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Why would a company care about the price of its own shares in the stock market?
Fiduciary They are obligated by the rules of the exchanges they are listed with. Furthermore, there is a strong chance that people running the company also have stock, so it personally benefits them to create higher prices. Finally, maybe they don't care about the prices directly, but by being a good company with a good product or service, they are desirable and that is expressed as a higher stock price.  Not every action is because it will raise the stock price, but because it is good for business which happens to make the stock more valuable.