Theory of Consumer Behaviour

93 questions

Question 1Question

A consumer's total utility (TUTU) schedule from consuming successive bottles of soft drink is presented in the table below:

Quantity of Soft Drink (Bottles)Total Utility (TUTU in utils)
140
275
3102
4120
5130

Based on the table above, what is the marginal utility (MUMU) derived from consuming the 4th bottle of soft drink?

Show answer & explanation

Answer: 18

Answer

The marginal utility derived from consuming the 4th bottle of soft drink is 18 utils.
Marginal Utility (MUMU) is defined as the additional utility derived from the consumption of one extra unit of a commodity. From the schedule, total utility increases from 102 utils to 120 utils when moving from 3 to 4 bottles. Thus, MU4=120102=18MU_4 = 120 - 102 = 18 utils.

Step-by-Step Solution

1
Find total utility values from the schedule for Q=4Q = 4 and Q=3Q = 3
TU4=120TU_4 = 120 utils and TU3=102TU_3 = 102 utils
Marginal utility measures the extra satisfaction gained from consuming one additional unit.
2
Apply the Marginal Utility formula MU=ΔTU/ΔQMU = \Delta TU / \Delta Q
MU4=120102=18MU_4 = 120 - 102 = 18 utils
Subtracting previous total utility from current total utility gives the additional utility contributed by the 4th unit.

Key Concept

Marginal Utility Calculation from Total Utility Schedule
Question 2Question

Match each utility concept on the left with its corresponding mathematical or economic description on the right.

Click a left item, then click its matching right item

Items

Total Utility (TUTU)
Marginal Utility (MUMU)
Average Utility (AUAU)
Point of Saturation

Matches

Show answer & explanation

Answer

Total Utility corresponds to the overall satisfaction obtained from consuming a specific total quantity of a commodity. Marginal Utility corresponds to the additional satisfaction gained from consuming one more unit of a commodity. Average Utility corresponds to the satisfaction derived per unit of commodity consumed. Point of Saturation corresponds to the consumption state where Total Utility reaches its maximum and Marginal Utility equals zero.
Total Utility represents cumulative satisfaction (TUTU), Marginal Utility represents the change in total utility per additional unit consumed (ΔTUΔQ\frac{\Delta TU}{\Delta Q}), Average Utility represents satisfaction per unit (TUQ\frac{TU}{Q}), and the Point of Saturation is the boundary where Total Utility peaks and Marginal Utility drops to zero.

Step-by-Step Solution

1
Define Total Utility (TUTU)
Identified that TUTU measures total aggregate satisfaction.
By definition, Total Utility sums all satisfaction up to a specific consumption level.
2
Define Marginal Utility (MUMU)
Identified that MU=ΔTUΔQMU = \frac{\Delta TU}{\Delta Q}.
Marginal utility isolates the incremental effect on satisfaction from one extra unit.
3
Define Average Utility (AUAU)
Identified that AU=TUQAU = \frac{TU}{Q}.
Average utility expresses satisfaction on a per-unit basis.
4
Define Point of Saturation
Identified that at saturation, TUTU is at its maximum and MU=0MU = 0.
Consuming beyond this point yields negative marginal utility (disutility).

Key Concept

Concepts of Utility (Total, Average, and Marginal Utility)
Estimated Time:1m 0s
Question 3Question

The table below presents the utility schedule for a consumer consuming successive units of commodity XX:

Units of Commodity XX (QQ)Total Utility (TUTU in utils)
118
232
342
448
548

What is the marginal utility (MUMU) derived from consuming the 4th4^{\text{th}} unit of commodity XX?

Show answer & explanation

Answer: 66 utils

Answer

The marginal utility derived from consuming the 4th unit of commodity X is 6 utils.
Marginal utility (MUMU) is defined as the addition to total utility derived from the consumption of an extra unit of a commodity (MU=ΔTUΔQMU = \frac{\Delta TU}{\Delta Q}). For the 4th unit, MU=TU4TU3=4842=6MU = TU_4 - TU_3 = 48 - 42 = 6 utils.

Step-by-Step Solution

1
Identify the formula for Marginal Utility (MU)
The formula is MUn=TUnTUn1MU_n = TU_n - TU_{n-1}, where nn is the unit number.
Marginal utility measures the extra satisfaction gained from consuming one additional unit of a good.
2
Extract Total Utility values from the table for Q=4Q = 4 and Q=3Q = 3
TU4=48TU_4 = 48 utils and TU3=42TU_3 = 42 utils.
To calculate the addition to total utility from the 4th unit, we compare total utility at 4 units with total utility at 3 units.
3
Compute the difference to find MU4MU_4
MU4=4842=6MU_4 = 48 - 42 = 6 utils.
Subtracting TU3TU_3 from TU4TU_4 yields the exact marginal contribution of the 4th unit.

