Answer to Question #297128 in Microeconomics for Fethi

Question

The total cost function of a firm is given by c = 100 + 40 q + 5q2.

A. Find Total fixed cost

B. Find the Marginal cost equation and the marginal cost of the 5th unit

C. Find Average variable cost equation and the AVC of the 4th unit

D. Find average fixed cost equation and the AVC of the 6th unit

E. Find average total cost equation and the ATC

Answer 1

Solution:

A.). Total fixed cost = 100

B.). Marginal cost = $\frac{\partial TC} {\partial Q} = 40 + 10Q$

The marginal cost of the 5^th unit = TC to produce 5 units – TC to produce 4 units

425 – 340 = 85

 

C.). Average variable cost = $\frac{Variable \; cost} {Q} = \frac{40q + 5q^{2} } {q} = 40 + 5q$

AVC of the 4^th unit = 60

 

D.). Average fixed cost equation = $\frac{TFC} {Q} = \frac{100} {Q}$

AVC of the 6^th unit = 70

 

E.). Average total cost equation = $\frac{TC} {Q} = \frac{100 + 40q + 5q^{2} } {q} = \frac{100} {q} + 40 + 5q$