The demand for diamonds is given by PZ = 680 - 2QZ where QZ is the number of diamonds demanded if the price is PZ per diamond. The total cost (TCZ) of the De Beers Company (a monopolist) is given by TCZ = 100 + 50QZ + 0.5Q2Z where QZ is the number of diamonds produced and put on the market by the De Beers Company. Suppose 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 marginal cost.
a. What is social welfare when De Beers acts as a single- price monopolist? (Note: Social welfare is the sum of consumer and producer welfare. It might be easier to graph the problem so that you can visualize the surpluses areas)
b. What is 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?