Question

A firm's total cost function is given by the equation: TC = 4000 + 5Q + 10Q2.

(1) Write an expression for each of the following cost concepts:

a. Total Fixed Cost

b. Average Fixed Cost

c. Total Variable Cost

d. Average Variable Cost

e. Average Total Cost

f. Marginal Cost

(2) Determine the quantity that minimizes average total cost and minimizing average variable cost.

(3) Why does its average variable cost curve achieve its minimum at a lower level of output than the average total cost curve?

Answer 1

Total Cost Function= TC = 4000 + 5Q + 10Q2.

1 Total fixed cost – The constant part of the equation is total fixed cost Ot means it will be 4000

2 . Average Fixed Cost= Total Fixed Cost/ Total Output

=4000/Q

3 Total Variable Cost= Except the Fixed cost all the other part of the Total Cost Function is total variable cost= 5Q + 10Q2.

4 Average Variable Cost= Total variable cost/total output

=(5Q + 10Q²)/Q

= 5 + 10Q

5 Average Total Cost = Total cost/Total output

   = (4,000 + 5Q + 10Q2)/Q

6 Marginal Cost= d(total Cost)/dQ

= d(4,000 + 5Q + 10Q²)/dQ

= 5 + 20Q