Question

Commercial Recording, Inc., is a manufacturer and distributor of reel-to-reel recording decks for commercial recording studios. Revenue and cost relations are: TC = $100,000 + $1,500Q + $0.1Q2 A) what is the total variable cost (TVC) at Q= 250? B) what is the average total cost (ATC) at Q=250? C) what is the average variable cost (AVC) at q= 250? D) what is the average fixed cost (AFC) at Q= 250? E) what is the marginal cost (MC) at Q= 250?  

Answer 1

As given  Revenue and cost relations are TC = $100,000 + $1,500Q + $0.1Q2 .

Total variable cost (TVC) at Q= 250.

MC = dTC/dQ = d($100,000 - $1,500Q +$0.1Q²)/dQ = -1,500+0.2Q

Assume MC equals to zero MC = 0

-1,500 + 0.2Q = 0

Q = 7,500 (As second derivative is greater than0, total cost is at minimum at output level of 7,500 units.)

Q is the level of output at whichtotal cost is minimizing. --> dMC/dQ = d(-1,500+0.2Q)/dQ = 0.2

B) AC = TC/Q = (100,000 - 1,500Q +0.1Q²)/Q = (100,000/Q) -1,500 + 0.1Q

AC is at its minimum when it isequal to MC.

Equating MC and AC -

-1,500 + 0.2Q = (100,000/Q) -1,500 +0.1Q

Q = 1,000 (The average cost minimizingoutput (Q) is 1,000 units.)