For students who like calculus: You can show the condition for profit maximization easily using calculus. Define TP (q ) = total profits, TC ( q ) = total costs, and TR ( q) = total revenues. Marginal this-or-that is the derivative of this-or-that with respect to output, so dTR/ dq = TR' (q) = MR = marginal revenue.
a. Explain why TP = TR - TC.
b. Show that a maximum of the profit function comes where TC' ( q) = TK ( q). Interpret this finding.