why might it be a plus for a company to have such a high share price that trading in its stock is discouraged?

Then would they be able to own more of their own stock and control the board of directors??

Or would this keep the number of owners down so there would be fewer people on the board?

What other scenarios can you think of?

Having a high share price can be seen as a plus for a company in certain situations, as it may discourage trading in its stock. Here's an explanation:

1. Stability and solidity: A high share price might indicate that the company is stable and has a strong financial position. Investors may view this as a positive signal, as it suggests that the company has a solid foundation and is less likely to run into financial troubles.

2. Long-term focus: When a company has a high share price, it may discourage short-term traders from buying and selling its stock frequently. This can be beneficial for a company that wants to maintain a long-term investor base, as it may help align investors' interests with the company's long-term goals and strategies.

3. Reduced speculative trading: High share prices can deter speculative traders who prefer lower-priced stocks with higher volatility. These short-term traders often engage in rapid buying and selling, which may increase stock price volatility and create instability. By reducing speculative trading, a company's stock price might experience smoother and more consistent performance.

4. Increased credibility and prestige: A high stock price can enhance a company's reputation and prestige in the market. It may be perceived as a mark of success and investor confidence, which can attract more institutional investors and potentially positive media coverage.

It's important to note that while a high share price can have these advantages, it also presents certain challenges. For example, it may limit the pool of potential investors who can afford to buy the stock, potentially reducing liquidity. Additionally, a high stock price might attract short-sellers who believe the stock is overvalued, which can create downward pressure on the price.

To determine whether a high share price is advantageous for a company, other factors such as market conditions, industry norms, and the company's individual circumstances should also be considered.