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Cournot with Conjectural Variations

Cournot with Conjectural Variations. Varying Reactions. Here we introduce a new parameter,  , which measures the elasticity of rivals’ output with respect to firm i’s output. For our 2 firm example  =  q 2 / q 2  q 1 / q 1 If  = 0 then we have the basic Cournot assumption.

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Cournot with Conjectural Variations

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  1. Cournot with Conjectural Variations

  2. Varying Reactions • Here we introduce a new parameter, , which measures the elasticity of rivals’ output with respect to firm i’s output. For our 2 firm example •  =  q2 / q2 •  q1 / q1 • If  = 0 then we have the basic Cournot assumption. • If = 1then firm i will believe that a reduction or increase in output of 1 per cent will be mirrored by its rivals. • = -1 then firm i will believe that a reduction or increase in output of 1 per cent will be offset by symmetrically opposite responses by its rivals.

  3. Our example revisited • P = 30 – Q • MC = 12 • Reaction curve of both firms • Q1 = 9 – 0.5 (Q2) • Q2 = 9 – 0.5 (Q1) • By adding  we get • Q1 = 9 – 0.5 (1 + ) Q2 • Q2 = 9 – 0.5 (1 + )Q1 • So we can draw the reaction curves for  = 0,  = 1,  = -1 • When  = 0 the normal Cournot case prevails.

  4. Cournot conjectures  =0 and  = -1

  5. Cournot conjectures  =0 and  = 1

  6. Solutions • In general • Qi = 18 • 3 +  • So if •  = 0, Qi = 6 •  = 1, Qi = 4.5 •  = -1, Qi = 9 •  = 0.5, Qi = 5.14 •  = -0.5, Qi = 7.2 Can you identify the welfare outcomes associated with these conjectures?

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