Suppose there are two firms with one demand function. This same (common) demand function is: [from HW]

Q = 1,000 , 40P with MR = 25 , 0.05Q

However, each firm has its own cost function which is different. These two different cost functions are shown below respectively:

Firm 1: 4,000 + 5Q
Firm 2: 3,000 + 7Q

a. What price should each firm charge if it wants to maximize its profit (or minimize its loss)? 

b. If price war breaks out, most likely price will fall. Two most likely prices in that event are $13 and $12. Which company, firm 1 and firm 2, is more vulnerable to price war when P = $13 and why? 

c. Which company, firm 1 or firm 2 is more vulnerable to price war when P = $12 and why?

d. In view of your answers in (b) and (c), discuss advantage and disadvantage of cost structure between firm 1 and firm 2.

e. Long run average cost curve decreases when output elasticity is greater than one.What is the implication of your answer in (b) and (c) for the shape of long run average cost curve?