To answer the question, we need to model the outcome when there are two firms in the industry. Neither the competitive model nor the monopoly model is appropriate---we really need a model of oligopoly.
But we can do a preliminary analysis if we make the (somewhat unreasonable) assumptions that the monopolist sells its output before another firm enters and does not anticipate entry when choosing its output and, when deciding whether or not to enter, a firm assumes that the monopolist will not react.
Under these assumptions, the question is: given the residual demand---the demand remaining after the monopolist has sold its output---is there any output for an entrant that yields it a positive profit? That is, is there any output for which the residual demand curve lies above the entrant's AC curve?
To find the residual demand, we simply subtract the amount sold by the monopolist from the total demand. The model is illustrated in the following figure. The origin for the monopolist is denoted 0. The monopolist produces the output for which MR is equal to MC and charges the price p*. The entrant's origin is 0E, and its marginal cost and average cost curves, relative to this origin, are MCE and ACE. Equating MC with MR, it produces the output yE (measured from the origin 0E) and charges the price pE, and makes a profit equal to the area of the small light purple rectangle.
Examples and exercises on monopoly and entry