Hello. Is it natural to use much alone in these sentences:

This shirt costs much.
I'm sleeping much.
I need to run much.
I eat much.
I'm afraid none of these sound natural. They will all be fine if you use 'a lot' instead of much.
Hi, Mr. M,

Do you think, though, that in the first example the "find it difficult to" creates a non-assertive context similar to "can't"? In that way, maybe this one isn't really an exception to the usual pattern? What do you think?

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Part of the unnaturalness comes from the informality of the simple example sentences. In ordinary conversation, 'much' is usually reserved for questions and negations, and is replaced, as Nona says, by 'a lot of' in affirmations. In formal writing, however, 'much' appears more often and without much awkwardness:

'Children find it difficult to study much when the television is blaring.'
'Psychiatrists have discovered that sleeping much does not recover previously lost sleep.'
 CalifJim's reply was promoted to an answer.
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Yes, it crossed my mind. Assertive 'much' does not occur much as an adverb of a verb, I admit. But when I think much about it, I can still find an example or two.