Key Concept

Calculation and Interpretation of Marginal Utility
Estimated Time:1m 0s
Question 4Question

A consumer spends their entire monthly budget of 2,400\text{₦}2,400 on two commodities, Good XX and Good YY. The market price of Good YY (PyP_y) is 30\text{₦}30 per unit. At utility-maximizing equilibrium under ordinal utility analysis, the consumer purchases 2020 units of Good XX and 4040 units of Good YY. What is the magnitude of the Marginal Rate of Substitution of Good XX for Good YY (MRSxyMRS_{xy}) at this equilibrium point?

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Answer: 2

Answer

The Marginal Rate of Substitution of Good X for Good Y (MRS_xy) at equilibrium is 2.
Under ordinal utility theory, consumer equilibrium occurs at the point of tangency between the budget line and the highest attainable indifference curve. At this point, the slope of the indifference curve (MRSxyMRS_{xy}) equals the absolute slope of the budget line (PxPy\frac{P_x}{P_y}). First, calculating PxP_x from the budget equation 2400=20Px+30(40)2400 = 20 P_x + 30(40) yields Px=60P_x = \text{₦}60. Then, substituting PxP_x and PyP_y into the equilibrium condition gives MRSxy=6030=2MRS_{xy} = \frac{60}{30} = 2.

Step-by-Step Solution

1
Formulate the budget line equation using total income and expenditures.
2400=20Px+30(40)2400 = 20 P_x + 30(40)
Total expenditure on both goods must equal total income at budget exhaustion.
2
Calculate the price of Good X (PxP_x).
Px=60P_x = \text{₦}60
Finding the price of Good X is necessary to establish the price ratio.
3
Calculate the Marginal Rate of Substitution at consumer equilibrium.
MRSxy=PxPy=6030=2MRS_{xy} = \frac{P_x}{P_y} = \frac{60}{30} = 2
At consumer equilibrium under ordinal utility, the indifference curve is tangent to the budget line, meaning MRSxy=PxPyMRS_{xy} = \frac{P_x}{P_y}.

Key Concept

Consumer Equilibrium Condition under Ordinal Utility Analysis
Estimated Time:2m 0s
Question 5Question

The table below displays a consumer's utility schedule from consuming consecutive cups of tea:

Quantity (Units)Total Utility (Utils)Marginal Utility (Utils)
12020
23515
345XX
4505
5500
646-4

Based on the table, what is the value of XX (the marginal utility of the 3rd unit), and at which level of consumption does the consumer reach the point of satiety?

Show answer & explanation

Answer: X=10X = 10 utils, and the point of satiety is reached at 5 units.

Answer

X=10X = 10 utils, and the point of satiety is reached at 5 units.
The marginal utility of the 3rd unit is calculated as TU3TU2=4535=10TU_3 - TU_2 = 45 - 35 = 10 utils. Satiety represents full consumer satisfaction, which occurs at 5 units where total utility reaches its maximum of 50 utils and marginal utility drops to zero.

Step-by-Step Solution

1
Calculate the Marginal Utility (XX) for the 3rd unit consumed.
X=TU3TU2=4535=10X = TU_3 - TU_2 = 45 - 35 = 10 utils.
Marginal utility measures the addition to total utility derived from consuming one extra unit of a commodity (MUn=TUnTUn1MU_n = TU_n - TU_{n-1}).
2
Determine the point of satiety from the utility schedule.
Satiety occurs at 5 units of consumption, where TU=50TU = 50 (maximum) and MU=0MU = 0.
The point of satiety is defined as the level of consumption where total utility is maximized and marginal utility becomes zero.

Key Concept

Law of Diminishing Marginal Utility and Point of Satiety
Estimated Time:1m 30s
Question 6Question

Match each utility condition or stage of consumption on the left with its corresponding mathematical and economic relationship on the right.

Click a left item, then click its matching right item

Items

Point of Satiety (Consumer Saturation)
Stage where Total Utility (TU\text{TU}) increases at a diminishing rate
Onset of Disutility (Negative Marginal Utility region)
Point of Maximum Average Utility (AU\text{AU})

Matches

Show answer & explanation

Answer

Point of Satiety matches with zero Marginal Utility and peak Total Utility (MU=0\text{MU} = 0); Total Utility increasing at a diminishing rate matches positive but declining Marginal Utility (MU>0\text{MU} > 0); Onset of Disutility matches declining Total Utility (MU<0\text{MU} < 0); and Maximum Average Utility matches the intersection where Marginal Utility equals Average Utility (MU=AU\text{MU} = \text{AU}).
Each pair correctly reflects the calculus and economic relationships governing utility curves. At satiety, TU\text{TU} reaches its maximum peak while MU=0\text{MU} = 0. When TU\text{TU} grows at a diminishing rate, MU\text{MU} is positive but decreasing. When consumption brings disutility (MU<0\text{MU} < 0), TU\text{TU} drops. Finally, the mathematical identity between average and marginal variables dictates that average utility is maximized where MU=AU\text{MU} = \text{AU}.

Step-by-Step Solution

1
Analyze the derivative relationship between Total Utility (TU\text{TU}) and Marginal Utility (MU\text{MU}).
Marginal Utility is the first derivative of Total Utility with respect to quantity (MU=dTUdQ\text{MU} = \frac{d\text{TU}}{dQ}).
Understanding MU\text{MU} as the slope of the TU\text{TU} curve allows exact matching of critical points like maxima and inflection points.
2
Identify the point of satiety.
When TU\text{TU} reaches its maximum, its slope is zero (MU=0\text{MU} = 0).
Point of satiety defines complete satisfaction where no more utility can be added.
3
Analyze the diminished growth of TU\text{TU} and negative MU\text{MU}.
Diminishing TU\text{TU} growth implies MU>0\text{MU} > 0 but declining. Once MU<0\text{MU} < 0, TU\text{TU} begins falling.
This reflects the fundamental Law of Diminishing Marginal Utility.
4
Examine the relationship between Average Utility (AU\text{AU}) and Marginal Utility (MU\text{MU}).
AU\text{AU} reaches its maximum where MU=AU\text{MU} = \text{AU}.
When marginal value equals average value, the average value is stationary at its peak.

Key Concept

Interrelationships among Total, Average, and Marginal Utility concepts
Estimated Time:1m 0s
Question 7Question

The table below presents the total utility schedule for a consumer consuming successive units of commodity ZZ:

Units of ZZTotal Utility (utils)
118
232
342
448
550

If the market price of commodity ZZ is N6\mathbb{N}6 per unit and 1 util=N11\text{ util} = \mathbb{N}1, what is the consumer surplus at the equilibrium level of consumption?

Show answer & explanation

Answer: \mathbb{N}24

Answer

\mathbb{N}24
The option specifying \(\mathbb{N}24\) is correct. Marginal utility per unit is derived as: Unit 1 = 18, Unit 2 = 14, Unit 3 = 10, Unit 4 = 6, Unit 5 = 2. With price \(P_Z = \mathbb{N}6\), consumer equilibrium condition \(MU_Z = P_Z\) is satisfied at 4 units of consumption. At 4 units, Total Utility is \(\mathbb{N}48\) and Total Expenditure is \(4 \times \mathbb{N}6 = \mathbb{N}24\). Consumer surplus is \(48 - 24 = \mathbb{N}24\).

Step-by-Step Solution

1
Calculate Marginal Utility (MU) for each unit consumed
MU1=18MU_1 = 18, MU2=14MU_2 = 14, MU3=10MU_3 = 10, MU4=6MU_4 = 6, MU5=2MU_5 = 2
Marginal utility is the change in total utility resulting from consuming one additional unit (MUn=TUnTUn1MU_n = TU_n - TU_{n-1}).
2
Determine the consumer equilibrium quantity
Equilibrium occurs at 4 units because MU4=N6=PZMU_4 = \mathbb{N}6 = P_Z
Under cardinal utility analysis, a consumer maximizes utility for a single commodity when MU=PMU = P (in monetary terms).
3
Calculate Total Expenditure at equilibrium
\text{Total Expenditure} = 4 \times \mathbb{N}6 = \mathbb{N}24
Total expenditure is calculated by multiplying the equilibrium quantity by the unit price.
4
Compute Consumer Surplus
\text{Consumer Surplus} = \text{Total Utility} - \text{Total Expenditure} = \mathbb{N}48 - \mathbb{N}24 = \mathbb{N}24
Consumer surplus is the net monetary gain derived from consumption, calculated as the total utility minus total amount paid.

Key Concept

Cardinal Consumer Equilibrium and Consumer Surplus Calculation
Estimated Time:1m 30s
Question 8Question

A consumer obtains an average utility (AUAU) of 1515 utils from consuming 44 units of bottled water. When the 5th5^{\text{th}} unit is consumed, the marginal utility (MUMU) derived is 2525 utils. If consuming the 6th6^{\text{th}} unit brings the consumer's total utility (TUTU) to 9696 utils, what is the average utility (AUAU) per unit, in utils, when 66 units are consumed?

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Answer: 16

Answer

The average utility per unit when 6 units are consumed is 16 utils.
To find the average utility after 6 units, determine total utility at 4 units (15×4=6015 \times 4 = 60 utils). Adding the marginal utility of the 5th unit (2525 utils) gives a total utility of 8585 utils for 5 units. Since total utility for 6 units is given as 9696 utils, dividing by quantity (96/696 / 6) yields an average utility of 1616 utils.

