1. Guards patrolling the mall provide a service without rivalry: all the stores in the mall are simultaneously protected. The demand for the electronics store, which suffer a big loss if thieves strike, is Q1 = 9 - 0.5P, where Q1 is demand of guards per hour, and P is the price of guard service. The ice-cream parlor, which loses less from a theft, demands fewer guards at any given price. Its demand is Q2 = 7 - P. A competitive market supplies as many guards as the stores want at $10.
(a) If stores act independently, what is the competitive market equilibrium? How many guards each store will hire? Show the results mathematically.
(b) What is the marginal benefit to society of guard service, given that a guard patrolling the mall protects both stores at once?
(c) Is the competitive market equilibrium optimal to the society? If yes, explain why. If no, find the optimal level of guard service and explain why.