Maximizing profit with total revenue and total cost

148 Part III: Market Structures and the Decision-Making Environment

Similarly, marginal cost is the change in total cost, so it’s represented as the derivative of total cost taken with respect to the quantity of output produced

As previously indicated in Figure 9-2, the profit-maximizing quantity of output is determined where marginal revenue equals marginal cost.

The market-determined price for your good is $80. Therefore, your total revenue equals

Marginal revenue equals the derivative of total revenue taken with respect to quantity or

Again note that marginal revenue and price are the same in perfect competition.

If your total cost function is

Marginal cost equals

In order to determine the profit-maximizing quantity of output, you simply set marginal revenue or price equal to marginal cost and solve for q.

1. Set marginal revenue equal to marginal cost.

2. Solve for q.

The profit maximizing quantity of output is 700 units. Note this is the same answer you obtain when you maximize the total profit equation by using calculus.