Long-Run Competitive Equilibrium: Price, MC and Minimum ATC
Long-run competitive equilibrium connects price taking, the best output and zero economic profit. Work through P = MR = MC = minimum ATC, distinguish productive from allocative efficiency, and try three original interactive questions.
The constant-cost benchmark is price = marginal cost = minimum average total cost.
Compare Three Equilibrium Cases
Assume identical price-taking firms, free entry and exit, a homogeneous product and a standard U-shaped long-run average-cost curve. Firms can choose their least-cost plant size and all relevant opportunity costs are counted. The efficiency claim also requires that private marginal benefits and costs reflect social ones, without other distortions. These are model conditions, not a description of every real market.
Which result indicates productive efficiency for a competitive firm in long-run equilibrium?
- Price exceeds marginal cost.
- The firm produces at minimum average total cost.
- Economic profit is maximized at any output.
- Marginal revenue is zero.
- Average variable cost equals fixed cost.
The firm produces at minimum average total cost. Producing at minimum ATC means output is made at the lowest attainable average resource cost.
After entry and exit have ended in a constant-cost competitive industry, which set of equalities describes a representative firm?
- MR=0
- P>MC and P>ATC
- P=AVC<ATC
- P=MC=min ATC
- P<MC
P=MC=min ATC Price taking gives P=MR=MC, while free entry and exit drive price to minimum ATC and economic profit to zero.
A price-taking industry has completed entry and exit, firms use the least-cost plant size, and no firm earns economic profit. Which set of equalities describes the resting point?
- Price = average variable cost
- Price = marginal revenue = marginal cost = minimum average total cost
- Demand = marginal revenue
- Price = maximum average total cost
- Marginal cost = average fixed cost
Price = marginal revenue = marginal cost = minimum average total cost Price equals marginal revenue for a price taker, marginal revenue equals marginal cost at the best output, and zero profit at efficient scale places price at minimum average total cost. Every equality answers a different part of the long-run result.
Video Lesson: Long-Run Competitive Profit
A focused video lesson from Khan Academy.
Explain Each Equality
Read the chain one link at a time. P = MR comes from taking the market price as given. MR = MC identifies an interior candidate for the best output, checked against other outputs and shutdown. P = ATC means revenue covers total economic cost. Under the stated cost shape, their long-run combination places output at minimum ATC.
Distinguish Three Economic Meanings
P=MC is the firm’s marginal output condition and supports allocative efficiency when private MC equals social marginal cost and price reflects marginal social benefit. Production at minimum ATC gives productive efficiency for the stated technology. P=ATC gives zero economic profit; the normal return is included in cost, so zero economic profit does not mean the owner receives nothing.
Connect Choice with Entry and Exit
The equalities arise from different mechanisms. Profit maximization and price taking give the candidate condition P=MC. Free entry and exit produce P=ATC in the identical-firm benchmark. For a positive-output equilibrium on the standard U-shaped cost curves, MC meets ATC at its minimum. Equality by itself needs the stated curve shape; it is not a universal mathematical test that every stationary cost point is a minimum.
Read the Equality Reference Table
| Equality | Meaning | Mechanism |
|---|---|---|
P=MC |
Firm output rule; allocative efficiency only with aligned private and social margins | Price taking plus profit maximization |
P=ATC |
Zero economic profit | Entry or exit |
MC=ATC |
Minimum ATC under the stated U-shaped cost assumption | Marginal-average relationship |
Track a Lasting Demand Increase
Demand rises in a constant-cost industry. Short-run price and profit rise. Entry expands supply until price returns to the original minimum-ATC level. Long-run market quantity remains higher because more firms each produce the efficient firm output.
Suppose minimum ATC is $12 at 40 units per firm. Long-run equilibrium price is $12 and each firm produces 40. If market demand later supports 4,800 units at $12, the industry needs 120 identical firms. The market quantity and firm count adjust while the representative firm’s efficient scale remains 40.
Separate Zero Profit from Zero Income
Zero economic profit is compatible with positive revenue, accounting profit, and producer surplus. Revenue covers variable cost, fixed opportunity cost, owner labor, and the normal return on capital. “Zero” refers only to the excess after all economic costs.
Know the Benchmark’s Limits
The zero-profit benchmark assumes identical firms and free entry. Different costs or scarce firm-specific resources can support rents in a competitive market. Constant industry costs are needed to restore an unchanged old price after a demand shift; they are not required for the same equilibrium equalities to hold at changed cost curves. Review the separate industry-cost lesson for that distinction.
