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Please help me to understand how the hypothetical introduction of wealth tax will affect the markets.

In my understanding, many of the super-rich own most of their wealth in shares of their own company (take heads of tech giants as an example).

Let's say that country X introduced an annual wealth tax of 3%. Let's also assume that a wealthy individual A owns 75% of their company B. The capitalization of B remains on about the same level. This would mean that after 37 years after the introduction of the tax, individual A will keep less than a quarter of company B shares ($0.75 * (1-0.03)^{37} ≈ 0.24$) and will hand more than a half over to the government. Would it mean that the government can take over the company by means of collecting a wealth tax? (unless the original owner has some kind of a super-voting stock)

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No, this is not how wealth tax works. Wealth taxes do not transfer company ownership to the government.

In order to understand how wealth taxes work consider following example. Let us assume that there is individual owning 10 shares each worth \$10,000 dollars in company A. The individual has no debts or nothing else directly affecting the wealth of individual.

Given the numbers assumed above the wealth of that individual would be 10x\$10,000 = \$100,000.

Next let us assume no deductible so the wealth tax is applied to whole \$100,000. Lastly, lets set the wealth tax to 3% as in your question.

In the case above the wealth tax will be:

$$ (0.03) {\\\$} 100,000 = {\\\$}3000$$

per year. However, government does not get any of the shares in the company. The individual is free to get the \$3000 to pay the wealth tax from their labor income or from their dividend income, profits from some venture or rent they get etc (neither of which are wealth). So even with 3% wealth tax they get to keep their company and shares in their company forever.

The individual could pay for the wealth tax by selling some of their shares in the company, for example in year 1 they could sell 1 share for \$10,000 to someone else pay \$3000 tax to the government and consume rest or keep the rest on bank account for future. But the individual does not need to sell it to the government.

If government would want to buy the shares it could presumably do that on the same capital market where individual will sell their \$10000 share, but the government would have to compete with other buyers there or the individual could also just decide to sell it someone directly where government would have no access to actually buy the share (although I don't know why would government want to do that in the first place).

Consequently, even with 3% wealth tax it might take anything between 1 year (in case if the person just decides to directly sell all shares on market) or infinity number of years (in case that individual (and their descendants) will never decide to sell their shares, or never sell them to the government) for government to get more than 50% ownership in a firm owned by an individual that is being taxed.

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