utility.

Show answer & explanation

Answer: $MRS_{xy} = 5$ ; it confirms that indifference curves are convex to the origin due to a diminishing marginal rate of substitution.

Answer

MRS_{xy} = 5

; it confirms that indifference curves are convex to the origin due to a diminishing marginal rate of substitution.

Moving from combination II

(2X, 12Y)

to combination III

(3X, 7Y)

requires sacrificing

5

units of Good

Y

to gain

1

unit of Good

X

, giving an

MRS_{xy}

of

5

. Across the entire schedule, the rate of sacrifice decreases (

6 \rightarrow 5 \rightarrow 4 \rightarrow 2

). This law of diminishing marginal rate of substitution is the fundamental reason standard indifference curves are convex to the origin.

Step-by-Step Solution

1

Calculate the Marginal Rate of Substitution (

MRS_{xy}

) between combination II and combination III.

\Delta X = 3 - 2 = 1

unit;

\Delta Y = 12 - 7 = 5

units.

MRS_{xy} = \left| \frac{\Delta Y}{\Delta X} \right| = \frac{5}{1} = 5

.

The Marginal Rate of Substitution measures the amount of Good

Y

a consumer is willing to give up to obtain an additional unit of Good

X

while keeping total utility constant.

2

Analyze the pattern of

MRS_{xy}

across all consecutive combinations in the schedule.

From I to II:

MRS_{xy} = \frac{18 - 12}{1} = 6

. From II to III:

MRS_{xy} = \frac{12 - 7}{1} = 5

. From III to IV:

MRS_{xy} = \frac{7 - 3}{1} = 4

. From IV to V:

MRS_{xy} = \frac{3 - 1}{1} = 2

.

Tracking the full schedule reveals whether the willingness to substitute is increasing, constant, or diminishing.

3

Relate the diminishing trend of

MRS_{xy}

to the geometric property of indifference curves.

The progression

6 \rightarrow 5 \rightarrow 4 \rightarrow 2

shows a diminishing

MRS_{xy}

, which geometrically ensures that the indifference curve is convex to the origin.

As a consumer acquires more of Good

X

, its marginal utility relative to Good

Y

falls, leading to a flatter slope (diminishing rate of substitution) moving left to right.

Key Concept

Marginal Rate of Substitution (

MRS_{xy}

) and Convexity of Indifference Curves

Estimated Time:1m 30s

Question 22Question →

A consumer's demand function for petrol in a local Nigerian market is given by the linear equation $P = 200 - 8Q$ , where $P$ represents the price per liter in Naira and $Q$ represents the quantity demanded in liters. If the current market price of petrol is established at $\text{N}80$ per liter, calculate the consumer surplus in Naira.

Show answer & explanation

Answer: 900

Answer

The value of the consumer surplus is 900 Naira.

Consumer surplus is the difference between total willingness to pay and total actual expenditure. Graphically, for a linear demand curve, it is the area of the triangle bounded by the price axis, the market price line, and the demand curve. With market price P = 80 Naira and quantity Q = 15 liters, the price intercept is 200 Naira. The area of the triangle is calculated as 0.5 * 15 * (200 - 80) = 900 Naira.

Step-by-Step Solution

1

Determine quantity demanded at the market price

Q = 15 liters

Substitute P = 80 into the demand equation P = 200 - 8Q and solve for Q.

2

Find the maximum willingness to pay (vertical axis intercept)

P_max = 200 Naira

At zero quantity consumed (Q = 0), the maximum price the consumer is willing to pay is 200 Naira.

3

Calculate the area of the triangular consumer surplus region

Consumer Surplus = 900 Naira

Consumer Surplus = 0.5 * Base * Height = 0.5 * 15 * (200 - 80) = 900.

Key Concept

Calculation of Consumer Surplus from a Linear Demand Function

Estimated Time:2m 0s

Question 23Question →

Along an indifference curve that is concave to the origin, the Marginal Rate of Substitution ( $MRS_{xy}$ ) increases as a consumer substitutes Good $X$ for Good $Y$ , indicating that the consumer is willing to give up progressively larger amounts of Good $Y$ to acquire each additional unit of Good $X$ .

True

False

Show answer & explanation

Answer: True

Answer

The statement is True.

The statement is correct because concavity to the origin mathematically implies an increasing absolute slope along the indifference curve as consumption of Good

X

increases. Consequently,

MRS_{xy}

increases rather than diminishes, requiring larger sacrifices of Good

Y

for additional units of Good

X

.

Step-by-Step Solution

1

Define the Marginal Rate of Substitution (

MRS_{xy}

) in terms of indifference curve geometry.

