This might appear weird to you at first sight. People usually speak of “the power of entry” or “limited entry” in monopoly industries. And we know that the power of entry can give existing players exorbitant profits. The power of exit, however, seems to be rather counterfactual: Why do you need a power to exit? What does it apply to?
The power of exit has important implications in the sphere of social sciences. Democracy provides people with the right to exit. Voting gives people the chance to reject certain leaders if they feel unsatisfied with them. This is the most manifest in the Liberalist view. Social hierarchy can deny people’s right of exit. A serfdom arrangements prevents people from exiting the system once they sign the contract (or hereditary even without a contract). In public finance, the power of exit also means a great deal of freedom and sometimes better social welfare. I was looking into the pre-primary school voucher scheme in Hong Kong, and I discovered that the poor people might be better off if the voucher could be redeemed for other uses (I have a post on this issue). By setting the voucher value to be only redeemable in education, the government is essentially forcing the poor to consume more of the education good instead of other goods which might be more valuable for them.
Economic models used to suppose that capital is restricted to a particular country and could be taxed efficiently. But in the contemporary world where factors of production are highly mobile, this is no longer the case. The tax on producers are often transmitted to land owners simply because they don’t have the right to exit for land is immobile.