A wizard begins play with a spellbook containing all 0-level wizard spells (except those from his prohibited schools, if any; see Arcane Schools) plus three 1st-level spells of his choice. The wizard also selects a number of additional 1st-level spells equal to his Intelligence modifier to add to the spellbook. At each new wizard level, he gains two new spells of any spell level or levels that he can cast (based on his new wizard level) for his spellbook. At any time, a wizard can also add spells found in other wizards' spellbooks to his own (see Magic ).
An alchemist may know any number of formulae. He stores his formulae in a special tome called a formula book. He must refer to this book whenever he prepares an extract but not when he consumes it. An alchemist begins play with two 1st-level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier. At each new alchemist level, he gains one new formula of any level that he can create. An alchemist can also add formulae to his book just like a wizard adds spells to his spellbook, using the same costs, pages, and time requirements. An alchemist can study a wizard's spellbook to learn any formula that is equivalent to a spell the spellbook contains. A wizard, however, cannot learn spells from a formula book. An alchemist does not need to decipher arcane writings before copying them.
I believe they start with it for free, which may be why they have a lower starting wealth on average. I cant point to a specific rule off hand but i seem to remember a developer posting that somewhere.
I was wondering about this for the cavalier's banner ability also, but not seeing a price for it until UE i just assume they automatically receive any class feature for free.
It does a darn sight more than imply it. As a class ability, the wizard/alchemist "begins play" with the book, in the same way that a fighter gets a bonus feat, or a Druid may choose an animal companion, or a cavalier gets a mount. The cost of spell books is only when the first (free) one gets full.
What about spell component pouches or holy symbols? I've never had my players pay for them unless they wanted spares (in short, characters ALWAYS start play with everything necessary to use their class abilities in our games).