Step-by-Step Solution

1
Calculate Total Utility for 4 units (TU4TU_4)
TU4=60TU_4 = 60 utils
Total utility is calculated by multiplying average utility by the quantity consumed: TU4=AU4×4=15×4=60TU_4 = AU_4 \times 4 = 15 \times 4 = 60 utils.
2
Calculate Total Utility for 5 units (TU5TU_5)
TU5=85TU_5 = 85 utils
Total utility of 5 units equals total utility of 4 units plus the marginal utility of the 5th unit: TU5=TU4+MU5=60+25=85TU_5 = TU_4 + MU_5 = 60 + 25 = 85 utils.
3
Identify Total Utility for 6 units (TU6TU_6)
TU6=96TU_6 = 96 utils
The total utility after consuming 6 units is given directly in the problem description as 96 utils.
4
Calculate Average Utility for 6 units (AU6AU_6)
AU6=16AU_6 = 16 utils
Average utility is calculated by dividing total utility by total units consumed: AU6=TU66=966=16AU_6 = \frac{TU_6}{6} = \frac{96}{6} = 16 utils.

Key Concept

Mathematical interrelationships between Total Utility (TU), Average Utility (AU), and Marginal Utility (MU)
Question 9Question

A consumer purchasing two goods, XX and YY, attains equilibrium when the marginal utility of Good XX (MUxMU_x) is 4040 utils and its price (PxP_x) is 10\text{₦}10. If the price of Good YY (PyP_y) is 5\text{₦}5, what is the marginal utility of Good YY (MUyMU_y) in utils at consumer equilibrium?

Show answer & explanation

Answer: 20 utils; 20; 20utils

Answer

The marginal utility of Good YY at consumer equilibrium is 20 utils.
Under cardinal utility analysis, consumer equilibrium for two commodities is achieved when the ratio of marginal utility to price is equal for both commodities (MUxPx=MUyPy\frac{MU_x}{P_x} = \frac{MU_y}{P_y}). Substituting MUx=40MU_x = 40, Px=10P_x = 10, and Py=5P_y = 5 gives 4010=MUy5\frac{40}{10} = \frac{MU_y}{5}, which simplifies to 4=MUy54 = \frac{MU_y}{5}. Solving for MUyMU_y gives 2020 utils.

Step-by-Step Solution

1
State the equimarginal condition for consumer equilibrium when consuming two goods.
MUxPx=MUyPy\frac{MU_x}{P_x} = \frac{MU_y}{P_y}
According to cardinal utility analysis, a consumer maximizes utility when the marginal utility per monetary unit spent is equal across all commodities.
2
Substitute the given values (MUx=40MU_x = 40, Px=10P_x = 10, Py=5P_y = 5) into the formula.
4010=MUy5\frac{40}{10} = \frac{MU_y}{5}
Substituting the known parameters sets up an algebraic equation for the unknown marginal utility of Good YY.
3
Solve the equation for MUyMU_y.
4=MUy5    MUy=4×5=20 utils4 = \frac{MU_y}{5} \implies MU_y = 4 \times 5 = 20\text{ utils}
Multiplying the marginal utility per naira spent (4 utils/naira) by the price of Good YY (₦5) gives the marginal utility of Good YY.

Key Concept

Equimarginal Principle of Consumer Equilibrium
Estimated Time:1m 30s
Question 10Question

In consumer utility theory, as a consumer moves downward from left to right along a standard, origin-convex indifference curve for two commodities, XX and YY, how does the Marginal Rate of Substitution (MRSxyMRS_{xy}) behave?

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Answer: It diminishes continuously as more units of XX are substituted for YY.

Answer

The Marginal Rate of Substitution (MRSxyMRS_{xy}) diminishes continuously as more units of XX are substituted for YY.
The correct answer accounts for the principle of diminishing marginal rate of substitution. As a consumer increases consumption of Good XX, its marginal utility (MUxMU_x) decreases relative to that of Good YY (MUyMU_y). Consequently, the consumer yields smaller amounts of YY for each extra unit of XX, making MRSxyMRS_{xy} diminish and conferring a convex shape to the indifference curve.

Step-by-Step Solution

1
Define Marginal Rate of Substitution (MRSxyMRS_{xy})
MRSxy=ΔYΔX=MUxMUyMRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}
MRSxyMRS_{xy} measures the rate at which a consumer is willing to give up Good YY to obtain one additional unit of Good XX while keeping total utility constant.
2
Analyze the impact of moving downward along the curve
As consumption of XX increases, MUxMU_x falls (due to diminishing marginal utility), while MUyMU_y rises as YY becomes scarcer to the consumer.
The principle of diminishing marginal utility dictates that as a good becomes more abundant, its marginal valuation declines.
3
Determine the curvature property resulting from this behavior
The slope of the curve (MRSxyMRS_{xy}) flattens, making the curve convex to the origin.
A diminishing ratio of MUxMUy\frac{MU_x}{MU_y} directly accounts for the origin-convex shape of standard indifference curves.

