Break-even Analysis with Curvilinear Functions.

Abstract The article presents two break-even models with assumptions stated and justified with respect to the realism of cost and market structures for typical firms. Break-even points and the maximum profit production level are determined, using differential calculus. For each model an exhibit is presented that reflects the relationships of revenue, cost, and profit at various production levels. Employing differential calculus techniques to break-even analysis permits most realistic assumptions for revenue and cost functions than is permitted under traditional "linear simplification" break-even analysis. Total revenue for the firm is determined by demand for the firm's products. Differential calculus may be used to calculate break-even points for curvilinear revenue and cost functions. Also, by determination of first and second derivatives, it is possible to find the level which will provide maximum profits for the firm. Linear break-even analysis suggests there is only one break-even point and the analysis does not provide for determination of the sales level which provides maximum profits. Beyond a certain level, however, total costs may exceed total revenue.