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23456789 Output per time period (units)

marginal

Change in the dependent variable caused by a one-unit change in an independent variable marginal revenue

Change in total revenue associated with a one-unit change in output marginal cost

Change in total cost following a one-unit change in output marginal profit

Change in total profit due to a one-unit change in output explanation. A marginal relation is the change in the dependent variable caused by a one-unit change in an independent variable. For example, marginal revenue is the change in total revenue associated with a one-unit change in output; marginal cost is the change in total cost following a one-unit change in output; and marginal profit is the change in total profit due to a one-unit change in output.

Table 2.2 shows the relation among totals, marginals, and averages for a simple profit function. Columns 1 and 2 display output and total profits. Column 3 shows the marginal profit earned for a one-unit change in output, whereas column 4 gives the average profit per unit at each level of output. The marginal profit earned on the first unit of output is $19. This is the change from $0 profits earned when zero units of output are sold to the $19 profit earned when one unit is produced and sold. The $33 marginal profit associated with the second unit of output is the increase in total profits (= $52 - $19) that results when output is increased from one to two units. When marginal profit is positive, total profit is increasing; when marginal profit is negative, total profit is decreasing. Table 2.2 illustrates this point. The marginal profit associated with each of the first seven units of output is positive, and total profits increase with output over this range. Because marginal profit of the eighth unit is negative, profits are reduced if output is raised to that level. Maximization of the profit function—or any function, for that matter—occurs at the point where the marginal switches from positive to negative.

When the marginal is greater than the average, the average must be increasing. For example, if a firm operates five retail stores with average annual sales of $350,000 per store and it opens a sixth store (the marginal store) that generates sales of $400,000, average sales per store will increase. If sales at the new (marginal) store are less than $350,000, average sales per store will decrease. Table 2.2 also illustrates the relation between marginal and average values. In going from four units of output to five, the marginal profit of $39 is greater than the $34 average profit at four units; therefore, average profit increases to $35. The $35 marginal profit of the sixth unit is the same as the average profit for the first five units, so average profit remains identical between five and six units. Finally, the marginal profit of the seventh unit is below the average profit at six units, causing average profit to fall.

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