Question

6. If TC= 50 + 20Q- 10Q2? +Q3, find TVC, AVC, MC. Also find the level of output at which MC is
minimum.​

Answer 1

Answer:

(a) TC= 120 + 50Q - 10Q2 +Q3

TVC = 50Q - 10Q2 +Q3

AVC = TVC / Q = 50 - 10Q + Q2

MC = 50 - 20Q + 3Q2

(b) AVC will be minimum where first derivative of AVC function is equal to 0.

=> -10 + 2Q = 0

=> 2Q = 10

=> Q = 10/2 = 5

The second derivative of AVC is 2. since second derivative of AVC is positive, it means AVC is U-shaped.

MC will be minimum where first derivative of MC function is equal to 0.

=> -20 + 6Q = 0

=> 6Q = 20

=> Q = 20/6 = 3.33 (let it be 3)

The second derivative of MC is 6. since second derivative of AVC is positive, it means MC is U-shaped.

(c) AVC = 50 - 10Q + Q2 = 50 - 10(5) + 52 = $25

MC = 50 - 20Q + 3Q2 = 50 - 20(5) + 3(5)2 = $25