In: Economics
A firm’s total cost curve is T C = Q 3 – 6 0 Q 2 + 91 0 Q + 15 0. Its marginal cost is 3 Q 2 – 12 0 Q + 91 0. Find the firm’s fixed cost, variable cost, average total cost, and average variable cost. Find the output level at which average variable cost is minimized.
TC= Q^3- 60.Q^2 + 910Q +150
MC= ∆TC/∆Q
MC= 3.Q^2-120Q+910
Fixed cost= Cost which is independent of output Q
Fixed cost= 150
Variable cost= Cost which depends on output Q
Variable cost= Q^3- 60.Q^2 + 910Q
Average total cost= TC/Q
ATC= [Q^3 - 60Q^2 +910Q+150]÷Q
ATC= Q^2 -60Q +910 +(150/Q)
Average variable cost= Variable cost/Q
AVC= [ Q^3- 60Q^2 +910Q] ÷ Q
AVC= Q^2 -60Q +910
AVC is minimised when AVC= MC
Q^2- 60Q +910 = 3Q^2 -120Q + 910
2Q^2-60Q=0
2Q(Q-30) = 0
Q= 30
At, Q=30 AVC is minimised.