Question
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  1. A firm has an average cost function,
(a) Find an expression for the TC function and calculate TC when . 4 marks
(b) Write down the equations for FC and TVC.
2 marks
© Find an expression for the MC function.
3 marks
3. Find the maximum and/or minimum values (if any) for each of the functions below.
(a)
5 marks
(b)
5 marks
1
Question Two
  1. Find from the first principles of differentiation.
    (a)
2 marks
(b)
3 marks
2. Determine the intervals along which each of the following curves is increasing or decreasing (consider the positive half of the plane, )
(a)
5 marks
(b)
5 marks
3. Sketch the following functions over the stated interval.
(a)
5 marks
(b)
5 marks
Question Three
  1. Find the derivatives of the following functions;
    (a)
3 marks
(b)
3 marks
©
3 marks
2. The demand function for a good is given as .
(a) Write down expressions for the TR and MR functions.
2 marks
(b) Calculate the output at which TR is a maximum and confirm that marginal

Upstudy AI Solution

Tutor-Verified Answer

Answer

Question 2:
(a) Total Cost (TC) when is 2625.
(b) Fixed Cost (FC) is 150, and Total Variable Cost (TVC) is .
© Marginal Cost (MC) is .

Solution

Sure, let’s tackle Question 2 step by step.

Question 2

A firm has an average cost function:

(a) Find an expression for the TC function and calculate TC when . (4 marks)

Solution:
  1. Understanding the Relationship:
    The Average Cost (AC) is related to Total Cost (TC) by the formula:
    Therefore, to find TC, multiply AC by Q:
  2. Substituting the Given AC Function:
  3. Simplifying the Expression:
    So, the Total Cost (TC) function is:
  4. Calculating TC When :
    Substitute into the TC function:
    Therefore, when , .

(b) Write down the equations for FC and TVC. (2 marks)

Solution:
  1. Total Cost (TC) Breakdown:
  2. From the TC Function:
    • Fixed Cost (FC): This is the part of TC that does not depend on .
    • Total Variable Cost (TVC): This comprises all terms in TC that depend on .
Therefore:

© Find an expression for the MC function. (3 marks)

Solution:
  1. Marginal Cost (MC): It’s the derivative of Total Cost (TC) with respect to .
  2. Differentiate the TC Function:
    So,
Therefore, the Marginal Cost (MC) function is:

If you need assistance with the other questions or further clarifications, feel free to ask!

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To find the total cost (TC) function, recall that average cost (AC) is defined as TC divided by quantity (Q). Therefore, you can multiply the AC function by Q to get TC. For , substituting into the AC function gives you the TC value.
Now, let’s dive into fixed cost (FC) and total variable cost (TVC). Since fixed costs do not vary with output, you’ll assess the constant elements in your AC function at to find the FC. For TVC, subtract FC from TC, and you’ll have the variable costs related to changes in output.
If you’re looking for further understanding, consider exploring economic theory textbooks like “Microeconomics” by Pindyck and Rubinfeld for in-depth analysis and practical examples of cost functions and their applications in real-world situations. Or, for a lighter read, check out “Freakonomics” by Levitt and Dubner that examines unexpected economic outcomes and encourages thinking outside the box!

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