Always Round Tire's new division, Start-up Batteries, finds that its total cost curve, TC = 300 + 2Q + 2Q2 and its demand curve, P = 130 ? 2Q. If the division is operated as an independent profit center, what will be the price and quantity sold each day? Will the division make a profit? If the division is operated purely as a revenue center, how many batteries will they sell each day? If the division is operated as a cost center and told to produce 20 batteries per day, what would be the cost per battery?

Question

What will be an ideal response?

Answer 1

Using a calculus approach, marginal cost is the first derivative of TC: MC = 2 + 4Q. From the demand curve, we know that MR = 130 ? 4Q. Setting MR=MC and solving for Q yields the profit maximizing output of Q = 16 batteries per day. To sell this quantity of batteries, the price should be $98 per battery. The resulting total cost will be $844 per day and total revenue $1,568, yielding a profit. 

If the division operates as a Revenue Center, it will maximize total revenue. Assuming it has pricing authority, the division will choose a price and output accordingly. Maximum total revenue occurs at an output where MR = 0, or 130 ? 4Q = 0, or Q=32.5 batteries. 

If the division operates as a cost center with a target of Q = 20, TC = 300 + 2(20) + 2(20)2 = $1,140. The cost per battery is $1,140/20 = $57.