The government is considering subsidizing the marginal costs of the monopolist described in the question above. What level of subsidy should

the government choose if it wants the monopolist to produce the socially optimal amount of output?

The government should choose a subsidy level that is equal to the difference between the marginal cost of production and the marginal benefit of production. This will ensure that the monopolist produces the socially optimal amount of output, as the marginal benefit of production will be equal to the marginal cost of production.