Question

A firm has a Total Cost function that depends on its output Q: T C ( Q ) = 62 + 17 Q - 2.8 Q^2 + 0.42 Q^3 To the nearest $0.01/unit (no $ sign), what is the firm's Exit Quantity (optimal production at the Exit Price)?

Answer 1

Given, TC = 62 + 17Q – 2.8Q^2 + 0.42Q^3

Total variable cost (TVC) = 17Q – 2.8Q^2 + 0.42Q^3

AVC = TVC / Q = (17Q – 2.8Q^2 + 0.42Q^3) / Q

                        = 17 – 2.8Q + 0.42Q^2

The exit price is AVC. Optimal production could be found if the derivative of AVC is 0.

(d/dQ) AVC = (d/dQ) [17 – 2.8Q + 0.42Q^2]

0 = 0 – 2.8 + (0.42 × 2) Q ^(2 – 1)

0 = 0 – 2.8 + 0.84Q

0.84Q = 2.8

Q = 2.8 / 0.84

    = 3.33

The required quantity is 3.33 units.