Read the Tangency on a Graph
On the usual smooth U-shaped long-run ATC curve, the equilibrium price line is tangent at its minimum and MC passes through that point. A price line meeting ATC elsewhere generally does not satisfy the firm’s best-output condition. Use both the marginal condition and the break-even condition, together with the relevant shape and entry assumptions.
Check the Social Margin
Productive efficiency concerns average resource cost for the given technology. Allocative efficiency concerns marginal social value and marginal social cost. Without an externality, and under the other competitive assumptions, private P=MC can express that social margin. With pollution or an unpriced benefit, the relevant condition is MSB = MSC, so the private equality can fail to establish social efficiency. Efficiency also does not by itself settle fairness or income distribution.
Allow Technology to Change Costs
If technology lowers every firm’s minimum ATC, the long-run zero-profit price also falls. Firms may earn temporary profit at the old price while entry and output adjust. Zero profit is an equilibrium condition, not a rule freezing price when demand or cost fundamentals change.
Use the New Input Costs
A permanent input-price increase similarly raises minimum ATC and the long-run break-even price, inducing exit during adjustment. The three equalities hold at the new cost curves, not necessarily at the old numerical price and output.
For example, adding a $4 per-unit input cost to the model below changes MC to 0.3q + 4 and minimum ATC to $16 at q = 40. A price of $16 then covers $640 total cost for forty units. The new zero-profit price differs even though the same equilibrium logic applies; the output at minimum ATC happens to stay forty for this particular cost shift.
Read the Entry and Efficiency Explanations
OpenStax’s entry and exit lesson explains the zero-profit benchmark. Its competitive efficiency lesson separates productive and allocative efficiency and discusses the model’s limits. The calculations and questions below are original teaching examples.
Verify All the Conditions with One Cost Function
Let a firm’s total economic cost be TC = 0.15q² + 240, with MC = 0.3q. The $240 is fixed over the short-run operating period and avoidable on long-run exit. For positive q, ATC = 0.15q + 240/q. Its minimum is $12 at q = 40 because ATC − 12 = 0.15(q − 40)²/q, which is nonnegative.
At P = $12 and q = 40, MR = MC = ATC = $12. Revenue is $480; variable cost is $240 and total economic cost is $480. Economic profit is zero, while producer surplus defined here as revenue minus variable cost is $240. It covers fixed economic cost over the period rather than representing excess profit.
| Price | Firm q | Revenue | Total economic cost | Economic profit |
|---|---|---|---|---|
| $12 | 40 | $480 | $480 | $0 |
| $18 | 60 | $1,080 | $780 | $300 |
At the higher price of $18, the firm chooses q = 60 where MC = $18, yet ATC is $13 and economic profit is $300. Thus P = MC alone does not establish zero profit or minimum ATC. The full operating-profit expression at this price is 300 − 0.15(q − 60)², so sixty is the global maximizing operating output. A shutdown payoff of −$240 is worse than operating at either tabled price.
Follow the Entry Response
Initially ten firms face demand Q = 800 − (100/3)P. At P = $12 they each produce forty, so industry output is 400. Demand now shifts to Q = 1,200 − (100/3)P while firm costs remain unchanged. What changes before and after entry?
Check your reasoning
Before entry, each firm chooses q = P/0.3 = (10/3)P. Ten firms supply Q = (100/3)P. Equating this to the new demand gives P = $18, Q = 600 and q = 60. Each firm earns $300 economic profit, as the table shows.
After free entry with unchanged costs, price returns to minimum ATC of $12. New demand at that price is Q = 800, supplied by twenty firms producing forty units each. Firm output returns to forty while market output doubles from the original 400. These are technical adjustment stages, not a fixed calendar duration.
At the two prices, profit can be written as (5/3)P² − 240 − 0.15[q − (10/3)P]². This verifies the best operating output for any given price in this example. Comparing with shutdown and, in the long run, the ability to avoid fixed costs supplies the remaining decision checks.
Try Three Equilibrium Questions
Choose one answer, then check your reasoning. These are short learning checks, not an exam score. If the controls are unavailable, the explanations remain readable below each question.
Answer B. MC = 0.3q = 18 gives q = 60. Revenue is $1,080 and TC is 0.15(60²) + 240 = $780, leaving $300. Free entry has not yet removed the profit gap.
Answer C. Economic profit subtracts total economic cost: 480 − 480 = 0. Producer surplus as defined here subtracts variable cost: 480 − 240 = 240. That surplus covers fixed economic cost over the period.
Answer D. Add the $3 external harm to private marginal cost: MSC = 12 + 3 = 15. That exceeds MSB of $12. The private P = MC condition therefore does not establish the social marginal condition for allocative efficiency.
Connect Equilibrium with Adjustment and Costs
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