Finding Profit-Maximizing Output from a Table

A table already has every number you need. List quantity, total revenue, and total cost, then compute profit at each quantity as total revenue minus total cost. The quantity with the highest profit is the answer. You can also work it marginal unit by marginal unit: find marginal revenue (the change in total revenue from one more unit) and marginal cost (the change in total cost). As long as marginal revenue is greater than marginal cost, producing that next unit adds to profit, so keep going. Once marginal cost climbs above marginal revenue, that unit would subtract from profit, so stop one unit before that happens.

For a price-taking firm, marginal revenue is just the market price, since every unit sells for the same amount and adds exactly that much to revenue. So the rule 'produce where marginal revenue equals marginal cost' becomes 'produce where price equals marginal cost.' With a table of costs, you do not need marginal revenue to equal marginal cost exactly; you pick the last quantity where marginal revenue still exceeds marginal cost.

This table method is the arithmetic twin of the graph students draw later with marginal revenue and marginal cost curves crossing. Once a firm has found this output, the next step in the unit is checking whether price covers average total cost to see if the firm earns a profit, breaks even, or should shut down. Finding the output comes first; judging whether it is worth running comes second.