What are the formulas for variable cost and average variable cost for the startup?

A) $VC(q) = 300q + 2q^2$; $AVC(q) = \frac{300q + 2q^2}{q}$

B) $VC(q) = 20000 + 300q + 2q^2$; $AVC(q) = \frac{20000 + 300q + 2q^2}{q}$

C) $VC(q) = 300q + 2q^2$; $AVC(q) = 300 + 2q$

D) $VC(q) = 20000 + 300q + 2q^2$; $AVC(q) = 20000 + 300q + 2q^2$

Question

22-03-2024
Business

High School

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What are the formulas for variable cost and average variable cost for the startup?

A) $VC(q) = 300q + 2q^2$; $AVC(q) = \frac{300q + 2q^2}{q}$

B) $VC(q) = 20000 + 300q + 2q^2$; $AVC(q) = \frac{20000 + 300q + 2q^2}{q}$

C) $VC(q) = 300q + 2q^2$; $AVC(q) = 300 + 2q$

D) $VC(q) = 20000 + 300q + 2q^2$; $AVC(q) = 20000 + 300q + 2q^2$

Answer :

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Final answer:

The correct formula for calculating a startup's variable cost is VC(q) = 300q + 2q², and the average variable cost is AVC(q) = (300q + 2q²) / q. The formulas indicate that the costs depend on the quantity of goods produced and do not include fixed costs. Therefore, the correct option is (c).

Explanation:

When discussing a startup's costs, determining the variable cost (VC) and the average variable cost (AVC) is essential for understanding production expenses relative to output levels. The variable cost refers to expenses that vary with the level of output, which typically includes costs such as labor, materials, and utilities. The formula for VC that only considers variable components is VC(q) = 300q + 2q², where 'q' represents the quantity of goods produced.

The average variable cost is calculated by dividing the total variable cost (TVC) by the quantity of output (q). Thus, the formula for AVC would be AVC(q) = VC(q) / q. Substituting the VC formula into this, we get AVC(q) = (300q + 2q²) / q. Simplifying this, we find that AVC depends on the quantity produced and is represented as AVC(q) = 300 + 2q.

It’s important to note that fixed costs are not considered in the calculation of AVC, as they do not vary with output. Therefore, the correct options for the formulas are VC(q) = 300q + 2q² and AVC(q) = (300q + 2q²) / q, which corresponds to option (c).