Perfect Competition: Long-Run Equilibrium and Efficiency

Hundreds of growers bring identical apples to a wholesale market. A crate sells for $25. One grower marks hers $25.01: one cent more. How many crates does she sell? This is Module 3.7, Perfect Competition: the side-by-side graphs behind the long free-response question in 2023, 2024 and 2025.

A perfectly competitive market has many buyers and sellers, each too small to move the price, one identical product, full information, and no barriers to entry or exit. So no firm has market power. Each is a price taker: it takes the market price as given and sells all it wants at that price. Back to $25.01. Buyers get the identical crate a cent cheaper next door, so all of them leave. Her total revenue drops to $0. Exam trap: all her buyers leave, not some. "Some customers switch" was a listed error on a recent exam.

She never needs to charge less: she sells every crate she wants at $25. So her demand is flat at the market price.

Quick refresher: total revenue is price times quantity; marginal revenue is the extra revenue from one more unit. At $25, 80 crates bring in $2,000 and 81 bring in $2,025. That extra $25 is the price.

So what just happened? One: a cent above the market price, every buyer left. Two: at $25, she sells all she wants. Three: her demand is flat; marginal revenue equals price.

Now the side-by-side graphs: market on the left, one typical firm on the right. Market first: downward-sloping demand, D, and upward-sloping supply, S, both solid.

Quick refresher: equilibrium is where supply and demand cross. Dotted lines run from there left to the price, $25, labeled PM, and down to the quantity, QM.

Now the firm. Label its vertical axis Price, Cost, and its horizontal axis Quantity. Then extend the dotted line from PM across to the firm's vertical axis, and label the price there PF. From PF, draw a horizontal line labeled d = MR: the firm's demand, which is also its marginal revenue. Exam trap: the memory aid MR. DARP is fine for remembering, but a run-together MRDARP label is not accepted. Write it with equals signs, d = MR = AR = P, and keep PF on the vertical axis. Next, a rising marginal cost curve, labeled MC. The firm's quantity, QF, is where MC crosses d = MR, dotted down to the axis.

Quick refresher: profit peaks where marginal revenue equals marginal cost. Below 80 crates, each extra crate costs under $25, so it adds profit; past 80, each costs over $25, so it cuts profit. So QF is 80.

Last, average total cost, labeled ATC: a steep U with one clear lowest point, and MC passing up through it. Our ATC bottoms out at $17 at 40 crates, and MC at 40 crates is also $17: that's where they cross. Exam trap: a flat-bottomed ATC counts as many lowest points and loses the point. Draw a steep U with one clear lowest point, and MC through it.

So what just happened? One: the market, with PM and QM. Two: a dotted line to PF, and a flat d = MR. Three: QF where MC crosses it. Four: ATC, with MC through its bottom.

ATC's position tells the profit story. At QF, 80 crates, ATC is $19, below the $25 price: economic profit.

Quick refresher: economic profit is price minus ATC, times quantity: a rectangle whose height is profit per crate and whose width is the number of crates.

Height: $25 minus $19 is $6 a crate. Width: 80 crates. Profit: $6 times 80 is $480. Shade it completely: from the price line down to ATC, from zero across to QF. On one recent exam, only 4 students in 10 earned that point.

So what just happened at $25? One: QF is 80 crates. Two: ATC there is $19, so each crate earns $6. Three: $6 times 80 is $480, fully shaded.

If the price is below ATC's bottom, ATC sits above d = MR at QF: price minus ATC is negative, a loss. Keep the minus sign. If the price is exactly at ATC's bottom, ATC just touches d = MR at QF: zero economic profit.

So what just happened? At QF, ATC below the price line: profit. ATC above it: a loss. ATC just touching it: zero economic profit.

Now the long run. That $480 of economic profit, with no barriers to entry, draws new orchards in.

Quick refresher, the four-step chain: one, price sets profit or loss. Two, profit draws firms in; losses push them out. Three, the number of firms shifts supply. Four, supply moves price.

