# Section 2.7: Marginal Analysis in Business and Economics

## Marginal Cost, Revenue, and Profit

If x is the number of units of a product produced in some time interval, then:

 total cost = C(x) marginal cost = C'(x) total revenue = R(x) marginal revenue = R'(x) total profit = P(x) = R(x) - C(x) marginal profit = P'(x) = R'(x) - C'(x)

Drag the x slider to see how cost, revenue, and profit change with the number of units produced.

### Marginal Cost and Exact Cost

If C(x) is the total cost of producing x items, then the exact cost of producing the (x + 1)st item is:

C(x + 1) - C(x)

The marginal cost function approximates the exact cost of producing the (x + 1)st item:

C'(x) ≈ C(x + 1) - C(x)

Similar statements can be made for total revenue functions and total profit functions.

x = 1

## Marginal Average Cost, Revenue, and Profit

If x is the number of units of a product produced in some time interval, then:

 average cost = C(x) = C(x)/x marginal average cost = C'(x) = d/dx C(x) average revenue = R(x) = R(x)/x marginal average revenue = R'(x) = d/dx R(x) average profit = P(x) = P(x)/x marginal average profit = P'(x) = d/dx P(x)