Question

Explain why the gap between ProPainters' total cost and total variable cost is the same no matter how many houses are painted.

Short answer

The gap between TC and TVC is the Fixed Costs, which remain constant.

Step-by-step solution

- Define Total Cost (TC)

Total Cost (TC) is the sum of all costs incurred by a business to produce a certain output. It includes both fixed costs (FC) and variable costs (VC). Mathematically, this is expressed as: \[ TC = FC + VC \]

- Define Total Variable Cost (TVC)

Total Variable Cost (TVC) consists of costs that vary directly with the level of output. As more houses are painted, variable costs like paint, labor, and other materials increase.

- Identify Fixed Costs (FC)

Fixed Costs (FC) are costs that do not change with the level of output. These might include rent, salaries of permanent staff, and costs of equipment. These costs remain constant regardless of the number of houses painted.

- Calculate the Gap (TC - TVC)

To find the gap between Total Cost (TC) and Total Variable Cost (TVC), we use the equation derived in Step 1: \[ TC - TVC = (FC + VC) - VC = FC \]Thus, the gap is just the Fixed Costs (FC).

- Interpret the Result

Since Fixed Costs (FC) are constant and do not vary with the output, the gap \( TC - TVC \) will remain the same regardless of the number of houses painted. This is because only variable costs change with output.

Key concepts

Fixed Costs

Fixed costs (FC) are expenses that remain constant regardless of how much output a company produces. For ProPainters, these might include:

• Rent for the workspace
• Salaries of permanent administrative staff
• Depreciation on painting equipment

No matter how many houses ProPainters paints, these costs do not change. They are independent of the business activity level and must be paid even if no houses are painted. This consistency makes fixed costs an important consideration when calculating the total cost.

Variable Costs

Variable costs (VC) change in direct proportion to the level of output. The more houses ProPainters paints, the higher these costs will be. Common examples for ProPainters include:

• Cost of paint and other materials
• Wages for temporary painting crews
• Transportation and fuel costs

If ProPainters doesn't paint any houses, these costs can drop to zero. Conversely, as the number of painted houses increases, the variable costs will rise correspondingly. This direct relationship with output level is what differentiates variable costs from fixed costs.

Calculation of Total Cost

The total cost (TC) is the sum of both fixed and variable costs. Mathematically, it is expressed as:
\[ TC = FC + VC \]
For ProPainters, the total cost to paint a certain number of houses includes all fixed costs plus the variable costs that vary with the number of houses painted. To find the gap between total cost (TC) and total variable cost (TVC), use this equation:
\[ TC - TVC = (FC + VC) - VC = FC \]
This shows that the gap is equal to the fixed costs (FC), which do not change with the number of houses painted. For example, if the fixed costs are \(1,000, this difference, or 'gap', will always be \)1,000 no matter how many houses are painted. This makes it clear why the gap between total cost and total variable cost remains the same regardless of output volume.