Question

Peter’s Pipers produces plumbing pipe. The long-run total cost of Peter’s pipes is LTC = 20,000Q – 200Q² + Q³, where Q is measured as thousands of feet of piping. The long-run marginal cost of Peter’s pipes is given as LMC = 20,000 – 400Q + 3Q².

Divide total cost by Q to obtain Peter’s long-run average cost of producing pipe.

Answer 1

The long-run average cost for Peter's Pipers is found by dividing the long-run total cost by quantity, resulting in the formula LRAC = 20,000 - 200Q + Q². This equation shows the cost per thousand feet of piping as quantity varies.

Step-by-step explanation:

To calculate the long-run average cost (LRAC) for Peter's Pipers, we simply divide the long-run total cost (LTC) by the quantity (Q). The formula given for the long-run total cost is LTC = 20,000Q - 200Q² + Q³. To find the LRAC, we take this formula and divide each term by Q, resulting in:

LRAC = (20,000Q - 200Q² + Q³) / Q

Breaking it down, we get:

LRAC = 20,000 - 200Q + Q²

This equation represents Peter's long-run average cost of producing plumbing pipe measured in thousands of feet. As Q changes, this formula will show how the cost per thousand feet of pipe will vary.

The marginal cost (MC) is related but distinct from average cost; it measures the additional cost of producing one more unit of output. It's important to know when analyzing production decisions, as it can determine the most economically efficient point of production.