# The Relationship Between Total and Marginal Values

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The Relationship Between Total and Marginal Values

Total Values TR Cost/Revenue Output/Sales
Total Revenue is price x quantity sold. (TR = P x Q) A firm facing a downward sloping demand curve must lower price to sell successive units of its product. TR therefore rises at first but the rate at which it rises begins to slow down and will eventually fall. Cost/Revenue The slope of the TR curve varies at each point. This is because the amount added to TR from each sale is slightly less than before. A positive slope suggests TR is rising, a negative slope that TR is falling. TR Output/Sales

TC FC TR Cost/Revenue Output/Sales
At this point the slope of the TR and TC curves are equal. At this point MC = MR since MC and MR are the slopes of the TR and TC curves. (Students of calculus should recognise this!) Hence profit maximisation occurs where MC = MR. Profit = TR – TC Maximum profit will be made where the distance between TR and TC are at their greatest. Total Cost (TC) is the sum of fixed costs (FC) and variable costs (VC). TC = FC + VC It cuts the vertical axis at a point indicating the level of fixed costs. Cost/Revenue TC FC TR Output/Sales

Total and Marginal Values
Price At the point where the MR cuts the horizontal axis, MR = O. That means that the addition to TR from selling one extra unit was 0. This is the definition for unit price elasticity of demand. Therefore the equivalent point on the D curve is where Ped = - 1 Marginal Revenue (MR) is the addition to TR as a result of selling one extra unit of output. If the D curve is downward sloping, each unit is sold at a progressively lower price. The MR curve lies under the D(AR) curve. Under normal conditions, the demand curve facing the firm is downward sloping from left to right. This implies that to sell increasing items of a product a firm must accept a lower price for each successive unit. AR = TR/Q. The area under the curve represents TR Ped = -1 D = AR Sales MR

Total and Marginal Values
Price It follows that when MR is negative, the addition to TR must be negative. If this is the case then a reduction in price by 10% would lead to Qd rising by less than 10% meaning TR would fall. Elasticity in this range of the demand curve must therefore be between infinity and -1 or elastic. When price elasticity of demand is elastic, the % change in Qd is > % change in P. In such circumstances, a reduction in price of 10% would see D rising by more than 10% and TR would rise. The addition to TR must therefore be positive shown by the highlighted area on the MR curve. Ped in this range is between infinity and -1 D = AR Sales MR

Total and Marginal Values
Price When MR is negative, the addition to TR must be negative. If this is the case then a reduction in price by 10% would lead to Qd rising by less than 10% meaning TR would fall. Elasticity in this range of the demand curve must therefore be between 0 and -1 - inelastic Ped in this range is between 0 and -1 D = AR Sales MR

Putting the two together:
Cost / Revenue TC Putting the two together: If a firm was to target revenue maximisation as an objective, this would not necessarily correlate with the profit maximising output – revenue maximisation occurs where TR is at a maximum (MR = 0) If we put the two diagrams together we can see that profit maximisation occurs where the difference between TR and TC is greatest (where MC = MR) TR Output/Sales MC D = AR Output/Sales Q1 Q2 MR