Key Concept

Diminishing Marginal Rate of Substitution and Indifference Curve Convexity
Estimated Time:1m 0s
Question 11Question

An indifference curve is convex to the origin because the marginal rate of substitution (MRSxyMRS_{xy}) increases as a consumer substitutes commodity XX for commodity YY along the curve.

Show answer & explanation

Answer: False

Answer

The statement is False. Indifference curves are convex to the origin due to a diminishing marginal rate of substitution (MRSxyMRS_{xy}), not an increasing one.
The statement is false because standard indifference curves are convex to the origin due to the Principle of Diminishing Marginal Rate of Substitution. As a consumer substitutes good XX for good YY, they are willing to give up successively fewer units of good YY for each additional unit of good XX.

Step-by-Step Solution

1
Identify the relationship between the slope of an indifference curve and the Marginal Rate of Substitution (MRSxyMRS_{xy})
The slope of an indifference curve at any point represents the marginal rate of substitution (MRSxy=ΔYΔX=MUxMUyMRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}).
Convexity to the origin describes how this slope changes as a consumer moves down the curve from left to right.
2
Analyze how MRSxyMRS_{xy} changes along a convex indifference curve
As the consumer acquires more units of XX and fewer units of YY, the marginal utility of XX (MUxMU_x) falls while the marginal utility of YY (MUyMU_y) rises, causing the ratio MUxMUy\frac{MU_x}{MU_y} to decrease (diminish).
This behavior follows the law of diminishing marginal utility under ordinal utility analysis.
3
Evaluate the validity of the statement
Because MRSxyMRS_{xy} diminishes (decreases) rather than increases along the curve, the statement is false.
An increasing MRSxyMRS_{xy} would produce a concave indifference curve to the origin.

Key Concept

Diminishing Marginal Rate of Substitution and Indifference Curve Convexity
Estimated Time:1m 0s
Question 12Question

The table below presents the utility schedule of a consumer consuming successive portions of roasted maize:

Quantity (QQ)Total Utility (TUTU) in utilsMarginal Utility (MUMU) in utils
11818
23416
3PP12
454QmQ_m
5584
6580
752-6

Based on the table, what is the combined value of P+QmP + Q_m, and at which unit of consumption does the consumer reach the point of satiety?

Show answer & explanation

Answer: 5454 utils and the 6th unit

Answer

The combined value of P+QmP + Q_m is 5454 utils, and the point of satiety is reached at the 6th unit.
To find PP, add the marginal utility of the 3rd unit (1212) to the total utility of the 2nd unit (3434), yielding P=46P = 46. To find QmQ_m, subtract the total utility of the 3rd unit (4646) from the total utility of the 4th unit (5454), yielding Qm=8Q_m = 8. Summing these gives 46+8=5446 + 8 = 54 utils. The point of satiety is the quantity at which marginal utility is zero (MU=0MU = 0), which occurs at the 6th unit where total utility peaks at 5858 utils.

Step-by-Step Solution

1
Calculate the unknown Total Utility PP at the 3rd unit.
P=TU2+MU3=34+12=46P = TU_2 + MU_3 = 34 + 12 = 46 utils.
Total utility at quantity QQ equals total utility at Q1Q-1 plus marginal utility at QQ.
2
Calculate the unknown Marginal Utility QmQ_m at the 4th unit.
Qm=TU4TU3=5446=8Q_m = TU_4 - TU_3 = 54 - 46 = 8 utils.
Marginal utility at quantity QQ is the change in total utility resulting from consuming that unit.
3
Sum PP and QmQ_m.
P+Qm=46+8=54P + Q_m = 46 + 8 = 54 utils.
Simple addition of the calculated values.
4
Identify the point of satiety.
The 6th unit.
The point of satiety (maximum total satisfaction) occurs at the consumption level where Marginal Utility equals zero (MU=0MU = 0) and Total Utility reaches its maximum.

Key Concept

Law of Diminishing Marginal Utility and Relationship between Total Utility and Marginal Utility
Question 13Question

Match each specific utility condition or phase of consumer satisfaction listed on the left with its exact mathematical relationship involving Total Utility (TUTU), Marginal Utility (MUMU), or Average Utility (AUAU) on the right.

