Assignment 2
Assignment 2
NAME: _______________________________________
STUDENT NUMBER:_______________________________________
SECTION NUMBER: _______________________________________
PROFESSOR: _______________________________________
Instructions:
1. Commerce 295 is a large, closely coordinated, multi-section course. It is necessary to be strict about rules regarding the assignment. Otherwise, marking and handling the assignments will be very difficult. These rules will help make the marking as fair and as timely as possible.
2. This assignment is due (in hardcopy form) by the beginning of your class on the date shown above. Assignments up to 24 hours late will receive a 25% penalty. Assignments more than 24 hours late will not be accepted. Late assignments can be given to Helen Ho in HA 266 or to Ines Bilec in the Undergraduate office or can be given to your instructor.
3. Extensions are possible only for genuine emergencies. Permission for the extension must be in advance (i.e. at least 24 hours before the assignment is due) and must be accompanied by appropriate documentation. See Ines Belic in the Undergraduate Office.
4. Show your working for all questions and make sure markers can understand the method you are using. Please be concise with your answers, and clearly identify the answer to the specific question you are being asked. Please carry 2 non-zero digits to the right of the decimal for answers that do not work out to whole numbers.
5. Please use these pages as a template.You may type in your answers before printing out the document or you may print out the document and print your answers neatly by hand.Your answers must be neat and easily readable. If not, marks will be deducted or the answer will be ignored entirely. If in doubt, type your answer. Please confine your answer to the allowed space.
6. Some of the questions have lines on which you are to write the answer. Do not exceed this space. Part of your task is to choose the right thing to say in a small space.
7. Students often like to work together in doing assignments. However, this is NOT a group assignment. It is primarily an individual effort. The basic rule about joint work is that it is acceptable to discuss questions with classmates but you must do the actual write-up of the assignment on your own. You must not copy someone else's answer. Copied or plagiarized answers will be subject to appropriate penalties.
8. You may use pen or pencil but if you use pencil we cannot review situations where you think there is a marking mistake (except addition errors).
9. There are 10 questions. Each question is worth 10 marks. All questions have two parts and each is worth 5 marks.
10. The assignment is challenging. Do not leave it to the last minute. When doing each question it is a good idea to find and read the relevant sections of the textbook first. Good Luck.
Marks:
Q1 ________
Q2 ________
Q3 ________
Q4 ________
Q5 ________
Q6 ________
Q7 ________
Q8 ________
Q9 ________
Q10 ________
TOTAL: ___________
Each question is worth 10 pts. Show your working. Unless otherwise stated each part of each question is worth 5 pts.
1. Oligopoly and Cartels
Recall the Cournot duopoly model of quantity competition between two firms (pp. 360-365). Suppose Firm 1 has a constant marginal cost equal to $10 and Firm 2 has a constant marginal cost equal to $20. Fixed costs are zero for both firms. Market demand is Q = 300 – 4P. Calculate each firm’s best response function as determine the Nash equilibrium quantities. Show the best response functions and the Nash equilibrium quantities on your graph.
Suppose Firm 2 proposes to Firm 1 that they should form a cartel. According to their agreement the entire quantity of the product will be produced by the firm with the lower marginal cost (Firm 1) and they will split the profits evenly. Would Firm 1 benefit from such an agreement? Explain. (Hint: Calculate the profits for Firm 1 from Cournot competition and from the cartel.)
2. Monopolistic Competition and Bertrand Oligopoly
Consider a market with many identical firms selling identical products and free entry (Monopolistic Competition – pp. 378-380). Illustrate the long-run equilibrium outcome for a representative firm including cost curves. What can you say about each firm’s profit? Is this outcome efficient (surplus maximizing)? Explain.
Consider a market with a small number of identical firms selling identical products without free entry where firms compete by setting prices (Bertrand Oligopoly – pp. 374-377). There are 200 customers, each of whom will purchase one unit of output at the lowest available price. (Thus demand is perfectly inelastic at Q = 200.) Also assume that each firm has a constant marginal cost of 8 and no fixed costs. What is the Nash equilibrium price (i.e. the Bertrand equilibrium price) charged by each firm? What can say you about firms’ profits? What important aspects of the Bertrand equilibrium would change if products were differentiated?
