Ayn Rand did not think the state would wither away to nothing, as Marx suggested, but saw that some government would exist, and need to be paid for.
She suggested commercial transactions as a major possibility for revenue. Credit transactions (and thus financial activity) would be prominent sources. Excerpts from Chapter 15 of The Virtue of Selfishness:
There are many possible methods of voluntary government financing. A government lottery, which has been used in some European countries, is one such method. There are others.
As an illustration (and only as an illustration), consider the following possibility. One of the most vitally needed services, which only a government can render, is the protection of contractual agreements among citizens. Suppose that the government were to protect – i.e., to recognize as legally valid and enforceable – only those contracts which had been insured by the payment, to the government, of a premium in the amount of a legally fixed percentage of the sums involved in the contractual transaction. Such an insurance would not be compulsory; there would be no legal penalty imposed on those who did not choose to take it – they would be free to make verbal agreements or to sign uninsured contracts, if they so wished. The only consequence would be that such agreements or contracts would not be legally enforceable; if they were broken, the injured party would not be able to seek redress in a court of law.
All credit transactions are contractual agreements. A credit transaction is any exchange which involves a passage of time between the payment and the receipt of goods or services. This includes the vast majority of economic transactions in a complex industrial society. When one considers the magnitude of the wealth involved in credit transactions, one can see that the percentage required to pay for such governmental insurance would be infinitesimal – much smaller than that paid for other types of insurance – yet it would be sufficient to finance all the other functions of a proper government. (If necessary, that percentage could be legally increased in time of war; or other, but similar, methods of raising money could be established for clearly defined wartime needs.)
This particular “plan” is mentioned here only as an illustration of a possible method of approach to the problem – not as a definitive answer nor as a program to advocate at present. The legal and technical difficulties involved are enormous: they include such questions as . . . the need of objective standards (or safeguards) for establishing the amount of the premiums, which cannot be left to the arbitrary discretion of the government, etc. Any program of voluntary government financing is the last, not the first, step on the road to a free society – the last, not the first, reform to advocate.
Source: http://sqapo.com/complete_text__rand__the_virtue_of_selfishness.htm, which says this:
“This SquaPo version is adapted from a version widely reproduced in free media elsewhere. Ayn Rand is theoretically still in copyright, though she herself denounced the idea of collecting royalty payments. All enquiries to her estate, and to her ‘Objectivist Newsletter’ have yeided no information as to the copyright status of ‘The Virtue of Selfishness‘, so Squashed Philosophers has taken it that the text is now in the Public Domain, as its author would have required.”
UPDATE, 20 November 2017: Ms. Rand’s contract premiums as a government financing mechanism would need an enormous amount of work to be thought through. Has anyone done such work?