Five questions. need detail calculation and explain. I will uploaded the chapter lecture and sample questions solution to show the answer step.PLEASE FOLLOW THE SAMPLE QUESTIONS TO MAKE THE SOLUTIONS.
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Detail questions list will uploaded. If it is the calculation and diagram hard to type in, hand writing photocopy will be ok too.
1. (12 marks) Consider the following game between Toshiba, a manufacturer of HD-DVD, and
Columbia Pictures, a movie studio. Each firm must decide whether to use the HD-DVD or Blu-ray
Toshiba to make DVD players, Columbia to release its movies for rental of purchase.
Columbia Pictures
HD-DVD Blu-ray
Toshiba HD-DVD 20, 10 0, 0
Blu-ray 0, 0 10, 20
a) Restrict attention to pure strategies. Does either firm have a dominant strategy? What is (are) the
Nash equilibrium (equilibria) of this game?
b) Is there a mixed strategy Nash equilibrium in this game? If so, what is it?
c) Plot the best-response functions of the two firms in a strategic space and show ALL Nash
equilibria.
Restrict attention again to pure strategies, but now focus on a sequential-move game in which
Toshiba chooses its strategy first.
d) Draw a tree diagram of this sequential-move game and show a subgame perfect Nash equilibrium
(SPNE).
e) A SPNE eliminates Nash equilibria that involve non-credible threats. State clearly the noncredible
threat and explain why it is not credible.
2. (10 marks) Consider a Bertrand model with two firms facing the market demand Qp 100 p .
Both firms have a constant marginal cost of 20. It is assumed that each firm has a capacity large
enough to meet the market demand all by itself.
a) Derive the best-response functions of the firms.
b) Plot the best-response functions and show the Bertrand Nash equilibrium.
c) What are the Bertrand Nash equilibrium and equilibrium profits of the firms?
Suppose now that firm 2 discovered a new technology that lowers its marginal cost to 10.
d) How does this affect the best-response function for firm 2? Plot the best-response functions
and show the new Bertrand Nash equilibrium.
e) Does the Bertrand Paradox hold in this case?
2
3. (14 marks) Suppose that there are two firms in an industry. Both firms have the same production
technology, which can be summarized by a cost function, ci qi 40qi , (i 1, 2) with the marginal
cost of 40. The market demand is given by pQ 400 2Q , whereQ q1 q2 . Each firm has a
capacity large enough to meet the demand all by itself.
Suppose that the firms choose quantities simultaneously (i.e., Cournot competition).
a) Find the Cournot Nash equilibrium. What are the profits of the firms?
b) Graph the best-response functions for the firms and show the Cournot Nash equilibrium.
c) Suppose that the firms collude. Find their joint profit-maximizing price, output and profit.
What is the profit of each firm?
d) By using the graph you draw in b), show that the firms have an incentive to increase output.
Suppose now that the firms choose quantities sequentially. Specifically, firm 1 (a Stackelberg leader)
decides how much to produce in period 1. In period 2, after observing firm 1s quantity choice, firm 2
(a Stackelberg follower) decides how much to produce.
e) Find the Stackelberg Nash equilibrium. What are the profits of the firms?
4. (5 marks) Consider the firms described in Question 1. As before, the firms compete over prices, but
each firm has a production capacity of 25 units.
a) If Firm 1 believes that Firm 2 will use up all of its capacity, what price does it charge? In a
diagram, show Firm 1s residual demand and the profit-maximizing price.
b) What do you expect the Nash equilibrium to be for this capacity constraint Bertrand
competition? Explain your answer.
5. (10 marks) Augie and Corinne are mineral spring duopolists facing a market demand given by the
equation pQ 24 Q , whereQ qA qC . Fixed costs are zero for both, but Augie has a constant
marginal cost of $6 per unit, whereas Corinnes marginal cost is zero.
a) Assuming that both behave as Cournot duopolists, derive the best-response functions of the
two firms. What are the equilibrium levels of output, the market price, the profit of each firm
and the value of consumer surplus?
b) If Corinne could effectively bribe Augie to shut down his production completely, regardless
of the market price, so that she supplied the entire market, what is the maximum amount she
would be willing to pay? What is the minimum amount Augie would accept?
c) Should such bribery be allowed? Explain your answer.