The

MRS_{xy}

is represented by the absolute value of the slope of the indifference curve at any point, calculated as

MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}

.

Establishing the link between curve slope and

MRS_{xy}

is essential for analyzing indifference curve curvature.

2

Analyze how slope changes along a curve that is concave to the origin.

As a consumer moves down along a concave curve (increasing consumption of Good

X

and decreasing consumption of Good

Y

), the curve grows progressively steeper.

Increased steepness from left to right means that the magnitude of

\frac{\Delta Y}{\Delta X}

gets larger.

3

Relate the changing slope to consumer trade-offs and

MRS_{xy}

.

Because the curve gets steeper,

MRS_{xy}

increases. This confirms that the consumer must give up larger quantities of Good

Y

for each additional unit of Good

X

.

This validates that the statement correctly describes the behavioral implications of a concave indifference curve.

Key Concept

Indifference Curve Curvature and Marginal Rate of Substitution

Question 24Question →

A consumer is willing to pay a maximum of ₦8,500 for a new textbook, but purchases it in the market for ₦5,800. What is the value of the consumer surplus in Naira?

Show answer & explanation

Answer: 2700

Answer

The consumer surplus is ₦2,700.

Consumer surplus is calculated by deducting the actual price paid from the maximum price the consumer was willing to pay: ₦8,500 - ₦5,800 = ₦2,700.

Step-by-Step Solution

1

Identify maximum willingness to pay and actual price

Maximum Willingness to Pay = ₦8,500; Market Price = ₦5,800

Consumer surplus is determined by comparing what the buyer is willing to pay against the market price.

2

Subtract the market price from the maximum willingness to pay

Consumer Surplus = ₦8,500 - ₦5,800 = ₦2,700

Consumer Surplus represents the financial gain or net benefit enjoyed by the consumer.

Key Concept

Consumer surplus is the difference between the total amount that consumers are willing and able to pay for a good or service and the total amount that they actually pay.

Estimated Time:45s

Question 25Question →

A consumer's consumption schedule for glasses of fresh juice reveals the following Total Utility ( $TU$ ) values: $36$ utils for $3$ glasses, $48$ utils for $4$ glasses, $55$ utils for $5$ glasses, $55$ utils for $6$ glasses, and $49$ utils for $7$ glasses. Based on this utility schedule, match each utility metric or milestone listed on the left with its corresponding calculated value or quantity on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Average Utility at 4 units matches 12 utils per glass; Marginal Utility of the 5th unit matches 7 utils; Quantity at point of saturation matches 6 glasses; Marginal Utility of the 7th unit matches -6 utils.

Each utility concept correctly pairs with its mathematical derivation from the schedule:

AU

at

4

units equals

12

utils per glass (

48/4

);

MU

of the

5^{\text{th}}

unit equals

7

utils (

55-48

); saturation point is reached at

6

glasses where

MU = 0

; and

MU

of the

7^{\text{th}}

unit equals

-6

utils (

49-55

).

Step-by-Step Solution

1

Calculate Average Utility (

AU

) at

4

glasses.

AU_4 = \frac{TU_4}{Q_4} = \frac{48}{4} = 12

utils per glass.

Average Utility is defined as Total Utility divided by the total number of units consumed.

2

Calculate Marginal Utility (

MU

) for the

5^{\text{th}}

glass.

MU_5 = TU_5 - TU_4 = 55 - 48 = 7

utils.

Marginal Utility measures the change in Total Utility resulting from consuming one additional unit.

3

Identify the point of saturation (

MU = 0

).

At

Q = 6

,

TU

remains unchanged at

55

utils, giving

MU_6 = 55 - 55 = 0

. Thus,

6

glasses is the saturation point.

Consumer saturation occurs when Total Utility reaches its maximum level and Marginal Utility drops to zero.

4

Calculate Marginal Utility (

MU

) for the

7^{\text{th}}

glass.

MU_7 = TU_7 - TU_6 = 49 - 55 = -6

utils.

When consumption exceeds the saturation point, Total Utility decreases, yielding negative Marginal Utility (disutility).

Key Concept

Concepts of Utility (Total, Average, and Marginal Utility)

Estimated Time:1m 30s

Question 26Question →

A consumer in a local market is willing to pay a maximum of ₦1,200 for a pair of sandals, but purchases them at the prevailing market price of ₦800. What is the value of the consumer surplus derived from this purchase?

₦400

₦800

₦1,200

₦2,000

Show answer & explanation

Answer: ₦400

Answer

₦400

The consumer surplus is ₦400 because it represents the difference between the maximum amount the consumer was prepared to pay (₦1,200) and the price actually paid in the market (₦800).