Click a left item, then click its matching right item

Items

Point of Total Saturation (Satiety)
Phase of Increasing Utility at a Decreasing Rate
Point where Average Utility (AUAU) Reaches Maximum
Phase of Disutility (Dissatisfaction)

Matches

Show answer & explanation

Answer

Point of Total Saturation matches MU=0MU = 0 with peak TUTU; Phase of Increasing Utility at a Decreasing Rate matches MU>0MU > 0 and falling; Point where AUAU Reaches Maximum matches MU=AUMU = AU; Phase of Disutility matches MU<0MU < 0 causing TUTU to decline.
The correct pairings accurately reflect the differential relationships governing total, average, and marginal utility: saturation corresponds to MU=0MU = 0 and peak TUTU; positive but declining MUMU causes TUTU to increase at a decreasing rate; maximum AUAU occurs where MU=AUMU = AU; and disutility occurs when MU<0MU < 0, causing TUTU to fall.

Step-by-Step Solution

1
Analyze the Saturation Point condition
Saturation occurs when consumption yields zero additional satisfaction (MU=0MU = 0). Beyond this, TUTU cannot increase, meaning TUTU is at its maximum.
By definition, the peak of TUTU occurs where the derivative or incremental gain (MUMU) is zero.
2
Analyze the Increasing Utility at a Decreasing Rate phase
As long as MU>0MU > 0, total satisfaction (TUTU) keeps growing. Because MUMU is falling, the rate of increase of TUTU slows down.
This reflects the core principle of diminishing marginal utility prior to reaching saturation.
3
Analyze the mathematical property of Average Utility (AUAU) peak
Average Utility (AU=TUQAU = \frac{TU}{Q}) rises when MU>AUMU > AU and falls when MU<AUMU < AU. Therefore, AUAU reaches its maximum at the point of intersection where MU=AUMU = AU.
This represents the classic mathematical relationship between average and marginal values.
4
Analyze the Disutility phase
Disutility occurs when additional units yield negative utility (MU<0MU < 0), causing the cumulative satisfaction (TUTU) to drop.
Negative marginal utility subtracts from total accumulated utility.

Key Concept

Interrelationships among Total Utility, Marginal Utility, and Average Utility
Estimated Time:1m 30s
Question 14Question

A consumer allocates a total income of ₦6,000 exclusively to purchase good XX and good YY. Good XX is plotted on the horizontal axis and costs ₦600 per unit, while good YY is plotted on the vertical axis and costs ₦300 per unit. What is the absolute value of the slope of this consumer's budget line?

Show answer & explanation

Answer: 2.02.0

Answer

The magnitude of the slope of the budget line is 2.02.0.
The slope of a budget line when good XX is on the horizontal axis and good YY is on the vertical axis equals PXPY-\frac{P_X}{P_Y}. Taking the absolute value gives 600300=2.0\frac{600}{300} = 2.0, which reflects the opportunity cost of purchasing one additional unit of good XX in terms of good YY.

Step-by-Step Solution

1
Identify the given economic parameters from the problem statement.
Total Income (II) = ₦6,000; Price of Good XX (PXP_X) = ₦600; Price of Good YY (PYP_Y) = ₦300.
Establishing the price and budget parameters is required to set up the budget equation.
2
State the standard formula for the slope of the budget line.
Slope = PXPY-\frac{P_X}{P_Y}, so the absolute value of the slope is PXPY\frac{P_X}{P_Y}.
The slope of the budget constraint measures the market opportunity cost of good XX in terms of good YY foregone.
3
Substitute the prices of good XX and good YY into the ratio.
Absolute Slope = 600300=2.0\frac{600}{300} = 2.0.
Dividing the price of the horizontal-axis good by the price of the vertical-axis good provides the relative price ratio.

Key Concept

Budget Line Slope and Relative Price Ratio
Question 15Question

An equal proportionate increase in a consumer's nominal income and the prices of both goods consumed will cause the budget line to shift outward parallel to its original position.

Show answer & explanation

Answer: False

Answer

The statement is False. An equal proportionate increase in nominal income and all commodity prices leaves real purchasing power and the budget line completely unchanged.
The statement is false because multiplying nominal income and all product prices by the same scalar leaves real purchasing power and relative price ratios unchanged, keeping the budget line in its exact original position.

Step-by-Step Solution

1
State the standard budget line equation and intercepts
The budget equation is PXX+PYY=IP_X X + P_Y Y = I, with horizontal intercept X=IPXX = \frac{I}{P_X}, vertical intercept Y=IPYY = \frac{I}{P_Y}, and slope PXPY-\frac{P_X}{P_Y}.
Establishing the mathematical parameters of the budget constraint is necessary to evaluate positional changes.
2
Apply a proportional scaling factor k>1k > 1 to nominal income and prices
The new equation becomes (kPX)X+(kPY)Y=kI(k P_X) X + (k P_Y) Y = k I.
An equal percentage increase scales nominal income and both prices by the same factor kk.
3
Simplify the scaled budget equation and determine the effect on the line
Dividing both sides by kk yields PXX+PYY=IP_X X + P_Y Y = I. The new intercepts kIkPX=IPX\frac{k I}{k P_X} = \frac{I}{P_X} and kIkPY=IPY\frac{k I}{k P_Y} = \frac{I}{P_Y} are identical to the original intercepts.
Because neither the intercepts nor the slope change, the budget line does not shift outward.

