Difficulty: Intermediate | Prerequisites: cost functions (TC, MC, ATC, AVC), basic calculus, understanding of market structure
Perfect competition is the benchmark market structure in microeconomics: many firms, identical products, free entry and exit. This set of notes covers the firm's short-run output decision (set P = MC), how to compute profit, the breakeven price (where profit is exactly zero), and the long-run equilibrium condition that determines how many firms survive in the market. You need to be comfortable with total cost, marginal cost, and average total cost before starting here.
A perfectly competitive firm maximises profit by producing where P = MC. Profit equals TR minus TC. The breakeven price is the minimum of ATC, where profit is exactly zero. In the long run, free entry drives all firms to the breakeven price, and you can solve for the number of firms by dividing market quantity at that price by each firm's output.
Perfect competition
A market structure with many buyers and sellers, homogeneous products, free entry and exit, and perfect information. Each firm is a price-taker: it faces a horizontal demand curve at the market price.
In simple terms, no single firm can influence the price. You sell at whatever the market says.
Profit-maximising output rule (P = MC)
A price-taking firm maximises profit by producing the quantity where price equals marginal cost. This comes from setting marginal revenue (which equals price in perfect competition) equal to marginal cost.
Economic profit
Profit = TR minus TC = (P × q) minus TC(q). This includes all opportunity costs. Zero economic profit means the firm is earning a normal return, covering all costs including the owner's opportunity cost.
Breakeven price
The price at which economic profit is exactly zero. It equals the minimum of the average total cost curve. At this price, P = MC = ATC.
Think of it as the lowest price at which the firm can survive in the long run without losses.
Shutdown price
The price below which the firm should stop producing in the short run. It equals the minimum of the average variable cost curve. Below this price, the firm cannot even cover its variable costs.
Long-run equilibrium
The state where no firm wants to enter or exit the market. Price equals the breakeven price (minimum ATC), every firm earns zero economic profit, and the number of firms adjusts so that total market supply equals market demand at that price.
Given: variable cost = 4q², MC = 8q, fixed cost F = 256, market price P = 104
Set P = MC: 104 = 8q, so q = 13
The firm produces 13 units to maximise profit
Total revenue: TR = P × q = 104 × 13 = 1,352
Total cost: TC = 4q² + 256 = 4(169) + 256 = 676 + 256 = 932
Profit: π = TR minus TC = 1,352 minus 932 = 420
The firm earns a positive economic profit of 420
The breakeven price is where MC = ATC (equivalently, the minimum of ATC)
ATC = TC/q = (4q² + 256)/q = 4q + 256/q
To minimise ATC, take the derivative and set it to zero: dATC/dq = 4 minus 256/q² = 0
Solving: 256/q² = 4, so q² = 64, giving q = 8
At q = 8: ATC = 4(8) + 256/8 = 32 + 32 = 64
The breakeven price is 64
Check: MC at q = 8 is 8(8) = 64, confirming MC = ATC at the minimum
In the long run, P = breakeven price = 64. Each firm produces q = 8.
Market demand: P = 448 minus 3Q, so at P = 64: 64 = 448 minus 3Q, giving Q = 128
Total market quantity Q = n × q, so 128 = n × 8, giving n = 16
In long-run equilibrium, there are 16 identical firms in the market
Each firm earns zero economic profit
\pi = TR - TC = P \cdot q - TC(q)ATC = \frac{TC(q)}{q}\frac{dATC}{dq} = 0 \implies \text{breakeven } qBreakeven price = MC = ATC at the quantity that minimises ATC.
Long-run number of firms: n = Q / q, where Q comes from the market demand curve at P = breakeven price.
Agricultural markets come close to perfect competition: thousands of wheat farmers produce an identical commodity, and no single farm can influence the market price. When wheat prices spike above long-run average cost, new acreage comes into production (entry), pushing prices back down toward breakeven. This is the entry-and-exit mechanism that drives the long-run equilibrium result.
Students often confuse the breakeven price with the shutdown price. Breakeven is minimum ATC (profit = 0). Shutdown is minimum AVC (the firm cannot cover variable costs). They are different prices.
A common mistake in long-run equilibrium problems is forgetting that each firm's output q is determined by the breakeven condition, not by the market demand curve. You find q from MC = ATC, then use the demand curve to find total Q, then divide.
Students sometimes think zero economic profit means the firm is failing. It means the firm is covering all costs, including opportunity costs. The owner is earning a normal return on their investment.
When computing profit, students occasionally use ATC instead of TC. Profit = TR minus TC, not TR minus ATC. (Though you can also compute it as (P minus ATC) × q.)
⚠️ The P = MC rule for profit-maximising output is tested on nearly every exam covering perfect competition. Be able to apply it quickly.
⚠️ Finding the breakeven price requires minimising ATC. This means taking a derivative, setting it to zero, and solving. Practise the algebra.
⚠️ Long-run equilibrium questions ("how many firms?") combine three separate pieces: the breakeven price, the individual firm's output at that price, and the market demand curve. Be ready to chain them together.
⚠️ Make sure you can distinguish between short-run (positive or negative profit possible, fixed costs sunk) and long-run (zero profit, entry/exit adjusts the number of firms).
Fill in the blank: A perfectly competitive firm maximises profit by producing where ______ = ______.
P = MC.
True or False: The breakeven price is the minimum of the average variable cost curve.
False. It is the minimum of average total cost.
If TC = 4q² + 256 and P = 104, what is the profit-maximising q?
MC = 8q. Set 104 = 8q, so q = 13.
True or False: In long-run equilibrium, each firm earns zero economic profit.
True.
Fill in the blank: The number of firms in long-run equilibrium equals ______ divided by ______.
Total market quantity Q divided by each firm's output q.
Q: A perfectly competitive firm has VC = 4q² and FC = 256. The market price is $104. How much output should the firm produce, and what is its profit?
A: MC = 8q. Set P = MC: 104 = 8q, so q = 13. TR = 104(13) = 1,352. TC = 4(169) + 256 = 932. Profit = 1,352 minus 932 = 420.
Q: For the same firm, what is the breakeven price?
A: ATC = 4q + 256/q. Minimise: dATC/dq = 4 minus 256/q² = 0, so q² = 64, q = 8. ATC at q = 8: 32 + 32 = 64. The breakeven price is 64.
Q: If market demand is P = 448 minus 3Q and all firms are identical with the cost structure above, how many firms are in long-run equilibrium?
A: In the long run, P = 64 and each firm produces q = 8. From demand: 64 = 448 minus 3Q, so Q = 128. Number of firms: n = 128/8 = 16.
Q: At the breakeven price, what is the firm's profit? Explain why.
A: Profit is zero. At the breakeven price, P = ATC, so TR = TC. The firm covers all costs, including opportunity costs, but earns no surplus above that.
The breakeven and shutdown analysis here connects directly to the firm's supply curve: the supply curve is the MC curve above the shutdown price. In monopoly and oligopoly, the P = MC rule no longer holds because the firm faces a downward-sloping demand curve, so MR replaces P. The long-run zero-profit result also ties to the elasticity material: in the long run, entry makes the market supply curve more elastic, which is why competitive markets tend toward lower prices over time.
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