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Concept and Calculation of Consumer Surplus

11 questions

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Question 1Question →

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?

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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 1400−800=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: 1400−800=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
Question 2Question →

A consumer's demand function for petrol in a local Nigerian market is given by the linear equation P=200−8QP = 200 - 8Q, where PP represents the price per liter in Naira and QQ represents the quantity demanded in liters. If the current market price of petrol is established at N80\text{N}80 per liter, calculate the consumer surplus in Naira.

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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 3Question →

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?

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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 4Question →

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?

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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 5Question →

A consumer derives a total utility worth N1,500\text{N} 1,500 from consuming 55 units of a commodity. If the market price of the commodity is N200\text{N} 200 per unit, what is the consumer surplus in Naira?

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Answer: 500

Answer

The consumer surplus is N500\text{N} 500.
Consumer surplus is calculated as Total Utility (total willingness to pay) minus Total Expenditure (P×QP \times Q). Here, Total Utility is N1,500\text{N} 1,500, and Total Expenditure is 5×N200=N1,0005 \times \text{N} 200 = \text{N} 1,000. Subtracting N1,000\text{N} 1,000 from N1,500\text{N} 1,500 gives a consumer surplus of N500\text{N} 500.

Step-by-Step Solution

1
Calculate total actual expenditure on the commodity
Total Expenditure = 5×N200=N1,0005 \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 = N1,500−N1,000=N500\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 6Question →

A consumer's maximum willingness to pay for four successive bags of rice is ₦15,000, ₦13,000, ₦11,000, and ₦9,000 respectively. If the prevailing market price per bag is ₦9,000, what is the total consumer surplus derived in Naira?

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Answer: 12000

Answer

The total consumer surplus derived by the consumer is ₦12,000.
Consumer surplus is the difference between total willingness to pay and total actual expenditure. The total willingness to pay for the 4 bags of rice is ₦15,000 + ₦13,000 + ₦11,000 + ₦9,000 = ₦48,000. Since each bag costs ₦9,000, total expenditure for 4 bags is 4 × ₦9,000 = ₦36,000. Subtracting ₦36,000 from ₦48,000 gives a consumer surplus of ₦12,000.

Step-by-Step Solution

1
Sum the maximum willingness to pay for all consumed units to find Total Willingness to Pay.
Total Willingness to Pay = ₦15,000 + ₦13,000 + ₦11,000 + ₦9,000 = ₦48,000.
Total utility or willingness to pay is the cumulative value derived from consuming all 4 units.
2
Multiply the number of purchased units by the market price per unit to calculate Total Actual Expenditure.
Total Expenditure = 4 × ₦9,000 = ₦36,000.
The market price applies uniformly to all units purchased.
3
Subtract Total Expenditure from Total Willingness to Pay to calculate Consumer Surplus.
Consumer Surplus = ₦48,000 - ₦36,000 = ₦12,000.
Consumer surplus is defined as the net benefit (Total Willingness to Pay minus Total Expenditure).

Key Concept

Concept and Calculation of Consumer Surplus

Alternative Method

Alternatively, calculate the individual surplus for each unit (Willingness to Pay - Market Price) and sum them up: 1st unit (₦15,000 - ₦9,000 = ₦6,000), 2nd unit (₦13,000 - ₦9,000 = ₦4,000), 3rd unit (₦11,000 - ₦9,000 = ₦2,000), 4th unit (₦9,000 - ₦9,000 = ₦0). Total Consumer Surplus = ₦6,000 + ₦4,000 + ₦2,000 + ₦0 = ₦12,000.
Estimated Time:1m 0s
Question 7Question →

A consumer's evaluation of total utility derived from consuming successive tubers of yam in a local Nigerian market (expressed in monetary terms) is presented in the table below:

Quantity of Yam (Tubers)Total Utility (₦)
11,800
23,300
34,500
45,400
56,000
66,300

If the prevailing market price of a tuber of yam is ₦900, what is the total value of consumer surplus (in ₦) enjoyed by the consumer at equilibrium?

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Answer: 1800

Answer

The consumer surplus enjoyed by the consumer at equilibrium is ₦1,800.
To find consumer surplus, one must first establish the consumer's profit-maximizing equilibrium quantity where Marginal Utility (MU) equals Price (P). From the Total Utility (TU) values, the MU for successive units is ₦1,800, ₦1,500, ₦1,200, and ₦900. At the 4th unit, MU equals the market price of ₦900. Total utility for 4 units is ₦5,400 and total outlay is 4×900=₦3,6004 \times 900 = \text{₦}3,600. Subtracting total outlay from total utility yields a consumer surplus of ₦1,800.

