How to Calculate Marginal Profit

Marginal profit is the derivative of the profit function (the same is true for cost and revenue). Use this marginal profit function to estimate the amount of profit from the "next" item to be produced. An example follows each step in brackets. Note that the character "^" is used to represent an exponent.

Instructions

1. Write down the marginal profit question to be answered. For example: "A company produces DVD players at a cost of $80 each. Its fixed cost is $4,000 and its variable cost is denoted by the function 0.02x^2 + 50x. What is marginal profit of producing the 1,001st DVD player?"

2. Determine the item number on which the marginal profit is to be calculated. It is labeled as x. [x=1,000]

3. Determine the fixed cost. This is usually a given: $4,000.

4. Determine the variable cost. This is usually a given: 0.2x^2 + 50x.

5. Determine the revenue function. It is labeled as R(x): R(x) = 80x.

6. Determine the cost function, which includes variable and fixed costs. It is labeled as C(x): C(x) = 0.2x^2 + 50x + 4000.

7. Determine the profit function, which is the revenue function minus the cost function. It is labeled as P(x) = R(x) - C(x): P(x) = 80x - (0.2x^2 + 50x + 4000).

8. Determine the marginal profit function, which is the marginal revenue minus the marginal cost. It is labeled as P'(x) = R'(x) - C'(x), which means that the derivatives of the revenue and cost functions need to be calculated now: P'(x) = 80 - (0.04x + 50).

9. Plug in the value for x, which is the number of the item produced where marginal profit is to be calculated: P'(x) = 80 - ((0.04(1000) + 50)).

10. Perform the math processes denoted in the marginal profit function: P'(x) = 80 - (40 + 50) = 80 - 90 = -10.

11. Determine the marginal profit or loss: The estimated marginal profit of producing the 1,001st DVD player is -$10 or a marginal loss of $10.

References

• Principles of Accounting: Reporting Techniques in Support of Managerial Decision Making