Answered: QUESTION 7 In the hotelling model,…

QUESTION 7 In the hotelling model, suppose firm 2 locates at 45 meters. Which of the following location choices for firm 1 gives highest profits? O 50 meters O 49 meters O 44 meters

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
The model initial setup is• The number of vacancies posted in the economy during a particular month is v = 100.• There were initially u = 225 unemployed workers at the beginning of the month.• Suppose that the average wage is 0.6 relative to their productivity. Unemployed workersreceive benefits that are half the wage, i.e., b = 0.3 relative to productivity.• Suppose that the number of matches between firms and workers are given by thefollowing matching functionsM = Au^0.5v^0.5• Suppose that 45 workers were able to find a job by the end of the month.Answer the following questions.a) What is the monthly job finding rate?b) What is the probability that an average vacancy is filled in a month?c) What is the job creation cost, k?d) What is the value of A?e) Explain how introducing a searching cost to this model would affect the queue length,the number of vacancy and unemployment rate, and wage.
[The soft drink industry is dominated by two cola firms- DEW and HEW. The market is worth $8 billion. Each firm can decide whether to advertise or not, but advertising costs $2 billion to any firm undertaking it. Moreover, advertising will create only negligible new demand as the market is already saturated. So, for the purpose of this question, assume that the market remains at $8 billion regardless of advertising. If one firm advertises and the other does not, then the former captures the whole market. If both firms advertise, then DEW captures 60% of the market and HEW captures 40% of the market, but the advertising must be paid for. If neither firm advertises, then the market is again split 60:40, with 60% going to DEW and 40% to HEW.] [Draw the payoff matrix for this game where each player’s payoff is equal to the value of market it captures less the cost of advertisement. [Do any of the firms have dominant strategies? If so, what are they? Is there a dominant strategy…
[The soft drink industry is dominated by two cola firms- DEW and HEW. The market is worth $8 billion. Each firm can decide whether to advertise or not, but advertising costs $2 billion to any firm undertaking it. Moreover, advertising will create only negligible new demand as the market is already saturated. So, for the purpose of this question, assume that the market remains at $8 billion regardless of advertising. If one firm advertises and the other does not, then the former captures the whole market. If both firms advertise, then DEW captures 60% of the market and HEW captures 40% of the market, but the advertising must be paid for. If neither firm advertises, then the market is again split 60:40, with 60% going to DEW and 40% to HEW.] Draw the payoff matrix for this game where each player’s payoff is equal to the value of market it captures less the cost of advertisement. (please explain how you calculate the payoff matrix)
Let’s use the Fisher effect to use two known values to learn about the unknown third one. Consider the table, with some values given and some missing. ?i ??Eπ ?EquilibriumrEquilibrium 5% 2% 3% 5% 1% ___ 5% ___ 8% ___ 10% 2% 6% ___ 2% 0% -2% ___ Compute the missing values in the table. ?=5%,??=1%,?Equilibrium=i=5%,Eπ=1%,rEquilibrium= % ?=5%,?Equilibrium=8%,??=i=5%,rEquilibrium=8%,Eπ= % ??=10%,?Equilibrium=2%,?=Eπ=10%,rEquilibrium=2%,i= % ?=6%,?Equilibrium=2%,??=i=6%,rEquilibrium=2%,Eπ= % ?=0%,??=−2%,?Equilibrium=
An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ? (b) If they buy 700 shares of retail stock, how many shares of the other stocks should they buy? computer ? shares utility ? shares What if they buy 1400 shares of retail stock? computer ? shares utility ? shares (c) What is the minimum number of shares of computer stock they should buy?? sharesWhat is the…
The soft drink industry is dominated by TCCC and PSC. The market is worth $6 billion. Each firm can decide whether to advertise, but advertising costs $1 billion to any firm undertaking it. Moreover, advertising will create only negligible new demand as the market is already saturated. So, for the purpose of this question, assume that the market remains at $6 billion regardless of advertising. If one firm advertises and the other does not, then the former captures the whole market. If both firms advertise, then TCCC captures 60% of the market and PSC captures 40% of the market, but the advertising must be paid for. If neither firm advertises, then the market is again split 60:40, with 60% going to TCCC and 40% to PSC. 1. Draw the payoff matrix for this game where each player’s payoff is equal to the value of market it captures less the cost of advertisement. 2. Do any of the firms have dominant strategies? If so, what are they? Is there a dominant strategy equilibrium? If so,…
A firm plans to expand its product line and faces a dilemma whether to build a small or largefacility to produce new products. If it builds a small facility and demand is low, the NPV afterdeducting for building costs will be four hundred thousand pesos. If demand is high, the firm caneither maintain the small facility or expand it. Expansion would have an NPV of four hundredfifty pesos while maintaining the small facility would have an NPV of fifty thousand pesos. If alarge facility is built and demand is high, the estimated NPV would be eight hundred thousandpesos. If demand turns out to be low, the NPV would be a loss of ten thousand. The probabilitythat the demand is high is estimated to be sixty percent.a. Analyze using a decision tree.b. Compute for EVPI.c. Determine the range over which each alternative would be best in terms of the valuewhen demand is low.
DERIVATIVES Differentiate f(x)=(4x4+3x)(2x4+2x) Let u(x)=(4x4+3x) and v(x)=(2x4+2x)
(Symmetric mixed strategy Nash equilibrium) A profile α∗ of mixed strategies in a strategic game with vNM preferences in which each player has the same set of actions is a symmetric mixed strategy Nash equilibrium if it is a mixed strategy Nash equilibrium and α∗ i is the same for every player i. Solve this problem: At a large round table sit n ≥ 2 players, each holding 3 cards: one white, one black, and one red. Each player must secretly choose one of their cards and then, when the bell rings, simultaneously reveal it publicly with all the others. If all players choose the white card, each of them receives 6 points. If player i chooses the white card, and at least one of the other players chooses a card of a different color, player i receives 1 point. If player i chooses the black card, they receive 3 points, regardless of the decisions of the other players. If player i chooses the red card, they receive 0 points, regardless of the decisions of the other players. Find all symmetric…
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…