## Info

125,000 \$50,000

155,000 30,000

180,000 25,000

200,000 20,000

210,000 10,000

### Total and Marginal Functional Relationships

Geometric relations between totals and marginals offer a fruitful basis for examining the role of marginal analysis in economic decision making. Managerial decisions frequently require finding the maximum value of a function. For a function to be at a maximum, its marginal value (slope) must be zero. Evaluating the slope, or marginal value, of a function, therefore, enables one to determine the point at which the function is maximized. To illustrate, consider the following profit function:

profit maximization

Activity level that generates the highest profit, MR = MC and Mn = 0

breakeven point

### Output level at which total profit is zero

Here n = total profit and Q is output in units. As shown in Figure 2.3, if output is zero, the firm incurs a \$10,000 loss because fixed costs equal \$10,000. As output rises, profits increase. A breakeven point is reached at 28 units of output; total revenues equal total costs and profit is zero at that activity level. Profit is maximized at 100 units and declines thereafter. The marginal profit function graphed in Figure 2.3 begins at a level of \$400 and declines continuously. For output quantities from 0 to 100 units, marginal profit is positive and total profit increases with each additional unit of output. At Q = 100, marginal profit is zero and total profit is at its maximum. Beyond Q = 100, marginal profit is negative and total profit is decreasing.

Another example of the importance of the marginal concept in economic decision analysis is provided by the important fact that marginal revenue equals marginal cost at the point of profit maximization. Figure 2.4 illustrates this relation using hypothetical revenue and cost functions. Total profit is equal to total revenue minus total cost and is, therefore, equal to the vertical distance between the total revenue and total cost curves at any output level. This distance is maximized at output QB. At that point, marginal revenue, MR, and marginal cost, MC, are equal; MR = MC at the profit-maximizing output level.

The reason why QB is the profit-maximizing output can be intuitively explained by considering the shapes of the revenue and cost curves to the right of point QA. At QA and QC, total revenue equals total cost and two breakeven points are illustrated. As seen in Figure 2.4, a breakeven point identifies output quantities where total profits are zero. At output quantities just beyond QA, marginal revenue is greater than marginal cost, meaning that total revenue is rising faster than total cost. Thus, the total revenue and total cost curves are spreading farther apart and profits are increasing. The divergence between total revenue and total cost curves continues so long as total revenue is rising faster than total cost—in other words, so long as MR > MC. Notice that marginal revenue is continuously declining while marginal cost first declines but then begins to increase. Once the slope of the total revenue curve is exactly equal 