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- 4. A model of network externalities. Suppose that there are 50 potential consumers in the market for a new technology that exhibits network effects. There is a uniform distribution of consumers with individual valuations, v, ranging from S1, $2,.., S50. Consumer valuation from consuming the technology is given by vN, where N is the number of consumers adopting the technology. Consumers with purchase the product as long as their valuation is greater or equal to the price, so that the marginal consumer has a valuation such that p3vN. The number of consumers adopting the technology is given by the number of people with valuation greater than y, i.e. N = 50 - v. %3D a) Using the information above, derive the relationship between the price of the product and the number of consumers adopting the product, N. Characterize this relationship – does it reflect a typical market demand curve? b) If the price for the product is $600, find the three equilibrium number of adopters in the market. c)…10. Game theorybelow cost? That is, explain a rationale of loss leaders, using your U4. The coconut-milk carts from Exercise S7 set up again the next day. Nearly 172 [CH. 5] SIMULTANEOUS- MOVE GAMES a dollars of a pound of cheese. (a) Initially, L'Épicerie runs La Boulangerie and La Fromagerie as if the were separate firms, with independent managers who each try to maximize their own profit. What are the Nash equilibrium quanti- ties, prices, and profits for the two divisions of L'Épicerie, given the new quantity equations? (b) The owners of L'Épicerie think that they can make more total profit by coordinating the pricing strategies of the two Yuppietown divi- sions of their company. What are the joint-profit-maximizing prices for bread and cheese under collusion? What quantities do La Bou- langerie and La Fromagerie sell of each good, and what is the profit that each division earns separately? (c) In general, why might companies sell some of their goods at prices below cost? That is, explain a…
- 34. Which one would have the greatest effect38 Refer to the normal-form game of advertising shown below. Firm A Advertise Do Not Advertise Multiple Choice Suppose there is a 10 percent chance that the advertising game depicted in Figure 10-17 will end next period. What is the present value to firm A of agreeing to the strategy (do not advertise, do not advertise]? $237.50 Firm B Advertise $0, $0 $10, $175 $1,250 Do Not Advertise $175, $10 $125, $125Exercise 6.2. If the companies that make up a duopoly agreed on the amount they are most interested in offering to the market, what amount would they choose? Why? If, on the other hand, each of the companies acted on its own, would they produce between the two a greater or lesser amount than in the previous situation? Graphically represent and explain your answers.
- 1. Suppose the following prisoner's dilemma is played twice with the payoff for the entire game being the sum of the payoffs from the two stages. Assume there is no discounting. Player 1 B Player 2 B 2,6 3,3 A 5,5 6,2 a. What is the Nash equilibrium for stage two? b. Show what the game in stage 1 amounts to when the players anticipate the Nash equilibrium for stage 2. c. Provide the subgame-perfect outcome for this game.Кееp production $200 million $300 million Using what you know about the prisoner's dilemma, what would be the profit for Antel and constant IMD in millions? (cooperate Antel profit Antel profit is $20 million is $200 million Antel options IMD profit is IMD profit is $20 million $100 million Increase production (act independently) Antel profit Antel profit is $100 million is $300 million Antel profit: S million million IMD profit: S What would be the best collective option for both firms? Select all of the reasons Antel and IMD would make more profit at the original constant production level? соорerate Because overall demand for computer chips act independently will increase Because they can both charge more for the product at the given level of production Because it restricts the supply of computer chipsThe ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F - 5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0:0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0;0
- The Old Familiar and The Beehive are the only two bistros in town. Each is trying to decide whether or not it should advertise in the local newspaper. The accompanying payoff table gives their weekly profits under each possible outcome. The Beehive The Beehive does advertise | does not advertise The Old Familiar The Old Familiar earns $X in profits. earns $3,500 in profits. The Old Familiar does advertise The Beehive The Beehive earns $Y in profits. earns $2,250 in profits. The Old Familiar The Old Familiar earns $2,000 in profits. earns $2,500 in profits. The Old Familiar does not advertise The Beehive The Beehive earns $4,000 in profits. earns $3,500 in profits. a. Which combination or combinations of X and Y would make a situation in which The Old Familiar does not advertise and The Beehive advertises a Nash equilibrium? A Nash equilibrium occurs ifU9. Consider a revised version of the game from Exercise S9: PROFESSOR PLUM Revolver Knife Wrench Conservatory 1,3 2,-2 0,6 MRS. PEACOCK Ballroom 3,2 1,4 5,0 (a) Graph the expected payoffs from each of Professor Plum's strategies as a function of Mrs. Peacock's p-mix. (b) Which strategies will Professor Plum use in his equilibrium mixture? Why? (c) What is the mixed-strategy Nash equilibrium of this game?Jagtar and Ravi both grow mangoes, which they sell in the same local market. They are deciding whether to pick 5 baskets worth of mangoes or 10 baskets, and have the following profit matrix: Jagtar 5 1 17 5 1 22 16 14 Ravi 1 24 14 a. What is the Nash equilibrium if both individuals make their decisions simultaneously? b. Does your analysis change if the local market charges a lump-sum fee of 12 to set up a stall and sell the mangoes in the space it provides? c. What would happen if the local market were instead to charge a lump-sum fee of 18?