Public Goods: 13. There are two major department stores at the mall: Sears and JC Penny. They both benefit from the mall security patrol. Assume that the quantity of the mall patrol is Q units and that we can write down the marginal benefits and the total benefits provided by mall security for each store as: Sears: MPB sears_ 5 - 0.5Q Total Benefit sears = 5Q - 0.25Q2 JC penny: MPB_JC = 2 - 0.25Q Total Benefit JC = 2Q - 0.125Q2 The marginal cost of hiring one additional unit of mall patrol is always $4. That is MC = 4. Answer the following questions: a. Assume Sears is the first department store in the mall. How many units of mall patrol will Sears choose to hire? What is the net benefit (its total benefit minus its total cost) to Sears of hiring this amount of mall security? b. Now JC Penny opens a store in the mall. Notice that the mall security patrols that Sears hired also benefit JC Penny. That is both stores can consume this mall security: mall security is not rival and also is not excludable (JC Penny can benefit from the mall security even when it does not pay for any mall security). Now, that JC Penny is in business at the mall, does JC Penny want to hire any more units of mall security patrols? Explain your answer. What is JC Penny's net benefit after its decision? c. Now the leasing manager for the mall is in charge of determining how many mall security units should be hired. The manager will make her decision based upon the total marginal benefits of hiring mall security units. How many units of mall security will she hire? Explain your answer. d. Suppose the manager charges Sears $3 per unit of mall security patrols and charges JC Penny $1 dollar per unit of mall security patrols. Will the two stores both accept this price? e. What is the net benefit to the manager of hiring the amount of mall security patrols on the basis of the total marginal benefits of these patrols? What's the net benefit for both of these two department stores? How does your result compare with parts (a) and (b)