The cost curve which is a rectangular hyperbola is:

Question

Accepted Answer

The correct answer to the question is Option 3: AFC curve. Let's delve into the reasoning behind this choice and why the other options are incorrect.

### Explanation for Option 3: AFC Curve

The Average Fixed Cost (AFC) curve is a rectangular hyperbola. This is because the AFC is calculated by dividing the Total Fixed Cost (TFC) by the quantity of output produced (Q). Mathematically, it is expressed as:

$$ \text{AFC} = \frac{\text{TFC}}{Q} $$

As the quantity of output increases, the AFC decreases, but it never reaches zero. This relationship creates a hyperbolic shape when plotted on a graph. The curve approaches both axes asymptotically, meaning it gets closer and closer to the axes but never actually touches them. This characteristic is what defines a rectangular hyperbola.

### Explanation for Why Other Options are Incorrect

1. **Option 1: TFC Curve**
   - The Total Fixed Cost (TFC) curve is a horizontal line on a graph because fixed costs do not change with the level of output. They remain constant regardless of the quantity produced. Therefore, it cannot be a rectangular hyperbola.

2. **Option 2: TVC Curve**
   - The Total Variable Cost (TVC) curve typically has a positive slope, reflecting the increase in variable costs as output increases. It is generally upward sloping and not hyperbolic. The TVC curve does not exhibit the characteristics of a rectangular hyperbola.

3. **Option 4: AVC Curve**
   - The Average Variable Cost (AVC) curve is typically U-shaped due to the law of diminishing returns. Initially, AVC decreases as output increases, reaches a minimum point, and then starts to increase. This U-shape is not characteristic of a rectangular hyperbola.

In conclusion, the AFC curve is the only one among the options that forms a rectangular hyperbola due to its mathematical relationship with output quantity. This justifies why Option 3 is the correct answer.