It's from the Wall Street Journal article.
Twitter Employees Face ‘Chaos Tax’
I understand that the article describes Tweeter in chaotic situation. But I can't guess what chaos tax implies exactly. I can't find any example of the expression.
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You probably can't find any example of the expression because it isn't a known idiom. It is also not a real tax!
There are many kinds of literal taxes and the word is often used as part of a compound noun to identify them - for example 'income tax', 'road tax', 'council tax' etc.
However, 'tax' is also sometimes used figuratively to suggest that something has been taken away, or there is some kind of loss to individuals. For example, in the UK, a government plan to reduce benefits (payments to persons on low incomes) from people who had spare rooms in their house was often referred to as the 'bedroom tax' by the media, even though it wasn't a form of taxation. This is because it was viewed as if people were having something taken away from them on the basis of them possessing something else.
'Chaos tax' suggests that individuals or the organisation are suffering a 'loss' because of chaos, or uncertainty - in the case of your example, the uncertainty surrounding jobs at Twitter caused by the recent takeover. I would not take this to mean a financial loss necessarily, but possibly feelings of financial insecurity.
Let’s take a closer look at the context in which the metaphor appears. From the article, with emphasis added:
Internal conversations and Slack channels are awash in distress and anger over the criticism [from Elon Musk], while company leaders who themselves have no way to know the outcome have responded with repeated staff meetings to try to soothe the angst and encourage people to press forward, according to current and former staffers and internal communications viewed by The Wall Street Journal.
“I expect the ‘chaos tax’ and ups and downs to continue,” Jay Sullivan, Twitter’s new head of product, wrote on May 13 in an internal message to thousands of employees that was viewed by the Journal. “As I know more, I will find ways to share with this group!”
Mr. Sullivan replaced one of the two executives that CEO Parag Agrawal fired earlier this month and is filling in for the other on an interim basis. In an internal memo circulated in mid-May, Mr. Agrawal attributed the hiring freeze to another cloud looming over Twitter: a weakening global economy intensified in part by the war in Ukraine.
So, “chaos tax” is Jay Sullivan’s metaphor. In this context, it means a cost or burden imposed by chaos. A Business Insider article used a very similar metaphor when it said, “The drama is taking a toll on employee morale.” According to the WSJ article quoted above, this takes two forms: a financial cost (a hiring freeze caused by economic uncertainty) and an emotional cost (distress and anger over getting a new boss who sharply criticized them in public).