Short-Run Supply — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: The short-run shut-down rule, the firm's short-run supply curve, derivation of the short-run market supply curve, profit/loss calculation for operating vs shut down, and the link between marginal cost and supply for perfectly competitive firms.

You should already know: Short-run cost definitions (TFC, TVC, AVC, MC, ATC); the profit-maximization rule MR = MC for perfectly competitive firms; the core characteristics of perfect competition.

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 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, 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. In AP Microeconomics, this topic is part of Unit 3: Production, Cost, and Perfect Competition, which makes up 20–30% of the overall AP exam score, with short-run supply itself accounting for roughly 4–6% of total exam points. Short-run supply is tested in both multiple-choice questions (MCQ) and as a core component of longer free-response questions (FRQ) focused on perfect competition. You will often be asked to derive supply curves, apply the shut-down rule, calculate profit/loss for operating vs shut down, or find short-run market equilibrium. This topic is specific to perfectly competitive markets, because firms in imperfect competition do not have a well-defined supply curve. Common notation used in this topic: $P$ for market price, $Q$ for quantity, $AVC$ for average variable cost, $MC$ for marginal cost, $TFC$ for total fixed cost.

2. 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 (the 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 ($TR-TVC$). Rearranging this logic gives us the rule:

• Operate (produce positive output) if $TR\ge TVC$
• Shut down (produce 0 output) if $TR<TVC$

Dividing both sides of the inequality by quantity $Q$, we get the simpler, more commonly used form: $$\text{Operate if }P\ge AVC;\text{Shut down if }P<AVC$$ 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 $AV{C}_{min}$ will always result in a shut down.

Worked Example

A wheat farmer has a fixed land lease cost of $1500pergrowingseason(cannotbecanceledmid-seasonintheshortrun).Attheprofit-maximizingquantityof600bushelsofwheat,theaveragevariablecost(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. First, identify the values we need: $P=\$4.00$, $AVC$ at profit-maximizing $Q=600$ is $\$4.20$.
2. Compare $P$ to $AVC$: $4.00<4.20$, so $TR=600\ast 4=\$2400$, $TVC=600\ast 4.20=\$2520$, so $TR<TVC$.
3. Calculate loss if operating: $TC=TVC+TFC=2520+1500=\$4020$, so $\text{Loss}=4020-2400=\$1620$.
4. Calculate loss if shutting down: The farmer still owes the lease, so $\text{Loss}=TFC=\$1500$.
5. Conclusion: The farmer should shut down, because it reduces total loss by $120 this growing season.

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

3. 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: the short-run supply curve is 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 relationship is unique to perfect competition: because the firm is a price-taker, there is a one-to-one relationship between price and profit-maximizing quantity, which creates the well-defined supply curve. In imperfect competition, firms set price instead of taking it, so no such supply curve exists.

Worked Example

A small t-shirt manufacturer has the following cost schedule for daily production:

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

1. First find $AV{C}_{min}$: the minimum AVC is $\$2$ at $Q=1$, so the firm will operate for all $P\ge 2$.
2. For $P=\$3.75$: The firm produces the largest quantity where $MC\le P$. $MC$ at $Q=3$ is $\$4$, which is greater than 3.75, so the profit-maximizing quantity is $Q=2$, where $MC=3\le 3.75$.
3. Check $AVC$ at $Q=2$: $AVC=2.5<3.75$, so the firm operates, supplies 2 t-shirts.
4. For $P=\$2.25$: $P\ge 2=AV{C}_{min}$, so the firm operates. The largest quantity where $MC\le 2.25$ is $Q=1$, where $MC=2\le 2.25$. $AVC$ at $Q=1$ is $2<2.25$, so the firm supplies 1 t-shirt.
5. This matches the rule: supply follows MC above AVC, so at every price, the quantity is read directly from the MC curve above AVC.

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 shade or label the portion of MC below AVC as part of supply. Examiners always check for this distinction.

