The whole sentence is "Prices to be set when the collection arrives". I guess it's a future tense but in a passive voice tense form, So it's not very clear for me why we didn't use "will be set" instead of "to be set" and when we use it? Thanks in advance
First of all, as Drew pointed out in the comments, "Prices to be set..." is short for "Prices are to be set..." The shorthand may have been used for brevity, to save space or printing costs, etc.
Now to answer your question: this particular type of passive construction is frequently used in contexts where the text could be legally binding. As you pointed out, in casual speech we might simply say "Prices will be set..." But in legally binging context (legal documents, advertising "small print", etc.) saying that something "will be" done might be construed as a commitment. The purpose of the sentence, however, is not to legally commit to setting prices immediately upon the arrival of the collection, but to make it clear to the reader that the general procedure is to set prices after the arrival. In other words, they're letting you know that you should definitely NOT expect prices to be set BEFORE the arrival of the collection, while at the same time NOT promising that they'll be set immediately after the arrival, either.
"Prices will be set when the collection arrives":
- Indicates what will happen in the future
- Sounds like a statement of fact or a commitment
- Can be legally binding
- Can be a legal liability for the person/entity issuing the statement
"Prices are to be set when the collection arrives":
- Indicates a vague expectation of an action
- Sounds like a description of a procedure or polite instructions
- Is more difficult to interpret as a legal commitment
- Protects the issuer of the statement from liability by creating ambiguity
Just FYI, please note that both versions are in the passive voice. In both cases, something is being done TO the prices, by an unspecified subject. Active voice would be something like "We will set the prices..."
What is the context of the sentence in question? If it is a headline, then it contains the common use of the to infinitive as an alternative to will + infinitive or the going to construction.
This use of language is called headlinese. Quirk et al., in section 11.46 (Newspaper Headlines) of A Comprehensive Grammar of the English Language note:
To is commonly used to express the future or a predicted arrangement
- Senator to seek reelection ['The senator is to seek reelection']
The Wikipedia article on Headlinese has this extract:
Most verbs are in the simple present tense, e.g. "Governor signs bill", while the future is expressed by an infinitive, with to followed by a verb, as in "Governor to sign bill".
As far as the passive is concerned, Garner in Modern American Usage (p414) in his entry on Headlinese states:
... the passive voice is far more common in in headlines than in general prose ... .
There is a similar question elsewhere on this site: To + verb in sentence without any other verb
Of course, headlinese is not restricted to newspaper headlines alone and is often used in contexts where there are space restraints.