Question 7 (2 points) Consider the following Bertrand competition model with cost asymmetries. Two chocolate bar...

Transcribed Image Text:

Question 7 (2 points) Consider the following Bertrand competition model with cost asymmetries. Two chocolate bar manufacturers, Firm 1 and Firm 2, face a market of 100 people. Each of these 100 people has a maximum willingness to pay for one chocolate bar of $20, and each will buy at most one chocolate bar. Each consumer will buy from whichever firm charges the lowest price. If the two firms charge the same price, they will each sell to half the market (i.e. to 50 people). Firm 1 has a constant marginal cost of production of c = 5, while Firm 2 has a constant marginal cost of production of c = 7. Firms can only choose integer prices, and will do so to maximise their expected profit. (a) (0.5 points) If Firm 2 chooses a price of 8, what is Firm 1's best response? (If Firm 1 has more than one best response, write the lowest price that constitutes a best response) (b) (0.5 points) If Firm 1 chooses a price of 8, what is Firm 2's best response? (If Firm 2 has more than one best response, write the lowest price that constitutes a best response) c) (0.5 points) If Firm 1 chooses a price of 4, what is Firm 2's best response? (If Firm 2 has more than one best response, write the lowest price that constitutes a best response) (d) (0.5 points) This game has one Nash equilibrium in which both firms charge the same price. What price do they charge in this Nash equilibrium? Question 7 (2 points) Consider the following Bertrand competition model with cost asymmetries. Two chocolate bar manufacturers, Firm 1 and Firm 2, face a market of 100 people. Each of these 100 people has a maximum willingness to pay for one chocolate bar of $20, and each will buy at most one chocolate bar. Each consumer will buy from whichever firm charges the lowest price. If the two firms charge the same price, they will each sell to half the market (i.e. to 50 people). Firm 1 has a constant marginal cost of production of c = 5, while Firm 2 has a constant marginal cost of production of c = 7. Firms can only choose integer prices, and will do so to maximise their expected profit. (a) (0.5 points) If Firm 2 chooses a price of 8, what is Firm 1's best response? (If Firm 1 has more than one best response, write the lowest price that constitutes a best response) (b) (0.5 points) If Firm 1 chooses a price of 8, what is Firm 2's best response? (If Firm 2 has more than one best response, write the lowest price that constitutes a best response) c) (0.5 points) If Firm 1 chooses a price of 4, what is Firm 2's best response? (If Firm 2 has more than one best response, write the lowest price that constitutes a best response) (d) (0.5 points) This game has one Nash equilibrium in which both firms charge the same price. What price do they charge in this Nash equilibrium?