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"Consider a risk-averse individual with Von Neumann-Morgenstern utility and who invests in a risky asset. If the return on the risky asset is taxed, so the consumer has an incentive to invest less in this asset." - FALSE

This alternative was given as false, but I can't understand the argument behind it. Can anyone help me? Tks!

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    $\begingroup$ Is "tks" a general new variant of "thx", or is this the spelling in some other language's online culture? $\endgroup$
    – Giskard
    Commented Mar 5 at 7:03
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    $\begingroup$ @Giskard: Seems so ... en.wiktionary.org/wiki/tks $\endgroup$
    – VARulle
    Commented Mar 5 at 10:04
  • $\begingroup$ @VARulle tks for the link (: $\endgroup$
    – Giskard
    Commented Mar 5 at 11:32

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There are not enough details to provide a general answer. Perhaps they mean that there are cases when, despite the tax, the investment does not decrease.

It is easy to concoct such an example: if the risky asset returns 200% of the investment with 50% chance and 400% of the investment with 50% chance (so it is always a win to invest in it) then the consumer will invest all their wealth in the risky asset.

On the other hand, it is also easy to concoct examples where the statement is true, e.g., when a loss is possible and there is a 100% tax on positive returns.

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