The book is $2 cheaper at our shop.
The book is $2 costlier at our shop.
Are the above two sentences fine to native speakers?
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Yes, you can certainly write an amount before the word “cheaper” like this.
“it’s 2cm shorter”
“that way is 1km longer”
“my house is 50 years older than yours”
However, there is an error in your second example. We say “$2 more costly” and never use the word “costlier”. (Actually, in ordinary usage in Australia “$2 more expensive” would be far more common. But this may depend on the variety of English.)
This is a complicated and illogical part of English. Learners just have to remember for each word when you use the “more —-er” structure and when you don’t.
10kg fatter - correct 10kg more fatter - incorrect 10% intelligenter - incorrect 10% more intelligent - correct
For some, both are correct. Such as, “simpler” and “more simple”.