The total tax revenue of the US is 2.6 trillion. The total GDP is around 14.2 trillion. In other words, tax revenue is a small percentage of the country's total GDP. How can tax dollars be used to replace innovation portion of the 14.2 trillion? Just take the pharmaceutical industry alone. If we get rid of patents, large companies have no incentive to invest tons of money developing a drug that can be immediately replaced by generics. So your proposal is to create incentive through tax dollars.
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A study by the consulting firm Bain & Company reported that the cost for discovering, developing and launching (which factored in marketing and other business expenses) a new drug (along with the prospective drugs that fail) rose over a five year period to nearly $1.7 billion in 2003.
That's 1.7 billion for a single drug! Tax dollars simply cannot cover the massive cost of innovation.