Question: The demand for diamonds is given by

P = 980 – 2Q

where Q is the number of diamonds demanded if the price is P per diamond. The total cost (TC) of the De Beers Company (a monopolist) is given by

TC = 100 + 50Q + 0.5Q²

where Q is the number of diamonds produced and put on the market by the De Beers Company. Suppose that the government could force De Beers to behave as if it were a perfect competitor; that is, via regulation, force the firm to price diamonds at the marginal cost.

a. What is social welfare (producer surplus and consumer surplus) when De Beers acts as a single price monopolist?

b. What is the social welfare when De Beers acts as a perfect competitor?

c. How much does social welfare increase when De Beers moves from monopoly to competition?