Step-by-Step Solution

1

Identify the consumer's maximum willingness to pay and the actual price paid in the market.

Maximum Willingness to Pay = ₦1,200; Market Price Paid = ₦800.

Consumer surplus measures the economic benefit received by paying less than maximum willingness.

2

Apply the consumer surplus formula: Consumer Surplus = Maximum Willingness to Pay - Actual Price Paid.

Consumer Surplus = ₦1,200 - ₦800 = ₦400.

Subtracting actual expenditure from total monetary valuation yields the net benefit.

Key Concept

Consumer surplus is the difference between the maximum amount a consumer is willing to pay for a commodity and the actual amount paid.

Question 27Question →

In ordinal utility theory, a consumer maximizes satisfaction within a given budget at the point of tangency between the indifference curve and the budget line. At this equilibrium position, the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) is equal to which of the following?

The price ratio of the two commodities,

\frac{P_x}{P_y}

The inverse price ratio of the two commodities,

\frac{P_y}{P_x}

The point where total utility derived from both goods reaches zero

A constant slope along the entire length of the indifference curve

Show answer & explanation

Answer: The price ratio of the two commodities, $\frac{P_x}{P_y}$

Answer

The price ratio of the two commodities,

\frac{P_x}{P_y}

Under ordinal utility analysis using indifference curves, consumer equilibrium is achieved at the tangency point between the budget line and the highest attainable indifference curve. At this tangency point, the slope of the indifference curve (

MRS_{xy}

) equals the slope of the budget line (

\frac{P_x}{P_y}

).

Step-by-Step Solution

1

Identify the slope of the indifference curve

The slope of the indifference curve represents the Marginal Rate of Substitution (

MRS_{xy} = -\frac{\Delta Y}{\Delta X}

).

It measures the rate at which a consumer is willing to substitute Good

Y

for Good

X

while maintaining the same level of utility.

2

Identify the slope of the budget line

The slope of the budget line is given by the relative price ratio of the two goods (

-\frac{P_x}{P_y}

).

It represents the rate at which the market allows the consumer to trade Good

X

for Good

Y

given their prices.

3

Equate the slopes to find the consumer equilibrium condition

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

Equilibrium occurs at the point of tangency where the rate at which the consumer is willing to substitute goods equals the market rate of substitution.

Key Concept

Consumer Equilibrium Condition in Ordinal Utility Analysis

Question 28Question →

A consumer derives a total utility worth $\text{N} 1,500$ from consuming $5$ units of a commodity. If the market price of the commodity is $\text{N} 200$ per unit, what is the consumer surplus in Naira?

Show answer & explanation

Answer: 500

Answer

The consumer surplus is

\text{N} 500

.

Consumer surplus is calculated as Total Utility (total willingness to pay) minus Total Expenditure (

P \times Q

). Here, Total Utility is

\text{N} 1,500

, and Total Expenditure is

5 \times \text{N} 200 = \text{N} 1,000

. Subtracting

\text{N} 1,000

from

\text{N} 1,500

gives a consumer surplus of

\text{N} 500

.

Step-by-Step Solution

1

Calculate total actual expenditure on the commodity

Total Expenditure =

5 \times \text{N} 200 = \text{N} 1,000

Total expenditure is the actual amount spent by the consumer, found by multiplying price per unit by the number of units bought.

2

Subtract total expenditure from total utility to find consumer surplus

Consumer Surplus =

\text{N} 1,500 - \text{N} 1,000 = \text{N} 500

Consumer surplus is the net economic benefit, calculated as the total monetary utility derived minus total expenditure.

Key Concept

Calculation of Consumer Surplus from Total Utility and Total Expenditure

Question 29Question →

Match each condition of Marginal Utility ( $MU$ ) on the left with its corresponding effect on Total Utility ( $TU$ ) on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: Positive and falling Marginal Utility corresponds to Total Utility increasing at a decreasing rate; Marginal Utility equal to zero corresponds to Total Utility reaching its maximum level (satiety point); Negative Marginal Utility corresponds to Total Utility beginning to decline.

Under the Law of Diminishing Marginal Utility, as consumption increases, positive marginal utility means total utility continues to rise at a decreasing rate. At the point of satiety, marginal utility equals zero and total utility reaches its maximum. If consumption continues, marginal utility becomes negative and total utility begins to diminish.

Step-by-Step Solution

1

Examine the relationship between Marginal Utility (

MU

) and Total Utility (

TU

).

MU

represents the rate of change of

TU

with respect to quantity consumed (

MU = \frac{\Delta TU}{\Delta Q}

).

Understanding

MU

as the slope of

TU

clarifies how changes in

MU

dictate the behavior of

TU

.

