Exercise 2 : Bertrand competition We consider two firms, denoted by 1 and 2, competing in price in the sense that they simultaneously choose their prices. The demand function is given by : DAP.P2) = 4-2, +Pje where i # j (1.2) The two firms have the same production technology such that their cost function is : C(q) = 45 where is the production of firm i = 1.2. 1. Determine cach firm's profit expression and its reaction function. 2. Draw the reaction functions in a graph (P2). 3. Determine the prices and decided at the Nash equilibrium. 4. Determine the equilibrium quantities and the associated profits. Questions: 1. What welfare criteria are usually used by economists! Explain their differences. 2. What may justify that some players use mixed strategies. Exercise 2 : Bertrand competition We consider two firms, denoted by 1 and 2, competing in price in the sense that they simultaneously choose their prices. The demand function is given by : DAP.P2) = 4-2, +Pje where i # j (1.2) The two firms have the same production technology such that their cost function is : C(q) = 45 where is the production of firm i = 1.2. 1. Determine cach firm's profit expression and its reaction function. 2. Draw the reaction functions in a graph (P2). 3. Determine the prices and decided at the Nash equilibrium. 4. Determine the equilibrium quantities and the associated profits. Questions: 1. What welfare criteria are usually used by economists! Explain their differences. 2. What may justify that some players use mixed strategies