Drawing and interpretation of diagrams that show how changes in output affect costs of production

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

Learning Objective

Draw and interpret diagrams that show how changes in output affect the costs of production.

Key Concepts

• 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\$
• Marginal Cost (MC): The additional cost of producing one more unit. \$MC = \frac{\Delta TC}{\Delta Q}\$
• Total Revenue (TR): Price multiplied by quantity sold. \$TR = P \times Q\$
• Marginal Revenue (MR): Additional revenue from selling one more unit. \$MR = \frac{\Delta TR}{\Delta Q}\$
• Profit (π): Difference between total revenue and total cost. \$\pi = TR - TC\$

Cost Curves – Shapes and Relationships

The following table summarises the typical shapes of the cost curves for a firm operating in the short run.

Step‑by‑Step Guide to Drawing the Cost Diagram

1. Draw the vertical (cost) and horizontal (output, Q) axes. Label the vertical axis “Cost (£)” and the horizontal axis “Output (Q)”.
2. Plot a horizontal line for Fixed Cost (FC) at the level of the firm’s fixed expenses.
3. From the origin, sketch an upward‑sloping curve for \cdot ariable Cost (VC). Ensure it is convex to reflect increasing marginal cost.
4. Add the Total Cost (TC) curve by vertically shifting the \cdot C curve upward by the amount of FC.
5. Derive the Average Fixed Cost (AFC) curve: a hyperbola that falls as Q increases.
6. Derive the Average \cdot ariable Cost (A \cdot C) curve: a U‑shaped curve that lies below the ATC curve.
7. Derive the Average Total Cost (ATC) curve: another U‑shaped curve that is the vertical sum of AFC and A \cdot C.
8. Plot the Marginal Cost (MC) curve: a U‑shaped curve that cuts the A \cdot C and ATC curves at their lowest points.
9. Label all curves clearly and indicate the points where MC intersects A \cdot C and ATC.

Interpreting Changes in Output

When a firm changes its level of output, the following interpretations apply:

• Increasing output from a low level: MC falls initially because of increasing marginal returns, causing A \cdot C and ATC to fall.
• Beyond the point of diminishing returns: MC rises, pulling A \cdot C and ATC upward. The firm’s cost per unit starts to increase.
• Impact on profit: Profit maximisation occurs where Marginal Revenue = Marginal Cost (MR = MC), provided price is above ATC at that output.
• Short‑run shutdown decision: If price falls below A \cdot C at the profit‑maximising output, the firm should shut down temporarily because it cannot cover variable costs.
• Long‑run entry/exit: In the long run, firms compare price with ATC. If price > ATC, firms earn economic profit and new firms may enter; if price < ATC, firms incur losses and may exit.

Example Calculation

Assume a firm has the following data:

From the table, calculate:

• Average Total Cost at Q = 20: \$ATC = \frac{TC}{Q} = \frac{£460}{20} = £23\$
• Marginal Cost between Q = 20 and Q = 30: \$MC = \frac{£590-£460}{30-20} = \frac{£130}{10} = £13\$
• Since price (£30) > MC (£13) and price > ATC (£23) at Q = 20, the firm should increase output to raise profit.

Summary Checklist for the Exam

• Know the definitions and formulas for FC, VC, TC, AFC, A \cdot C, ATC, MC, TR, MR and profit.
• Be able to sketch the seven cost curves on one diagram and label the key points (minimum A \cdot C, minimum ATC, MC intersections).
• Explain how a change in output moves the firm along the MC curve and how this affects A \cdot C and ATC.
• State the profit‑maximising rule (MR = MC) and the shutdown rule (P < A \cdot C).
• Interpret the diagram to answer questions about cost efficiency, economies of scale and short‑run decisions.

Suggested Practice Question

“A firm operates in a perfectly competitive market where the market price is £25 per unit. Using the diagram you have drawn, explain how the firm decides the profit‑maximising level of output and whether it should continue to produce in the short run if its average variable cost at that output is £22.”