Suppose there are two firms A and B in a duopol... - SS2 Economics Price And Quantity Determination Under Duopoly Question
Suppose there are two firms, A and B, in a duopoly market. The market demand and cost functions are given as follows:
Demand function: P = 100 - Q
Cost function: C = 20Q
where P is the market price, Q is the total quantity of goods produced by both firms, and C is the total cost of production. Assuming that firm A and firm B have equal production costs, what is the Nash equilibrium price and quantity in this duopoly market?
We need to determine the total quantity produced by both firms. Since each firm has equal production costs, they will produce the same quantity. Therefore, the total quantity produced, Q, can be written as
Q = QA + QB
We need to find each firm's profit-maximizing quantity given the other firm's quantity. Since the firms have equal costs, we can assume that they will split the market equally:
QA = (100 - QB - 20)/2
QB = (100 - QA - 20)/2
Solve for QA and QB where QA = QB.
Substituting QB = QA into the best response function for firm A, we get:
QA = (100 - QA - 20)/2
2QA = 80
QA = 40
Similarly, we can find QB = 40.
We need to calculate the market price, which can be found by substituting Q = 80 into the demand function:
P = 100 - Q
P = 100 - 80
P = 20
Thus, the Nash equilibrium price and quantity in this duopoly market are P = 20 and Q = 80, respectively.
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