Questions, instructions below

2. Model of sales There are 5 bookstores selling our IO textbook. They each have to pay $100 per copy from the publisher. There are 500 students who need a copy, which they value it at $200. Assume 150 students visits all bookstores every week (they are keen readers), so they know the prices charged by all bookstores. The remaining 350 students can only buy from his/ her nearest bookstore (they are non-readers). Assume that each bookstore has a share of 70 non-readers. Each bookstore can randomize over the price it charges for the textbook. Our objective is to identify a symmetric-equilibrium mixed strategy, denoted by distribution function F (p). You may assume without proof that this F has no mass point and no "gap", so it has a density function f with f (p) > 0 only over some interval E, )3]. (Remark: This question differs from the model we discussed in class in two main ways. First, the number of rms are exogenously xed here. Second, the marginal cost and average cost is constant. Nonetheless, much of the logics explained in class is still applicable here, so the resulting equilibrium will still share a number of similar features.) 4 (a) Given all other firms use mixed strategy F (p), what is an individual firm's expected profit of charging a price of $200? (b) Explain why p = 200 in the equilibrium mixed strategy. (c) Given all other firms use mixed strategy F (p), what is an individual firm's expected profit of charging a price pe [p, p]? (d) Using parts (a) to (c) above, what is the lowest price p in equilibrium? (e) Compute the symmetric-equilibrium mixed strategy F (p). Check that it indeed satisfies the assumptions made