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ECMC41-Lec4

# ECMC41-Lec4 - ECMC41 Lecture 4 Lecture 4 Outline 1 Q&A Lec3...

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ECMC41 – Lecture 4

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2 Lecture 4 - Outline 1. Q&A: Lec3 2. Price discrimination (1) Conditions for price discrimination (2) Types of price discrimination (3) Perfect and the 3 rd degree price discrimination: models and their welfare implications
3 Non-cooperative Oligopoly Models Cournot model: Bertrand model(s) Three steps Step 1: Objective and decision variable Step 2: F.O.C to obtain firm’s best response function Step 3: NE by equating best response functions

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4 Example: Cournot model - Decision variable: output ( 29 1 1 2 1 1 10 100 1 q q q q Max q - - - = π ( 29 2 2 2 1 2 10 100 2 q q q q Max q - - - = π ( 29 2 1 2 1 2 1 1 1 2 1 45 : 0 10 2 100 q q q BR q q q - = = - - - = π ( 29 1 2 1 2 1 2 2 2 2 1 45 : 0 10 2 100 q q q BR q q q - = = - - - = π * 900 \$ 10 * 40 \$ ) 30 30 ( 100 * 100 30 2 30 45 30 2 45 4 3 4 1 2 45 4 1 2 45 45 2 1 45 2 1 45 2 1 45 2 * 1 * 1 * 1 * * 2 * 1 1 1 1 1 2 1 π π = = - = = + - = - = = - = →→ = →→ = + = + - = - - = - = q q p Q p q q q q q q q q y y x x MC AC MC AC = = = = 10 , 10
5 Example: Bertrand models - Decision variable: price x y y y x x P P q P P q + - = + - = 2 100 , 2 100 ( 29 ( 29 y x x x P P P P Max x + - - = 2 100 10 π ( 29 ( 29 X Y Y Y P P P P Max Y + - - = 2 100 20 π ( 29 ( 29 ( 29 y x y x x y x x x P P p BR P P P P 4 1 30 : 0 10 2 2 100 + = = - - + - = π ( 29 ( 29 67 . 50 33 . 41 33 . 45 * 2 100 67 . 62 33 . 45 33 . 41 * 2 100 33 . 45 4 1 35 , 33 . 41 4 1 35 4 1 30 * * * * * = + - = = + - = = + = →→ = →→ + + = y x x Y x x x q q P P P P P y y x x MC AC MC AC = = = = 20 , 10 ( 29 ( 29 ( 29 X Y X Y Y X Y Y Y P P p BR P P P P 4 1 35 : 0 20 2 2 100 + = = - - + - = π

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6 Some considerations 1. Cournot-Nash Equilibrium : 1. If entry is not limited: - Relationship between the shape of cost (and demand ) curves and the number of the firms in a market (1) MC =AC = constant (i.e. FC = 0) (2) MC is constant, AC is declining (i.e. FC > 0) (3) MC & AC increasing as output rises ( 29 ( 29 ( 29 ( 29 2 2 1 2 2 1 2 1 2 1 1 2 1 1 , , , , q for q q q q q for q q q q C C C C C C π π π π
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