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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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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.
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.
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?