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NOTESOLIss6

# NOTESOLIss6 - Econ 467 Summer 2006 Oligopoly Theory...

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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.

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