Graphing Costs in Microeconomics: Cost Curves and Their Relationships

Graphing Costs in Microeconomics

Introduction to Cost Curves

Understanding cost curves is fundamental in microeconomics, especially when analyzing firm behavior and market structures. Cost curves illustrate how different types of costs change as output (quantity) varies. The main curves include Marginal Cost (MC), Average Total Cost (ATC), Average Variable Cost (AVC), and Average Fixed Cost (AFC).

Shape of the Cost Curves

• U-Shaped Curves: The MC, AVC, and ATC curves are typically U-shaped due to the law of diminishing marginal returns.

• AFC Curve: As output increases, the Average Fixed Cost (AFC) curve gets smaller and smaller, approaching zero but never touching the axis.

Key Cost Relationships

• Relationship of ATC, AVC, and AFC:

  • $ATC = AVC + AFC$

  • As output increases, the distance between ATC and AVC gets smaller because AFC decreases.

• Relationship of Marginal Cost and Average Cost:

  • The marginal cost curve crosses the ATC and AVC curves at their minimum points.

  • When marginal cost is below ATC and AVC, these averages are falling; when MC is above, they are rising.

Cost Table Example

The following table summarizes the relationships between output and various cost measures:

Total Quantity of Pizza	Marginal Cost per Pizza	ATC = TC/Q	AFC = FC/Q	AVC = VC/Q	ATC = TOC/Q or AVC + AFC
40	2.50	5.00	2.50	2.50	5.00
80	2.00	3.75	1.25	2.50	3.75
120	2.50	3.33	0.83	2.50	3.33
160	3.00	3.13	0.63	2.50	3.13
200	4.00	3.50	0.50	3.00	3.50

Definitions of Key Terms

• Total Cost (TC): The sum of fixed and variable costs at each level of output.

• Average Total Cost (ATC): Total cost divided by quantity produced. $ATC = \frac{TC}{Q}$

• Average Fixed Cost (AFC): Fixed cost divided by quantity produced. $AFC = \frac{FC}{Q}$

• Average Variable Cost (AVC): Variable cost divided by quantity produced. $AVC = \frac{VC}{Q}$

• Marginal Cost (MC): The increase in total cost from producing one more unit. $MC = \frac{\Delta TC}{\Delta Q}$

Examples and Applications

• Example 1: If average total cost is $10, quantity produced is 10, and total fixed cost is $100, then total variable cost is:

  • $ATC = \frac{TC}{Q} \Rightarrow TC = ATC \times Q = 10 \times 10 = 100$

  • $TC = TFC + TVC \Rightarrow TVC = TC - TFC = 100 - 100 = 0$

• Example 2: At a quantity of 100, if AFC is $2, then total fixed cost is $2 \times 100 = $200.

• Example 3: When a firm is producing zero output, total cost equals fixed cost, since variable cost is zero at zero output.

Summary Table: Cost Curve Relationships

Curve	Shape	Key Property
MC	U-shaped	Crosses ATC and AVC at their minimum points
ATC	U-shaped	Distance from AVC decreases as output increases
AVC	U-shaped	Always below ATC; gap narrows as output rises
AFC	Downward sloping	Declines as output increases

Practice Questions (with Answers)

1. If average total cost is $10, quantity produced is 10, and total fixed cost is $100, what is the total variable cost for the output of 10?

   • Answer: $0$

2. Based on the graph, at a quantity of 100, AFC is equal to:

   • Answer: $2$

3. When a firm is producing zero output, total cost equals:

   • Answer: Fixed cost

Additional info: The above notes expand on the graphical and tabular analysis of cost curves, providing definitions, relationships, and practice applications relevant to microeconomics students.