Suppose there are 50 companies in a commercial building. Initially there is no automatic fire sprinkler system in the public area of the building. Each company has identical individual demand curve for the fire sprinklers, which is given by the equation: P = 10 - 0.5 Q, where P is the price of fire sprinkler and Q is the quantity of fire sprinkler. (a) Explain why the automatic fire sprinkler system can be considered a public good. (Hint: try to explain beyond repeating the definitions.) (b) Suppose each fire sprinkler costs $100. What is the optimal quantity of fire sprinklers to be installed? (Hint: explain how you obtain the social marginal benefit function of the fire sprinklers before you do the calculation.) (c) Explain why it is difficult for this commercial building to install the optimal quantity of fire sprinklers if there is no central party to coordinate the installation.