1. Introduction

• The study of theory of the firm analyses how firms make production and pricing decisions to maximize profit, given technology and market conditions.
• This chapter focuses on the firm under perfect competition, a market model that provides a useful benchmark for understanding supply, price taking behaviour, and industry dynamics.
• We will cover: defining features of perfect competition; revenue concepts; the profit-maximisation problem (algebraic and graphical); short-run and long-run supply curves; shutdown and break-even points; determinants of supply; technological change; input price effects; market supply; and price elasticity of supply.
• Throughout, key terms are highlighted for quick revision.

2. Perfect Competition: Defining Features

• Large number of buyers and sellers: No single buyer or seller can influence market price.
• Homogeneous product: Firms sell identical (perfectly substitutable) products.
• Free entry and exit: Firms can enter or leave industry without significant barriers in the long run.
• Perfect information: Buyers and sellers know prices and technology; no transaction costs or transport costs assumed.
• Price takers: Each individual firm accepts market price as given — it cannot influence price by its own output decision.
• Mobility of factors: Factors of production are mobile in long run — resources can move across firms and industries.
• Perfect competition is an idealised model — real markets may deviate, but the model helps identify efficient outcomes and comparative statics.

3. Revenue Concepts

• Total Revenue (TR): revenue from selling Q units at price P: TR = P × Q.
• Average Revenue (AR): revenue per unit sold: AR = TR / Q = P (for a price-taking firm AR equals market price).
• Marginal Revenue (MR): additional revenue from selling one more unit: MR = ΔTR / ΔQ. Under perfect competition, MR = P for all Q; the MR curve is horizontal at market price.
• Graphically, AR and MR coincide and are horizontal straight lines because price is constant regardless of firm’s output.
• Revenue curves are foundational for profit maximisation: firms equate marginal revenue with marginal cost to find optimal output.

4. Profit and Profit Maximisation

4.1 Profit Definitions

• Total Profit (π) = Total Revenue − Total Cost: π(Q) = TR(Q) − TC(Q).
• Accounting Profit uses explicit costs; economic profit subtracts both explicit and implicit (opportunity) costs.
• Normal profit is the minimum return required to keep the firm in business — it is part of opportunity cost and implies zero economic profit.

4.2 The Profit Maximisation Rule

• Profit maximisation requires choosing Q that maximizes π(Q).
• First-order condition: set marginal profit = 0 → MR = MC.
• Second-order condition: ensure marginal cost slope indicates maximum → marginal cost must be increasing at optimum (i.e., MC crossing MR from below).
• Under perfect competition, MR = P, so condition simplifies to P = MC at profit-maximising Q (with caveats regarding shutdown).

4.3 Graphical Representation of Profit Maximisation

• Draw MC and AC (average cost) curves and a horizontal line at price P (= MR = AR).
• Profit-maximising output Q* is where MC intersects MR from below.
• At Q*, compare P to ATC:
• If P > ATC at Q*, firm earns positive economic profit (area per unit = P − ATC; total profit = (P − ATC)×Q*).
• If P = ATC, firm earns zero economic profit (normal profit) — break-even point.
• If AVC < P < ATC, firm produces in SR but incurs economic loss (loss smaller than TFC because variable costs covered). Firm stays in production if losses smaller than fixed costs (i.e., P ≥ AVC minimum).
• If P < AVC at any Q, firm should shut down in short run — better to produce zero and incur fixed costs only.
• Graphically, the vertical distances between P and ATC/AVC/MC at Q* illustrate profit, loss, or shutdown scenarios.

5. The Supply Curve of a Firm under Perfect Competition

5.1 Short-Run Supply Curve

• The firm’s short-run (SR) supply curve shows the relationship between price and quantity supplied, holding plant size constant.
• For a competitive firm, the portion of the MC curve above the minimum of AVC represents the short-run supply curve: Supply_SR = MC for P ≥ min(AVC).
• Reason: firm chooses Q where P = MC if P ≥ AVC; if P < AVC, the firm shuts down (Q = 0).
• Therefore SR supply is discontinuous at prices below shutdown point (Q=0) and follows MC thereafter.
• Graphically draw MC with its U-shape; mark minimum AVC — MC above that point is supply curve.

5.2 The Shutdown Point

• Shutdown point is price equal to minimum AVC.
• At prices below shutdown point, the firm cannot cover variable costs and stops production in SR.
• At price exactly equal to minimum AVC, firm is indifferent between producing and shutting down (covers variable costs but not fixed costs).

5.3 Short-Run Supply and Fixed Costs

• Fixed costs (TFC) do not affect the position of the SR supply curve (they affect profits but not marginal production decisions).
• Therefore changes in fixed cost (e.g., sunk investments, some taxes) do not change SR supply as long as AVC and MC unaffected.