2

Evaluate the behavior of Total Utility at key Marginal Utility thresholds (

MU > 0

,

MU = 0

,

MU < 0

).

As long as

MU > 0

,

TU

grows. When

MU = 0

,

TU

stops growing and attains maximum height. When

MU < 0

,

TU

drops.

This directly applies the Law of Diminishing Marginal Utility to consumer utility schedules.

Key Concept

Relationship between Total Utility and Marginal Utility under the Law of Diminishing Marginal Utility

Question 30Question →

A consumer spends a fixed weekly income $I$ on Good $X$ (plotted on the horizontal axis) and Good $Y$ (plotted on the vertical axis) with unit prices $P_x$ and $P_y$ . Suppose the government imposes a $20\%$ ad valorem tax on Good $X$ while simultaneously providing the consumer with a lump-sum income subsidy equal to $20\%$ of their initial total income $I$ , leaving $P_y$ unchanged. Which of the following correctly describes the structural transformation of the consumer's budget line?

The vertical intercept increases by

20\%

, the horizontal intercept remains unchanged, and the budget line pivots counter-clockwise around the fixed horizontal intercept to become steeper.

The budget line shifts outward in a parallel direction because both nominal income and the price of Good

X

increased by the same proportion.

The horizontal intercept decreases by

20\%

while the vertical intercept remains unchanged because the lump-sum grant exactly neutralizes the price increase of Good

X

.

The slope of the budget line remains constant because the relative price ratio

P_x/P_y

is offset by the

20\%

increase in purchasing power.

Show answer & explanation

Answer: The vertical intercept increases by $20\%$ , the horizontal intercept remains unchanged, and the budget line pivots counter-clockwise around the fixed horizontal intercept to become steeper.

Answer

The vertical intercept increases by 20%, the horizontal intercept remains unchanged, and the budget line pivots counter-clockwise around the fixed horizontal intercept to become steeper.

The initial budget line has a horizontal intercept at

I/P_x

, vertical intercept at

I/P_y

, and slope of magnitude

P_x/P_y

. Following the policy changes, the new income is

1.20I

and the new price of

X

is

1.20P_x

. The new horizontal intercept is

(1.20I)/(1.20P_x) = I/P_x

, which is unchanged. The new vertical intercept is

(1.20I)/P_y

, representing a

20\%

increase. The slope magnitude increases to

(1.20P_x)/P_y = 1.20(P_x/P_y)

, making the budget line steeper. Graphically, anchoring the budget line at the same point on the horizontal axis while pushing its vertical endpoint upward corresponds to a counter-clockwise pivot around the fixed horizontal intercept.

Step-by-Step Solution

1

Express the initial budget equation and its key boundary intercepts and slope.

Initial equation:

P_x X + P_y Y = I

. Horizontal intercept (

X

-axis) =

\frac{I}{P_x}

, Vertical intercept (

Y

-axis) =

\frac{I}{P_y}

, Slope =

-\frac{P_x}{P_y}

.

Establishing initial parameter values allows direct comparison with post-tax and post-subsidy values.

2

Determine the updated price of Good

X

and updated nominal income.

P_x' = (1 + 0.20) P_x = 1.20 P_x

;

I' = (1 + 0.20) I = 1.20 I

;

P_y' = P_y

.

The

20\%

tax inflates

P_x

by a factor of

1.20

, and the

20\%

income subsidy inflates

I

by a factor of

1.20

.

3

Calculate the new horizontal intercept, vertical intercept, and slope.

New Horizontal Intercept =

\frac{I'}{P_x'} = \frac{1.20 I}{1.20 P_x} = \frac{I}{P_x}

(Unchanged).
New Vertical Intercept =

\frac{I'}{P_y'} = \frac{1.20 I}{P_y} = 1.20 \left(\frac{I}{P_y}\right)

(

20\%

increase).
New Slope =

-\frac{P_x'}{P_y'} = -\frac{1.20 P_x}{P_y} = 1.20 \left(-\frac{P_x}{P_y}\right)

(

20\%

magnitude increase, steeper).

Comparing the relative scaling factors reveals which intercept shifts and how the opportunity cost ratio changes.

4

Synthesize the geometrical movement of the budget line.

Since the

X

-intercept is fixed while the

Y

-intercept shifts outward, the budget line pivots counter-clockwise around the

X

-intercept, making it steeper.

A fixed horizontal intercept combined with a higher vertical intercept results in a counter-clockwise rotation.

Key Concept

Budget Line Intercepts and Slope Transformation under Asymmetric Price and Income Changes

Estimated Time:2m 0s

Question 31Question →

For a normal good, the substitution effect and the income effect operate in opposite directions following a change in the price of the good.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. For a normal good, the substitution effect and the income effect operate in the same direction.

