Suppose the daily demand for Coke and Pepsi in a small city are given by Q_C = 90 - 100P_C + 400(P_P - P_C)and Q_P = 90 - 100P_P + 400(P_C - P_P),where Q_C and Q_P are the number of cans Coke and Pepsi sell,respectively,in thousands per day.P_C and P_P are the prices of a can of Coke and Pepsi,respectively,measured in dollars.The marginal cost is $0.45 per can for both Coke and Pepsi.What is the Nash equilibrium price for Coke? A) $0.016 B) $0.45 C) $0.53 D) $0.38

Question

Quizplus · Accepted Answer

To find the Nash equilibrium price for Coke, we need to find the price at which neither Coke nor Pepsi has an incentive to change their price, assuming the other firm's price is fixed. Mathematically, this occurs when each firm's profit is maximized given the other firm's price. The profit function for Coke is: πC = (P_C - 0.45)Q_C πC = (P_C)(90 - 100P_C + 400(P_P - P_C)) - 0.45Q_C Similarly, the profit function for Pepsi is: πP = (P_P - 0.45)Q_P πP = (P_P)(90 - 100P_P + 400(P_C - P_P)) - 0.45Q_P To find the Nash equilibrium, we need to solve for the prices that maximize each firm's profit given the other firm's price. This can be done by setting the derivative of each firm's profit function with respect to price equal to zero and solving for price. Taking the derivative of πC with respect to P_C and setting it equal to zero, we get: 90 - 300P_C + 400P_P - 0.9 = 0 Taking the derivative of πP with respect to P_P and setting it equal to zero, we get: 90 - 300P_P + 400P_C - 0.9 = 0 Solving these two equations simultaneously, we get: P_C = $0.53 P_P = $0.53 Therefore, the Nash equilibrium price for Coke is $0.53. This means that both Coke and Pepsi will sell their product at $0.53, since neither has an incentive to change their price given the other firm's price.

Suppose the Daily Demand for Coke and Pepsi in a Small