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Short-Run
Production Costs

Master the relationship between fixed costs, variable costs, and output: how firms decide what to produce and at what price in the short run.

AP Microeconomics

What Is the Short Run?

In economics, the short run is a period in which at least one input is fixed. A bakery can hire more workers tomorrow, but it cannot build a new oven overnight. That fixed oven is what makes it "short run."

Fixed Inputs
Cannot be changed: factory size, major equipment, long-term leases
Variable Inputs
Can be adjusted: labor hours, raw materials, electricity usage

Three Cost Categories

Fixed Costs (FC)
Do not change with output. Rent, insurance, loan payments: you pay them even if \( Q = 0 \).
Variable Costs (VC)
Rise as output rises. Labor wages, raw materials, energy: more production means more spending.
Total Cost (TC)
\( TC = FC + VC \). The sum of everything a firm spends to produce a given quantity.

Visualizing FC, VC, and TC

Quantity (Q) Cost ($) FC VC TC FC gap

Per-Unit Cost Measures

Firms care about cost per unit because it determines profitability. We divide total costs by quantity to get average measures.

AFC
\( AFC = \frac{FC}{Q} \). Always declining: spreading the fixed cost over more units.
AVC
\( AVC = \frac{VC}{Q} \). U-shaped: falls then rises due to diminishing returns.
ATC
\( ATC = \frac{TC}{Q} = AFC + AVC \). Also U-shaped, always above AVC.

The Most Important Curve: Marginal Cost

Marginal Cost (MC) is the additional cost of producing one more unit. It drives every profit-maximizing decision a firm makes.

MC Intersects ATC and AVC at Their Minimums

Quantity (Q) Cost per unit ($) AFC AVC ATC MC min AVC min ATC

Why Does MC Cross at the Minimum?

Think of it like a grade point average. If your next test score (marginal) is below your GPA (average), your GPA falls. If it's above, your GPA rises. They meet exactly when the next score equals the current average.

1
When \( MC < ATC \), producing one more unit pulls the average down.
2
When \( MC > ATC \), producing one more unit pushes the average up.
3
When \( MC = ATC \), the average is neither rising nor falling: it's at its minimum.

ATC vs. MC: Know the Difference

ATC MC
Formula \( \frac{TC}{Q} \) \( \frac{\Delta TC}{\Delta Q} \)
Measures Cost per unit on average Cost of the next unit
Includes FC? Yes No
Shape U-shaped U-shaped (steeper)
Decision use Break-even pricing Profit-maximizing output

Diminishing Marginal Returns Drive the Curves

The law of diminishing marginal returns says that as you add more of a variable input (labor) to a fixed input (capital), the marginal product of that input eventually falls.

Rising MP
Early workers specialize and collaborate: MP rises, so MC falls.
Falling MP
Too many workers crowd the fixed capital: MP falls, so MC rises.

How to Calculate Short-Run Costs

1
Identify FC and VC. FC is the cost at \( Q = 0 \). Everything else is VC.
2
Compute TC. Add them: \( TC = FC + VC \).
3
Find per-unit costs. Divide: \( ATC = \frac{TC}{Q} \), \( AVC = \frac{VC}{Q} \), \( AFC = \frac{FC}{Q} \).
4
Calculate MC. \( MC = \frac{\Delta TC}{\Delta Q} \) between consecutive rows.
5
Check relationships. Verify MC crosses AVC and ATC at their minimums.

Example 1: Building a Cost Table

A firm has \( FC = \$100 \). Use the data below to fill in all cost measures.

Q VC TC MC ATC AVC
0$0$100———
1$50$150$50$150$50
2$80$180$30$90$40
3$100$200$20$66.67$33.33
4$140$240$40$60$35
5$200$300$60$60$40
6$290$390$90$65$48.33

Example 2: Graphing the Curves

Using the table from Example 1, here are the per-unit cost curves plotted:

Q $ per unit 0 30 60 90 120 150 1 2 3 4 5 6 ATC AVC MC

Example 3: Profit or Loss?

Suppose the market price is $65. From Example 1, at \( Q = 6 \): \( ATC = \$65 \) and \( MC = \$90 \). Should the firm produce 6 units?

1
Find profit-maximizing \( Q \). Produce where \( P = MC \). At \( Q = 5 \), \( MC = \$60 \); at \( Q = 6 \), \( MC = \$90 \). So optimal \( Q \) is 5 units.
2
Check profit. At \( Q = 5 \): Revenue \( = 5 \times \$65 = \$325 \). Cost \( = TC = \$300 \). Profit \( = \$325 - \$300 = \) $25.
3
Per-unit check: \( P - ATC = \$65 - \$60 = \$5 \) profit per unit \( \times 5 = \$25 \). ✓ Consistent.

Common Mistakes to Avoid

✕ Confusing MC with ATC
MC is the cost of the next unit; ATC is the average of all units. They are equal only at the minimum of ATC.
✕ Forgetting FC at Q = 0
TC is never zero in the short run. At \( Q = 0 \), \( TC = FC \). The TC curve starts at FC, not the origin.
✕ Saying MC "includes" FC
MC measures only the change in TC, and since FC is constant, \( \Delta FC = 0 \). MC reflects only variable costs.

Summary of Short-Run Cost Curves

Curve Formula Shape Key Fact
FC Constant Horizontal line Exists at \( Q = 0 \)
VC Varies with Q S-shaped (increasing) Starts at origin
TC \( FC + VC \) S-shaped (shifted up by FC) Starts at FC
AFC \( \frac{FC}{Q} \) Always declining Approaches 0 but never reaches it
AVC \( \frac{VC}{Q} \) U-shaped MC crosses at its minimum
ATC \( \frac{TC}{Q} \) U-shaped MC crosses at its minimum
MC \( \frac{\Delta TC}{\Delta Q} \) U-shaped Drives output decisions

Question 1 of 5

If a firm's fixed cost is $200 and its total cost at 10 units is $500, what is the average variable cost at 10 units?

Question 2 of 5

Which of the following is true about marginal cost (MC) in the short run?

Question 3 of 5

When marginal cost is below average total cost, ATC is:

Question 4 of 5

A firm produces 4 units with \( TC = \$240 \), then produces 5 units with \( TC = \$310 \). What is the marginal cost of the 5th unit?

Question 5 of 5

The law of diminishing marginal returns explains why, in the short run: