1. Comenius project Partners in Patterns 2006-2009 Underlying patterns in economic models Madrid – November 2007 – Italian partners Prof. G. Arcidiacono e P. Ronchi

2. Our proposal 1.To look for underlying pattern in economic models. 2.To built and publish on the web an Encyclopedia of mathematical and economic terms using the languages of the European partners. An example…….

3. ANALYSIS BREAKBREAK EVENEVEN

4. BREAK EVEN ANALYSIS Aims to analyze the potential profitability of an expenditure in a sales-based business. Meaning Analysis of total costs – sale of product-total revenue

5. OBJECTIVE The break even point for a product is the point where total revenue received equals total costs associated with the sale of the product It is typically calculated in order for businness to determine if it would be profitable to sell a proposed product, as opposed to attempting to modify an existing product instead so it can be made lucrative. BREAK EVEN POINT in economics is the point at which cost or expenses and income are equal - there is no net loss or gain, one has "broken even".

6. 1. 1. ALGEBRIC ALGEBRIC : BEP quantity is calculated by the profit equation: Profit=Revenues-cost 2. BY CHART: CHART: In its simplest form, the break even chart is a graphical representation of costs at various levels of activity shown on the same chart as the variation of income. Solution methods:

7. 1. ALGEBRIC METHOD q = quantity of product and quantity sold cv = variable cost per unit p= selling price per unit CF=total fixed cost per unit CV=progressive variable costs per year CT=total costs per year RT=total revenues per year CT = CF + CV = CF + cv x q RT = p x q CT=RT B.E.P. occurs when

8. CF + cv x q=p x q CT=RT p – cv = margine unitario di contribuzione, con il quale ogni prodotto partecipa alla copertura dei costi fissi CF q= p - cv

9. 2. BY CHART

10. In the diagram above, the line OA represents the variation of income at varying levels of production activity ("output"). B C represents the total fixed costs in the business. As output increases, variable costs are incurred, meaning that total costs (fixed + variable) also increase. At low levels of output, Costs are greater than Income. At the point of intersection, P, costs are exactly equal to income, and hence neither profit nor loss is made. WIRIS GRAPHIC Italian WIRIS server O A P B C

11. B.E.P. using worksheet worksheet B.E.P. using wwww oooo rrrr kkkk ssss hhhh eeee eeee tttt