A firm is developing a new technology to produce walls more cheaply. The annual demand is Q=100-p. The existing industry produces at marginal cost of 50. The new technology would reduce marginal cost to 40. There are no fixed costs in production using either old or new technology. A patent lasts for T years, and the interest rate is 0.

Unfortunately, the world will end in 20 years (so you don't have to calculate infinite series, either).

(i)Now suppose that the existing technology is monopolized and the inventor is another firm. Calculate the profits for the potential entrant of getting this innovation, and the increase in welfare from the innovation. Assume that there will be Cournot competition following the invention.

(ii)Given the assumptions of (i), calculate the maximum expenditure the innovator should be willing to spend to get the invention.

(iii)Given the assumptions of (i), and assuming that no subsidy is possible, are there conditions where the government should extend the patent? If so, describe.