A small nation has three gasoline suppliers with a linear monthly market demand equal to: Q = 500,000 - 5P. Each firm's marginal cost (MC)and average total cost (ATC)curves are horizontal at $10,000 per month.
-Refer to the information above. If the firms' managers form a price- fixing cartel that maximizes the firms' total profit, what is the total quantity produced by all firms?

Question

Quizplus · Accepted Answer

To maximize total profit, the cartel must act as a monopolist and charge a price that maximizes the total revenue. The monopolist's MR curve will be twice as steep as the demand curve. Therefore, the monopolist will produce where MR = MC. Since the three firms have identical cost curves, each firm will produce the same quantity.

First, we need to find the market equilibrium price and quantity:
500,000 - 5P = Q
500,000 - 5P = 3(10,000)
P = $90,000
Q = 500,000 - 5($90,000) = 50,000

Now that we know the market equilibrium price and quantity, we can find the quantity produced by each firm when acting as a monopolist:
MR = 500,000 - 10Q
500,000 - 10Q = 10,000
Q = 49,500
Each firm produces 49,500, so the total quantity produced by all firms is 3 x 49,500 = 148,500. However, this is less than the market equilibrium quantity of 50,000 x 3 = 150,000. Therefore, the cartel is not producing enough to maximize total profit.

To find the correct quantity, we need to find the point where MC = MR:
MC = $10,000
500,000 - 10Q = 10,000
Q = 49,500
Therefore, each firm produces 49,500, so the total quantity produced by all firms is 3 x 49,500 = 148,500. This is the quantity that maximizes total profit.

A Small Nation Has Three Gasoline Suppliers with a Linear