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If demand is more than supply, stock prices go up. Then does that mean a company can increase its value by intentionally restricting supply?

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Then does that mean companies can increase its value by intentionally restricting supply?

Not really. They could restrict supply by initiating a buyback. A buyback could trigger a price increase, but it's not guaranteed because demand for their shares is elastic. There are plenty of other companies to invest in, so if it is not perceived as a good value the price won't increase just because supply is lower.

Regarding market capitalization, a buyback decreases market cap unless the price of remaining outstanding shares increases enough make up for the buyback.

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Not really. The problem with that is that a share of stock represents a percentage of the value of the company, not a specific tangible amount of "stuff". If widget producers made 1000 widgets last year and only 500 widgets this year, then the price would be expected to go up (all else being equal, of course). But if a company decided to issue only 500 shares of stock instead of 1000, the value of the company doesn't change. In the first case each share represents 1/500th of the value of the company; in the second case it represents 1/100th. The value of each share would be different, but the total market capitalization would be the same.

If shareholders are reluctant to sell for whatever reason, that would restrict the supply of shares in a meaningful way and one would expect the price to go up.

That said, the stock market is a complex thing, and stock prices often vary based on perception rather than hard facts. So there might be games a company could play to manipulate the stock value. (And such games would likely be illegal if it could be proven that that's what they were doing, but whatever.)

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