Consider the following average variable cost of XYZ company

Consider the following average variable cost of XYZ company:

AVC = 20-3Q+0.25Q2

A. What is the marginal cost?

B. At what output is AVC minimum?

C. What is the minimum value for AVC?

D. If price (P) = $15, should this firm continue to operate or shut down?

a) If AVC = 20-3Q+0.25Q²

TVC = AVC*Q = 20Q-3Q²+0.25Q³

MC = Differentiation of TVC w.r.t.Q

MC = 20-6Q+0.5Q²

b) AVC is minimum when first derivative of AVC is zero and second derivative is positive

First derivative of AVC = -3+0.5Q = 0

0.5Q = 3

Q = 30/5 = 6 units.

c) 20-3(6)+0.25(36)

20-18+9 = 11

d) Firm should continue to operate because price is more than minimum of AVC. It means, firm is able ot recover its variable cost.