James: I make 10000 USD a month.
Alice: Wow, you have a highly paid job.
Is the phrase “highly paid job” correct?
I think yes, but also wish to ask the native speakers here.
I assume that “high paid job” is an incorrect alternative.
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Basically yes, that phrase sounds fine, though I might hyphenate highly and paid:
You have a highly-paid job.
I might also paraphrase it to sounds slightly more natural (though this is subjective):
Wow, you're highly paid!
"High paid job" is grammatically incorrect because "highly" needs to be an adverb to modify the verb "paid".
High can be an adverb (with comparative and superlative forms) as well as an adjective:
adv. higher, highest
At, in, or to a lofty position, level, or degree ... [flew high]
In an extravagant or luxurious way: made a fortune and lived high. [AHDEL]
In that it has the same form as the adjective, it is known as a flat adverb
Obviously, the related -ly form exists:
He was rated highly by the judges.
That being said, I really want to see the splitting off of degree-modifiers (such as the prototypical very as in very quickly, very bright) and other secondary modifiers (such as mystifyingly silent, obviously troubled, off-puttingly tedious, oppressively close, overweeningly devoted, painfully obvious / shy, perilously close - to name but a few) into a separate word-class. Admittedly, they are almost always isoformal with related adverbs, but their function is very different - in fact, very can't even modify a verb, except whimsically (How very dare you!)
Returning to the possibility of using 'high paid' rather than 'highly paid', it depends on whether high may be used as a degree modifier as well as an adverb. Apart from very, most secondary modifiers are of the -ly form. Well isn't of the -ly form, and is only used very informally as a degree modifier (He's well cheeky!) However, in a high-flying aeroplane, we see that it can, though it does require the hyphen here. On the other hand, a highly paid job or a highly-paid job would seem to sound more natural.
I assume that "high paid job" is an incorrect alternative.
It's not incorrect. Here's an example:
Research reveals that they are seriously under-represented in higher-paid jobs.
Reference: Collins Cobuild Dictionary
Also see here.
However, here are some alternatives: