Demand Schedules for Three Individuals
Quantity Person A: WTP Person B: WTP Person C: WTP
1 $50 $80 $30
2 $40 $10 $30
3 $20 $0 $25
4 $10 $0 $25

The table above represents the individual demand curves for three different people for a good. Assume also that the market as as whole is made up of the three consumers in total.

Assume the good is a public good (e.g. a ticket to turn the lights on in an open-access play area for 15-minutes). If the price is set to $35 per ticket, what is the socially optimal quantity of tickets that should be purchased?

Note: enter answer with only numerical values (no commas) and round up to the nearest tenth. For example, if you think the answer is "$1,101.58" then enter the answer "1101.6" in the space below.

Question

Demand Schedules for Three Individuals
Quantity	Person A: WTP	Person B: WTP	Person C: WTP
1	$50	$80	$30
2	$40	$10	$30
3	$20	$0	$25
4	$10	$0	$25

The table above represents the individual demand curves for three different people for a good. Assume also that the market as as whole is made up of the three consumers in total.

Assume the good is a public good (e.g. a ticket to turn the lights on in an open-access play area for 15-minutes). If the price is set to $35 per ticket, what is the socially optimal quantity of tickets that should be purchased?

Note: enter answer with only numerical values (no commas) and round up to the nearest tenth. For example, if you think the answer is "$1,101.58" then enter the answer "1101.6" in the space below.

BlackTom AI · Accepted Answer

To tackle a public good problem, we use the Samuelson condition: the sum of individuals' marginal valuations (willingness to pay for the next unit) should be compared to the price (cost) of providing that unit.

First, examine unit 1: add up each person's WTP for the first unit. A1 = 50, B1 = 80, C1 = 30. Sum = 50 + 80 + 30 = 160. Since 160 > 35, supplying the first unit increases total welfare, so unit 1 should be provided.

Next, unit 2: consider the second unit for each person. A2 = 40, B2 = 10, C2 = 30. Sum = 40 + 10 + 30 = 80. Because 80 > 35, the second unit should also be provided.

Then unit 3: WTPs for the third unit are A3 = 20, B3 = 0, C3 = 25. Sum = 20 + 0 + 25 = 45. Since 45 > 35, the third unit should be provided as well.

Finally, unit 4: WTPs for the fourth unit are A4 = 10, B4 = 0, C4 = 25. Sum = 10 + 0 + 25 = 35. This exactly equals the price, so providing the fourth unit yields zero net gain but does not reduce welfare; in standard marginal cost equals marginal benefit criteria, we can justify providing it, though in some analyses one might exclude if strictly prefer to avoid zero net gain.

Summarizing the marginal totals:
- Unit 1: total WTP 160 > 35 → include
- Unit 2: total WTP 80 > 35 → include
- Unit 3: total WTP 45 > 35 → include
- Unit 4: total WTP 35 = 35 → include (tie can justify inclusion depending on convention)

Therefore, the socially optimal quantity, given the data and the price of 35, is the number of units up to which the summed marginal valuations meet or exceed the price, which reaches the fourth unit under the common convention that a tie at the margin justifies provision. Note that if one required strictly greater than, unit 4 would be excluded, yielding a quantity of 3; with the equality case commonly included, the quantity is 4.

End result (based on the standard rule and the provided values): the marginal comparison supports providing up to four units, since the fourth unit’s total marginal benefit equals the price and therefore does not reduce welfare.

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