After an investigation carried out by the National Economic Prosecutor's Office (FNE), the cement cartel operating in the town of Pinto was dismantled.  With this, it is expected that there will be changes in the market and they hire you to calculate them.  The FNE tells him that the companies acted jointly maximizing their profits, like a monopoly, and that after the FNE's intervention they should act in a perfectly competitive manner.

In your investigation, you find that the Total Aggregate Cost function is given by CT (Q) = Q^2+100 and that the Aggregate Demand is given by Q^d = 30−0.5P.

Considering this information, answer the following questions:

(a) Find the quantity produced and the price charged by the cement cartel, prior to the intervention of the FNE.

(b) Calculate the market equilibrium after the intervention of the FNE.  What happens to the amount traded and the price charged in the market?

(c) Compare the equilibrium found before and after the intervention of the FNE.  Is social welfare increased?  Support your answer, calculate how much the total surplus changed and show both scenarios graphically.