The only way to eliminate black-market marijuana is to remove the profit... the only incentive.  To do this the price of the legal stuff has to be low enough to accomplish that.
Fact is... legal marijuana will likely be highly taxed and priced high, allowing the black market to remain in business, and perhaps even thrive.
The same thing is currently happening with cigarettes... a thriving black market that outsells legal product.
The ability to "grow your own" might have an impact on black-market distribution however.