Question

Stations A and B are the only gas stations in town and battle for customers according to Bertrand competition. MCA = 6 and MCB = 5 reflect costs for the stations. Resident demand for gasoline is defined by Q = 50 - P, where Q is the total quantity of gasoline demanded. If opportunity costs are zero and we assume that prices can only be set to the nearest dollar in this strange town, what is the output of each gasoline station?

Answer 1

In Bertrand's competition, each gas station sets its price based on its marginal cost. The output of gas station A is 44 and the output of gas station B is 45.

Step-by-step explanation:

In Bertrand's competition, each gas station sets its price based on its marginal cost. In this case, gas station A has a marginal cost of 6, and gas station B has a marginal cost of 5. The demand for gasoline in the town is given by Q = 50 - P, where Q is the quantity demanded and P is the price. The stations are only allowed to set prices to the nearest dollar.

To determine the output of each gas station, we need to find where their marginal costs intersect with the demand curve. At this point, the price will be set and the corresponding quantity will be their output.

Let's find the intersection for gas station A:

Marginal cost of gas station A (MCA) = 6

Demand curve: Q = 50 - P

Set MCA equal to the demand curve:

6 = 50 - P

Subtract 6 from both sides:

P = 44

So, the output of gas station A is 44.

Now, let's find the intersection for gas station B:

The marginal cost of gas station B (MCB) = 5

Demand curve: Q = 50 - P

Set MCB equal to the demand curve

5 = 50 - P

Subtract 5 from both sides:

P = 45

So, the output of gas station B is 45.