Consider a differentiated product duopoly market with symmetric, linear demand system 12-2p1 + P2 32 =...

 

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Consider a differentiated product duopoly market with symmetric, linear demand system 12-2p1 + P2 32 = 12-2p2 + P1 and in which both firms have constant unit costs of $5 per unit. The firms compete in prices, with Firm 1 choosing first (the leader) and Firm 2 second (the follower). Y1 = When answering the following questions, please round figures to 2 dec- imal places when necessary. (a) Write down the profit function of Firm 1. (b) Write down the reaction function of Firm 2. (You can use the formula derived in the Class Prep video for Week 5.) (c) Substitute Firm 2's reaction function into Firm 1's profit function and determine Firm 1's profit-maximising choice of p₁. (d) What price will Firm 2 choose? (e) Draw a diagram with p₁ measured on the horizontal axis and p2 on the vertical axis. Sketch the reaction function for Firm 2 in your diagram, and indicate the point corresponding to the values of p₁ and p2 that you found in (c) and (d). (f) Does this market have a first-mover or a second-mover advantage? Consider a differentiated product duopoly market with symmetric, linear demand system 12-2p1 + P2 32 = 12-2p2 + P1 and in which both firms have constant unit costs of $5 per unit. The firms compete in prices, with Firm 1 choosing first (the leader) and Firm 2 second (the follower). Y1 = When answering the following questions, please round figures to 2 dec- imal places when necessary. (a) Write down the profit function of Firm 1. (b) Write down the reaction function of Firm 2. (You can use the formula derived in the Class Prep video for Week 5.) (c) Substitute Firm 2's reaction function into Firm 1's profit function and determine Firm 1's profit-maximising choice of p₁. (d) What price will Firm 2 choose? (e) Draw a diagram with p₁ measured on the horizontal axis and p2 on the vertical axis. Sketch the reaction function for Firm 2 in your diagram, and indicate the point corresponding to the values of p₁ and p2 that you found in (c) and (d). (f) Does this market have a first-mover or a second-mover advantage?