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I don't know if this is the right place to ask this question, if not, please be so kind and refer me to the right place, much appreciated!

Say if a company releases a million share with 10 each, and a transaction is made with 11 for a thousand share, then the total value of sotcks will be $999,000*10+1,000*11=10,001,000$, so now the price for each share becomes $10.001$. Am I correct?

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In a frictionless world, all outstanding shares are perfectly identical as they give you the same rights and claims to control and cash flows. So the observed market price for one share is the same as for all other shares. In your example, all shares would now be worth 11. Why would you pay 11 if there are other share worth 10 you could buy?

In practice, things may be a bit more complicated due to at least two reasons.

  1. Sole control over a firm is potentially more valuable than a single share. Investors may be willing to overpay for marginal shares allowing them to gain full control compared to the first share you might buy. That explains merger and acquisition premia.
  2. Market prices are only reliable if there is sufficient liquidity. In stocks where hardly anyone trades, you can observe people artificially inflating prices. An example is the 100 million dollar deli in New Jersey: https://www.cnbc.com/2021/04/15/theres-a-single-new-jersey-deli-doing-35000-in-sales-valued-at-100-million-in-the-stock-market.html
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