3. Static Games.Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below.
Are there any Nash equilibria in pure strategies? If so, what are they? (State the strategies chosen and the payoffs.) Would the Pareto Criterion help firms coordinate? Explain. (See pp. 391-402.)
If the managers of both firms are conservative and each follows a maximin strategy, what will be the outcome? If Firm 1 uses a maximin strategy and Firm 2 knows this, what will Firm 2 do to maximize profit? Justify your reasoning. (See pp. 408-411)
4. Dynamic Games
a) Repeated Games: Question 2.3 on page 384 of your textbook assumes that two quantity-setting duopolists, each with a marginal cost of $60 per unit, face a market demand p = 150 – Q where Q = q_{1} + q_{2}. The table below shows the profits earned by each firm under various output combinations (e.g., q_{1} = 22.5 and q_{2} = 30). Suppose the firms play the quantity setting game repeatedly and for an infinite number of periods. Provide an example of a trigger strategy that results in an equilibrium where for each period each firm earns $1012.50 in profits rather than the $900, which is the amount earned in the Nash-Cournot equilibrium of a one=shot static game. Explain, using numbers, why neither firm would want to use a different strategy. (Hint: See Ch. 13.1: pp. 430-435).
b) Stackelberg Oligopoly: Convert the game matrix in part (a) into an extensive form diagram similar to that shown in Figure 13.1 (page 437) of the text. When doing this assume that Firm1 is the leader and as such is able to set its quantity before Firm 2. Assume this sequential game is played only once. Solve this Stackelberg leader-follower game using backward induction, and identify the sub-game perfect Nash equilibrium. What is the most that Firm1 would be willing to pay to be a Stackelberg leader rather than earning $900 in the one-shot (static) Nash-Cournot game?
5. Credibility and Commitment in Sequential Games
a) Airbus is designing a new jet and will contract with Rolls-Royce to supply the engines. Airbus must choose between a long range jet and a large capacity jet. Either type of jet can be fitted with a type A or type B Rolls-Royce engine. First Airbus decides on what type of jet to order. Rolls-Royce is informed of this decision, then decides on which engine type to provide. The extensive form game diagram is shown below. What is the subgame perfect Nash equilibrium in this game? Now suppose that the two firms engage in pre-play communication and that Rolls-Royce “threatens” to produce one of the types “no matter what”. Which engine type will it threaten to produce if it is trying maximize its profit? Is the threat credible? Explain briefly.
b) Now suppose that Rolls-Royce produces type A engines in factory A and type B engines in factory B. Before the game is played Rolls-Royce can “sabotage” one of its factories, raising the cost and reducing the profit from that factory by an amount D. Airbus will find out what the new payoffs for Rolls-Royce are before it chooses which type of jet to order. Will Rolls-Royce have an incentive to sabotage one its factories? Which one? How large would D need to be for Rolls-Royce to benefit from this self-sabotage? Explain briefly.
6. Entry Deterrence:Two firms produce luxury auto seat covers: Northwest Seat Covers (NW) and J&J Seat Cover Company (J&J). The market demand for these seat covers is represented by the inverse demand function: P = 100 - Q, where Q = q_{1} +q_{2}. Each firm has a cost function given by C(q) = 10q.
a) The Cournot solution implies that each firm produces an output of 30. If the two firms formed a cartel, the total cartel output would be 45. Fill in each cell with the profits for each firm, carefully showing the steps in your calculation. Suppose the two firms must independently and simultaneously decide which of these two outputs to choose. What is the Nash equilibrium in the one shot game? Is this game a prisoners’ dilemma?
b) Now suppose that NW is initially the only firm in this market. However, it is concerned that J&J may enter the market. If J&J enters the market it must pay an up-front fixed investment cost of 300 in addition to its production costs. NW can prevent entry by obtaining a patent on these seat covers. Obtaining the patent would cost 1000. Draw the extensive form of the entry deterrence game and determine the subgame perfect Nash equilibrium. Briefly explain your reasoning. What term would you use to describe this outcome? (See pp. 441-442).
