You may be able to close the sale but at what cost? Not only have you allowed someone to pay you less than you’re worth but now you’ve also busied yourself with an underpaying client. The time you spend working for underpaying clients reduces the time you have available to nurture relationships with other prospective clients who recognize the value of your services and will gladly pay for it.
Give your real prices. Give each prospective client the opportunity to decide for themselves. You’ll notice that those who really want to work with you will pay you.