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I am trying to better understand how shares work from a mathematical perspective. I am curious about how stocks work with companies to better understand how they work. Here is an example:

Let's say the number of shares of a company is 100. Person A owns 20 shares and person B owns 80 shares of a 10 dollar stock.

Q1) Person A sells one share and no one buys it. Does that mean the company has 99 shares where person B owns 0.8(100-1)=79.2 dollars and person A owns 0.2(100-1)=19.8 dollars? Or does the number of shares of a company always remain the same and something else happens? I think the share price would go down but not sure how.

Q2) Also, let's say person C buys a share and no one sells. I believe the stock price for person A would go up in this process but again am not sure how. How would you determine how much person A owns for a total amount of his 20 shares?

Q3) Let's say person A sells one share. Then, person C buys it. Would that mean the stock price moves up?

Q4) Can a company move a stock up and down? Here they start out with a $1000 market cap. If the company decides to spend $30 dollars, that means the amount person A owns will be 0.2(1000-30)=194 dollars. But then say the company makes 50 dollars of revenue spending that $30 dollars. When does that money get allocated to the shareholder person A, so that way he owns 0.2(1000-30+50)=204 dollars?

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    Person A never gets their share of the $20 profit if the board doesn't issue a dividend. – chepner Sep 11 '20 at 19:02
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    Throughout Q1-3, you seem to think that buying and selling are isolated transactions. Who do you think the seller is selling to, if not a buyer? – Daniel R. Collins Sep 11 '20 at 20:04
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    "Person A sells one share and no one buys it": that just can't happen. You need to sell a share to someone. If no one buys it, you can't sell it. It's like saying you sold your house but no-one bought it. – jcaron Sep 11 '20 at 21:30
  • I’m voting to close this question because it's a combination of theoretical, and nonsense. The premise makes no sense. How would any answers help a future visitor? Or the OP? – JTP - Apologise to Monica♦ Sep 11 '20 at 22:00
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Let's say the number of shares of a company is 100. Person A owns 20 shares and person B owns 80 shares of a 10 dollar stock.

Q1) Person A sells one share and no one buys it.

This is not possible. For each seller, there must be a buyer.

Q2) Also, let's say person C buys a share and no one sells.

The same.

Q3) Let's say person A sells one share. Then, person C buys it. Would that mean the stock price moves up?

Here the dynamic of the market comes in play:

Assume, A places a limit sell order of $10.10. C places a market order (to buy at any price). Then A sells to C at $10.10.

If C doesn't want to buy at any price, they place a limit buy order instead, e. g. for $9.90. In this case, nothing happens. But then everyone has the opportunity to either sell for $9.90 (to C) or to buy for $10.10 (form A). The "current" price is usually the last price at which a deal has taken place.

Q4) Can a company move a stock up and down? Here they start out with a $1000 market cap. If the company decides to spend $30 dollars, that means the amount person A owns will be 0.2(1000-30)=194 dollars. But then say the company makes 50 dollars of revenue spending that $30 dollars. When does that money get allocated to the shareholder person A, so that way he owns 0.2(1000-30+50)=204 dollars?

In this case, the company doesn't wilfully move the price, But the "real" value of the company changes, and so does the "real value" of the shares. Person A still owns 20 shares (assuming they didn't sell them), but as the company now has a value of $1020, each share has a current value of $10.20. But that's not to say that the price which can be obtained follows this movement. Maybe the shareholders (the public) isn't aware of the fact that the company's value has increased, or they don't consider it relevant, or whatever.

Anyway, the incentive for a buyer (e. g. C) to pay more for a share is greater if the company has a higher value, so they likely will place a buy order for $10.20 or maybe $10.25.

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    Just to add (or confuse) things a little - it's a fundamental law that you cannot sell without a buyer and you cannot buy without a seller. This is the same for stocks as well as physical objects. However, sometimes a company will buy their own stock. They are the buyer. In this case, there is simply less stock on the market. The company may use that stock for employee bonuses, or sell it again later if the market price has risen. – Istanari Sep 11 '20 at 17:34
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    This is a great answer. I think it's also valuable to note that the company and its profits are in a very real way decoupled from the stock and its value. Stock price doesn't change because a company's value goes up and down; it changes because people are willing to pay more or less (often based on company value, but that's indirect: it's perception of value that sets the stock price). This was one of the hardest concepts for me to grasp at first, and seems to be the root of one of the errors the OP has made. – Nicholas Sep 11 '20 at 18:54
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Q1 and Q2: As @glglgl points out, your first two questions are impossible. You can't sell a share if no buys it or buy a share if no one sells it to you. In this sense, buying and selling stock is just like buying and selling anything else. If I said, "Suppose I sell my used car and no one buys it. What happens?" What happens is that I TRIED to sell it, but I didn't actually sell it.

Q3: In the most immediate sense, what causes stock prices to move up and down is the supply and demand for the stock. Suppose that C wants to buy 1 share and D wants to buy one share. A is not willing to sell and B is only willing to sell 1 share. So we have two people who want to buy and only one who wants to sell. Who will he sell to? He'll sell to whoever offers the higher price. If C is willing to pay $9 and D is willing to pay $11, he'll sell to D. So now the stock exchange will record that the last price at which the stock sold was $11. The value of the stock is now $11. Their total market capitalization goes up: It's now 100 shares x $11 = $1,100.

In real life, stocks in big companies are being bought and sold constantly. There are hundreds or thousands or sometimes millions of sellers everyday, and similar numbers of buyers. But the principle is still the same. If the price that sellers are demanding is higher than the price that buyers are willing to pay, then either some buyers say forget it or some sellers lower their price until the number of buyers and sellers is in sync.

If you're a big shot trading millions of dollars, you may explicitly negotiate a price. For the average small investor, when you place a buy order, you typically say "I'll pay up to $11.37 per share" or whatever number. If your broker can't buy shares at that price, the order is unfilled and eventually cancelled. Similarly when you sell you specify the minimum you will accept.

Q4: How much a company spends or earns does not directly affect the stock price. A company's market capitalization, i.e. it's share price times the number of shares outstanding, is not the same as its assets. A company could have a billion dollars in assets and market capitalization of $10 million or vice versa. So the fact that a company spent money on some expense or earned some profit does not directly affect the share price.

In the long term, how profitable a company is has a lot to do with its share price. If a company is losing money its share price is going to tend to go down and if they're making bundles of money their share price will tend to go up. But it's not a simple relationship.

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You are confusing a sell-order with a sale. A sell-order is just an offer to sell. It get listed on some exchange, but the offer does not become an actual sale until someone accepts it.

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