Question

Suppose a cost function of the form C(q)=aq³+bq²+cq+d where a=0.5,b=−4,c=20 and d=120 Assuming the firm is using resources efficiently, what is the total variable cost (VC) when q= 66?

Answer 1

To find the total variable cost (TVC) for q=66 with the cost function C(q)=0.5q³-4q²+20q+120, we calculate TVC=0.5(66³)-4(66²)+20(66) which results in TVC(66) = 129644.

Step-by-step explanation:

To calculate the Total Variable Cost (TVC) using the given cubic cost function C(q) = aq³ + bq² + cq + d, where q is the quantity, and substituting the provided values a, b, c, and d, the fixed cost component (d) must be excluded to derive the TVC. The TVC is the portion of total cost that varies with production level.

Substituting the values into the equation without the fixed cost yields TVC(q) = 0.5q³ - 4q² + 20q.

For q = 66:

\[ \text{TVC}(66) = 0.5(66^3) - 4(66^2) + 20(66) \]

Calculating this expression results in TVC(66) = 0.5(287496) - 4(4356) + 20(66) = 143748 - 17424 + 1320 = 129644.

Therefore, the Total Variable Cost for the given production quantity of q = 66 is 129,644 units.