"The contract is valid if the woman accepts it; a valid contract doesn't require that the rates be stated upfront so long as the terms are disclosed and consented to by both parties."

Actually, it depends on the type of contract, and where in the world you are.

In the US, UCC contracts don't require a price term, but other contracts do. Since UCC does not cover services contracts, Picasso's contract would have required a price term, or some other show of consideration.

In the specific case of lawyers, most states require fee agreements that state prices up front in writing.