Why is profit maximization by itself an inappropriate goal and what is meant by the goal of maximization of shareholder wealth?
Shareholder wealth is measured in terms of the market value of the stock held by them. A company's objective should be to increase shareholder wealth rather than just an increase in the total profits.
Total profits can be increased in many ways, many of these do not lead to an increase in shareholder wealth, instead they may actually lead to a fall in the market value of the stock and decrease the wealth of the present shareholders. Examples of this could include raising additional capital by issuing more stock but not using the capital raised for projects that give a yield matching the expectations of investors. Profit could also be increased by investments made in high risk projects that can increase the revenue substantially when they are started but there is no guarantee that the same level of returns would continue to flow in over a long duration of time.
If a management only focuses on increasing total profits and is not concerned with the actual increase in the earnings per share or takes up unsustainable and high risk projects that cannot yield a consistent return over a long period of time or starts projects that do not result in revenue growth for a long time, the stock of the firm is no longer attractive.
Buyers of the stock of a firm do not look merely at the total profits reported, instead they are interested in becoming shareholders of companies that have a strategy for consistent growth in profits and a minimization of risk for the shareholders. Companies that do this instead of trying to merely report a higher total profit are more attractive and there is an increase in the value of their stock which leads to an increase in shareholder wealth.