The statement is false because for any normal good, a price decrease creates a substitution effect and an income effect that both work in the same direction to increase total quantity demanded.

Step-by-Step Solution

1

Examine the substitution effect direction upon a price decrease.

The substitution effect always induces a consumer to purchase more of a good when its relative price falls.

The good becomes relatively less expensive compared to alternative substitute goods.

2

Examine the income effect direction for a normal good.

The increase in real purchasing power leads to an increase in the quantity demanded of the normal good.

By definition, the demand for a normal good rises as real income increases.

3

Combine both effects to determine their directional relationship.

Both the substitution effect and the income effect push quantity demanded in the same upward direction.

Because both effects act constructively together, they do not oppose each other for normal goods.

Key Concept

Directional interaction of income and substitution effects for normal goods

Question 32Question →

A consumer derives a total utility of $50$ utils from consuming $4$ packs of biscuits and $62$ utils after consuming the $5^{\text{th}}$ pack. What is the marginal utility of the $5^{\text{th}}$ pack of biscuits?

12

utils

62

utils

12.4

utils

112

utils

Show answer & explanation

Answer: $12$ utils

Answer

The marginal utility of the

5^{\text{th}}

pack of biscuits is

12

utils.

Marginal utility measures the addition to total utility derived from consuming one extra unit of a good. Subtracting the total utility of

4

packs (

50

utils) from the total utility of

5

packs (

62

utils) yields

12

utils.

Step-by-Step Solution

1

Identify the formula for Marginal Utility (MU)

\text{MU} = \frac{\Delta \text{TU}}{\Delta Q} = \text{TU}_n - \text{TU}_{n-1}

Marginal Utility measures the extra satisfaction gained from consuming one more unit of a commodity.

2

Substitute the given values into the formula

\text{MU}_5 = 62 - 50 = 12

utils

Subtracting the total utility of

4

units (

50

utils) from the total utility of

5

units (

62

utils) gives the marginal utility of the

5^{\text{th}}

unit.

Key Concept

Marginal Utility Calculation

Estimated Time:45s

Question 33Question →

A consumer's total utility ( $TU$ ) from consuming $3$ units of commodity X is $45$ utils. Consuming the $4^{\text{th}}$ unit provides a marginal utility ( $MU$ ) of $9$ utils. The $5^{\text{th}}$ unit brings the consumer to the point of satiety (saturation), while consuming the $6^{\text{th}}$ unit results in a marginal utility of $-3$ utils. What is the average utility ( $AU$ ) derived from consuming $5$ units of commodity X?

10.8

utils

12.6

utils

9.0

utils

10.2

utils

Show answer & explanation

Answer: $10.8$ utils

Answer

The average utility derived from consuming 5 units of commodity X is

10.8

utils.

The correct answer of

10.8

utils is obtained because total utility at

3

units (

45

utils) plus the marginal utility of the

4^{\text{th}}

unit (

9

utils) equals

54

utils. At the point of satiety (

5^{\text{th}}

unit), marginal utility is

0

, leaving total utility unchanged at

54

utils. Dividing

54

utils by

5

units yields an average utility of

10.8

utils.

Step-by-Step Solution

1

Calculate Total Utility for 4 units (

TU_4

)

TU_4 = TU_3 + MU_4 = 45 + 9 = 54

utils

Total utility at

n

units is the sum of total utility at

n-1

units and the marginal utility of the

n^{\text{th}}

unit.

2

Determine Marginal Utility (

MU_5

) and Total Utility (

TU_5

) at the point of satiety

MU_5 = 0

utils, so

TU_5 = TU_4 + MU_5 = 54 + 0 = 54

utils

At the point of satiety (saturation point), Total Utility reaches its maximum, which means Marginal Utility is exactly zero.

3

Compute Average Utility for 5 units (

AU_5

)

AU_5 = \frac{TU_5}{5} = \frac{54}{5} = 10.8

utils

Average utility is defined as total utility divided by the quantity consumed (

AU = \frac{TU}{Q}

).

Key Concept

Relationship between Total Utility, Marginal Utility at the point of satiety, and Average Utility calculation.

Question 34Question →

A consumer's marginal utility ( $MU$ ) for the first three consecutive glasses of fruit juice consumed is $27$ utils, $35$ utils, and $23$ utils respectively. If consuming the $4\text{th}$ glass brings total utility ( $TU$ ) to $97$ utils, and the consumer reaches the satiety point at the $6\text{th}$ glass where total utility is maximized at $101$ utils (with $TU$ for the $5\text{th}$ glass also equal to $101$ utils), which of the following correctly identifies the unit at which the Law of Diminishing Marginal Utility first sets in, the $MU$ of the $4\text{th}$ glass, and the $MU$ at the satiety point?

