Q.Will the monopolist firm continue to produce in the short run if a loss is incurred at the best short run level of output?

In the short run, fixed costs are unavoidable whether or not the firm produces, so the decision turns on whether price covers average variable cost. …

In the short run the firm's fixed costs must be paid whether it produces or not, so they are not relevant to the produce-or-shut-down decision; only the variable costs are. The firm compares the price it receives (its average revenue) with its average variable cost ($AVC$): …