More orchards mean more sellers, so market supply shifts right, S1 to S2. The price falls, labeled P2; quantity rises, labeled Q2. Exam trap: shift supply, not demand. Shifting demand left also lowers the price; on a recent exam, it was the most common error. Entry continues until the profit is gone, at the bottom of ATC. So P2 is $17. On the firm's graph, run a dotted line from P2 to the firm's axis, label it P*, and draw the new flat d2 = MR2.

The new quantity, Q*, is 40 crates, where P* = MR2 = MC = minimum ATC. Economic profit: ($17 minus $17) times 40 is zero, called normal profit. Exam trap: under 4 in 10 earned this point on a recent exam. The listed error: no link from P2. Draw the dotted line or write P* = P2.

So what just happened in the long run? One: profit drew orchards in. Two: supply shifted right; the price fell to $17. Three: each orchard makes 40 crates at minimum ATC, with zero profit.

Losses run it backward: firms exit, supply shifts left, and the price rises to the bottom of ATC. Ours is a constant-cost industry: entry doesn't change firms' costs, so the long-run price is the $17 minimum ATC. All three released long questions on this model said constant-cost. In an increasing-cost industry, firms' costs rise as the industry grows, so after a demand increase the long-run price ends above where it started. In a decreasing-cost industry, costs fall as it grows, so the price ends below where it started.

Last, efficiency, in two ways. Quick refresher from Unit 1: keep going while marginal benefit is at least marginal cost. Buyers stop when the last crate is worth just $17 to them; growers stop when it costs $17.

So the last crate's marginal benefit and marginal cost both equal the $17 price: allocative efficiency. No crate worth its cost is skipped, and none costing more than it's worth is grown. The $17 price carries that message: it tells buyers what another crate costs to grow, tells growers what it's worth to buyers, and gives both a reason to act on it. Second, each orchard makes 40 crates at the bottom of ATC, $17 a crate. Producing at minimum ATC is productive efficiency.

So what just happened? One: price equals marginal benefit and marginal cost: allocative efficiency. Two: production at minimum ATC: productive efficiency. Three: zero economic profit is normal profit.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

Question 1. Thousands of farms sell identical oats, and new farms enter freely. Which of the following is true for one oat farm? A) It can raise its price and keep some buyers. B) Its demand curve slopes downward. C) Its marginal revenue equals the market price. D) Market demand is horizontal at the farm's price. E) Its marginal revenue is below the market price.

The answer is C. A price taker gets the market price for every extra unit it sells, so marginal revenue equals price. A is the some-buyers-stay error. B and E describe a firm with market power. D swaps firm and market: the farm's demand is flat, not the market's.

Question 2. In side-by-side graphs, the market price is $7. The firm's MC crosses d = MR at 50 units, where ATC is $15. MC crosses ATC's lowest point, $11, at 150 units. What is the firm's economic profit at its profit-maximizing output? A) -$600 B) -$400 C) -$200 D) $350 E) $400

The answer is B. ($7 - $15) × 50 = -$8 × 50 = -$400. Use ATC at QF, and keep the minus sign: it's a loss. A uses the wrong crossing: ($7 - $11) × 150. C uses ATC's lowest point instead of ATC at QF. D is total revenue, $7 × 50. E drops the minus sign.

Free response, 1 point. Ridgeline Farm sells pumpkins in a perfectly competitive market. Draw correctly labeled side-by-side graphs for the pumpkin market and the farm, showing the market price and quantity, labeled PM and QM, and the farm's profit-maximizing price and quantity, labeled PF and QF.

These graphs are scored point by point; here's the one students miss most. One: a horizontal line on the firm's graph, labeled d = MR. Two: a dotted line from PM, or PF = PM written. Three: PF on the vertical axis. The costly mistakes: no d = MR label, a run-together MRDARP, no link to PM, or a downward-sloping firm demand curve. Fewer than half earned this point on the AP exam, three years running.

So what earned the point? One: a flat line labeled d = MR. Two: a dotted line from PM. Three: PF on the firm's vertical axis.

Recap: a price taker's d = MR is flat at the market price; it produces where MC crosses it. ATC's position shows profit or loss. Long run: P = MC = minimum ATC. Next: the Unit 3 test, worked.