Answer
This statement is true under certain conditions.
Work Step by Step
If a firm is producing at a level where Price is less than Average total cost but greater than the average variable cost, it will be losing money. However, in this case business should stay in business because at least it is able to pay some of it's fixed costs right now. If it shuts down, it won't be able to pay any fixed cost. Hence, in this case the firm should stay in business, even if it is losing money.
