From today's front-page NYT article on the 9-9-9 plan:
"From that exchange emerged the plan that Mr. Cain calls 9-9-9: a flat 9 percent individual income tax rate, a 9 percent corporate tax rate and a 9 percent national sales tax."
Again, the "corporate tax" here is in fact a sales tax, no less than the sales tax in the plan is a sales tax. These things matter.
By the way, suppose that we didn't have an income tax - say, because Congress had replaced it with a progressive consumption tax, such as either the David Bradford X-tax or a "consumed income tax" on individuals. BTW, as I've discussed in various places, such as here, I would strongly prefer this to the existing income tax, at least if we could make optimistic assumptions about how Congress would actually implement it. (This is a problem that these plans admittedly would share with 9-9-9.)
If that happened, then we wouldn't need a "corporate tax." The main purpose that the corporate income tax serves today is to backstop the income tax on individuals, which would become a joke if people could avoid it by earning their income through corporate entities. Thus, suppose I could hire myself out to "Shaviro, Incorporated," a newly formed corporation to be entirely owned by myself and close family members, and arranged for it to contract with NYU for my teaching services. It would then pay me (to meet current consumption expenses) only a fraction of my actual salary. Unless we either taxed this company directly or made the income currently taxable at the worker or owner level, we would have shot a huge and pointless whole in the income tax.
Many people nonetheless seem to want a "corporate tax" as an end in itself, not just to backstop the income tax if we have one. This appears to reflect the "pathetic fallacy" of personifying corporate entities. As it happens, concern about this way of thinking was an important reason why David Bradford came to prefer the X-tax to a purely individual-level consumed income tax - he thought it would be more salable politically because corporations would literally be taxpayers (i.e., they would be remitting VAT-like payments to the government).
9-9-9 fails to use its "corporate tax" as a proper backstop to the individual tax, given that nonpayment of owner-employees' salary reduces tax liability at the full 9% individual rate. And it gestures towards the public sentiment for a "corporate tax" by doing something that is entirely misleading - although, again, I see no reason to doubt that the proponents are themselves misled. It would be nice if the New York Times could do more to help public understanding on this front.