The inverse demand function on the route is P=40-2(qA + qB)
The Correct Answer and Explanation is:
Correct Answer:
The inverse demand function is:
P=40−2(qA+qB)P = 40 – 2(q_A + q_B)P=40−2(qA+qB)
This function represents the price PPP as a function of the total quantity demanded on the route, where qAq_AqA and qBq_BqB are the quantities provided by Firm A and Firm B, respectively.
Explanation:
An inverse demand function expresses the price of a good as a function of the total quantity sold in the market. In this case, the inverse demand function is given by:P=40−2(qA+qB)P = 40 – 2(q_A + q_B)P=40−2(qA+qB)
Here, PPP denotes the market price of the service on a specific route, while qAq_AqA and qBq_BqB represent the quantities (such as the number of seats, flights, or units of service) offered by two competing firms, A and B.
The term (qA+qB)(q_A + q_B)(qA+qB) indicates that the price depends on the total quantity supplied in the market. This captures the effect of competition between the two firms. As the total quantity increases due to increased supply from either firm, the price falls. The coefficient of -2 shows the rate at which price decreases in response to an increase in quantity. For every additional unit of total quantity, the price drops by 2 units.
This type of linear inverse demand function is common in models of Cournot competition, where firms choose quantities simultaneously and independently to maximize profits. Each firm understands that its output decision affects the market price, but takes the output of the rival as given.
In equilibrium, each firm selects its optimal quantity based on the marginal revenue derived from this inverse demand function, minus its marginal cost. The strategic interaction between firms, influenced by this demand function, determines the equilibrium prices and quantities in the market.
This framework helps to analyze outcomes such as market efficiency, price sensitivity, and the welfare implications of competition. By modeling the interaction through an inverse demand curve, economic insights can be drawn about how firms’ decisions impact market prices and consumer surplus.
