Principles of Microeconomics / Unit 8 MIC 0717 worked example, 60 to 90 seconds
Finding the Monopolist's Quantity, Price and Profit
The idea
Three steps. First, compare marginal revenue with marginal cost row by row and take every unit whose marginal revenue is at least its marginal cost; the last such row is the quantity. Second, read the price at that quantity from the demand schedule, not from the marginal revenue column. Third, compute average total cost at that quantity and take price minus average cost, times quantity, for profit. A fourth check: marginal revenue at the chosen row should be positive.
In practice
Worked example: the medicine's marginal revenue per dose for each added thousand runs eleven, nine, seven, five, three, one, and its marginal cost runs two, two, three, four, five, six. The fourth thousand has marginal revenue five against marginal cost four and pays; the fifth has three against five and does not. Quantity: four thousand doses. Price from demand at four thousand: eight dollars. Total cost is the ten-thousand fixed cost plus two, two, three and four thousand, twenty-one thousand, so average cost is five twenty-five. Profit is eight minus five twenty-five, times four thousand: eleven thousand dollars a week.
Where people slip
Two errors. Pricing at the crossing, five dollars here, when the demand curve says eight. And treating profit as guaranteed; had fixed cost been fifty thousand, the same rule would give the same quantity and a loss, and the monopolist would face the shutdown test like anyone else.
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