Principles of Microeconomics / Unit 17 MIC 1622 worked example, 60 to 90 seconds
Sample Question Eight: Quantity from a Total-Cost Table
The idea
Given a price and a table of total cost by quantity, compute marginal cost as the change in total cost between successive rows. Produce every unit whose marginal cost is at most the price and stop at the first that exceeds it; the last unit produced is the answer. Check by profit: revenue, price times quantity, minus total cost, should be highest at that row. Report the quantity and profit.
In practice
Worked example: total cost is twenty, twenty-five, thirty-one, thirty-eight, forty-six, fifty-six, sixty-eight and eighty-three dollars for zero through seven units, so marginal cost is five, six, seven, eight, ten, twelve and fifteen. At a price of thirteen, the sixth unit costs twelve at the margin and the seventh fifteen: produce six. Revenue seventy-eight, total cost sixty-eight, profit ten; at five units profit is nine and at seven it is eight, so six is the maximum. At a price of nine, produce four: revenue thirty-six, cost forty-six, a loss of ten, which beats the loss of twenty from shutting down, since fixed cost is twenty.
Where people slip
Marginal cost comes from differences between rows, never from a row divided by its quantity, which is average cost. And a loss at the best quantity is not a reason to produce less; the marginal rule finds the best of a bad set, and the shutdown test decides whether to produce at all.
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