Key Concept

Homogeneity of the Budget Constraint (Real vs. Nominal Changes)
Estimated Time:1m 0s
Question 16Question

Under the ordinal utility approach, a consumer optimizes satisfaction subject to a budget constraint when purchasing two commodities, Good XX and Good YY. Which condition must hold true at this point of consumer equilibrium?

Show answer & explanation

Answer: The Marginal Rate of Substitution of Good XX for Good YY (MRSxyMRS_{xy}) is equal to the price ratio of the two goods (PxPy\frac{P_x}{P_y}), and the indifference curve is convex to the origin.

Answer

Consumer equilibrium is attained where the Marginal Rate of Substitution of Good XX for Good YY (MRSxyMRS_{xy}) equals the ratio of their prices (PxPy\frac{P_x}{P_y}), and the indifference curve is convex to the origin.
The statement specifying that MRSxy=PxPyMRS_{xy} = \frac{P_x}{P_y} and that the indifference curve is convex to the origin is correct because consumer equilibrium in ordinal utility analysis requires the indifference curve to be tangent to the budget line at a point where the marginal rate of substitution is diminishing.

Step-by-Step Solution

1
Identify the slope of the indifference curve and budget line
Slope of Indifference Curve = MRSxy-MRS_{xy}; Slope of Budget Line = PxPy-\frac{P_x}{P_y}.
The indifference curve represents consumer preferences, while the budget line represents consumer expenditure capacity.
2
Apply the tangency condition for utility maximization under ordinal analysis
MRSxy=PxPyMRS_{xy} = \frac{P_x}{P_y}.
At the point of equilibrium, the rate at which the consumer is willing to substitute Good XX for Good YY equals the rate at which the market allows substitution.
3
Verify the second-order condition for equilibrium
The indifference curve must be strictly convex to the origin.
Convexity ensures a stable equilibrium point where the marginal rate of substitution is diminishing.

Key Concept

Consumer Equilibrium under Ordinal Utility
Estimated Time:1m 0s
Question 17Question

For a normal good, a decrease in price creates substitution and income effects that operate in the same direction, thereby reinforcing an increase in total quantity demanded.

Show answer & explanation

Answer: True

Answer

The statement is true because for normal goods, both the substitution effect and the income effect increase quantity demanded when the price falls.
For a normal good, a reduction in price makes the commodity relatively cheaper (inducing a positive substitution effect on quantity demanded) and increases the consumer's real income (inducing a positive income effect on quantity demanded). Consequently, both components work together in the same direction to boost overall demand.

Step-by-Step Solution

1
Analyze the direction of the substitution effect following a price decrease.
The substitution effect is always negative with respect to price change; a fall in price makes the good relatively cheaper, leading to an increase in quantity demanded.
Consumers substitute away from relatively more expensive goods toward the cheaper good.
2
Analyze the direction of the income effect for a normal good when price falls.
A lower price increases real purchasing power. For a normal good, an increase in real income leads to an increase in quantity demanded.
Normal goods have a positive income elasticity of demand.
3
Synthesize the total price effect by combining both components.
Since both the substitution effect and the income effect push in the direction of higher consumption, the total price effect is positive (quantity demanded increases).
Total Price Effect = Substitution Effect + Income Effect.

Key Concept

Income and Substitution Effects on Normal Goods
Question 18Question

A consumer allocates a fixed income between Good XX and Good YY. At their current consumption combination, the Marginal Rate of Substitution of XX for YY (MRSxyMRS_{xy}) is 33, while the market price of Good XX (PxP_x) is 150\text{₦}150 and the market price of Good YY (PyP_y) is 30\text{₦}30. Assuming strictly convex indifference curves, what adjustment should the consumer make to attain consumer equilibrium under ordinal utility analysis?

Show answer & explanation

Answer: Decrease consumption of Good XX and increase consumption of Good YY

Answer

The consumer should decrease consumption of Good XX and increase consumption of Good YY.
Under ordinal utility analysis, consumer equilibrium is attained where the indifference curve is tangent to the budget line, satisfying MRSxy=PxPyMRS_{xy} = \frac{P_x}{P_y}. Given Px=150P_x = \text{₦}150 and Py=30P_y = \text{₦}30, the price ratio is 55. Since the current MRSxyMRS_{xy} is 33, the marginal rate of substitution is less than the market price ratio (3<53 < 5). To increase MRSxyMRS_{xy} toward equilibrium, the consumer must decrease consumption of Good XX and increase consumption of Good YY, moving to a higher indifference curve tangency point.

