From the article: How to Find Out Your Client's Budget
Finding our your client's budget without providing them with an estimate first can be difficult. If your client does reveal their budget, however, it can improve your relationship with them by avoiding a lot of the uncomfortable talk about money. It can also save you time, if you can avoid research and proposal writing for projects below your desired price. Share your experience and advice below on your success in getting client's to disclose their budgets.