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