Barriers of entry

Please see the attached file.

-In everyday discussions, people tend to talk about monopoly firms "setting high prices," but in this chapter we have talked about choosing a profit-maximizing level of output. Are these two approaches saying the same thing? What kind of rule would a monopoly follow if it wished to choose a profit-maximizing price? Why not charge the highest price possible?
-Why are barriers to entry crucial to the success of a monopoly firm? Explain why all monopoly profits will show up as returns to the factor or factors that provide the barrier to entry.
-A single firm monopolizes the entire market for Nixon masks and can produce at constant average and marginal costs of AC = MC = 10 Originally, the firm faces a market demand curve given by Q = 60 - P and a marginal revenue function given by MR = 60 - 2Q
a- Calculate the profit-maximizing price-quantity combination for the firm. What are the firm's profits?
b- Now assume that the market demand curve becomes steeper and is given by Q = 45 - .5P
with the marginal revenue function given by MR = 90 - 4Q What is the firm's profit-maximizing price-quantity combination now? What are the firm's profits?

c- Instead of the assumptions in part b, assume that the market demand curve becomes flatter and is given by Q = 100 - 2P with the marginal revenue function given by MR = 50 - Q.
What is the firm's profit-maximizing price-quantity combination now? What are the firm's profits?

d- Graph the three different situations of part a, part b, and part c. Using your results, explain why there is no meaningful "supply curve" for this firm's mask monopoly.

-Commercial fishing is an industry that is often given as an example of quantity competition, as in the Cournot model. Can you think of others? Can you give examples of industries in which firms compete in prices? In which of these cases are capacity constraints important, so that the two-stage model of capacity investment and price competition might apply?
-The Bertrand Paradox relies on the assumption that the demand for any one firm's product is very responsive to pricing by the other firm. Why is this assumption crucial for the competitive results in the Bertrand model? How would those results be affected if consumers were reluctant to shift purchases firm to another because of consumer switching costs? What other assumptions are crucial for the Bertrand Paradox?
-The pricing game between two firms, which can each set either a low or a high price, is given by the following normal form.
B
Low Price High Price
A Low Price 2,2 4,1
High Price 1,4 3,3
a-Find the Nash equilibrium or equilibria of the game.
b-How would you label the actions to make this a quantity game like Cournot?