In class, we examine the Cournot duopoly equilibrium assuming the product of duopolists are identical. In...

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In class, we examine the Cournot duopoly equilibrium assuming the product of duopolists are identical. In this exercise, we will relax such assumption and explore an extension of the Cournot model with differentiable product. Intel and AMD are duopolists in the CPU market. Their products (Intel Core(R) and AMD Ryzen™) are slightly different, and the demand functions for their products are q1= 10-2P1+ PA QA = 10-2PA + PI Notice that, the demand for each firm's product is higher if its own price is lower or if it's competitor's price is higher. Assuming marginal cost of CPU is 4 for both Intel and AMD. Derive the (Cournot) equilibrium production for Intel and AMD. (a) find the inverse demand function P₁, PA as functions of quand q4. (Hint: AMD's demand function implies P₁ = 2PA+ A-10. Substitute PA out using Intel's demand function. You then have AMD's inverse demand function with P₁on the left-hand-side, and qA and qr on the right-hand-side. Apply the similar procedure to find Intel's inverse demand function with PA on the left-hand-side, and qA and qr on the right-hand-side.) (b) Find the equilibrium price of CPU given the inverse demand functions from part (a), In class, we examine the Cournot duopoly equilibrium assuming the product of duopolists are identical. In this exercise, we will relax such assumption and explore an extension of the Cournot model with differentiable product. Intel and AMD are duopolists in the CPU market. Their products (Intel Core(R) and AMD Ryzen™) are slightly different, and the demand functions for their products are q1= 10-2P1+ PA QA = 10-2PA + PI Notice that, the demand for each firm's product is higher if its own price is lower or if it's competitor's price is higher. Assuming marginal cost of CPU is 4 for both Intel and AMD. Derive the (Cournot) equilibrium production for Intel and AMD. (a) find the inverse demand function P₁, PA as functions of quand q4. (Hint: AMD's demand function implies P₁ = 2PA+ A-10. Substitute PA out using Intel's demand function. You then have AMD's inverse demand function with P₁on the left-hand-side, and qA and qr on the right-hand-side. Apply the similar procedure to find Intel's inverse demand function with PA on the left-hand-side, and qA and qr on the right-hand-side.) (b) Find the equilibrium price of CPU given the inverse demand functions from part (a),

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a We have QI 10 2PI PA and QA 10 2PA PI Take the second demand function QA 1... View the full answer