Problem 5 (20 points) Consider the following Cournot duopoly model. Firms 1 and 2 produce the...

 

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Problem 5 (20 points) Consider the following Cournot duopoly model. Firms 1 and 2 produce the same good. They simultaneously choose their output levels y₁, y2, and the resulting price is given by the inverse demand function p = 1 — Y₁ — Y2. If firm 1 produces a (strictly) positive output level, it incurs a fixed cost k but no variable cost. Thus, its cost function is 0 if y₁ = 0, k if y₁ > 0. Firm 2 faces no cost at all; its cost function is C2 (Y2) = 0 for all y2 ≥ 0. Show that (i) there is a unique Cournot-Nash equilibrium if the fixed cost k is below a lower threshold k or above an upper threshold k+ and (ii) there are two Cournot-Nash equilibria when k≤ k ≤ kt. Compute the thresholds k, k and the equilibrium output levels explicitly. C₁ (31) = { Problem 5 (20 points) Consider the following Cournot duopoly model. Firms 1 and 2 produce the same good. They simultaneously choose their output levels y₁, y2, and the resulting price is given by the inverse demand function p = 1 — Y₁ — Y2. If firm 1 produces a (strictly) positive output level, it incurs a fixed cost k but no variable cost. Thus, its cost function is 0 if y₁ = 0, k if y₁ > 0. Firm 2 faces no cost at all; its cost function is C2 (Y2) = 0 for all y2 ≥ 0. Show that (i) there is a unique Cournot-Nash equilibrium if the fixed cost k is below a lower threshold k or above an upper threshold k+ and (ii) there are two Cournot-Nash equilibria when k≤ k ≤ kt. Compute the thresholds k, k and the equilibrium output levels explicitly. C₁ (31) = {

Answer rating: 100% (QA)

i There is a unique CournotNash equilibrium if the fixed cost k is below a lower thresho... View the full answer