{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

NOTESOLIss6 - Econ 467 Summer 2006 Oligopoly Theory...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 467 - Summer 2006 Oligopoly Theory / Strategic Trade (third market case) I - Homogeneous Products, 2 Firms . Typical Demand function: p= A - b (q 1 + q 2 ), Costs (identical or not): MC 1 = c 1 , MC 2 = c 2 (1) Firms choose quantities simultaneously. We look for the NE in quantities or Cournot equilibrium. Step 1: Calculate reaction functions by choosing q i to max. A i (q i , q j ) assuming q j is fixed. Let R i (q j ) be firm I’s reaction function. Step 2: Calculate the NE by finding the intersection of the two reaction functions (i.e. find the values of q 1 and q 2 that solve : q 1 = R 1 (q 2 ) and q 2 = R 2 (q 1 ) ). (2) Firms choose quantities sequentially (assume Firm 1 moves first). We look for the SPNE in quantities or Stackelberg equilibrium. Step 1: Calculate Firm 2's reaction function by choosing q 2 to max. A 2 (q 1 , q 2 ) assuming q 1 is fixed. Let R 2 (q 1 ) be firm 2’s reaction function. Step 2: Calculate the optimal q 1 by max. A 1 (q 1 , q 2 ) assuming q 2 = R 2 (q 1 ). Replacing the optimal q 1 into R 2 (q 1 ) we get the value of q 2 at the SPNE. Remark: A 1 > A 2 so the firm that goes first has an advantage. (3) Firms choose prices simultaneously. We look for the NE in prices or Bertrand equilibrium with homogeneous products. (i) If both firms have the same marginal costs (c 1 = c 2 ) no mathematical calculation needed. Just a clear argument to justify the NE prices. (ii) If c 1 < c 2 , there will be two cases depending on whether c 2 is bigger or smaller than the monopoly price for firm 1.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ 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