Growth, Capital, Accumulation, and the Economics of Ideas: End of Chapter Problem
Are we running out of ideas? Economist Paul Romer thinks not. As an example, Romer states that if we keep trying out different
molecules to search for interesting compounds like new drugs, new plastics, etc., the universe may end from heat death before
we finish analyzing them all. Do the math and prove it to yourself! Suppose we take 100 different atoms out of the 118 (and
increasing!) elements in the Periodic Table and limit ourselves to only combinations made up of 6 atoms. This would result in
$100^6$ different molecules.
a. If it takes a machine 1 minute to analyze each new 6-atom
molecule, how many years will it take for this one machine to
test out all $100^6$ molecules?
b. How many machines would it take to test out all of these
molecules within 100 years?
