Price And Quantity Determination Under Duopoly - SS2 Economics Past Questions and Answers - page 1

(Each firm produces less goods in a duopoly. Both firms need to consider the potential reactions of their competitor before setting their own strategy. This leads to a situation where both firms may end up producing less and charging a higher price than what they would have in a monopoly)

In a duopoly, the pricing strategy is determined by the actions and responses of each firm's competitor, whereas in a monopoly, the pricing strategy is solely determined by the monopolist.

The quantity of goods produced in a duopoly is higher than in a price war, as both firms end up producing less than what they would have produced in a monopoly, but more than what they would have produced in a price war.

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.