Fixed, Variable, and Marginal Costs

Cost Concepts and Profit Maximization

• Firms operate to maximize total profit:

$\pi = TR - TC$

• Total Cost ($TC$): Composed of fixed and variable costs.
• Fixed Costs ($FC$): Costs that do not vary with output quantity (e.g., rent, building maintenance).
• Variable Costs ($VC$): Costs that vary directly with output quantity and variable inputs.

Average and Marginal Cost Metrics

• Average Fixed Cost ($AFC$): Fixed cost allocated per unit of output:

$AFC = \frac{FC}{Q}$

• Average Variable Cost ($AVC$): Variable cost per unit of output:

$AVC = \frac{VC}{Q}$

• Average Total Cost ($ATC$): Total cost per unit of output, calculable by dividing total cost by output or summing average fixed and average variable costs:

$ATC = \frac{TC}{Q} = AFC + AVC$

• Marginal Cost ($MC$): The change in total cost resulting from producing one additional unit of output:

$MC = \frac{\Delta TC}{\Delta Q}$

Cost Curve Characteristics

• Marginal Cost ($MC$): Rises as the quantity of output increases.
• Average Total Cost ($ATC$): Forms a distinct U-shaped curve.
• Curve Intersection: The $MC$ curve intersects the $ATC$ curve precisely at the minimum point of $ATC$.
• Average Fixed Cost ($AFC$): Continuously declines as output rises due to fixed expenses spreading across more units.

Short-Run vs. Long-Run Costs

• Cost flexibility depends entirely on the operating time horizon.
• Short-Run: At least one input remains fixed; capital (such as factory size) is fixed while labour remains variable.
• Long-Run: All inputs are variable, allowing firms to adjust factory scale, acquire land, or purchase additional machinery.