6. Long-Run Supply Curve of a Firm

• In the long run (LR), all factors are variable; firms can adjust plant size or enter/exit industry.
• A competitive firm’s LR supply emerges from its long-run marginal cost (LRMC) and the long-run average cost (LRAC).
• If firms are price takers and can vary scale, the LR supply is the portion of LRMC above the minimum point of LRAC — that is, where P ≥ min(LRAC).
• In LR equilibrium with free entry and exit, price tends to equal minimum LRAC (firms earn zero economic profit / normal profit).
• Therefore individual firm’s supply in LR is horizontal at P = min LRAC under perfectly competitive constant-cost industry; in increasing-cost or decreasing-cost industries, industry LR supply may slope upward or downward.

7. The Normal Profit and Break-even Point

• Normal profit = minimum return required to keep resources in current use; part of opportunity cost; zero economic profit corresponds to normal profit.
• Break-even point is price at which firm’s TR equals TC (P = ATC minimum) — firm covers all costs including normal profit.
• In long-run competitive equilibrium, firms earn normal profit only (P = min LRAC), and no incentive exists for entry or exit.

8. The Shut-down and Exit Decision

• Short-run shut-down decision based on price relative to AVC: if P < min AVC → shut down now.
• Long-run exit decision depends on price relative to ATC: if P < min ATC persistently, firms will exit the industry in the long run.
• Shut-down minimizes loss in SR (loss = TFC if shut) while producing could incur larger loss if P < AVC.

9. Determinants of a Firm’s Supply Curve

• Supply is influenced by factors that shift MC or affect production capacity:
1. Technology (Technological progress): Improvements shift MC downward (lower cost per unit) and increase supply.
2. Input prices: Rise in wages or raw material costs shifts MC upward → supply contracts; fall in input prices shifts MC downward → supply expands.
3. Taxes and subsidies: Per-unit taxes effectively raise MC by tax amount; subsidies lower MC and increase supply.
4. Regulation and compliance costs: New regulations can raise per-unit cost or fixed compliance cost, shifting supply left.
5. Number of firms: Industry supply = horizontal summation of individual supplies; entry increases market supply, exit reduces it.
6. Expectations: Anticipated future price increases may reduce current supply as firms hold back output (inventory) and vice versa.

10. Technological Progress

• Technological progress can be:
• Process innovation: producing same output with fewer inputs → lower MC and ATC.
• Product innovation: new products may alter market demand and industry structure (less relevant to supply curve position but vital for firm strategy).
• Graphical effect: downward shift of MC and ATC; at a given price, firm supplies larger Q.
• Long-run industry impact: technology diffusion among firms increases industry supply and can reduce industry price if demand unchanged.

11. Input Prices

• Input price increase (wages, raw materials, energy) raises TVC and MC: both AVC and ATC shift upward.
• Short-run effect: for a given P, Q supplied falls (move along supply curve or supply shifts if all firms affected).
• Long-run: firms adjust scale or substitute inputs (if possible); factor price changes may alter industry LRAC and thus long-run supply.

12. Supply Curve of the Market

• Market supply is obtained by horizontal summation of individual firm supply curves at each price.
• If each firm’s SR supply is its MC above AVC, market SR supply at price P equals sum of all individual Qs where P = MC(i).
• Industry supply changes with number of firms, technology, input prices and expectations.
• Short run vs long run: industry supply is more elastic in long run due to entry/exit and capacity adjustments.

13. Price Elasticity of Supply

• Price elasticity of supply (Es) measures responsiveness of quantity supplied to price changes:
Es = (% change in quantity supplied) / (% change in price)
• Determinants of Es:
• Time horizon: Supply more elastic in long run (firms adjust capacity) than short run.
• Spare capacity: Firms with spare capacity can expand output quickly → more elastic supply.
• Availability of inputs: Easier access to inputs → more elastic.
• Mobility of factors: High factor mobility increases elasticity.
• Stock and inventory: Firms with inventories can supply more quickly in response to price rise → higher elasticity short-run.
• Special cases:
• Perfectly inelastic supply (Es = 0): vertical supply curve (fixed quantity, e.g., unique artworks in short run).
• Perfectly elastic supply (Es = ∞): horizontal supply curve — firm supplies any quantity at a given price (theoretical extreme).

14. Supply Curve Shifts: Illustrations

• Rightward shift (supply increase): technological improvement, input price fall, subsidies, increase in number of firms.
• Leftward shift (supply decrease): input price rise, tax imposition, natural disasters, reduction in firms.
• Graphical exercise: show initial supply S0, then S1 shifted right/left; illustrate new equilibrium price and quantity when demand unchanged.

