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Exam 2 ? Past Questions Managerial Economics Professor: Arce M. Points of Interest ? I am releasing these questions as a courtesy to you. I do not provide answers to these questions nor do I entertain...

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Exam 2 ? Past Questions Managerial Economics Professor: Arce M. Points of Interest ? I am releasing these questions as a courtesy to you. I do not provide answers to these questions nor do I entertain inquiries about them. I am fully confident that the questions can be capably vetted within your group because they were answered by past students during the time constraints of an exam. ? A typical in-class exam consists of 3-6 questions and lasts 1hr 15minutes. ? Some past exam questions are now part of your problem sets. These questions are not repeated here. ? Neither these questions nor the problem sets exhaustively represent all possible material for exam 1. You are responsible for all the material covered in the notes. ? It is unlikely that I will be asking any of these questions on your exam. Example of Exam Instructions: ? All answers (including short answer questions) must include artwork and/or algebra unless explicitly specified. ? Correct answers without accompanying (and correct) economic analysis will receive zero credit. ? To receive partial credit, you must show your work. ? Your answers are required to be concise and self-explanatory. Keep your creative writing skills on a leash. ? It is disingenuous to use one question to answer another unless they are explicitly related. Disingenuous answers will be penalized. ? Do not make irrelevant statements within your answers – you will be penalized if they are incorrect. 2 1. Consider a private-value auction where it is assumed that bidders have valuations that are uniformly distributed between 1 and 10. There are 3 bidders and your valuation is 7. a. What should you bid in a Dutch (oral descending price) auction for this item? b. What should bid in a 2nd price sealed-bid auction for this item? c. Explain how your answers to (a) and (b) CHANGE under a common value auction. Refer to LEGAL behavior only. 2. For the game to the right. a. Find the Nash equilibria for the game below. b. Identify the outcomes that are Pareto efficient. c. Is this game an example of the Prisoner’s Dilemma? Why or why not? 3. A discount clothing chain lists the prices of women’s clothing by date, where the price falls every two weeks (provided the item has not been previously sold). a. What degree of price discrimination is this? Explain. b. What type of auction is this? Explain. Note: no diagrams necessary here. 4. Three bidders: Dennis, Betsy, and Michael are bidding for two items: X and Y. The bidders’ (nonadditive) private valuations for the items are given to the right. The seller decides to hold three simultaneous sealed-bid auctions: X and Y are sold separately in second-price auctions and the bundle X&Y is sold in a first-price auction. The items are sold as a bundle if the high bid for X&Y meets or exceeds the sum of the separate prices for X and Y. Dennis’ bid is given by bD, Betsy’s by bB and Michael’s by bM. Suppose that the bidding for X is bD = 6; bB = 7 and bM = 1. The bidding for Y is bD = 4; bB = 1 and bM = 5; and the bidding for bundle X&Y is bD = 8; bB = 7 and bM = 6. Your answers to the questions below do not require the construction of a game box. Do not make any assumptions about the distribution of valuations. a. Given these bids who wins the item(s) and at what price(s)? b. Is this collection of bids a Nash equilibrium? Why or why not? C D A 2, 2 5, 1 B 0, 0 5, 1 ?Bidder Private Valuations X Y X&Y Dennis XXXXXXXXXXBetsy 7 1 8 Michael XXXXXXXXXXThe game to the right is an example of Chicken where T > R > P > S. Consider the following tit-for-tat strategy TFT = start with ; play whatever your opponent did in the previous period ? A ? ? a. Consider a repeated version of this game, where the ending period is finite, but unknown. Under what condition is (TFT, TFT) a Nash equilibrium? b. Is (TFT, TFT) a subgame perfect Nash equilibrium (SPNE)? Note: no illustrations are necessary to justify your answer but you do need to consider potentialities where TFT is paired with some strategy other than TFT. 6. Consider the data to the right. The firms in this market sell an undifferentiated product; hence, the firm charging the lower price will be the monopolist in the market. If they charge the same price, then they will split the monopoly profits. If there are two firms, with strategies as prices, and payoffs equal to profits, illustrate the corresponding game box and find the Nash equilibrium. ?Betsy\Susan? A I Acquiesce (A) R, R P, T Insist (I) T, P S, S Price Monopoly Profits XXXXXXXXXX504 7. Consider the game to the right. Player 1 can choose either meat (M) or fish (F). Player 2 chooses the wine (red or white). a. Write out the strategic form game box associated with this game. b. Find the Nash equilibrium for your answer in (a). c. Find the SPNE of the extensive form of this game XXXXXXXXXXM F R W r w XXXXXXXXXX
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Answered Same Day Dec 20, 2021

Solution

David answered on Dec 20 2021
125 Votes
Ans 1
a) the 2x2 infinitely repeated game with strategies defect and grim strategy is shown below
D GT
D (1+ Ï„)P,(1+ Ï„)P T+ Ï„P, S+ Ï„P
GT S+ Ï„P,T+ Ï„P (1+ Ï„)R, (1+ Ï„)R
Profit of player a when it defects, given that player other defects is P (in period 0) + P(in all Ï„
periods) = (1+ Ï„)P
Profit of a player when it defects given the other player plays grim strategy is T(in period 0) +
P(in all Ï„ periods)=T+ Ï„P
Profit of a player when it plays grim strategy given that the other player has defected is S(in
period zero) + P(in all Ï„ periods) = S+ Ï„P
Profit of a player when both the players are playing grim strategy is R(in all 1+ Ï„ periods) = (1+
Ï„)R
) Tit for tat strategy here is playing C in period 0 and in period T plays what the opponent
played.
Profit when playing TFT(both players) = R(in period 0)+R(in Ï„ periods) = R(1+ Ï„)
Profit when the player is playing TFT and opponent defects = S(in period 0) + P(in Ï„
periods)=S+ Ï„P
Profit when the player defects and opponent plays TFT=T(in period 0) + P(in all Ï„
periods) = T+ Ï„P
Profit of the player when both player and opponent defects = P(1+ Ï„)
D TFT
D (1+ Ï„)P,(1+ Ï„)P T+ Ï„P, S+ Ï„P
TFT S+ Ï„P,T+ Ï„P (1+ Ï„)R, (1+ Ï„)R
TFT is a nash equili
ium if
Profit from TFT,TFT> profit from D,TFT(or TFT,D) for the player who deviates
(1+ Ï„)R> T+ Ï„P
Ï„(R-P)>T-R
Ï„>(T-R)/(R-P)
c) T is basically the temptation to defect. R is reward for cooperation. P is the punishment
for defecting. Then the inequality can be interpreted as the...
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