Step-by-Step Solution

1
Calculate the price ratio of the two goods (Px/PyP_x / P_y).
Px/Py=15030=5P_x / P_y = \frac{150}{30} = 5.
The price ratio represents the slope of the budget line (the market rate of exchange between Good XX and Good YY).
2
Compare the Marginal Rate of Substitution (MRSxyMRS_{xy}) to the price ratio (Px/PyP_x / P_y).
MRSxy=3<Px/Py=5MRS_{xy} = 3 < P_x / P_y = 5.
Consumer equilibrium under ordinal utility requires MRSxy=PxPyMRS_{xy} = \frac{P_x}{P_y} at the point of tangency between the indifference curve and the budget line.
3
Determine the necessary change in consumption to restore equilibrium.
Since MRSxy<PxPyMRS_{xy} < \frac{P_x}{P_y}, the consumer values Good XX less than the market price demands. To raise MRSxyMRS_{xy} to 55, the consumer must reduce consumption of Good XX and increase consumption of Good YY along the budget line, relying on the principle of diminishing marginal rate of substitution.
Moving up and to the left along an indifference curve increases the slope (MRSxyMRS_{xy}) until it equals the slope of the budget line.

Key Concept

Consumer Equilibrium under Ordinal Utility (MRSxy=Px/PyMRS_{xy} = P_x / P_y)
Estimated Time:2m 0s
Question 19Question

When the price of Good X rises, a consumer experiences a substitution effect that reduces consumption of Good X by 6 units, and an income effect that increases consumption of Good X by 2 units. Which of the following statements correctly classifies Good X and describes the overall change in its quantity demanded?

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Answer: Good X is an inferior good, and total quantity demanded decreases by 4 units.

Answer

Good X is an inferior good, and total quantity demanded decreases by 4 units.
The correct response accurately applies the price effect identity (Total Effect = Substitution Effect + Income Effect). When the price of Good X rises, real income declines. A positive reaction in consumption (+2 units) from a fall in real income characterizes an inferior good. Combining the negative substitution effect (-6 units) and positive income effect (+2 units) yields a net reduction of 4 units in quantity demanded.

Step-by-Step Solution

1
Determine the type of good based on the income effect direction
Real income decreases when price increases. Since the income effect causes consumption of Good X to increase (+2 units) when real income drops, Good X must be an inferior good.
By definition, an inferior good has an inverse relationship between real income and quantity demanded.
2
Calculate the total price effect
Total Effect = Substitution Effect + Income Effect = -6 + 2 = -4 units.
The total change in quantity demanded is the algebraic sum of the substitution effect and the income effect.
3
Determine if the good is a Giffen good
Since the substitution effect (-6) outweighs the income effect (+2), total quantity demanded falls by 4 units. Thus, it obeys the law of demand and is not a Giffen good.
A Giffen good is a special inferior good where the income effect exceeds the substitution effect.

Key Concept

Decomposition of Price Effect into Income and Substitution Effects
Question 20Question

A consumer's maximum willingness to pay for successive packets of milk in a retail market is given in the schedule below:

Unit of MilkMaximum Willingness to Pay (₦)
1st500
2nd400
3rd300
4th200
5th100

If the market price of a packet of milk is fixed at ₦200, what is the total consumer surplus (in Naira) enjoyed by the consumer when purchasing 4 packets?

Show answer & explanation

Answer: 600

Answer

The total consumer surplus enjoyed by the consumer is 600 Naira.
Total willingness to pay for the 4 packets of milk is 500+400+300+200=1400500 + 400 + 300 + 200 = 1400 Naira. The actual total expenditure for 4 packets at the uniform market price of 200 Naira is 4×200=8004 \times 200 = 800 Naira. Subtracting the actual total expenditure from total willingness to pay gives a consumer surplus of 1400800=6001400 - 800 = 600 Naira.

Step-by-Step Solution

1
Calculate total willingness to pay for 4 packets
₦1,400
Sum the maximum prices the consumer is willing to pay for the first 4 units: 500+400+300+200=1400500 + 400 + 300 + 200 = 1400.
2
Calculate total actual expenditure
₦800
Multiply the market price per unit by the total number of units purchased: 4×200=8004 \times 200 = 800.
3
Subtract total actual expenditure from total willingness to pay
₦600
Consumer surplus is the net monetary gain obtained when total valuation exceeds total expenditure: 1400800=6001400 - 800 = 600.

Key Concept

Consumer Surplus is the difference between the maximum total amount a consumer is willing to pay for a commodity and the actual total amount paid at the prevailing market price.
Estimated Time:1m 30s
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