When clients request an expert, make it compulsory that they include their budget or per hour rate for the project.
I get the impression that many clients are looking for something for nothing. Inclusion of a budget in their request should weed out those who are not serious.

Currently each inquiry indicates if the Client has a budget, we will consider asking for the budget amount but that might be information the client is not willing to share.
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John-Payne commented
This would smoke out the "I want something for nothing clients". It would save client and expert time if the client can provides a rate per hour or indicate an acceptable range for rate per hour. I do not work for free.
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Laurence-Bacon commented
If they are not willing to reveal their budget, they should not have same qualms about revealing a rate per hour they are prepared to pay. If they will not reveal this, they should be blocked. Likewise if they state a rate they are prepared to pay, but fail to follow through for this reason (cost) alone, they should be blocked from future requests for a certain period to be determined.