Econ 483_Lecture 21_Public provision

Case i if rms do not merge cournot competition firms

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Unformatted text preview: ecture 21: Public Support of R&D, Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Case I: If …rms do not merge (Cournot competition)... Firms’ pro…t functions: πA πB = (100 = (100 qA qB ) qA 40qA 300 qA qB ) qB 40qB 300 In equilibrium, ∂π A ∂qA ∂π B ∂qB = 0 , 100 2qA qB 40 = 0 , qA = 30 = 0 , 100 qA 2qB 40 = 0 , qB = 30 Lecture 21: Public Support of R&D, Econ483: Econ of Innovation & Technology, Evangelia Chalioti 1 qB 2 1 qA 2 c A ll rights reserved. Solving the system, qA = 30 1 2 30 and thus, qB = 30 1 qA 2 , qA = 20 1 (20) , qB = 20 2 In equilibrium, Total output: Q = qA + qB = 40 Price: P = 100 40 = 60 Pro…ts: π A = (100 Lecture 21: Public Support of R&D, 40) 20 40 (20) 300 = 100 & π B = 100 Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Consumer surplus: CS = 1 (100 2 P )Q = 1 (100 2 60) 40 = 800 Total welfare before the merger: W = CS + λ (π A + π B ) = 800 + λ...
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