Suppose a monopolist faces demand Q=100-P. The marginal cost of production is 20.

1) Calculate the price P the monopolist will set, the corresponding Q, and the monopolist's profits.

2) Suppose there is a technology the monopolist can adopt, for a fixed cost C, that reduces the marginal cost to 10. For what values of C will the monopolist adopt the technology? Calculate P, Q, and the monopolist's profits when the technology is adopted.

3) Could the government ever increase total surplus by providing a subsidy to the monopolist to adopt the technology?