3rd glass,

12

utils, and

0

utils

2nd glass,

12

utils, and

0

utils

3rd glass,

24.25

utils, and

4

utils

4th glass,

12

utils, and

4

utils

Show answer & explanation

Answer: 3rd glass, $12$ utils, and $0$ utils

Answer

The Law of Diminishing Marginal Utility first sets in at the 3rd glass, the marginal utility of the 4th glass is

12

utils, and the marginal utility at the satiety point is

0

utils.

The correct response accurately applies the principles of cardinal utility theory. First, diminishing marginal utility begins when marginal satisfaction starts decreasing; since

MU_1 = 27

,

MU_2 = 35

, and

MU_3 = 23

, the decrease begins at the 3rd glass. Second, total utility after 3 glasses is

27 + 35 + 23 = 85

utils; subtracting this from

TU_4 = 97

utils yields

MU_4 = 12

utils. Third, the satiety point occurs where total utility reaches its peak (

101

utils), corresponding to

MU = 0

utils.

Step-by-Step Solution

1

Determine the unit where the Law of Diminishing Marginal Utility first sets in

The Law of Diminishing Marginal Utility sets in at the 3rd glass.

Marginal utility increases from the 1st glass (

MU_1 = 27

utils) to the 2nd glass (

MU_2 = 35

utils), but then decreases to the 3rd glass (

MU_3 = 23

utils). The law of diminishing marginal utility begins operating at the point where

MU

first starts to fall, which is at

Q = 3

.

2

Calculate total utility for 3 glasses (

TU_3

) and derive the marginal utility of the 4th glass (

MU_4

)

TU_3 = 85

utils and

MU_4 = 12

utils.

TU_3 = MU_1 + MU_2 + MU_3 = 27 + 35 + 23 = 85

utils. Given

TU_4 = 97

utils,

MU_4 = TU_4 - TU_3 = 97 - 85 = 12

utils.

3

Determine marginal utility at the point of satiety

MU_{\text{satiety}} = 0

utils.

The point of satiety is reached when Total Utility is at its maximum (

TU_5 = 101

utils and

TU_6 = 101

utils). At this point, additional consumption yields no added satisfaction, so

MU_6 = TU_6 - TU_5 = 101 - 101 = 0

utils.

Key Concept

Law of Diminishing Marginal Utility and Total Utility Relationship

Estimated Time:2m 0s

Question 35Question →

A consumer's total utility ( $TU$ ) from consuming $3$ units of a commodity is $29$ utils. Consuming the $4^{\text{th}}$ unit yields a marginal utility ( $MU$ ) of $15$ utils. If consuming the $5^{\text{th}}$ unit results in average utility ( $AU$ ) being equal to marginal utility ( $MU$ ), what is the total utility ( $TU$ ) derived from consuming $5$ units of the commodity?

55

utils

59

utils

44

utils

47

utils

Show answer & explanation

Answer: $55$ utils

Answer

The total utility (

TU

) derived from consuming

5

units of the commodity is

55

utils.

The correct answer is derived by first finding total utility at 4 units (

TU_4 = 29 + 15 = 44

utils). Applying the condition that average utility equals marginal utility at 5 units gives

\frac{TU_5}{5} = TU_5 - 44

. Solving this linear equation yields

TU_5 = 55

utils.

Step-by-Step Solution

1

Calculate the Total Utility at 4 units (

TU_4

)

TU_4 = TU_3 + MU_4 = 29 + 15 = 44

utils

Total utility is the cumulative sum of marginal utilities up to that quantity.

2

Express Average Utility (

AU_5

) and Marginal Utility (

MU_5

) in terms of

TU_5

AU_5 = \frac{TU_5}{5}

and

MU_5 = TU_5 - TU_4 = TU_5 - 44

By definition,

AU = \frac{TU}{Q}

and

MU = \Delta TU

for a unit increase.

3

Set

AU_5 = MU_5

as specified by the condition and solve for

TU_5

\begin{aligned} \frac{TU_5}{5} &= TU_5 - 44 \\ TU_5 &= 5(TU_5 - 44) \\ TU_5 &= 5TU_5 - 220 \\ 4TU_5 &= 220 \\ TU_5 &= 55 \text{ utils} \end{aligned}

Equating the average utility and marginal utility expressions allows solving for the unknown total utility.

