Calculation of TC, ATC, FC, AFC, VC and AVC

Microeconomic Decision‑Makers – Firms' Costs, Revenue and Objectives

1. Why cost calculations matter

Understanding the different types of cost enables a firm to:

• Determine the level of output that maximises profit.
• Make short‑run production decisions (e.g., whether to increase or decrease output).
• Set appropriate pricing strategies in competitive markets.
• Assess the impact of changes in input prices or technology.

2. Key cost concepts

The following terms are fundamental for any cost analysis:

• Fixed Cost (FC) – Costs that do not vary with output (e.g., rent, salaries of permanent staff).
• Variable Cost (VC) – Costs that change directly with the level of output (e.g., raw materials, hourly wages).
• Total Cost (TC) – The sum of fixed and variable costs: \$TC = FC + VC\$
• Average Fixed Cost (AFC) – Fixed cost per unit of output: \$AFC = \frac{FC}{Q}\$
• Average \cdot ariable Cost (A \cdot C) – Variable cost per unit of output: \$A \cdot C = \frac{VC}{Q}\$
• Average Total Cost (ATC) – Total cost per unit of output: \$ATC = \frac{TC}{Q} = AFC + A \cdot C\$

3. Relationship between the cost curves

In a typical short‑run diagram:

• The AFC curve declines as output rises because the same fixed cost is spread over more units.
• The A \cdot C curve is U‑shaped due to diminishing marginal returns.
• The ATC curve lies above the A \cdot C curve and is also U‑shaped, reflecting the addition of AFC to A \cdot C.

4. Calculating each cost type – Step‑by‑step method

1. Identify the total fixed cost (FC) for the period.
2. Identify the total variable cost (VC) for each level of output (Q).
3. Compute total cost: \$TC = FC + VC\$.
4. Calculate average costs:

   • \$AFC = \frac{FC}{Q}\$
   • \$A \cdot C = \frac{VC}{Q}\$
   • \$ATC = \frac{TC}{Q}\$

5. Example calculation

Suppose a small bakery has the following data for a week:

Fixed cost (FC) for the week is £500 (rent, equipment depreciation, manager’s salary).

Calculate TC, AFC, A \cdot C and ATC for each output level.

Interpretation:

• As output rises, AFC falls sharply because the fixed cost is spread over more loaves.
• A \cdot C falls initially (economies of scale) then begins to rise slightly, indicating the onset of diminishing marginal returns.
• ATC follows the combined pattern, reaching its minimum where the firm is most efficient.

6. Common pitfalls to avoid

• Confusing total cost with average cost – remember TC is a monetary total, ATC is cost per unit.
• Including fixed cost in the variable cost column – FC must remain constant regardless of output.
• Dividing by zero – AFC and A \cdot C are undefined at Q = 0; the cost curves start from the first positive output level.
• For short‑run analysis, treat at least one input as fixed; in the long run, all inputs become variable and FC = 0, so ATC = A \cdot C.

7. Quick revision checklist

1. Write down the formula for each cost concept before attempting a calculation.
2. Check that FC is the same for every output level in the short run.
3. Calculate \cdot C first, then add FC to obtain TC.
4. Derive average costs by dividing the appropriate total cost by Q.
5. Plot the resulting values to visualise the shape of the cost curves.

8. Extension – Linking costs to revenue

Profit (\$\pi\$) is the difference between total revenue (TR) and total cost (TC):

\$\pi = TR - TC\$

Where total revenue is price (P) multiplied by quantity (Q):

\$TR = P \times Q\$

In the short run, a firm should continue producing as long as:

\$TR \geq \cdot C \quad \text{(i.e., } P \geq A \cdot C\text{)}\$

In the long run, the condition becomes:

\$TR \geq TC \quad \text{(i.e., } P \geq ATC\text{)}\$

These criteria help students answer typical IGCSE exam questions on profit maximisation and shutdown decisions.