ajaz_eco204_2009_HW_19 - University of Toronto, Department...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain HW 19 Please help improve the course by sending me an email about typos or suggestions for improvements _____________________________________________________________________________________ Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 The CEO of Brr! Yani foods Ajax has been recently exploring opportunities for growth in South Korea. The table below contains the total market size, anticipated market capture and anticipated fixed and average variables costs (all figures in dollars): Total Market Size (annual units) Anticipated Market Capture (%) Annual Fixed Costs Average Variable Cost South Korea Market 500,000 40% $2m $30 (a) What is Brr! Yani's annual cost in millions of dollars if it is the only firm to enter the South Korean market? Show all steps and calculations. Ajax learns that a Japanese rival company VLM is also considering entering the South Korean market. Neither company knows the other company's actions. Wall and Bay Street analysts predict VLM and Brr! Yani's fixed cost and average variable to be identical. Ajax calculates that either firm, if it were the only entrant, could capture 40% of the total market size at a price of $55 per unit. If both companies were to enter the market, each firm is expected to sell 30% of the total market size at a price of $45. 1 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain (b) Fill the payoffs (in `000s of $) for South Korea entry game below. Show all steps and calculations. VLM Enter Brr! Yani Don't Enter Enter Don't Enter (c) Copy the payoffs from the table in part (b) below. Calculate the pure strategy Nash equilibriums for the simultaneous game below. Show all calculations and payoffs. VLM Enter Brr! Yani Don't Enter Enter Don't Enter Question 2 (20072008 Final Question) In a business deal, Gussy has been identified as sometimes being straightforward and at other times bluffing, while Jen has been identified as being sometimes trusting and at other times skeptical. The payoffs from a oneshot simultaneous game between Gussy and Jen are: Gussy Straightforward Bluffing Jen Trusting 20, 20 50, 10 Skeptical 10, 10 0, 0 (a) What is the pure strategy Nash equilibrium? (b) What is the mixed strategy Nash equilibrium? Show your calculations below, clearly stating any assumptions you've made: Question 3 (20072008 Final Exam Question) Courtney and Alma play a game: Courtney Left Right Alma Up 1, 1 0, 5 Down 5, 0 4, 4 2 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain (a) What is the pure strategy Nash equilibrium in a oneshot game? (b) Suppose Courtney and Alma play the game repeatedly forever. Predict the possible outcomes of the game. State any assumptions and show all calculations clearly. Question 4 Two hospitals compete on the basis of service to patients. The following table gives the profits (in millions of $): Basic Hospital A's Services All Purpose Specialty Basic 5, 7 4, 5 6, 10 Hospital B's Services All Purpose 5, 4 8, 7 3, 12 Specialty 12, 6 7, 4 3, 3 (a) Does either hospital have a dominant strategy? If so, solve the game by dominant/dominated strategies. Show all steps below. (b) Solve for the pure strategy Nash equilibrium. (c) If these hospitals merge and coordinate their hospital services, what actions should they take? Explain briefly. If necessary, show your reasoning below. 3 ...
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