A firm’s total cost curve is T C = Q 3 – 6 0 Q 2...

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.

Solutions

Expert Solution

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.

Rahul Sunny answered 2 years ago

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