Source: Lecture Notes of Prof. Guoqiang Tian, Texas A&M University
Tags: profit maximisation, competitive firm, price taker, marginal revenue, MR equals MC, shutdown rule, short-run supply curve, industry supply, long-run equilibrium, zero economic profit, entry and exit, price elasticity of supply, constant-cost industry, increasing-cost industry
A perfectly competitive firm is a price taker that maximises profit by producing where marginal cost equals price (MC = P). In the short run, the firm's supply curve is its MC curve above the minimum AVC. In the long run, free entry and exit drive economic profit to zero, so price settles at the minimum of long-run ATC. The industry supply curve depends on whether it is a constant-cost, increasing-cost, or decreasing-cost industry.
Competitive firm
A firm that is one of many producing identical products. It is a price taker in both input and output markets. Its individual demand curve is horizontal (perfectly elastic).
Profit
Total revenue minus total cost. pi = TR - TC.
Total revenue (TR)
Price times quantity. TR = P * q.
Average revenue (AR)
TR / q = P. For a competitive firm, average revenue equals the market price.
Marginal revenue (MR)
The change in total revenue from selling one more unit. MR = delta TR / delta q = P for a competitive firm.
Profit-maximising output rule
Produce where MC = MR = P, provided price covers average variable cost.
Shutdown rule
The firm should produce in the short run if and only if P >= AVC (equivalently, TR >= TVC). If P < AVC, the firm minimises losses by shutting down and losing only fixed costs.
Short-run supply curve of the firm
The portion of the MC curve that lies above the minimum AVC. Below that price, quantity supplied is zero.
Short-run industry supply curve
The horizontal sum of all individual firms' MC curves (above their AVCs).
Long-run competitive equilibrium
Occurs when three conditions hold simultaneously: each firm produces where P = LMC; firms earn zero economic profit (P = minimum LATC); and market quantity demanded equals market quantity supplied.
Zero economic profit
Normal profit is earned (the owner's opportunity cost is covered), but there is no surplus above that. This is the long-run equilibrium condition under perfect competition.
Price elasticity of supply
The percentage change in quantity supplied divided by the percentage change in price. Always positive when the supply curve slopes upward.
Constant-cost industry
Entry and exit of firms do not affect input prices. Long-run supply curve is horizontal.
Increasing-cost industry
Entry of firms bids up input prices, raising costs. Long-run supply curve slopes upward.
Decreasing-cost industry
Expansion of the industry lowers input costs (e.g. through external economies of scale). Long-run supply curve slopes downward.
Large numbers of buyers and sellers (no individual has market power).
Unrestricted mobility of resources (free entry and exit in the long run).
Homogeneous (identical) product.
All participants possess relevant information.
Because products are identical and firms are small, each firm faces a horizontal demand curve at the market price. P = AR = MR.
The firm's decision has two parts:
Should the firm produce at all?
Yes, if there exists some output where TR > TC (the firm earns positive profit).
Yes, if the firm cannot make a profit but can make a loss smaller than fixed costs. This happens when TR > TVC, i.e. P > AVC.
No (shut down), if P < AVC at all output levels. In this case, producing only adds to losses beyond fixed costs.
What quantity to produce?
Produce up to the point where MC = P (and MC is rising). It is worth producing any unit where MR > MC. It is not worth producing units where MR < MC.
P > ATC: the firm earns positive economic profit. Profit = (P - ATC) * q.
AVC < P < ATC: the firm operates at a loss, but the loss is smaller than TFC. Loss = (ATC - P) * q.
P < AVC: the firm shuts down. Loss = TFC.
P = ATC: the firm earns zero economic profit (normal profit).
The industry supply curve is the horizontal sum of all individual firms' MC curves (above minimum AVC). It slopes upward because each firm's MC slopes upward (due to diminishing marginal returns).
The intersection of industry supply and market demand determines the equilibrium price and total industry output.
In the long run, firms can adjust all inputs (including plant size) and can enter or exit the industry.
Entry eliminates profits: if existing firms earn economic profits, new firms enter. Supply increases, price falls, and profits shrink until P = minimum LATC and economic profit = 0.
Exit eliminates losses: if firms suffer economic losses, some exit. Supply decreases, price rises, and losses shrink until P = minimum LATC and economic profit = 0.
Long-run equilibrium conditions:
P = LMC (each firm maximises profit).
P = minimum LATC (zero economic profit, so no incentive for entry or exit).
Total industry output equals total quantity demanded.
With a given price, the long-run most profitable output may differ from the short-run most profitable output because the firm can adjust its scale of operations. In the long run, the firm operates on its long-run MC curve; in the short run, it is constrained by its current plant size.
Es = (% change in Qs) / (% change in P) = (delta Q / Q) / (delta P / P)
|Es| > 1: elastic supply
|Es| < 1: inelastic supply
|Es| = 1: unit elastic
|Es| = 0: perfectly inelastic (vertical supply)
|Es| = infinity: perfectly elastic (horizontal supply)
Constant-cost industry: entry/exit does not affect input prices. The long-run supply curve is horizontal at the minimum LATC.
Increasing-cost industry: entry bids up input prices, raising costs. The long-run supply curve slopes upward.
Decreasing-cost industry: expansion lowers per-unit costs (external economies). The long-run supply curve slopes downward.
Profit: pi = TR - TC = P * q - TC
Profit-maximisation condition: MC = MR = P
Shutdown condition: produce only if P >= AVC
Short-run supply = MC curve above min AVC
Long-run equilibrium: P = LMC = min LATC
Elasticity of supply: Es = (delta Qs / Qs) / (delta P / P)
⚠️ The profit-maximisation rule MC = P is the cornerstone of competitive firm analysis. Always confirm MC is rising at the chosen output.
⚠️ The shutdown rule compares P to AVC (not ATC) in the short run. Even at a loss, the firm should keep producing if it covers variable costs. Shutting down means losing all of TFC.
⚠️ In the long run, economic profit is zero. This does not mean the firm earns nothing; it earns normal profit (the opportunity cost of the owner's resources is covered).
⚠️ Know the difference between the short-run supply curve (MC above AVC) and the long-run supply curve (depends on industry cost structure).
⚠️ Entry/exit is the mechanism that drives long-run equilibrium. If you see positive economic profit, expect entry and a price decrease. If you see losses, expect exit and a price increase.
Q: A competitive firm has P = $12, ATC = $10, AVC = $8 at its profit-maximising output of 100 units. What is its economic profit?
A: Profit = (P - ATC) q = (12 - 10) 100 = $200.
Q: Should a competitive firm produce if P = $6, min AVC = $5, and min ATC = $9?
A: Yes. Since P ($6) > min AVC ($5), the firm should produce. It will operate at a loss because P < ATC, but the loss is smaller than TFC. Shutting down would lose the entire TFC.
Q: Why is the short-run industry supply curve upward sloping?
A: Because it is the horizontal sum of individual firms' MC curves, each of which slopes upward due to the law of diminishing marginal returns.
Q: In a constant-cost industry, what is the long-run effect of an increase in demand?
A: In the short run, price rises and firms earn economic profit. New firms enter, supply increases, and price falls back to the original level (min LATC). In the new long-run equilibrium, a larger quantity is supplied at the same price. The long-run supply curve is horizontal.
Q: What are the three conditions for long-run competitive equilibrium?
A: (1) Each firm produces where P = LMC (profit maximisation). (2) P = min LATC (zero economic profit, no incentive for entry or exit). (3) Market clears: total quantity supplied equals total quantity demanded.
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