Understanding Average Fixed Cost (AFC)

Average Fixed Cost (AFC) is defined as the total fixed cost (TFC) divided by the quantity of output produced (Q). Fixed costs are costs that do not change with the level of output, such as rent, salaries of permanent staff, and depreciation of machinery. The formula for AFC is:

\( AFC = \frac{TFC}{Q} \)

Since TFC is a constant value, the AFC depends inversely on the quantity of output. As the output (Q) increases, the fixed cost (TFC) is spread over a larger number of units, causing the Average Fixed Cost (AFC) per unit to decrease. Conversely, as output decreases, AFC increases.

Analyzing Statements about Average Fixed Cost

Let's examine each statement provided regarding the Average Fixed Cost (AFC) of a firm:

Statement (i): Its slope is always negative.

As discussed, when output (Q) increases, Average Fixed Cost (AFC) decreases, assuming TFC is positive. This inverse relationship between Q and AFC means that the curve representing AFC against output slopes downwards from left to right. A downward-sloping curve has a negative slope.

For example, if TFC = $100:

• If Q = 1, AFC = $100/1 = $100
• If Q = 2, AFC = $100/2 = $50
• If Q = 4, AFC = $100/4 = $25

As Q increases from 1 to 4, AFC decreases from $100 to $25. This shows a clear negative relationship.

Therefore, this statement is correct.

Statement (ii): Its slope is always greater than one.

As established, the slope of the Average Fixed Cost (AFC) curve is negative. A negative number is always less than a positive number like one. Therefore, the slope cannot be greater than one.

This statement is incorrect.

Statement (iii): Its slope is always equal to one.

Again, the slope of the Average Fixed Cost (AFC) curve is negative, not positive. Therefore, the slope cannot be equal to positive one.

This statement is incorrect.

Statement (iv): Elasticity with respect to output is equal to one.

Elasticity of Average Fixed Cost (AFC) with respect to output (Q) measures the percentage change in AFC resulting from a one percent change in Q. The formula for point elasticity is:

\( E_{AFC,Q} = \frac{\text{% Change in AFC}}{\text{% Change in Q}} = \frac{\frac{\text{d}AFC}{AFC}}{\frac{\text{d}Q}{Q}} = \frac{\text{d}AFC}{\text{d}Q} \cdot \frac{Q}{AFC} \)

We know \( AFC = \frac{TFC}{Q} \). Let's find the derivative of AFC with respect to Q:

\( \frac{\text{d}AFC}{\text{d}Q} = \frac{\text{d}}{\text{d}Q} \left( \frac{TFC}{Q} \right) = \frac{\text{d}}{\text{d}Q} (TFC \cdot Q^{-1}) \)

Using the power rule, \(\frac{\text{d}}{\text{d}Q}(Q^n) = nQ^{n-1}\):

\( \frac{\text{d}AFC}{\text{d}Q} = TFC \cdot (-1) Q^{-2} = -\frac{TFC}{Q^2} \)

Now, substitute this into the elasticity formula:

\( E_{AFC,Q} = \left( -\frac{TFC}{Q^2} \right) \cdot \frac{Q}{\frac{TFC}{Q}} \)

Simplify the expression:

\( E_{AFC,Q} = -\frac{TFC}{Q^2} \cdot \frac{Q^2}{TFC} = -1 \)

The elasticity of Average Fixed Cost (AFC) with respect to output is always -1. This indicates that a 1% increase in output leads to a 1% decrease in AFC. Statement (iv) claims the elasticity is equal to one, which is incorrect, as the elasticity is -1.

The AFC curve is a rectangular hyperbola, meaning that the product of AFC and Q (which is TFC) is constant. For any rectangular hyperbola \( xy = k \), the elasticity of y with respect to x is always -1.

This statement is incorrect.

Summary of Statement Analysis

Based on the analysis, only statement (i) is correct.

Conclusion on Average Fixed Cost Properties

The Average Fixed Cost (AFC) curve is always downward sloping, indicating a negative slope. This is because fixed costs are spread over increasing output, reducing the per-unit cost. The elasticity of AFC with respect to output is consistently -1, reflecting the rectangular hyperbola shape of the curve.

Therefore, only statement (i) accurately describes a property of the Average Fixed Cost (AFC) curve.

Correct Option

Based on the analysis, the correct option is the one stating that only statement (i) is correct.

Revision Table: Average Fixed Cost Facts

Additional Information: Fixed and Variable Costs

In the short run, a firm's total cost (TC) is divided into Total Fixed Cost (TFC) and Total Variable Cost (TVC).

• Total Fixed Cost (TFC): These costs do not change with the level of output. Examples include rent, insurance premiums, and salaries of administrative staff. TFC is constant regardless of whether the firm produces zero output or a large quantity.
• Total Variable Cost (TVC): These costs change with the level of output. Examples include raw material costs, wages for production workers, and electricity used in production. TVC is zero when output is zero and increases as output increases.

Total Cost (TC) = TFC + TVC.

Average costs are calculated by dividing the total costs by the quantity of output:

• Average Total Cost (ATC) = TC / Q = (TFC + TVC) / Q = AFC + AVC
• Average Variable Cost (AVC) = TVC / Q
• Average Fixed Cost (AFC) = TFC / Q

Understanding the behavior of these different cost curves, including the Average Fixed Cost (AFC) curve, is fundamental to analyzing a firm's production decisions and profitability in microeconomics.