Perfect Competition: Key Concepts & Quiz Explanations

Price-Taking Behavior in Perfect Competition

• Definition of a price-taking firm:
  • Operates in a market with many buyers and sellers, each too small to influence price individually.
  • Must accept the prevailing market price; attempting to charge more results in zero sales.
• Key implication:
  • The firm’s demand curve is perfectly elastic (horizontal) at the market price.
  • It can "sell all it wants" at that price, but not at a higher one.
• Mathematical representation:
  • Market price P is exogenous to the firm.
  • Marginal revenue MR equals P for every unit: MR = P.

Long-Run Exit Criterion

• Long-run decision rule:
  • A firm exits the market if it cannot cover total cost (TC) in the long run, i.e. when TR < TC.
  • Economic profit ( \pi = TR - TC ) is negative.
• Significance:
  • Ensures that resources flow out of inefficient uses toward alternative industries.
  • In perfect competition, long-run equilibrium drives firms to zero economic profit.

Output Decision Rules (Short-Run & General)

• Increase output if MR > MC:
  • Each additional unit adds more to revenue than to cost → profit rises.
  • Transcript phrasing: “An increase in output will increase the firm’s profit.”
• Decrease output if MC > MR:
  • Additional units cost more than they bring in → cutting back raises profit.
  • Transcript phrasing: “A decrease in output will increase the firm’s profit.”
• Profit-maximizing quantity q^* occurs where MR = MC (and MC is rising).

Revenue & Cost Calculations in a Competitive Setting

• With a constant price P:
  • Total revenue: TR = P \times Q.
  • Marginal revenue: MR = \frac{\Delta TR}{\Delta Q} = P (because price does not change with quantity).
• Tabular or graphical problems often supply a price column; students compute TR, MR, and compare to MC.

Market-Level Dynamics After a Demand Increase (Panel b Scenario)

• Short-run effect:
  • Demand curve shifts right → market equilibrium price P rises.
  • Existing firms, with unchanged cost curves, now earn positive economic profit (\pi > 0).
• Long-run adjustment:
  • Free entry attracts new firms.
  • Industry supply curve shifts right until price falls back to minimum average cost.
  • Economic profit is driven to zero; market "normalizes."
• Broader connection:
  • Demonstrates the self-correcting nature of perfectly competitive markets.

Long-Run Entry Process (Profits → Entry)

• Quiz statement: “New firms enter the market, eliminating profits.”
• Mechanism:
  1. \pi > 0 signals opportunity.
  2. Entry increases market supply S \uparrow.
  3. Price falls until P = ATC_{min} and \pi = 0.
• Essential principle: free, costless entry and exit equalize rates of return across industries.

Short-Run Shutdown Criterion

• Some inputs are fixed → exit not immediately feasible.
• Shutdown rule: produce nothing if price is below average variable cost (AVC).
  • Condition: P < AVC_{min}.
  • Rationale: the firm cannot even cover variable costs; operating would increase losses beyond fixed costs.
• If AVC < P < ATC: firm continues to produce, covering variable costs and some fixed cost, despite short-run losses.

The Firm’s Short-Run Supply Curve

• In perfect competition, the firm’s supply is its marginal cost (MC) curve above AVC_{min}.
  • Formally: qs(P) = MC^{-1}(P) for all P \ge AVC{min}; q_s = 0 otherwise.
• Why above AVC?
  • Below that point, the firm shuts down (zero supply).

Profit Maximization Condition Restated

• Universal rule in perfect competition:
  P = MR = MC at quantity q^*.
• Graphically: intersection of horizontal price line with upward-sloping MC curve above AVC.
• Ensures that neither expanding nor contracting output can raise profit.

Conceptual & Practical Connections

• Relation to earlier cost theory:
  • Average total cost (ATC) reaches minimum where it intersects MC.
  • Zero economic profit in long run corresponds to P = ATC_{min}.
• Real-world relevance:
  • Agricultural markets (e.g., wheat) approximate perfect competition; individual farmers are price takers.
• Ethical & policy implications:
  • Efficiency: resources allocated where P = MC, equating society’s marginal benefit and marginal cost.
  • Entry/exit freedoms foster innovation but also expose firms to risk; social safety nets may be debated.

Numerical Example (Hypothetical)

• Suppose P = \$10, MC schedule rises with quantity.
• Table snippet:
  • Q: 1 2 3 4 5
  • MC: 4 6 9 12 15
• Decision process:
  1. Compare P to MC: produce until MC exceeds P.
  2. Here Q^* = 3 (because MC3 = 9 < 10, but MC4 = 12 > 10).
  3. Profit per unit: P - ATC; compute ATC to verify \pi.

Key Formulas Recap

• TR = P \times Q
• AR = \frac{TR}{Q} = P
• MR = \frac{\Delta TR}{\Delta Q} = P (in perfect competition)
• \pi = TR - TC
• Shutdown: P < AVC_{min}
• Long-run exit: P < ATC_{min}
• Supply (firm): MC curve above AVC_{min}
• Profit max: P = MC

Study Tips

• Always start with cost curves—identify AVC{min}, ATC{min}, intersection with MC.
• Remember: in perfect competition, price is given; your task is selecting the optimal quantity.
• Distinguish between shutdown (short run) and exit (long run).
• For tables, compute TR and MR row by row; compare to MC.
• Practice drawing side-by-side graphs: industry supply–demand on left, firm cost curves on right, to visualize price transmission.