Plot demand separately from marginal revenue

Plot demand separately from marginal revenue

Question and evidence

Why is marginal revenue below price for a single-price seller?

A fictional monopolist faces price P=12−Q for integer quantities 0 through 6 and constant marginal cost 2. There are no fixed costs. One price applies to every unit sold.

This packet uses fictional data to isolate a mechanism. It is not an empirical estimate.

Mechanism and worked example

Total revenue is price times quantity. Under a downward-sloping single-price demand curve, marginal revenue subtracts the revenue lost on earlier units as price falls. Profit-maximizing output balances incremental revenue and cost; the selling price is then read from demand. Monopoly does not guarantee profit when fixed costs are substantial.

At Q=4, P=8 and revenue 32. At Q=5, P=7 and revenue 35, so fifth-unit MR=3. At Q=6, revenue 36, so sixth-unit MR=1 below MC=2. Profit peaks at Q=5: 35−10=25.

Complication

A faulty graph sets marginal revenue equal to price and chooses ten units, beyond this packet’s domain. Raising quantity lowers the price received on earlier units; the extra unit’s price is not the entire revenue change.

Your investigation

Plot the discrete demand points, label fifth- and sixth-unit revenue changes, then identify quantity and price using separate steps.

Revise your answer to “Why is marginal revenue below price for a single-price seller?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Vocabulary

Marginal revenue: The change in total revenue from selling one additional unit.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Independent extension

Independently extend the investigation “Plot demand separately from marginal revenue” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.