Problem 6 [Ramsey prices] Imagine that the production and distribution of electricity in a country is monopolized by one firm. This monopoly is able to perfectly distinguish the demand of electricity of households and industrial consumers, which are Q1 = 200 - 5 P1 and Q2 = 600 - 20 P2. In these expressions, P1 and P2 are the price for resident and industrial consumers, respectively. On the other hand, we assume that the cost to produce the electricity does not depend on the type of consumer. Specifically, the firm's total costs are TC(Q) = 60 + 5 Q. Use Mathematica to calculate the following results: A. Calculate the price of the electricity if the regulator sets a uniform price that maximizes the social welfare in the two markets? B. Calculate the Ramsey's prices. Offer an economic intuition for the Ramsey term. C. Calculate social welfare in the two previous scenarios and compare the I results