1) Consider the Akerlof's model of lemons. Assume the sellers have all the bargaining power: they can charge the buyers their expected value of buying the car. Suppose there are 3 possible car qualities: high, medium and low. Suppose also that the proportion of each type of car is 1/3. The values of buyers and sellers for different car qualities are tabulated below. Seller's value Buyer's value Low quality car Medium quality car High quality car 8 10 13 15 18 (a) Is there an equilibrium in which all types of qualities are traded? (b) Is there an equilibrium in which only low and medium qualities are traded? (c) Is there an equilibrium in which only low qualities are traded?

1) Consider the Akerlof's model of lemons. Assume the sellers have all the bargaining power: they can charge the buyers their expected value of buying the car. Suppose there are 3 possible car qualities: high, medium and low. Suppose also that the proportion of each type of car is 1/3. The values of buyers and sellers for different car qualities are tabulated below. Seller's value Buyer's value Low quality car Medium quality car High quality car 8 10 13 15 18 (a) Is there an equilibrium in which all types of qualities are traded? (b) Is there an equilibrium in which only low and medium qualities are traded? (c) Is there an equilibrium in which only low qualities are traded?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The market for lemons refers to a situation where sellers are better informed than buyers about the quality of the good for sale, like used cars. While sellers know the true quality of the car, buyers can’t distinguish the good cars from the bad cars (a.k.a. lemons). Consequently, from the buyer's perspective, there is a 50-50 chance that cars are either high or low quality, and therefore they will perceive all cars as medium quality cars. Which of the following statements are true? Multiple Choice From the seller's point of view, the price that buyers are willing to pay is too low. Therefore, they will find it difficult to sell their cars at "true" value. For the sellers who are selling lemons, the offered price will be higher than what they have expected. Therefore, they will sell lemons to the buyers at a higher price. Because buyers perceive all cars as medium quality cars they will pay a price that is between the price of good cars and the price of lemons.…
suppose in the market for used cars there is symmetric information and suppose that three cars are available with quality levels 0, 1, 2, 3, and 4. (a) If the sellers have a reservation price of $4,000 per unit of quality, and the buyers value cars at $5,000 per unit of quality, the equilibrium price per car will be? (b) if instead sellers know more about their cars than do buyers, what would be the equilibrium price? 9:28 PM /
Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n=10 people at the partywho are potential bidders. The owner of the $100 bill puts forth the following procedure: All bidders simultaneously submit a written bid. Only the highest bidders pay their bid (assuming that the highest bid is positive). If m people submit the highest bid, then each receives 1/m of the $100. Each person’s strategy set is {0,1,2,...,1000}{0,1,2,...,1000} so bidding can go as high as $1,000. The payoff of a player bidding bi is:0 if bi < max{b1,b2,…,bn},and 100/m − bi if bi = max {b1,b2,…,bn}where,m is the number of bidders whose bid equals max{b1,...,bn}. How many pure-strategy Nash equilibria does this game have? 1) 0 2) 1 3) 4 4) More than 4.
Exercise 1.8. Consider the following "third-price" auction. There are n≥ 3 bidders. A single object is auctioned and Player / values the object $v,, with V, > 0. The bids are simultaneous and secret. The utility of Player / is: 0 if she does not win and (v-p) if she wins and pays $p. Every non-negative number is an admissible bid. Let b, denote the bid of Player i. The winner is the highest bidder. In case of ties the bidder with the lowest index among those who submitted the highest bid wins (e.g. if the highest bid is $120 and it is submitted by players 6, 12 and 15, then the winner is Player 6). The losers don't get anything and don't pay anything. The winner gets the object and pays the third highest bid, which is defined as follows. Let be the winner and fix a Player j such that b₁ = max({b,,...,b,}\ {b}) [if GAME THEORY - Giacomo Bonanno 39 max({b,...,b}\{b;}) contains more than one element, then we pick one of them]. Then the third price is defined as max({b₁,...,b}\{b,,b;}).…
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1) Consider the following variant of the prisoner's dilemma with altruistic preferences. For simplicity, I'm adding 15 to the payoffs of the baseline normal form representation of the game we describe in class which results in the following: Player I\ Player 2 Cooperate Non-Cooperate Cooperate 8.8 0,15 Non Cooperate 15,0 14,14 Assume now that the players are not “selfish”; rather the preference of each player i are represented by the payoff (utility) function m; (a) + ßm; (a) where mi(a) is the payoff received by player i when the strategy profile is a, j is the other player, and ß is a given non-negative number. Player 1's payoff to the strategy profile (Cooperate, Cooperate), for example, is 8+8ß. A) Assume ß = 1. Write the normal form of the game. Is this game a prisoner's dilemma? What is the Nash equilibria of the game? B) Find the range of values of ß for which the resulting game is the prisoner's dilemma.
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Are these statements true or false? Provide a detailed explanation as to how you arrived at your answer: 1. If someone has linear indifference curves between contingent commodity bundles, then they must be risk averse and the risk premium is positive. 2. If a game has a Pareto efficient outcome, there exists a Nash equilibrium that leads to this outcome. 3. If a quantity tax is imposed on a profit maximising monopolist, consumer bear a higher burden of the tax than producers.
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