1. Guards patrolling the mall provide a service without rivalry: all the stores in the mall aresimultaneously protected. The demand for the electronics store, which suffer a big loss ifthieves strike, is Q1 = 9 – 0.5P, where Q1 is demand of guards per hour, and P is the priceof guard service. The ice-cream parlor, which loses less from a theft, demands fewerguards 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 manyguards each store will hire? Show the results mathematically and graphically.
(b) What is the marginal benefit to society of guard service, given that a guard patrollingthe mall protects both stores at once? Show and discuss your results with a graph.
(c) Is the competitive market equilibrium optimal to the society? If yes, explain why. Ifno, find the optimal level of guard service and explain why.
2. Two companies require identical skills and training from their workers. Both employ10,000 people. On average, Safety First has one worker fatality per year, while Safety Secondhas two worker fatalities per year. Jobs at Safety First pay $50,000/year, while jobs at SafetySecond pay $50,500/year.
(a) Why do these jobs with identical requirements pay different salaries, based on theinformation presented here?
(b) What is the risk for a worker of a fatal accident at each company? What is the paypremium associated with the higher risk?
(c) The value of a statistical life is the difference in wage divided by the difference in risk.What is the value of a statistical life for workers with these skills and training?
(d) Do you expect this value of a statistical life to be appropriate for the population as awhole? Why or why not?