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# Calculations are similar to a e using the first

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Unformatted text preview: a) e) Using the first mover’s profit function to derive their Firm 1’s optimum output and Firm 2’s optimum reaction ( ( ) ) ( ) Substituting Firm 2’s reaction function into since firm 1 already knows firm 1 is expected to react ( ) This the key difference between the Cournot and Stackelberg model, i.e. Substituting in the reaction fn FOC =0 Substituting into Firm 2’s reaction function to get firm 2’s optimal reaction ( Market Price: ( ) ) ( )( ( ) ) ( ) To summarize the outcome in each model, the following diagram have been drawn Firm 1 and 2' s Reaction function 99 ( )- firms ’s reaction fn Stackelberg Equilibrium Perfect Competition Equilibrium 49.5 Nash Cournot Equilibrium 33 Cartel/ Collusion 24.75 0 24.75 33 ( )-firm ’s reaction fn 9 9 49.5 Market Demand Curve 100 P 50.5 Cartel/ Collusion Cournot Equilibrium 34 25.75 Stackelberg Equilibrium Perfect Competition Equilibrium MCindustry Pc= 1 MR 49.5 66 74.25 Dindustry 99 100 Quantity, Q Problem 2 Market 1 Total firm MC and MR Market 2 400 MC P2 200 P1 M R1 D 2 M R2 Q1 ∑MR D2 Q2 Q1+ Q2 The diagram above shows the diagrammatic representation of the model. To profit maximise a firm must satisfy the condition be...
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