7. Uncertainty
An investor is considering 4 different investment strategies. The returns of the investor under two different states of the nature (good luck and bad luck) and the probabilities associated with these two states are shown in the following table:
Strategy | Return (R) with Bad Luck | Prob. of Bad Luck | Return (R) with Good Luck | Prob. of Good Luck |
A | 4 | 0.8 | 9 | 0.2 |
B | 5 | 0.3 | 8 | 0.7 |
C | 2 | 0.4 | 10 | 0.6 |
D | 4 | 0.7 | 8 | 0.3 |
a) Use Excel to calculate the expected return and the standard deviation of the return for each of the four strategies. Paste your spreadsheet into your answer. What can you say about which strategies would be chosen by a risk averse investor, a risk neutral investor, and a risk preferring investor?
A risk averse investor would __________________________________________________
because ___________________________________________________________________
A risk neutral investor would __________________________________________________
because ___________________________________________________________________
A risk preferring investor would ________________________________________________
because ___________________________________________________________________
b) Next, assume that the investor’s utility function is given by U(R) = R^{0.5}, where R is the return from the investment. Draw a diagram illustrating the utility function. For investment option A find the expected value of the return, the certainty equivalent, and the risk premium. Show all three in the diagram. Show your calculations and explain briefly what you are doing. (Hint: See pp. 472 – 474.)
8. Behavioral Economics
a) Consider a game with 10 players. Each person submits an integer between 0 and 100. The winner of the game is the person who submits a number closest to 60% of the average number submitted. The winner gets a prize of $1000 and no one else gets anything. If two or more people tie for the win they share the prize equally. Assuming that all players are fully rational and that rationality is common knowledge, what is the Nash equilibrium? If you were playing this game with randomly chosen first year UBC students, would you bid the Nash equilibrium value?
The Nash equilibrium is __________________________________________________________.
We know this is a Nash equilibrium because _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
If I were trying to win this game I would submit the value _________________________.
I think this offers the best chance of success because _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
b) The prospect theory utility function shown in Figure 14.6 can be used to explain framing effects. Draw the relevant diagram below, state what framing effects are, provide an example from the textbook and explain how the diagram applies to this case. Also indicate whether framing effects can explain the ultimatum game (pp. 454-55.)
The term “framing effect” means ________________________________________________________
___________________________________________________________________________________.
An example of the framing effect is ________________________________________________________.
The diagram suggests that in this case the framing effect arises because ____________________________
_____________________________________________________________________________________
____________________________________________________________________________________.
Framing (can or cannot) explain the ultimatum game because __________________________
___________________________________________________________________________.
9. Adverse Selection.Consider the used car example described in Q&A 15.1, except the numbers are different. Buyers value lemons at $5000 and good used cars at $10,000. The reservation price of lemon owners is $4000 and the reservation price of owners of good used cars is $7,500. Owners know the quality of the cars but buyers do not. (Show your working.)
a) Suppose that 40% of the used cars are good used cars and 60% are lemons. Describe the equilibrium.
b) Now suppose that 70% of the cars are good used cars and 30% are lemons. Describe the equilibrium now. What is the lowest percentage of good used cars that will allow for all cars to be sold in equilibrium?
10. Research Question.
(a) Explain how medical insurance diversifies the financial risk of unforeseen medical expenses?
Do medical insurance providers such as Sun Life face a similar problem(s) as does a insurance
buyer? Explain (in less than 200 words).
(b) (Refer lecture notes to answer this question). What could have Harvard done to prevent the adverse selection problem it faced in its Medical Insurance plan in 1990s? How does universal care of Canada take care of this Adverse Selection problem?