If a business is making a loss because total revenue is less than total costs, what should the business do: shut down or continue to operate?
If you are the manager of this company, you cannot know whether to shut down simply based on the factors that you ask about in this question. The total revenue and total costs are not the numbers that are used to determine whether to shut a business down. Instead, you need to determine what your marginal revenue (MR) is and what your average variable costs (AVC) are. If your MR is less than your AVC, then you shut down. If your MR is greater than your AVC, you keep producing, regardless of whether your total revenues are lower than your total costs.
Let us imagine that you own a hotel and that it is the off season for your area. Let us further imagine that your average fixed costs (for things like the mortgage on your hotel) are $50 per room per night. Let us assume that the AVC (for things like housekeeping services) is $45 per room per night. This means your total cost for renting a room out for the night is $95. What do you do if you can only charge $50 per night for the room? You are losing $45 per night, so shouldn’t you shut down?
The answer is no. You will actually lose more if you shut down. If you shut down, you still have to pay the $50 per night in fixed costs. By shutting down, you will lose $50 per room per night whereas by staying open you lose $45 per room per night. Staying open is the better option in the short run.
So, in this case, you cannot decide whether to shut down based on the information available. You need to know your MR and AVC, not just total revenue and total costs.