Starting with Moore's Law the technological outlook points to a post-silicon era after 2020. This is a world of artificial intelligence and quantum computing. If the cost of a car produced today followed Moore's law then cars would cost ten cents! Following this logic, computer chips of the future will cost pennies. I feel compelled to point out the flaw in this logic. I am not an economist, however, I would assume that cost reduction is only one possible trajectory in the technology advancement timeline and story of the chip. By 2020 and beyond the biological integration with technology could be prevalent throughout society so the linear relationship between computing power and cost reduction that Dr Kaku is proposing is one of many possible outcomes even if it doesn't violate Moore's law.
Touted by the Chicago Tribune as "An erudite, compelling, insider's look into the most mind-bending potential of science research." The journey is entertaining, to say the least. If the above video tweaks your interest then I would recommend reading, "Visions - How Science Will Revolutionize the 21st Century."