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Washington State ECONS 425 Industrial Organization Final Exam

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EconS 425;Final Exam;1. Consider the following game about trust that has been played in many experiments. The experimenter starts by giving player 1 ten dollars and player 2 zero dollars. The experimenter then asks player 1 how many dollars is he willing to give back to help player 2. If he chooses to give x dollars back;to the experimenter, then the experimenter gives player 3 3x dollars. Subsequently, player 2 has the;opportunity to give any or all (or none) of the money he has received to player 1.;(a) Assuming that the two players are risk neutral and care only about their own payo? FInd the;subgame perfect equilibrium of this game. (The subgame perfect equilibrium, by the way, is not;what seems to happen in experiments. Usually player 1 gives some, but not all of the money back;to the experimenter.);(b) Does the game have a Nash equilibrium in which the players receive higher payo?s?;(c) Suppose we modiFIed the game so that after the two stages above player 1 had the chance to;punch player 2. Suppose that this would reduce player 1?s utility by 1 dollar and reduce player;2?s utility by 5 dollars. Would this change your answers to parts (a) and (b)? How about if we;instead had the players play the game shown below after the second stage? Do these predictions;seem reasonable to you.;Player 2;A B;Player 1 A 5,5 -5,-5;B -5,-5 5,5;(d) An alternative explanation for the experimental results is that the players may be altruistic. Show;that the simplest representation of altruism ?each player maximizing a weighted sum of his own;dollar payo? and the other player?s dollar payo? ?cannot account for the experimental regularity except for one very special (and not compelling) choice of the weights. Can you think of utility;functions that might be used to account for the experimental result?;2. Prove the second part of Proposition 12.1 (page 309) using the same procedure as the one used in the;proof of the FIrst part.;3. A monopoly o?ers a product for sale. The product costs c = $60 to produce. The product may fail;with probability 0:5, hence it is fully operative with probability = 0:5. This probability is public;information in the sense that it is known to the seller and all buyers. The product can either be fully;functioning or totally defective. Consumers are willing to pay up to V = $240 for a fully-functioning;product. If the product is found to be defective, consumers do not gain any utility. Solve the following;problems.;(a) The monopoly provides a ?twice-replacement?warranty. That is, if the original purchase is found;to be defective, the consumer can have the product replaced free of charge. If the replacement;product is also found to be defective, it also gets replaced free of charged. However, the monopoly;will not replace the replacement of the replacement product if it also found to be defective.;Compute monopoly?s proFIt-maximizing price and the resulting expected proFIt.;(b) Now suppose the monopoly provides a money-back guarantee (instead of the twice-replacement;warranty). Compute monopoly?s proFIt-maximizing price and the resulting expected proFIt.;Microsoft and Apple produce di?erentiated goods, Microsoft Surface (MS) and iPad (iP), respectively.;There are two types of buyers in the economy, those who are FIrst time buyers (inexperienced consumers) and those who have purchased the product before (experienced consumers). The group of inexperienced consumers represents the 45% of the total group of consumers. Assume that the group of experienced consumers is divided into two subgroups: those who prefer to purchase MS over brand iP, and those who prefer iP over MS. Let;4. The inverse market demand function for MP3 players is given by p = 240 -2Q. Initially, firm A and;firm B produce at equal unit cost, c0. After investing heavily in R&D, firm A has managed to reduce;its unit production cost to c1 = $40 0 and FIrm 2;has the same marginal cost than FIrm 1. First, the potential entrant observes FIrm 1?s output level and;then it decides whether or not to enter. If FIrm 2 enters, both FIrms compete a la Cournot. Find the;range of values of F for which FIrm 1 (incumbent) decides to accommodate entry.;7. Microsoft and Apple produce di?erentiated goods, Microsoft Surface (MS) and iPad (iP), respectively.;There are two types of buyers in the economy, those who are FIrst time buyers (inexperienced consumers) and those who have purchased the product before (experienced consumers). The group of inexperienced consumers represents the 45% of the total group of consumers. Assume that the group of experienced consumers is divided into two subgroups: those who prefer to purchase MS over brand iP, and those who prefer iP over MS. Let B, 0 < B < 1, be the fraction of MS-oriented consumers (among experienced consumers). Hence, (1-B) is the fraction of iP-oriented consumers (among experienced consumers). In addition, FIrms must decide between two advertising methods: Persuasive (P) or Informative advertising (I).;a) Following Assumption 11.1 (page 292), identify the proFIt level for each FIrm and the aggregate;proFIt under all four possible outcome.;(b) Discuss under which conditions both FIrms will use informative advertising. Discuss your results.;8. Following Brander and Spencer 1983 and 1985, consider two countries denoted by i = X, Y, each of;which has one FIrm producing a homogeneous product only for export, to be sold in the international;market. Both FIrms compete a la Cournot in the international market. The inverse demand function;in the international market is P = 15 ? 0.5Q. In addition, assume that the preinnovation unit cost;of each FIrm is c = 4. Let ri denote the amount of R&D sponsored by the government in country i.;Assume that when the government i undertakes R&D at level ri, the unit production cost for the firm producing in country I is reduced to c-ri, I = X, Y. Finally, the total cost to government I of engaging in R&D at level ri, is TC;(a) Identify countries best response function.;6(b) What is the Nash equilibrium R&D level for each country? Discuss your results., t

 

Paper#68423 | Written in 18-Jul-2015

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