Key Concept

Mathematical Relationships between Total Utility (TU), Average Utility (AU), and Marginal Utility (MU)

Question 36Question →

The table below presents the total utility derived by a consumer from drinking successive glasses of water on a hot day:

Quantity of Water (Glasses)	Total Utility (Utils)
1	15
2	27
3	36
4	42
5	42

What is the marginal utility derived from consuming the 3rd glass of water?

9

utils

12

utils

27

utils

36

utils

Show answer & explanation

Answer: $9$ utils

Answer

The marginal utility derived from consuming the 3rd glass of water is

9

utils.

Marginal utility (

MU

) is the change in total utility (

TU

) resulting from a one-unit increase in consumption (

MU_n = TU_n - TU_{n-1}

). For the 3rd glass of water,

MU_3 = TU_3 - TU_2 = 36 - 27 = 9

utils.

Step-by-Step Solution

1

Identify the formula for Marginal Utility (

MU

)

MU = \Delta TU / \Delta Q = TU_n - TU_{n-1}

Marginal utility measures the addition to total utility from consuming one more unit of a good.

2

Extract Total Utility values for the 2nd and 3rd units from the table

TU_2 = 27

utils and

TU_3 = 36

utils

To find the marginal utility of the 3rd unit, subtract the total utility of 2 units from the total utility of 3 units.

3

Compute the difference in Total Utility

MU_3 = 36 - 27 = 9

utils

The extra satisfaction gained specifically from the 3rd glass of water is

9

utils.

Key Concept

Calculation of Marginal Utility from Total Utility Schedule

Estimated Time:45s

Question 37Question →

A consumer derives a total utility ( $TU$ ) of $50$ utils from consuming $4$ oranges. Upon consuming a $5^{\text{th}}$ orange, total utility increases to $62$ utils. What is the marginal utility ( $MU$ ) derived from consuming the $5^{\text{th}}$ orange in utils?

Show answer & explanation

Answer: 12

Answer

The marginal utility derived from consuming the 5th orange is 12 utils.

Marginal Utility (

MU

) represents the change in Total Utility (

TU

) resulting from consuming one additional unit of a good. Using

MU = \frac{\Delta TU}{\Delta Q}

, the change in total utility is

62 - 50 = 12

utils, and the change in quantity consumed is

5 - 4 = 1

orange. Therefore,

MU = \frac{12}{1} = 12

utils.

Step-by-Step Solution

1

Identify the total utility values before and after consuming the 5th orange.

TU_4 = 50

utils for

4

oranges, and

TU_5 = 62

utils for

5

oranges.

Marginal utility measures the addition to total utility from consuming one extra unit of a commodity.

2

Calculate Marginal Utility (

MU

) using the formula

MU_n = TU_n - TU_{n-1}

.

MU_5 = 62 - 50 = 12

utils.

Subtracting the previous total utility from the new total utility gives the marginal utility of the 5th unit.

Key Concept

Calculation of Marginal Utility from Total Utility

Question 38Question →

The table below shows the Total Utility ( $TU$ ) obtained by a consumer from consuming successive packs of plantain chips:

Packs Consumed ( $Q$ )	Total Utility ( $TU$ ) in utils
$1$	$10$
$2$	$22$
$3$	$30$
$4$	$34$
$5$	$34$
$6$	$30$

At which pack of plantain chips does the Law of Diminishing Marginal Utility FIRST set in for this consumer?

The

2^{\text{nd}}

pack

The

3^{\text{rd}}

pack

The

5^{\text{th}}

pack

The

6^{\text{th}}

pack

Show answer & explanation

Answer: The $3^{\text{rd}}$ pack

Answer

The Law of Diminishing Marginal Utility first sets in at the

3^{\text{rd}}

pack.

The Law of Diminishing Marginal Utility states that after a certain point, consuming additional units of a good yields progressively less extra satisfaction. Computing

MU = \Delta TU / \Delta Q

shows that

MU_1 = 10

,

MU_2 = 12

, and

MU_3 = 8

. Because marginal utility increases from the

1^{\text{st}}

to the

2^{\text{nd}}

pack and then drops for the

3^{\text{rd}}

pack, diminishing marginal utility first begins with the consumption of the

3^{\text{rd}}

pack.

Step-by-Step Solution

1

Calculate the Marginal Utility (

MU

) for each successive pack using the formula

MU_n = TU_n - TU_{n-1}

.

MU_1 = 10 - 0 = 10

utils;

MU_2 = 22 - 10 = 12

utils;

MU_3 = 30 - 22 = 8

utils;

MU_4 = 34 - 30 = 4

utils;

MU_5 = 34 - 34 = 0

utils;

MU_6 = 30 - 34 = -4

utils.

Marginal utility measures the extra utility derived from consuming one additional unit of a commodity.

