file - ww w ox di a Given name.c om Family name Student...

Info icon This preview shows pages 1–3. Sign up to view the full content.

Given name : Family name : Student number : Signature : UNIVERSITY OF TORONTO Faculty of Arts and Science ECO 380 F (Markets, Competition, and Strategy) Instructor: Zhe Yuan Midterm Jun 2nd 2015 Duration: 100 minutes No aids allowed This examination paper consists of 8 pages and 4 questions. Please bring any discrepancy to the attention of an invigilator. The number in brackets at the start of each question is the number of points the question is worth. Answer all questions. To obtain credit, you must give arguments to support your answers. For graders’ use: Score 1 (30) 2 (25) 3 (20) 4 (25) Total (100) Page 1 of 8 DownloaderID 17634 ItemID 16592 Downloader ID: 17634 Item ID: 16592 Downloader ID: 17634 Downloader ID: 17634
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

page 2 1. St. George is a street with a length of one mile. Two hotdog shops are potential entrants and they are considering locating their outlets. Each of them can open one outlet. Suppose both these two shops have constant marginal cost c . A mass 1 UT students are uniform distributed on St. George st. and they are looking for hotdogs. Their reservation value for hotdog is very high with V >> c . However, there is a transportation cost of walking to the hotdog shop which is a quaratic function of the distance between the consumer and the shop. For example, consumer who is located at x needs to suffer a cost of t ( x a ) 2 in order to walk to a . And we assume V >> t . (a) [5] Suppose these two shops are located in ( a, 1 b ), with a bracketleftbig 0 , 1 2 bracketrightbig . They are involved in a price competition with shop 0 charges p 0 and shop 1 charges p 1 . Find the marginal consumer. Given any location choice ( a, 1 b ), suppose the marginal consumer is x m V p 0 t ( x a ) 2 = V p 1 t (1 b x ) 2 Solve and get x m = a + 1 a b 2 + p 1 p 0 2 t (1 a b ) (b) [5] Suppose we can solve for the best response function of the two firms as a function of locations and competitor’s price. BR 0 ( p 1 ) = at (1 a b ) + t (1 a b ) 2 2 + p 1 + c 2 BR 1 ( p 0 ) = bt (1 a b ) + t (1 a b ) 2 2 + p 0 + c 2 If firm 0 is going to charge p 0 = 0, what is the optimal price for shop 1? If p 0 = 0, according to the best response function, BR 1 ( p 0 = 0) = bt (1 a b ) + t (1 a b ) 2 2 + 0 + c 2 = bt (1 a b ) + t (1 a b ) 2 2 + c 2 (c) [5] If firm 0 is going to charge p 0 + , what is the optimal price for shop 1? Firm 1 now is not going to decide price according to the best response function. Actually, Firm 1 will behave as the monopolist in the market. Since the V is high ( V >> t ), Firm 0 will maximize its profit by serve the whole market (Proof see Question 2 in PS2, no need to show here). So Firm 1 will set price such that the consumer at x = 1 is indifferent from purchase or no purchase, i.e., p 1 = V t (1 a ) 2 (d) [5] Find the Nash Equilibrium price for the two firms.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '12
  • CarlosSerrano
  • Game Theory, Tax Returns, Stackelberg competition

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern