We analyze the steady-state production of a product produced through the growth of microorganisms in both a continuous flow bioreactor and in an idealized continuous flow membrane reactor. The reaction is assumed to be governed by Monod growth kinetics subject to noncompetitive product inhibition. Although this reaction scheme is often mentioned in textbooks, a stability analysis does not appear in the literature. The steady-state solutions of the model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained. Knowledge of the steady-state solutions and their asymptotic limits may be useful to estimate parameter values from experimental data. The key dimensionless parameter that controls the degree of noncompetitive product inhibition is identified and we quantify the effect that this has on the reactor performance in the limit when product inhibition is 'small' and 'large'.