A firm is developing a new technology to produce roofing shingles more cheaply. The annual demand for such shingles 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 shingle production using either old or new technology. A patent lasts for T years, and (to simplify calculations) the interest rate is 0 (so that we don't have to discount future years). Unfortunately, the world will explode in 20 years (so you don't have to calculate infinite series, either).

(a) Assuming that the existing industry is perfectly competitive, calculate the profits of the innovator and the increase in welfare from the innovation (where welfare is the sum of profits and consumer surplus). Ensure that you account for all the 20 years remaining in the world.

(b) Given the assumptions of (a), calculate the maximum expenditure the innovator should be willing to spend to get the invention. Suppose that the invention costs more than this. Under what conditions should the government offer a subsidy?

(c) Now suppose that the existing technology is monopolized. Calculate the profits for the monopolist of getting this innovation (assuming that it will continue to be a monopolist), and the increase in welfare from the innovation.

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

(e) 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.

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

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