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    Bertrand & Cournot Models

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    Question 1:
    Consider the Bertrand model of price competition with two firms.Denote firm 1's (resp. firm 2's)marginal cost by c1(resp. c2),and assume c1< c2. Assume that the demand function x is given by x(p)= a-p,with a > c2 so that x(c2) > 0. Find all Nash equilibria of this model.

    Question 2:
    Consider a two-firm Cournot model. Let ci (i=1,2) denote firm i's cost per unit of output produced, and assume that c1 > c2 . Assume also that the inverse demand function is P(q)=a-bq, with a> c1 .
    (A) Derive the Nash equilibrium of this model. Under which conditions does it involve only one firm producing? Which one will this be?
    (B) When the equilibrium involves both firms producing, how do equilibrium outputs and profits vary when firm 1's cost changes?

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    Solution Summary

    Bertrand & Cournot Models are explicated.