Question 7.30 Choose the correct answerThe diagram depicts the demand curve of a product. Assume that there are 100 potential buyers who can choose to purchase one unit each. Based on this graph, read the following statements and select the correct one.

Question

BlackTom AI · Accepted Answer

A downward-sloping linear demand curve implies P = 10,000 − 100Q (since P = 10,000 at Q = 0 and P = 0 at Q = 100).

1) Relevant concepts
- Law of Demand: price and quantity demanded move inversely; a downward-sloping demand curve graphically illustrates this.
- Willingness to pay (WTP): the price each marginal buyer is willing to pay; total WTP (or total value) is the sum (area under the demand curve up to Q).
- Revenue: R(Q) = P(Q) × Q; for linear demand R(Q) = (10,000 − 100Q)Q.

2) Step-by-step reasoning and calculations
- Derive demand function: slope = (0 − 10,000)/(100 − 0) = −100, so P(Q) = 10,000 − 100Q.
- Check option a: “A quarter of buyers are not willing to pay more than £2,000.” Solve 2,000 = 10,000 − 100Q → 100Q = 8,000 → Q = 80. That means 80 buyers are willing to pay at least £2,000, so only 20 buyers (20%) are unwilling — not 25%. Option a is false.
- Check option b: “At output of 20, the willingness to pay of all 20 consumers who buy the product is £8,000.” P(20) = 10,000 − 100×20 = 8,000, so the marginal buyer’s WTP is £8,000, but the total WTP of all 20 buyers is the sum of each buyer’s WTP (area under the curve). Average WTP for first 20 units = (P(0)+P(20))/2 = (10,000+8,000)/2 = 9,000; total WTP = 20×9,000 = £180,000, so the statement as written is incorrect.
- Check option d: Revenue at Q = 100 is R(100) = 0×100 = 0. Revenue is maximized where dR/dQ = 0: R(Q) = 10,000Q − 100Q^2 → dR/dQ = 10,000 − 200Q = 0 → Q = 50. So selling all 100 units does not maximize revenue. Option d is false.

3) Why the correct answer is correct
The plotted curve is a classic downward-sloping demand curve showing that higher prices correspond to lower quantities demanded — exactly the Law of Demand. None of the other statements correctly interpret the graph or the economic calculations.

4) Conclusion
Therefore the correct choice is c. The diagram demonstrates the Law of Demand, which matches the provided answer.

Question 7.30 Choose the correct answerThe diagram depicts the demand curve of a product. Assume that there are 100 potential buyers who can choose to purchase one unit each. Based on this graph, read the following statements and select the correct one.单项选择题

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