Businesses do this all the time: banks offer high introductory interest rates to new accounts, cell phone providers offer 2-for-1 phones to new customers, etc. As you said, it's a good way for a business to drum up new business, but it means less profit in the short run. When you signed on with Square, did you get any sort of introductory incentive? We didn't, but since we are so satisfied with Square, we don't resent them offering these incentives.
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