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.

In this article, the author analyzes some of the unique accounting practices in foreign countries. A study of international accounting practices reveals an array of methods and procedures. Some nations still use the primitive accounting techniques which most industrialized nations considered outmoded fifty years ago; on the other hand, a number of nations now employ the most advanced accounting methods, supported by up-to-date laws. International accounting is important because it gives us the opportunity to study historical accounting methods supported. More than that, however, one can learn from the failures and successes of nations that have applied accounting methods different from ours to solve many of the same problems now facing people. The relative merits of flexibility as compared with uniformity of accounting principles, procedures and methods have been under much discussion in the United States. Although there is no space here for detailed investigation, it is interesting to note that there are still three nations in which complete or partial uniformity was or is still required by law.

I. The basic model, 455. — II. Analysis of global stability of growth equilibrium when both countries are incompletely specialized, 459. — III. Analysis of global stability of growth equilibrium when both countries are completely specialized, 463.

One of the continuing unsolved problems of accounting is that of joint costs of production. Generations of accountants have struggled in the definitional morass of joint products, major products, co-products, minor products, by-products, and scrap, waste, spoiled or defective products. For their part, economists have been quick to point out that, in many cases, cost allocations to joint products are arbitrary and thus unjustified. Be that as it may, for a number of mundane reasons well known to accountants, such as the preparation of balance sheets and income statements, evaluation of inventories, preparation of tax returns and public regulation. Some allocations are required and must be made. It proposes to relate accounting to economic theory and in so doing to make a very limited advance on the problem. In a joint cost situation, one input serves to produce two or more products, these two or more outputs may issue from the production process either in fixed proportions or in variable proportions.