Step-by-Step Solution

1
Calculate Marginal Utility (MU) for each unit consumed
MU values are ₦1,800 for the 1st tuber, ₦1,500 for the 2nd, ₦1,200 for the 3rd, ₦900 for the 4th, ₦600 for the 5th, and ₦300 for the 6th tuber.
Consumer equilibrium is reached when the marginal utility of a unit equals its market price.
2
Determine the equilibrium quantity consumed
The consumer purchases 4 tubers of yam.
For the 4th tuber, MU=₦900MU = \text{₦}900, which matches the prevailing market price of ₦900. Consuming a 5th tuber yields MU=₦600<₦900MU = \text{₦}600 < \text{₦}900, which reduces net utility.
3
Calculate the actual total expenditure
Total Expenditure=4×₦900=₦3,600\text{Total Expenditure} = 4 \times \text{₦}900 = \text{₦}3,600.
Total expenditure is equal to the quantity purchased multiplied by the market price per unit.
4
Subtract Total Expenditure from Total Utility to find Consumer Surplus
Consumer Surplus=₦5,400−₦3,600=₦1,800\text{Consumer Surplus} = \text{₦}5,400 - \text{₦}3,600 = \text{₦}1,800.
Consumer surplus measures the difference between total willingness to pay (Total Utility at 4 units) and actual expenditure.

Key Concept

Calculation of Consumer Surplus from Discrete Utility Schedules
Question 8Question →

A household's maximum willingness to pay for successive kegs of palm oil is given in the table below:

Unit (Keg)Maximum Willingness to Pay (₦)
1st500
2nd450
3rd400
4th350
5th300

If the market price per keg is ₦350, what is the total consumer surplus derived by the household?

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Answer: ₦300

Answer

The total consumer surplus derived by the household is ₦300.
The correct answer is ₦300. At a market price of ₦350, the household consumes 4 kegs of palm oil because willingness to pay equals price at the 4th unit. Total willingness to pay for 4 kegs is ₦500 + ₦450 + ₦400 + ₦350 = ₦1,700. The actual expenditure is 4 × ₦350 = ₦1,400. Thus, consumer surplus = ₦1,700 - ₦1,400 = ₦300.

Step-by-Step Solution

1
Determine the quantity of palm oil kegs the household will purchase at the market price of ₦350.
The consumer will buy up to the 4th keg because for the 4th keg, willingness to pay (���350) equals market price (₦350). The 5th keg will not be purchased because willingness to pay (₦300) is less than market price.
A rational consumer purchases additional units as long as willingness to pay is greater than or equal to market price.
2
Calculate the total willingness to pay (total monetary utility) for the 4 purchased kegs.
Total Willingness to Pay = ₦500 + ₦450 + ₦400 + ₦350 = ₦1,700.
Total willingness to pay is the sum of maximum prices the consumer is prepared to pay for each consumed unit.
3
Calculate the actual total expenditure incurred by buying 4 kegs at ₦350 each.
Total Expenditure = 4 units × ₦350 = ₦1,400.
Actual expenditure is calculated as total quantity purchased multiplied by prevailing market price.
4
Subtract actual total expenditure from total willingness to pay to obtain consumer surplus.
Consumer Surplus = ₦1,700 - ₦1,400 = ₦300.
Consumer surplus measures the net economic benefit or gain derived by consumers when paying less than their maximum willingness to pay.

Key Concept

Consumer Surplus from Marginal Utility / Willingness to Pay Schedule
Question 9Question →

A consumer's evaluation of marginal utility (maximum willingness to pay) for purchasing successive bottles of fruit juice is presented in the table below:

Unit (Bottle)Willingness to Pay (₦)
1st bottle500
2nd bottle400
3rd bottle300
4th bottle200
5th bottle100

If the prevailing market price per bottle is ₦200, what is the total consumer surplus derived from consuming the optimal quantity of fruit juice?

Show answer & explanation

Answer: ₦600

Answer

The total consumer surplus derived is ₦600.
The correct option is ₦600 because the consumer will buy 4 bottles (where willingness to pay ≥ ₦200). Total willingness to pay is ₦500 + ₦400 + ₦300 + ₦200 = ₦1,400, while total outlay is 4 × ₦200 = ₦800. Net consumer surplus is ₦1,400 - ₦800 = ₦600.

