Question

Consider the inverse market demand below for a market with two dominant firms:

P=200-3(Q1+Q2)
The first firm has the following total cost function: TC1=26Q1
The second firm has a different total cost function: TC2=32Q2
Which firm has the lowest average total cost? How about the firm with the lowest marginal cost?

Answer 1

The first firm has the lowest average total cost with a value of 26. The first firm also has the lowest marginal cost with a value of 26.

Step-by-step explanation:

In order to determine which firm has the lowest average total cost, we need to calculate the average total cost for each firm. The average total cost is calculated by dividing the total cost by quantity. For the first firm, the total cost function is TC1=26Q1. So, the average total cost for the first firm is TC1/Q1 = (26Q1)/Q1 = 26. Therefore, the first firm has an average total cost of 26.

For the second firm, the total cost function is TC2=32Q2. So, the average total cost for the second firm is TC2/Q2 = (32Q2)/Q2 = 32. Therefore, the second firm has an average total cost of 32.

Based on these calculations, the first firm has the lowest average total cost with a value of 26.

To determine which firm has the lowest marginal cost, we need to calculate the marginal cost for each firm. The marginal cost is calculated by dividing the change in total cost by the change in quantity. Since the total cost function for the first firm is TC1=26Q1, the marginal cost for the first firm is the derivative of the total cost function with respect to quantity, which is 26. Therefore, the first firm has the lowest marginal cost with a value of 26.