Understanding the Cost Function

The total cost function, denoted as $c(y)$, represents the total expenses incurred in producing a certain quantity of output, $y$. This total cost is typically broken down into two components:

• Total Fixed Cost (TFC): Costs that do not change with the level of output. These costs are incurred even if the production is zero.
• Total Variable Cost (TVC): Costs that vary directly with the level of output. These costs are zero when production is zero.

The relationship is expressed as: $c(y) = TFC + TVC$

Identifying Fixed and Variable Costs

Given the cost function $c(y) = y^2 + 1$:

• The constant term, $1$, represents the Total Fixed Cost (TFC). So, $TFC = 1$.
• The term that depends on the quantity $y$, which is $y^2$, represents the Total Variable Cost (TVC). So, $TVC = y^2$.

Calculating Average Variable Cost (AVC)

Average Variable Cost (AVC) is calculated by dividing the Total Variable Cost (TVC) by the quantity of output ($y$). The formula is:

Substituting the TVC identified from the cost function:

Simplifying the expression:

Therefore, the Average Variable Cost (AVC) for the given cost function is $y$. This matches option 4.