A monopoly with constant marginal costs m = $10 faces the inverse demand curve p = 50 - Q. The interest rate is r = 10%. An inventor discovers a way to reduce marginal costs to m = $6 (with no additional fixed costs) and receives a permanent patent for that invention. Up to how much is the monopoly prepared to pay for a permanent license to use the invention (i) if it is certain that the inventor will not offer the invention to any other firm? (ii) if it knows that the inventor may offer the invention to a potential entrant instead? How much is the potential entrant prepared to pay in the latter case, assuming it earns zero profits if it does not obtain the license?