Short-Run Costs — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: Total fixed cost, total variable cost, average fixed cost, average variable cost, average total cost, marginal cost, the law of diminishing marginal returns, and the relationship between marginal and average short-run costs.

You should already know: The short-run/long-run production distinction, marginal product of variable inputs, basic marginal vs. average calculation rules.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Short-Run Costs?

In microeconomics, short-run costs are all production costs a firm faces when at least one input (most often capital, like factory space or equipment) is fixed and cannot be adjusted to change output. Unlike the long run, where all inputs are variable, the short run’s fixed input creates the split between fixed and variable costs that defines all short-run cost measures. According to the AP Microeconomics Course and Exam Description (CED), this topic makes up roughly 20% of Unit 3 (Production, Cost, and Perfect Competition), which itself accounts for 20-25% of the total AP exam score. Short-run cost concepts appear in both multiple-choice questions (MCQ) as standalone calculations or graph interpretation, and as a core required foundation for free-response questions (FRQ) covering perfect competition, firm supply, and profit calculation. Standard notation for this topic uses $Q$ for quantity of output, $TC$ for total cost, $TFC$ for total fixed cost, $TVC$ for total variable cost, $AFC$ for average fixed cost, $AVC$ for average variable cost, $ATC$ for average total cost, and $MC$ for marginal cost, with all values denominated in dollars.

2. Total and Average Short-Run Costs

All short-run costs are split into two categories: fixed costs and variable costs. Total fixed cost ($TFC$) is the cost of fixed inputs, which is constant at all output levels, including when output is zero. Firms incur $TFC$ even if they shut down temporarily in the short run. Total variable cost ($TVC$) is the cost of variable inputs (most often labor and raw materials), which increases with output because more output requires more variable inputs. Total cost is the sum of fixed and variable cost: $$TC=TFC+TVC$$ Average costs are per-unit cost measures, used to compare cost per unit to the market price to calculate profit. The three average cost definitions are: $$AFC=\frac{TFC}{Q}AVC=\frac{TVC}{Q}ATC=\frac{TC}{Q}=AFC+AVC$$ A key feature of average fixed cost is that it always falls as output increases, because the same total fixed cost is spread over more units of output. This causes the gap between $ATC$ and $AVC$ to shrink as output rises, since $ATC-AVC=AFC$.

Worked Example

A food truck has monthly fixed costs of $1200forthetruckandpermit.Whenitproduces600tacospermonth,itstotalvariablecostforingredientsandlaboris$900. Calculate all total and average cost measures for this output level.

1. Identify given values: $TFC=\$1200$, $Q=600$, $TVC=\$900$.
2. Calculate total cost: $TC=TFC+TVC=1200+900=\$2100$.
3. Calculate average fixed cost: $AFC=1200/600=\$2$ per taco.
4. Calculate average variable cost: $AVC=900/600=\$1.50$ per taco.
5. Calculate average total cost: $ATC=2100/600=\$3.50$ per taco (check: $AFC+AVC=2+1.50=3.50$, which matches).

Exam tip: If a question asks for total cost when output is zero, the answer is just total fixed cost—there is no variable cost when no output is produced.

3. Marginal Cost and Diminishing Marginal Returns

Marginal cost ($MC$) is the additional cost of producing one more unit of output. Since total fixed cost does not change with output, the change in total cost equals the change in total variable cost, so marginal cost can be calculated two equivalent ways: $$MC=\frac{\Delta TC}{\Delta Q}=\frac{\Delta TVC}{\Delta Q}$$ Marginal cost is directly related to the marginal product of the variable input ($M{P}_L$). Higher marginal product means each additional worker produces more output, so the marginal cost of that output is lower. The relationship is inverse: $MC=w/M{P}_L$, where $w$ is the wage rate.

