Assume a monopolist that has cost = 0, and can produce with no output constraint. The market consists of five consumers and each purchase one unit. Consumers have the following distribution of willingness to pay: B1 = 1, B2= 0.8, B3= 0.6, B4= 0.4, and B5 = 0.2. What is the value created and the price charged by the monopolist?

Question

BlackTom AI · Accepted Answer

We are given a monopolist with zero costs and no output constraint, facing five consumers with the following willingness to pay (WTP): B1 = 1, B2 = 0.8, B3 = 0.6, B4 = 0.4, B5 = 0.2. Each consumer purchases at most one unit. For a given price P, the number of units sold equals the count of consumers with WTP ≥ P, and the value created is the total willingness to pay of those buyers (since costs are zero, value created equals consumer surplus plus revenue, but in this setup we consider value created as the sum of WTP of those who buy).

Option analysis:

Option A: P = $0.4, value created = $4.0
- At P = 0.4, which consumers buy? Those with WTP ≥ 0.4: B1 = 1, B2 = 0.8, B3 = 0.6, B4 = 0.4. That is 4 buyers.
- Value created would be the sum of their WTPs: 1 + 0.8 + 0.6 + 0.4 = 2.8, not 4.0. Moreover, the stated value 4.0 is inconsistent with the given WTPs. This option miscounts both the number of buyers and the total WTP.

Option B: P = $0.6, value created = $2.4
- At P = 0.6, buyers are those with WTP ≥ 0.6: B1 = 1, B2 = 0.8, B3 = 0.6. That yields 3 buyers.
- The value created is the sum of their WTPs: 1 + 0.8 + 0.6 = 2.4. This matches the definition of value created given zero costs.

Option C: P = $0.6, value created = $3.0
- Using the same price and buyer set as above (0.6 threshold), the value created is 2.4, not 3.0, since only B1, B2, and B3 contribute: 1 + 0.8 + 0.6 = 2.4.
- Therefore this option overstates the total WTP of buying consumers for this price.

Option D: P = $0.2, value created = $5.0
- At P = 0.2, all five buyers purchase (since all WTPs are at least 0.2).
- The value created would be the sum of all WTPs: 1 + 0.8 + 0.6 + 0.4 + 0.2 = 3.0, not 5.0. This option doubles the total available WTP and is inconsistent with the given numbers.

In summary, evaluating each option against the definitions and the given WTPs shows that Option B correctly aligns with the price threshold and the corresponding total value created, while the other options misstate either the buyer set or the sum of WTPs.

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