Average Cost, Marginal Cost, and Cost Curves in Microeconomics

Concept: The Relationship Between Average Cost and Marginal Cost

Definitions and Key Relationships

Understanding the relationship between average cost (AC) and marginal cost (MC) is essential in microeconomics, especially when analyzing production decisions and cost curves.

• Average Cost (AC): The total cost divided by the number of units produced. It represents the cost per unit on average.

• Marginal Cost (MC): The additional cost incurred by producing one more unit of output.

• Relationship: The average cost will rise or fall depending on the marginal cost of the next unit.

Key Points:

• If MC > AC, the average cost will increase when producing another unit.

• If MC < AC, the average cost will decrease when producing another unit.

Example: Semester and Cumulative GPA Analogy

This analogy helps illustrate how marginal changes affect averages:

Semester	Semester GPA	Cumulative GPA
1	3.00	3.00
2	3.50	3.25
3	2.00	2.83
4	4.00	3.13

• When the semester GPA (marginal) is higher than the cumulative GPA (average), the cumulative GPA increases.

• When the semester GPA is lower than the cumulative GPA, the cumulative GPA decreases.

Patterns in MC, AFC, AVC, and ATC Curves

Cost Curve Definitions

• Fixed Cost (FC): Costs that do not change with output.

• Variable Cost (VC): Costs that change with output.

• Total Cost (TC): $TC = FC + VC$

• Average Fixed Cost (AFC): $AFC = \frac{FC}{Q}$

• Average Variable Cost (AVC): $AVC = \frac{VC}{Q}$

• Average Total Cost (ATC): $ATC = \frac{TC}{Q} = AFC + AVC$

• Marginal Cost (MC): $MC = \frac{\Delta TC}{\Delta Q}$

Tabular Comparison of Cost Curves

Output (Pizzas)	Fixed Cost	Variable Cost	Total Cost	Marginal Cost	AFC = FC/Q	AVC = VC/Q	ATC = TC/Q
0	100	0	100	-	-	-	-
1	100	50	150	50	100.00	50.00	150.00
2	100	90	190	40	50.00	45.00	95.00
3	100	120	220	30	33.33	40.00	73.33
4	100	140	240	20	25.00	35.00	60.00
5	100	150	250	10	20.00	30.00	50.00

Patterns:

• As output increases, AFC falls (spreads fixed cost over more units).

• As output increases, AVC falls then rises (due to diminishing returns).

• As output increases, ATC falls then rises (reflects both AFC and AVC behavior).

• As output increases, MC falls then rises (due to marginal productivity changes).

Practice Questions and Applications

Question 1: Marginal and Average Cost Change

A firm is producing 100 units at an average total cost of $44 and a marginal cost of $32. If it increases production to 101 units, which is true?

• Answer: Average total cost would decrease (since MC < ATC).

Question 2: Government Imposes a Fixed Fee

The government imposes a $10,000 per year inspection fee on all restaurants. Which cost curves are affected?

• Answer: Average total cost and average fixed cost (fixed costs increase, affecting ATC and AFC).

Question 3: Marginal and Average Cost at Higher Output

A firm produces 1,500 units at a total cost of $15,000. If it increases production to 1,501 units, total cost rises to $15,012. What is true?

• Marginal cost: $MC = \frac{15,012 - 15,000}{1,501 - 1,500} = 12$

• Average total cost: $ATC = \frac{15,012}{1,501} \approx 10$

• Answer: Marginal cost is $12 and average total cost is $10.

Summary Table: Cost Curve Effects

Cost Curve	Affected by Fixed Cost Change?	Affected by Variable Cost Change?
Average Fixed Cost (AFC)	Yes	No
Average Variable Cost (AVC)	No	Yes
Average Total Cost (ATC)	Yes	Yes
Marginal Cost (MC)	No	Yes

Additional info:

• These concepts are foundational for understanding cost minimization and profit maximization in microeconomics.

• Cost curves are used to analyze firm behavior in both short-run and long-run production decisions.