Step-by-Step Solution

1
Determine the optimal quantity consumed.
4 bottles are purchased.
A rational consumer continues purchasing as long as Marginal Utility (willingness to pay) is greater than or equal to the market price (₦200). The 5th bottle is excluded because its willingness to pay (₦100) is below market price.
2
Calculate total willingness to pay (Total Utility in monetary terms) for the optimal quantity.
Total Willingness to Pay = ₦500 + ₦400 + ₦300 + ₦200 = ₦1,400.
Summing the consumer's maximum valuation for each of the 4 units purchased.
3
Calculate total expenditure paid by the consumer.
Total Expenditure = 4 units × ₦200 = ₦800.
Multiplying the quantity bought by the market price per unit.
4
Compute consumer surplus.
Consumer Surplus = ₦1,400 - ₦800 = ₦600.
Consumer surplus is the difference between total willingness to pay and total actual expenditure.

Key Concept

Consumer Surplus from Marginal Utility Schedule
Question 10Question →

A student in Lagos is willing to pay a maximum of \text{\mathbb{N}}2,500 for a transit pass, but the prevailing market price is \text{\mathbb{N}}1,600. What is the consumer surplus derived by the student from purchasing the pass?

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Answer: ₦900

Answer

The consumer surplus derived by the student is ₦900.
Consumer surplus is defined as the economic benefit gained by a consumer when they pay less for a product than the maximum amount they were willing to pay. Calculating \text{\mathbb{N}}2,500 - \text{\mathbb{N}}1,600 yields \text{\mathbb{N}}900, which accurately reflects this net monetary gain.

Step-by-Step Solution

1
Identify the total willingness to pay and actual expenditure
Maximum willingness to pay = ₦2,500; Actual market price = ₦1,600
Consumer surplus requires finding the difference between maximum willingness to pay and actual price.
2
Apply the consumer surplus formula
Consumer Surplus = ₦2,500 - ₦1,600 = ₦900
Consumer Surplus = Maximum Willingness to Pay - Actual Price Paid

Key Concept

Consumer surplus is the net monetary gain or benefit a consumer receives when paying a market price that is lower than the maximum price they were willing to pay.
Estimated Time:45s
Question 11Question →

A consumer's inverse demand function for bags of fertilizer in an agricultural zone is given by the equation P=200−10QP = 200 - 10Q, where PP is the price per bag in Naira (₦\text{₦}) and QQ is the quantity of bags demanded. If the prevailing market price of fertilizer is ₦80\text{₦}80 per bag, what is the consumer surplus in Naira (₦\text{₦})?

Show answer & explanation

Answer: 720

Answer

The consumer surplus derived from purchasing fertilizer at the market price is ₦720.
Consumer surplus is calculated as the area of the region under the linear demand curve and above the market price line. Given P=200−10QP = 200 - 10Q, substituting the market price P=80P = 80 yields Q=12Q = 12. The maximum price PmaxP_{max} at Q=0Q = 0 is ₦200₦200. Using the area formula 12×base×height=12×12×(200−80)=₦720\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times (200 - 80) = ₦720.

Step-by-Step Solution

1
Determine quantity demanded (QQ) at the prevailing market price (P=80P = 80)
Q=12Q = 12 units
Setting P=80P = 80 in the demand equation 80=200−10Q80 = 200 - 10Q yields 10Q=12010Q = 120, giving Q=12Q = 12.
2
Find maximum willingness to pay (PmaxP_{max}) when quantity demanded is zero (Q=0Q = 0)
Pmax=₦200P_{max} = ₦200
The vertical intercept of the linear demand curve represents the maximum price the consumer would consider paying.
3
Calculate the height of the consumer surplus triangle (Pmax−PmarketP_{max} - P_{market})
200−80=₦120200 - 80 = ₦120
This measures the net benefit per unit between maximum willingness to pay and the market price.
4
Calculate the total consumer surplus using the triangular area formula CS=12×Base×HeightCS = \frac{1}{2} \times \text{Base} \times \text{Height}
CS=12×12×120=₦720CS = \frac{1}{2} \times 12 \times 120 = ₦720
For a linear demand curve, consumer surplus is visually and mathematically represented by the triangular area below the demand curve and above the market price.

Key Concept

Calculation of Consumer Surplus using Linear Demand Equations
Concept and Calculation of Consumer Surplus Practice Questions — JAMB UTME | Examkin