The law of diminishing marginal returns explains the shape of the short-run marginal cost curve. Diminishing marginal returns states that as more variable input is added to a fixed amount of capital, eventually the marginal product of the additional variable input falls. When marginal product falls, marginal cost rises. This makes the short-run MC curve U-shaped: initially, specialization of new workers increases marginal product, so MC falls, but once diminishing returns set in, MC rises.

Worked Example

A small bakery has one fixed-size oven. The table below gives total cost at different output levels of loaves of bread. Calculate marginal cost for each 100-loaf increment of output, and identify where diminishing marginal returns set in.

1. Recall $MC=\Delta TC/\Delta Q$, and $\Delta Q=100$ for each increment.
2. $MC$ (0→100): $(400-300)/100=100/100=\$1$ per loaf.
3. $MC$ (100→200): $(480-400)/100=80/100=\$0.80$ per loaf (MC falling, increasing returns).
4. $MC$ (200→300): $(570-480)/100=90/100=\$0.90$ per loaf (MC rising).
5. $MC$ (300→400): $(680-570)/100=110/100=\$1.10$ per loaf (MC continuing to rise).
6. Diminishing marginal returns set in after 200 loaves, when MC begins to rise.

Exam tip: When marginal cost is calculated for output increments larger than 1 unit, always divide by the change in quantity—never just report the change in total cost as MC. This is a common point deduction on FRQs.

4. Relationship Between Marginal Cost and Average Costs

A core relationship tested repeatedly on the AP exam is the interaction between marginal cost and average costs: if marginal cost is less than average cost, it pulls the average down; if marginal cost is greater than average cost, it pulls the average up. As a result, marginal cost intersects both AVC and ATC exactly at their minimum points.

This relationship is intuitive if you think of your GPA: your current GPA is your average grade, and your new (marginal) course grade changes your average. If your new grade is lower than your current average, your average falls; if it is higher, your average rises. Only when your new grade equals your current average does your average stay the same, which occurs at the minimum point of the average curve.

Worked Example

At an output of 150 units, a firm’s average total cost is $20.Themarginalcostofthe151stunitis$18. Calculate the new average total cost at 151 units and confirm the relationship between MC and ATC.

1. Calculate total cost at 150 units: $T{C}_{150}=ATC\times Q=20\times 150=\$3000$.
2. Add marginal cost of the 151st unit to get total cost at 151 units: $T{C}_{151}=3000+18=\$3018$.
3. Calculate new average total cost: $AT{C}_{151}=3018/151\approx \$19.99$.
4. The new ATC ($19.99)islowerthantheoriginalATC($20), which confirms that when MC ($18)<ATC($20), ATC falls.

Exam tip: On graph-drawing FRQs, AP graders require you to draw MC crossing ATC and AVC exactly at their minimum points to earn full credit. Drawing the intersection anywhere else loses points.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Claims total fixed cost falls as output increases, instead of average fixed cost. Why: Students memorize that AFC always falls and incorrectly extend this pattern to total fixed cost. Correct move: Always note that TFC is constant at all output levels (including Q=0), only AFC falls as Q rises.
• Wrong move: Calculates marginal cost as $TC/Q$ instead of $\Delta TC/\Delta Q$. Why: Mixes up average total cost and marginal cost definitions, since both use total cost. Correct move: Circle the word "marginal" in any question and write a $\Delta$ symbol next to it to remind yourself you need the change in cost over change in output.
• Wrong move: Draws MC intersecting ATC at the minimum of AFC, or claims MC crosses AVC at AVC’s maximum. Why: Memorizes "MC crosses average at minimum" but mixes up which average. Correct move: For any average cost (ATC or AVC), MC crosses that average at its own minimum; there is no intersection relationship with AFC because AFC is always falling.
• Wrong move: Includes fixed costs when calculating marginal cost for output decisions. Why: Forgets that fixed costs are sunk and do not change with output in the short run. Correct move: When calculating MC, only use the change in variable cost, since change in TFC is always zero.
• Wrong move: Attributes the upward slope of short-run MC to diseconomies of scale. Why: Confuses short-run diminishing returns with long-run scale concepts. Correct move: Always attribute upward-sloping short-run MC to the law of diminishing marginal returns (a short-run concept with fixed inputs); diseconomies of scale are a long-run concept.

6. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

A firm produces 200 units of output with total fixed cost of $4,000andtotalvariablecostof$6,000. The marginal cost of the 201st unit of output is $25. What is the average total cost of 201 units of output? A) $49.75 B) $50.00 C) $49.88 D) $50.12

Worked Solution: First, calculate total cost at 200 units by adding fixed and variable cost: $TC=4000+6000=\$10,000$. Next, add the marginal cost of the 201st unit to get total cost at 201 units: $T{C}_{201}=10000+25=\$10025$. Average total cost is total cost divided by output: $ATC=10025/201\approx 49.88$. This calculation tests the ability to connect marginal cost to total cost and average cost, so the correct answer is C.

Question 2 (Free Response)

A taco truck operates in the short run with fixed costs of $1200 per month. The truck faces the following cost schedule:

(a) Calculate AFC, AVC, ATC, and MC for Q=200. (b) Explain why MC of the 200th to 300th taco is higher than MC of the 100th to 200th taco. (c) At Q=200, is MC above or below ATC? What does this imply about how ATC will change if output increases beyond 200?

Worked Solution: (a) $TFC=\$1200$ at all output levels. $AFC=TFC/Q=1200/200=\$6$ per taco $AVC=TVC/Q=500/200=\$2.50$ per taco $ATC=AFC+AVC=6+2.50=\$8.50$ per taco $MC=\Delta TVC/\Delta Q=(500-300)/(200-100)=200/100=\$2$ per taco

(b) The taco truck has a fixed amount of kitchen space and cooking equipment in the short run. As more workers (the variable input) are added to increase output, the law of diminishing marginal returns sets in: the marginal product of additional workers falls, so the marginal cost of additional output rises.

(c) At Q=200, MC ($2)isbelowATC($8.50). When marginal cost is below average total cost, increasing output pulls the average down, so ATC will decrease as output increases beyond 200.

Question 3 (Application / Real-World Style)

A small graphic design company rents a studio for $1800permonth(fixedcost).Itcurrentlyemploys3designersatatotalvariablecostof$12,000 per month, and produces 40 client projects per month. If the company hires one more designer for $3500 per month, it can produce 10 additional projects, for a total of 50 projects per month. Calculate the marginal cost per additional project, the original average total cost, and the new average total cost. Interpret your result.

Worked Solution:

1. Original total cost: $TC=1800+12000=\$13800$. Original ATC: $13800/40=\$345$ per project.
2. Change in total cost equals the additional variable cost of the new designer, since fixed cost does not change: $\Delta TC=\$3500$, $\Delta Q=10$.
3. Marginal cost per additional project: $MC=3500/10=\$350$ per project.
4. New total cost: $13800+3500=\$17300$. New ATC: $17300/50=\$346$ per project.

Interpretation: Average total cost increased from $345to$346, which confirms the core relationship: when marginal cost ($350) is higher than the original average total cost, it pulls the average up.

7. Quick Reference Cheatsheet

8. What's Next

Short-run costs are the foundation for all subsequent production and market structure topics in AP Microeconomics. Next you will extend cost concepts to the long run to study economies of scale, then apply short-run cost curves to find the profit-maximizing output and shutdown condition for perfectly competitive firms. Without mastering the relationships between MC, ATC, and AVC, you will not be able to correctly solve for profit, draw firm supply curves, or analyze long-run industry equilibrium, which are heavily tested on the AP exam. Short-run cost concepts also carry over to all other market structures, including monopoly, monopolistic competition, and oligopoly. Follow these next topics: Long-Run Costs and Economies of Scale Profit Maximization for Perfect Competition Firm Short-Run Supply and Shutdown Condition