Suppose the daily demand for Coke and Pepsi in a small city are given by and 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.What is the Nash equilibrium price for Pepsi? A) $.016 B) $0.45 C) $0.53 D) $0.38

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To find the Nash equilibrium, we need to find the point where neither firm has an incentive to change its price. This means that at the Nash equilibrium, each firm's profit must be maximized given the other firm's price. Let's assume that Pepsi is considering a price change. If Pepsi lowers its price, it will steal some of Coke's customers, but it will also make less profit on each can it sells. Conversely, if Pepsi raises its price, it will lose some of its customers to Coke but will make more profit on each can sold. To find the Nash equilibrium price, we need to find the point where Pepsi is indifferent between raising or lowering its price, given the price of Coke. In other words, Pepsi must be maximizing its profit with respect to its own price, holding Coke's price constant. The profit function for Pepsi is: Profit = P_P * Q_P - 0.45 * Q_P * (Q_P + Q_C) To find Pepsi's profit-maximizing price, we take the derivative of the profit function with respect to P_P and set it equal to zero: dProfit/dP_P = Q_P - 0.45 * (Q_P + Q_C) = 0 Solving for Q_P, we get: Q_P = 0.45 * Q_C / 0.55 Now, we can substitute the demand functions for Coke and Pepsi to find the quantities sold at the Nash equilibrium price: Q_P = 0.45 * (780 - 0.1 * P_C) / 0.55 Q_C = 780 - 0.1 * P_P Substituting for Q_P in the second equation, we get: Q_C = 525 + 0.05 * P_C Solving for P_C, we get: P_C = (780 - Q_C) / 10 P_C = (780 - (525 + 0.05 * P_C)) / 10 Solving for P_C, we get: P_C = $0.53 Therefore, the Nash equilibrium price for Pepsi is $0.53.

Suppose the Daily Demand for Coke and Pepsi in a Small