2

Analyze the trend of Marginal Utility (

MU

) values to identify where

MU

begins to decrease.

From the

1^{\text{st}}

to the

2^{\text{nd}}

pack,

MU

increases from

10

to

12

utils. From the

2^{\text{nd}}

to the

3^{\text{rd}}

pack,

MU

falls from

12

to

8

utils.

The Law of Diminishing Marginal Utility states that as more units of a commodity are consumed, the additional satisfaction derived from consuming each additional unit eventually decreases.

3

Determine the exact unit at which the decline in

MU

first occurs.

The decline in

MU

starts upon consumption of the

3^{\text{rd}}

pack.

The

3^{\text{rd}}

pack is the first unit where marginal utility (

8

utils) is less than the marginal utility of the preceding unit (

12

utils).

Key Concept

Onset of the Law of Diminishing Marginal Utility

Estimated Time:1m 0s

Question 39Question →

A consumer consumes successive cups of ice cream. The total utility ( $TU$ ) derived from the 1st, 2nd, 3rd, and 4th cups is $15$ utils, $25$ utils, $30$ utils, and $30$ utils respectively. What is the marginal utility ( $MU$ ) of the 4th cup of ice cream?

0

utils

30

utils

7.5

utils

5

utils

Show answer & explanation

Answer: $0$ utils

Answer

The marginal utility of the 4th cup of ice cream is

0

utils.

Marginal Utility (

MU

) measures the change in Total Utility (

TU

) resulting from consuming one additional unit of a good. Using

MU_4 = TU_4 - TU_3

, we subtract

30

utils (

TU_3

) from

30

utils (

TU_4

) to obtain

0

utils.

Step-by-Step Solution

1

Identify the Total Utility (

TU

) values for the 3rd and 4th units.

TU_3 = 30

utils and

TU_4 = 30

utils.

Calculating marginal utility requires comparing total utility before and after consuming the 4th unit.

2

Apply the Marginal Utility formula

MU_n = TU_n - TU_{n-1}

.

MU_4 = 30 - 30 = 0

utils.

The 4th cup adds zero extra utility, reaching the consumer's point of satiety.

Key Concept

Calculation of Marginal Utility from Total Utility

Question 40Question →

The table below presents the Total Utility ( $TU$ ) and Marginal Utility ( $MU$ ) derived by a consumer from drinking successive bottles of fruit juice on a warm day:

Quantity Consumed ( $Q$ )	Total Utility ( $TU$ ) in utils	Marginal Utility ( $MU$ ) in utils
1	24	24
2	42	18
3	$X$	12
4	60	$Y$
5	60	0
6	52	-8

Based on the table, what are the values of $X$ and $Y$ , and at which quantity consumed is the consumer's point of satiety reached?

X = 54

,

Y = 6

, and satiety is reached at the 5th unit.

X = 54

,

Y = 18

, and satiety is reached at the 4th unit.

X = 42

,

Y = 6

, and satiety is reached at the 6th unit.

X = 54

,

Y = 0

, and satiety is reached at the 3rd unit.

Show answer & explanation

Answer: $X = 54$ , $Y = 6$ , and satiety is reached at the 5th unit.

Answer

X = 54

,

Y = 6

, and the point of satiety is reached at the 5th unit of consumption.

To find

X

, add the marginal utility of the 3rd unit (

12

) to the total utility of the 2nd unit (

42

), giving

X = 54

. To find

Y

, subtract the total utility of the 3rd unit (

54

) from the total utility of the 4th unit (

60

), giving

Y = 6

. The point of satiety is the level of consumption where marginal utility reaches zero and total utility is maximized (

60

utils at

5

units). Thus, the option stating

X = 54

,

Y = 6

, and satiety at the 5th unit is correct.

Step-by-Step Solution

1

Calculate the unknown Total Utility

X

at

Q = 3

.

X = TU_3 = TU_2 + MU_3 = 42 + 12 = 54

utils.

Total Utility at any level of consumption is the cumulative sum of Marginal Utilities up to that level.

2

Calculate the unknown Marginal Utility

Y

at

Q = 4

.

Y = MU_4 = TU_4 - TU_3 = 60 - 54 = 6

utils.

Marginal Utility is the change in Total Utility resulting from consuming one additional unit (

MU_n = TU_n - TU_{n-1}

).

3

Identify the point of satiety.

Satiety occurs at

Q = 5

units.

The point of satiety (saturation point) is reached where Marginal Utility equals zero (

MU = 0

) and Total Utility attains its peak value (

TU = 60

).

Key Concept

Relationship between Total Utility and Marginal Utility; Point of Satiety

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