This is a point I find very confusing and very hard to justify to students. Depending on the books, one finds many different conventions regarding the sign of elasticities and marginal rate of substitution (MRS). Some define them taking absolute value, some don't, and one sometimes finds inconsistencies inside a single book or set of notes.
My questions are:
To your knowledge, what is the most conventional stance regarding the use of absolute value in the definition of
Own-price elasticity
Cross-price elasticity
MRS
Is it mere convention or is there somewhat of a rational for taking absolute value in some/all/none of the cases?