Cost Function And Marginal Cost

The cost function is

Marginal Cost (MC) is the derivative of the cost function with respect to :

Substitute :

Average Cost (AC) is the total cost divided by the quantity:

Substitute :

=

Hence, the correct answer is (c) and .

Given the cost function, we can calculate:

After calculating the values when , the correct order from smallest to largest is:
Hence, the correct answer is (b).

Step 1: Integrate the marginal cost function.
The total cost function is the integral of the marginal cost function . The marginal cost is given by: Integrating with respect to , we get: where is the constant of integration.

Step 2: Apply the fixed cost.
We are given that the fixed cost is 75, so when , . Thus:

Step 3: Conclusion.
Therefore, the total cost function is:

Step 1: Understanding the relationship.
The relationship between marginal cost (MC) and average cost (AC) is important in understanding cost behavior for a firm. The slope of AC and the relationship with MC helps in determining the behavior of cost at different levels of output.

Step 2: Analysis of options.
- (A) Slope of AC = : This is correct. The slope of the average cost curve is related to the difference between average cost and marginal cost.
- (B) and (C) are incorrect interpretations.
- (D) is incorrect as it involves an incorrect formula for the relationship.

Step 3: Conclusion.
The correct expression for the slope of AC in relation to MC is .