Final answer:
The statement is true; monopolists face the trade-off between setting higher prices and selling lower quantities. They must find a balance that maximizes profit without diminishing sales too much or failing to compensate for lower prices with higher volumes.
Step-by-step explanation:
The statement "even with market power, monopolists cannot achieve any level of profit they desire because they will sell lower quantities at higher prices." is true. This is because a monopolist's ability to set prices is constrained by the demand for the product. While a monopolist has market power and can set higher prices, this typically leads to lower quantities sold, as consumers may resist purchasing the product at inflated prices. Further, the monopolist also faces diminishing marginal revenue as additional units sold tend to reduce the overall market price. The monopolist's challenge is to find the profit-maximizing balance between the price it charges and the quantity it sells.
For a monopolist, total revenue is low at both very low and very high quantities of output because at low quantities not much is sold, and at very high quantities, products must be sold at a lower price. Thus, the monopolist aims to strike a balance to maximize profit without setting prices so high that sales volume drops significantly or so low that increased volume does not compensate for the lower price.