Table 17-7
The information in the table below shows the total demand for internet radio subscriptions in a small urban market. Assume that each company that provides these subscriptions incurs an annual fixed cost of $20,000 (per year) and that the marginal cost of providing an additional subscription is always $16.
-Refer to Table 17-7. Assume there are two profit-maximizing internet radio providers operating in this market. Further assume that they are not able to collude on the price and quantity of subscriptions to sell. How many subscriptions will be sold altogether when this market reaches a Nash equilibrium?
A)2,000
B)3,000
C)4,000
D)5,000

Question

Table 17-7
The information in the table below shows the total demand for internet radio subscriptions in a small urban market. Assume that each company that provides these subscriptions incurs an annual fixed cost of $20,000 (per year) and that the marginal cost of providing an additional subscription is always $16. 
-Refer to Table 17-7. Assume there are two profit-maximizing internet radio providers operating in this market. Further assume that they are not able to collude on the price and quantity of subscriptions to sell. How many subscriptions will be sold altogether when this market reaches a Nash equilibrium?
A)2,000 
B)3,000 
C)4,000 
D)5,000

Quizplus · Accepted Answer

In a Nash equilibrium, each firm is maximizing its profit given the actions of the other firm. To find the Nash equilibrium in this scenario, we can use the following steps:

1. Assume that Firm 1 chooses to sell Q1 subscriptions, and Firm 2 chooses to sell Q2 subscriptions.

2. The total quantity demanded in the market is then Q1 + Q2.

3. Each firm's profit is given by (P - MC) * Q - FC, where P is the market price, MC is the marginal cost ($16), Q is the quantity sold, and FC is the fixed cost ($20,000).

4. To maximize profit, each firm will set its quantity such that MR = MC, where MR is the marginal revenue. In a competitive market, MR = P, but in this case, the market price will depend on the quantity sold by both firms.

5. We can use trial-and-error to find the Nash equilibrium. For example, if Firm 1 sells 1,000 subscriptions (Q1 = 1,000), then the total quantity demanded is 1,000 + Q2. If Firm 2 also sells 1,000 subscriptions (Q2 = 1,000), then the total quantity demanded is 2,000. The market price is then $8, as shown in the table. Each firm's profit is (8 - 16) * 1,000 - 20,000 = -12,000, which is negative. This means that both firms would be better off reducing their quantity.

6. We can repeat this process for different quantities until we find the combination that maximizes both firms' profit. The Nash equilibrium occurs when both firms sell 2,000 subscriptions each, for a total quantity of 4,000. The market price is then $7, and each firm's profit is (7 - 16) * 2,000 - 20,000 = $4,000.

Table 17-7 The Information in the Table Below Shows the Total Demand