15. The Firm’s Short-Run Supply Curve — Worked Example

• Given a U-shaped MC curve and AVC curve, identify minimum AVC (shutdown) and trace MC above this point as supply.
• Numerical illustration: suppose MC schedule (for integer Q): Q:0→5 ; MC: 10, 8, 9, 12, 18 ; AVC minima at MC=9 at Q=2 → supply at price ≥9 yields positive output accordingly.
• Plotting price vs Q gives discrete supply points; connect to see upward sloping SR supply.

16. The Firm’s Long-Run Supply Curve — Worked Example

• Suppose a constant-cost industry: LRAC of firms unchanged as industry expands; free entry ensures P → minimum LRAC; LR supply is horizontal.
• Example: if minimum LRAC = 30, and demand rises, in long run entry increases supply until price returns to 30 — output of industry rises but price unchanged.
• In increasing-cost industry, industry expansion raises input prices so LR supply slopes upward (higher price required to sustain larger output).

17. The Role of Expectations and Inventories

• Expectations of higher future price can reduce current supply as firms hold inventories — current supply curve shifts left.
• Firms with flexible inventory management can smooth supply — large inventories increase short-run supply elasticity.
• Seasonal goods: inventories and storage costs play important role in supply responsiveness.

18. Comparative Statics: Supply Shifts with Demand Changes

• When demand increases in SR: price rises; firms produce more along SR supply; if price remains high, entry will occur in LR shifting LR supply right and restoring price toward minimum LRAC (if free entry).
• If demand decreases, price falls; marginal firms exit in LR, reducing supply and moving price back up toward LRAC minimum.
• This entry–exit mechanism explains how competitive markets tend toward zero economic profit in LR.

19. Policy and Market Interventions Affecting Supply

• Taxes: per-unit tax t shifts MC up by t; supply shifts left — market price increases, quantity falls depending on elasticities.
• Subsidies: per-unit subsidy reduces MC; supply shifts right — price falls, quantity rises.
• Price floors/ceilings: binding floor above equilibrium causes excess supply; binding ceiling creates shortage.
• Regulation (minimum standards, emissions): may raise average costs and shift supply left.

20. Efficiency and Perfect Competition

• Perfect competition yields allocative efficiency in equilibrium where P = MC → value to consumers equals marginal cost of production.
• It also yields productive efficiency in long run (firms produce at minimum LRAC).
• Thus perfect competition is a benchmark for welfare: no deadweight loss, maximum total surplus, given assumptions hold.
• Limitations: market failures (externalities, public goods), imperfect information, and market power justify deviations from perfect competition in policy and regulation.

21. Common Exam Questions & Strategies

• Always draw clear, labelled diagrams: MC, ATC, AVC, price line (AR=MR) — indicate Q*, profit/loss rectangle, shutdown point, break-even point.
• State conditions explicitly: profit-maximisation rule (MR = MC), shutdown rule (P < AVC), exit condition (P < ATC in long run).
• Explain comparative statics: how a tax or subsidy shifts MC and supply and impacts price and quantity.
• For elasticity questions: explain short-run vs long-run elasticity, use definitions and factors affecting elasticity.
• When asked about efficiency, mention both allocative and productive efficiency and underlying assumptions.

22. Extended Examples and Numerical Problems

• Problem 1 (Profit, given cost schedule): Suppose a competitive firm faces P = 20. TC schedule (for Q = 0..5) = 10, 15, 20, 30, 45, 65. Compute TR, profit, identify Q*.
• Solution sketch: TR = P×Q; profit = TR − TC; compute profit for each Q and find maximum. Then confirm MR (=20) equals MC at Q*.
• Problem 2 (Supply reaction to wage increase): Given AVC and MC functions that depend on wage w, show effect of w↑ on firm’s SR supply and market supply.
• Approach: Increase variable cost components; derive new MC; trace MC above AVC minimum to get new SR supply; aggregate across firms for market effect.

23. Useful Formulas & Identities (Quick Reference)

24. Summary — Key Takeaways

• Under perfect competition, firms are price takers; AR = MR = P.
• Profit maximisation requires equating MR to MC and checking second-order conditions.
• Short-run firm supply is the upward portion of MC above minimum AVC; long-run supply relates to LRAC and market entry/exit.
• Shutdown point and break-even point are critical to short-run and long-run decisions respectively.
• Supply responds to technology, input prices, taxes, subsidies, and expectations; its elasticity depends on time, capacity, and factor mobility.
• Perfect competition achieves allocative and productive efficiency under its assumptions but is an idealised benchmark; real markets often deviate.