# Short-Run Supply

> AP Microeconomics · Unit 3: Production, Cost, and Perfect Competition
> Source: https://www.owlsprep.com/study/ap-microeconomics-u3-short-run-supply/

This module covers the short-run shut-down rule, the firm's short-run supply curve, derivation of the short-run market supply curve, and profit/loss calculation for perfectly competitive firms, tested on both AP Microeconomics MCQ and FRQ.

**Prerequisites:** [Short-run cost definitions (TFC, TVC, AVC, MC, ATC)](https://www.owlsprep.com/study/ap-microeconomics-u3-short-run-costs/); [Profit-maximization rule MR = MC for perfectly competitive firms](https://www.owlsprep.com/study/ap-microeconomics-u3-perfect-competition-profit-maximization/); [Core characteristics of perfect competition](https://www.owlsprep.com/study/ap-microeconomics-u3-perfect-competition-characteristics/)

## Learning objectives

- Apply the short-run shut-down rule to decide between operating and shutting down
- Derive a perfectly competitive firm's short-run supply curve
- Calculate the short-run market supply curve for a market with fixed number of firms
- Compute profit/loss for operating vs shutting down in the short run

## Core Definition of Short-Run Supply

Short-run supply describes the quantity of output a perfectly competitive firm (or market) will produce at every possible market price in the short run. The short run is defined as the period where at least one input (typically capital, factory size, or lease agreements) is fixed, and new firms cannot enter or exit the market. This topic is specific to perfectly competitive markets, because firms in imperfect competition do not have a well-defined supply curve. It makes up roughly 4–6% of total AP Microeconomics exam points.

**Short-Run Supply** — The quantity of output a perfectly competitive firm or market will produce at every possible market price in the short run (a period with at least one fixed input and fixed number of firms).

## The Short-Run Shut-Down Rule

In the short run, fixed costs are sunk: they must be paid regardless of whether the firm produces output or shuts down. This means the firm’s decision to operate or shut down depends only on whether operating generates enough revenue to cover variable costs (costs that change with output, like labor and raw materials).

- If the firm shuts down, it loses all its total fixed cost ($TFC$)
- If it operates, it loses $TFC$ minus any excess revenue it earns after covering variable costs ($TR - TVC$)

$$\text{Operate if } P \geq AVC; \quad \text{Shut down if } P < AVC$$

where $AVC = \frac{TVC}{Q}$ is average variable cost *at the profit-maximizing quantity*. The minimum value of AVC across all quantities is the cutoff price: any price below $AVC_{min}$ will always result in a shut down.

**Worked example:** A wheat farmer has a fixed land lease cost of \$1500 per growing season (cannot be canceled mid-season in the short run). At the profit-maximizing quantity of 600 bushels of wheat, the average variable cost (seed, fertilizer, labor) is \$4.20 per bushel. The current market price for wheat is \$4.00 per bushel. Should the farmer operate or shut down this season? What is the difference in total loss between the two options?

1. Identify the key values given:

   $$P = \$4.00, \quad AVC \text{ at } Q=600 = \$4.20$$
2. Compare $P$ to $AVC$: $P < AVC$, so total revenue is less than total variable cost:

   $$TR = 600 \times 4 = \$2400, \quad TVC = 600 \times 4.20 = \$2520$$
3. Calculate total loss if the farmer operates:

   $$TC = TVC + TFC = 2520 + 1500 = \$4020, \quad \text{Loss} = 4020 - 2400 = \$1620$$
4. Calculate total loss if the farmer shuts down: the farmer still owes the fixed lease cost, so all fixed cost is lost:

   $$\text{Loss} = TFC = \$1500$$
5. Conclusion: Shutting down reduces total loss by \$120, so the farmer should shut down.

> **Exam tip:** Always compare $P$ to $AVC$ at the profit-maximizing quantity, not just the minimum AVC, and never use ATC for short-run shut-down decisions. ATC includes fixed cost, which is sunk and irrelevant to the short-run decision.

## The Firm's Short-Run Supply Curve

For a perfectly competitive firm, the profit-maximizing quantity at any price is found by setting $P = MC$, because $MR = P$ for price-taking firms. Combining this with the shut-down rule, we get the definition of the firm’s short-run supply curve.

**Firm's Short-Run Supply Curve** — The portion of the firm's marginal cost curve that lies above the average variable cost curve. For all prices below the minimum AVC, the firm supplies 0 output.

This one-to-one relationship between price and quantity supplied is unique to perfect competition: in imperfect competition, firms set price instead of taking it, so no well-defined supply curve exists.

| Q (t-shirts) | MC ($) | AVC ($) |
| --- | --- | --- |
| 0 | - | - |
| 1 | 2 | 2 |
| 2 | 3 | 2.5 |
| 3 | 4 | 3 |
| 4 | 5 | 3.5 |
| 5 | 6 | 4 |

**Worked example:** What quantity will the firm supply at $P = \$3.75$, and at $P = \$2.25$?

1. First find $AVC_{min}$: the minimum AVC is $\$2$ at $Q=1$, so the firm will operate for all $P \geq 2$.
2. For $P = \$3.75$: the firm produces the largest quantity where $MC \leq P$. $MC$ at $Q=3$ is $\$4 > 3.75$, so profit-maximizing quantity is $Q=2$.
3. Check $AVC$ at $Q=2$: $AVC = 2.5 < 3.75$, so the firm operates and supplies 2 t-shirts.
4. For $P = \$2.25$: $P \geq 2 = AVC_{min}$, so the firm operates. The largest quantity where $MC \leq 2.25$ is $Q=1$, so the firm supplies 1 t-shirt.
5. This matches our rule: supply follows the marginal cost curve above the AVC curve.

> **Exam tip:** If asked to draw the short-run supply curve on a graph, explicitly label the kink at the minimum of AVC, and do not label the portion of MC below AVC as part of supply. Examiners always check for this distinction.

## The Short-Run Market Supply Curve

In the short run, the number of firms in the market is fixed: entry of new firms and exit of existing firms only occur in the long run, because new firms need time to build production capacity and existing firms cannot exit to avoid fixed costs in the short run.

To derive the short-run market supply curve, we horizontally sum the supply curves of all individual firms in the market. For any given price, we add up the quantity supplied by each individual firm to get total market quantity supplied. For $n$ identical firms, this simplifies to multiplying the individual firm quantity by $n$.

$$Q_{\text{market}}(P) = \sum_{i=1}^{n} Q_i(P)$$

Since every individual firm’s MC curve is upward sloping, the short-run market supply curve is also always upward sloping.

**Worked example:** There are 80 identical coffee producers in a perfectly competitive regional market. Each firm’s individual short-run supply is: $Q_i = 0$ for $P < \$2$, and $Q_i = 15P - 30$ for $P \geq \$2$. What is the total market quantity supplied at $P = \$5$, and what is the equation for the short-run market supply curve?

1. Confirm $P = 5 \geq 2$, so every firm supplies positive output.
2. Calculate quantity per firm:

   $$Q_i = 15(5) - 30 = 45 \text{ bags of coffee per firm}$$
3. Multiply by the fixed number of firms to get total market quantity:

   $$Q_{\text{market}} = 80 \times 45 = 3600 \text{ bags}$$
4. Derive the full market supply equation:

   $$\text{For } P < 2: Q_{\text{market}} = 0; \quad \text{For } P \geq 2: Q_{\text{market}} = 80(15P - 30) = 1200P - 2400$$
5. Verify the equation is consistent with the shut-down rule: at $P=2$, $Q_{\text{market}} = 0$, which matches our expectation.

> **Exam tip:** Do not adjust the number of firms when calculating short-run market supply, even if firms earn negative economic profit. Entry and exit are long-run adjustments, so the number of firms is always fixed for short-run problems.

## Concept Check

**Check your understanding**

Test your understanding of short-run supply with this AP-style multiple-choice question:

1. A perfectly competitive firm has total fixed cost of \$500. At the profit-maximizing quantity of 100 units, average variable cost is \$8, and the market price is \$7. Which of the following is the firm's optimal short-run decision and what is its resulting profit/loss?

   - A) Operate, loss of \$100
   - B) Operate, loss of \$600
   - C) Shut down, loss of \$500
   - D) Shut down, loss of \$600

   *Answer:* C) Shut down, loss of \$500

   *Why:* Correct: $P < AVC$ so the firm shuts down, and loss equals fixed cost of \$500. If you chose D, you incorrectly added variable cost to the loss, which is not incurred when producing zero.

## Common pitfalls

- **Wrong:** Comparing $P$ to ATC instead of AVC for short-run shut-down decisions
  - Why it fails: Students confuse the short-run shut-down rule with the long-run exit rule, where exit occurs when $P < ATC$.
  - Correct: Always use AVC for short-run shut-down decisions; reserve ATC only for long-run exit decisions.
- **Wrong:** Drawing the entire marginal cost curve as the firm's short-run supply curve
  - Why it fails: Students forget that the firm shuts down and supplies zero when $P$ is below minimum AVC.
  - Correct: Only label the portion of the MC curve that lies above the minimum AVC as the short-run supply curve; all prices below minimum AVC correspond to $Q=0$.
- **Wrong:** Changing the number of firms when calculating short-run market supply in response to negative economic profit
  - Why it fails: Students mix up short-run and long-run market adjustments, where entry/exit change the number of firms in the long run.
  - Correct: Assume the number of firms is fixed for any short-run supply calculation, regardless of the current profit level.
- **Wrong:** Comparing $P$ only to the minimum AVC, and not checking AVC at the profit-maximizing quantity
  - Why it fails: Students memorize the minimum AVC cutoff but forget AVC rises at higher quantities, so AVC can be above $P$ even if $P$ is above the minimum AVC.
  - Correct: After finding profit-maximizing $Q$ where $P=MC$, check AVC *at that $Q$* to confirm $P \geq AVC$ before deciding to operate.
- **Wrong:** Calculating loss when shutting down as zero in the short run
  - Why it fails: Students think shutting down means no costs, but fixed costs are sunk and must still be paid in the short run.
  - Correct: Always remember that short-run shut down results in a loss equal to total fixed cost, not zero loss.

## Cheatsheet

| Category | Formula / Rule | Notes |
| --- | --- | --- |
| Short-Run Shut-Down Rule | Operate if $P \geq AVC$ <br> Shut down if $P < AVC$ | AVC is measured at the profit-maximizing $Q$ (where $P=MC$); applies only to the short run |
| Loss if Shut Down | $\text{Loss} = TFC$ | Fixed costs are sunk in the short run, so they are still incurred even if $Q=0$ |
| Loss if Operate | $\text{Loss} = TFC - (TR - TVC)$ | If $P \geq AVC$, $TR - TVC$ is positive, so loss is smaller than $TFC$ |
| Firm Short-Run Supply Curve | $S_f(P) = MC(P)$ for $P \geq AVC_{min}$ <br> $S_f(P) = 0$ for $P < AVC_{min}$ | Only the portion of MC above minimum AVC is the supply curve for perfectly competitive firms |
| Individual Supply (Linear MC) | If $MC = a + bQ$, then $Q_i = \frac{P - a}{b}$ for $P \geq AVC_{min}$ | Derived directly from the profit-maximization condition $P=MC$ |
| Short-Run Market Supply | $Q_S(P) = \sum_{i=1}^{n} Q_i(P)$ | Number of firms $n$ is fixed in the short run; sum horizontally across individual firms |
| Identical Firms Market Supply | $Q_S(P) = n \times Q_i(P)$ | Simplifies calculation when all firms have identical cost structures |

## What's next

Short-run supply is the foundation for understanding how competitive markets adjust to changes in demand and costs, and it is a required prerequisite for learning long-run supply and long-run competitive equilibrium, the next core topic in Unit 3. Without mastering the shut-down rule and the derivation of short-run market supply, you will not be able to correctly analyze how entry and exit shift the market supply curve in the long run, or explain why different industry types have different long-run supply elasticities. This topic also feeds into broader concepts like producer surplus and the welfare effects of government intervention in competitive markets.

- [Long-Run Supply](https://www.owlsprep.com/study/ap-microeconomics-u3-long-run-supply/)
- [Efficiency and Perfect Competition](https://www.owlsprep.com/study/ap-microeconomics-u3-efficiency-and-perfect-competition/)
- [Imperfect Competition Overview](https://www.owlsprep.com/study/ap-microeconomics-u4-overview/)

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