4. The Short-Run Market Supply Curve

In the short run, the number of firms in the market is fixed: entry (new firms entering the market) and exit (existing firms leaving) only occur in the long run, because new firms need time to build production capacity and existing firms cannot exit and avoid fixed costs in the short run. To get the market short-run supply curve, we horizontally sum the supply curves of all individual firms in the market. This means that for any given price, we add up the quantity supplied by each individual firm to get the total market quantity supplied. For n identical firms, this simplifies to multiplying the individual firm quantity supplied by n. The formula is: $$Q_{\text{market}}(P)=\sum _{i=1}^n{Q}_i(P)$$ where n is the fixed number of firms. 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 $P\ge \$2$. What is the total market quantity supplied at $P=\$5$, and what is the equation for the short-run market supply curve?

1. Check that $P=5\ge 2$, so each firm supplies positive output.
2. Calculate individual firm quantity: $Q_i=15(5)-30=75-30=45$ bags of coffee per firm.
3. Number of firms is fixed at 80 in the short run, so total market quantity is $80\ast 45=3600$ bags of coffee.
4. Derive the full market supply equation: For $P<2$, $Q_{\text{market}}=0$. For $P\ge 2$, $Q_{\text{market}}=80\ast (15P-30)=1200P-2400$.
5. Verify the cutoff: At $P=2$, $Q_{\text{market}}=1200(2)-2400=0$, which matches the shut-down condition, so the equation is consistent.

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.

5. Common Pitfalls (and how to avoid them)

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

6. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

A perfectly competitive firm has total fixed cost of $500.Attheprofit-maximizingquantityof100units,averagevariablecostis$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

Worked Solution: First, apply the shut-down rule: we compare P to AVC at the profit-maximizing quantity. P = $7andAVC=$8, so P < AVC, meaning the firm should shut down, eliminating options A and B. When the firm shuts down, it still owes all fixed costs, so total loss equals $500. Option D incorrectly adds variable cost to the loss, which the firm does not incur if it produces zero output. The correct answer is C.

Question 2 (Free Response)

Assume the portable power bank market is perfectly competitive, and all firms are identical. The short-run cost function for a single firm is $TC(Q)=150+8Q+Q^2$, so marginal cost is $MC(Q)=8+2Q$, and average variable cost is $AVC(Q)=8+Q$. There are 40 firms in the market in the short run. (a) What is the minimum price at which the firm will operate in the short run? Justify your answer. (b) Derive the equation for the individual firm's short-run supply curve, then derive the equation for the short-run market supply curve. (c) If the market demand curve is $Q_D=640-15P$, find the short-run equilibrium market price and quantity.

Worked Solution: (a) The firm operates if and only if $P\ge AV{C}_{min}$. $AVC=8+Q$ is increasing in Q for all $Q>0$, so its minimum value occurs at $Q=0$, where $AVC=8$. So the minimum price for operation is $\$8$. (b) For $P\ge 8$, the firm sets $P=MC$ to maximize profit: $P=8+2Q\to Q_i=0.5P-4$. For $P<8$, $Q_i=0$. For 40 identical firms, the short-run market supply is: for $P\ge 8$, $Q_S=40(0.5P-4)=20P-160$, and $Q_S=0$ for $P<8$. (c) Set $Q_D=Q_S$: $640-15P=20P-160\to 800=35P\to P\approx \$22.86$. Substitute back to find equilibrium quantity: $Q=640-15(22.86)\approx 297$ units. So equilibrium price is ~$\$22.86$ and equilibrium quantity is ~297 power banks.

Question 3 (Application / Real-World Style)

A food truck vendor has a fixed permit cost of $800persemester(cannotberefundedifthevendorstopsoperatingforasemester).Atthecurrentmarketpriceof$8 per taco, the profit-maximizing quantity is 300 tacos per week. The average variable cost (ingredients, labor, fuel) per taco is $8.50. Should the vendor continue operating in the short run, or stop vending for the semester? How much does the vendor save by making the optimal choice?

Worked Solution: First, compare P ($8)toAVC($8.50) at the profit-maximizing quantity: $P<AVC$, so the vendor should stop operating in the short run. Calculate loss if operating: $TR=8\ast 300=\$2400$, $TVC=8.50\ast 300=\$2550$, $TC=2550+800=\$3350$, so total loss is $3350-2400=\$950$. Loss if stopping equals the fixed permit cost of $800.Thevendorsaves$150 per semester by stopping operations in the short run, which makes sense because the permit cost is already sunk regardless of operation.

7. Quick Reference Cheatsheet

8. 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. Follow-up topics to study next: Long-Run Supply Perfect Competition Equilibrium Producer Surplus