– Need a full detailed answer for this bonus question.DescriptionSolution downloadThe QuestionNeed a full detailed answer for this bonus question.ECON101Winter, 2016Bonus QuestionPrice Competition with Search FrictionPolicy The bonus question is beyond the scope of the chapter. So it is completely ?ne if you don?t knowhow to solve it. If you are really interested in the material and willing to spend some time on it, pleasehave a try. It is OK that you ask your TA or look up some advanced textbook (Actually I encourage youto read something deeper). Overall, the bonus question can add upto 2% of your ?nal grade. If you tend toparticipate,? Email me your answer by 11pm, Feb 18th (Thursday).? Write your answer clearly.? You can form a small study group with upto 3 members.? There are four parts of the question. Grading is under all-or-nothing policy, meaning that if youranswer is wrong, no point will be given for the part. So it is risky.Enjoy!BackgroundIn real market, di?erent sellers may sell the same goods at di?erent prices. We call the phenomenon ?pricedispersion?. In some industry, the magnitude of such dispersion is very large. The phenomenon is puzzlingsince consumers tend to buy goods with lower price, which should drive sellers with higher prices out ofmarket. However, they actually survive.To resolve the puzzle, economists have being raising di?erent theories. One of the explanations is consumers?costly search behavior. For instance, you can by a bottle of ketchup by simply visiting Ralphs. Or you canvisit Trader Joes, Costco and many other stores, compare their prices and buy the cheapest one. However,visiting lots of stores are costly. If you are impatient, you may visit only one store and buy the item (if theprice is no higher than your reserved price).On the other hand, consumers? costly search behavior will de?nitely a?ect sellers? pricing strategy. In thebonus question, we try to setup a simple game theory model and study the issue.Model and QuestionSellers: There are two sellers i = A, B in the market. Each has only one unit of goods to sell. They are ofthe same quality and no production cost.Consumer: On the demand side, there is only one consumer, who needs only one unit of the goods andvalues it as v > 0.Price competition: The two sellers compete by choosing prices PA , PB 0. Since there is no cost, if theconsumer purchases from seller i, i?s pro?t is equal to Pi , and the consumer generates utility u = v Pi .Outside option: In addition, if the prices are larger than v, consumer will give up on purchasing and leavethe market. If so, both sellers and buyer get zero.In terms of consumer?s ?search? , we consider two alternative environments. Actually, the ?rst one is thestepstone to the second.1. Assume that with probability q, the consumer is a patient person. So he will visit both sellers andcompare the two prices. With probability 1 q, the consumer is impatient and will randomly visit one-1-ECON101Winter, 2016of the two sellers with equal probability. As long as the price of the store is lower than v, he will buyit even if the other seller?s price might be lower.Also, we assume that the sellers know the value of q and choose prices before consumer visits.(a) If q = 1, i.e. the consumer is patient for sure, what?s Nash Equilibrium PA , PB ? If q = 0, i.e. theconsumer is impatient for sure, what?s the Nash Equilibrium PA , PB ?(b) For any value 0 < q < 1, what?s Nash Equilibrium prices PA , PB ?Hints:? Check whether pure strategy NE exists or not.? If not, how about mixed NE?2. In ?rst environment, we assume consumers could be either patient or not. In the second environment,we assume that the consumer can choose between visiting only one seller or visit both.If he visi
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