Suppose there are 30 companies in a commercial building. Initially there is no fire sprinkler system in the public area of the building. The companies have 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.

Suppose each fire sprinkler costs $40. What is the optimal quantity of fire sprinklers to be installed? (Hint: calculate and explain the social marginal benefit function of the fire sprinklers.)