This statement is incorrect for at least two reasons.
First, the phrase “the highest price” is meaningless. There is no such thing as a “highest price.” It is at least mathematically possible to charge any price for any item. Therefore, there is no way to know what “the highest price” would be.
Second, and more to the point, it is not beneficial to a firm to charge a price that is too high. If it does so, it will not sell enough of its product. Instead, firms should charge the price that corresponds to their profit maximizing output.
Economists have proven that there is a level of output that always produces the maximum possible profit. This level of output is achieved when the marginal cost (MC) of making the final unit of output is equal to the marginal revenue (MR) the firm gets from selling it. When MC = MR, profit is maximized. Otherwise, the firm is not making as much money as it could.
So, what a firm needs to do (regardless of the market structure it is in) is to produce the output where MR = MC and then set the price at which all of the output will sell and no further output will be demanded (the market-clearing price). The firm must not simply set a very high price. If it does, it may well be making less profit than it could be.