The Theory of the Firm under Perfect Competition

2.1 Core concepts

• A perfectly competitive market has four defining features: (1) large number of buyers and sellers, (2) homogeneous product, (3) free entry and exit, and (4) perfect information (NCERT §4.1, p. 53).
• These four features together produce the single most distinguishing characteristic of perfect competition — price-taking behaviour: an individual firm cannot sell anything above the market price and has no incentive to sell below it (NCERT §4.1, p. 54).
• A firm's total revenue is TR = p x q, where p is the market price and q the output sold; when no unit is sold TR is zero (NCERT §4.2, p. 54, Table 4.1).
• Because p is constant for a price-taking firm, the total revenue curve is an upward-sloping straight line through the origin whose slope equals the market price p (NCERT §4.2, p. 55, Fig. 4.1).
• Average revenue AR = TR / q = p, so for a price-taking firm the AR curve is a horizontal price line at height p, and this same line is also the firm's perfectly elastic demand curve (NCERT §4.2, p. 55, Fig. 4.2).
• Marginal revenue MR is the change in TR per unit increase in output; algebra and intuition both show that for a perfectly competitive firm MR = AR = p (NCERT §4.2, pp. 55-56).
• A firm is a profit maximiser; profit π = TR - TC, and profits are maximum at the output q0 where MR = MC, which for a price-taking firm reduces to p = MC (NCERT §4.3 and §4.3.1, p. 56).
• For positive output to maximise profit, three conditions must hold at q0: (i) p = MC, (ii) MC must be non-decreasing at q0, and (iii) p >= AVC in the short run / p >= AC in the long run (NCERT §4.3, p. 56).
• Condition 2 rules out downward-sloping segments of the MC curve as profit maxima — at such a point reducing output would raise profit (NCERT §4.3.2, p. 57, Fig. 4.3).
• Condition 3 in the short run: if p < min AVC, the area of rectangle OpAq1 (TR) is less than the area of rectangle OEBq1 (TVC), so the firm's loss exceeds TFC and it does better shutting down and bearing only -TFC (NCERT §4.3.3 Case 1, pp. 57-58, Fig. 4.4).
• Condition 3 in the long run: if p < min LRAC, TR < TC, the firm makes a loss, and since a shut-down firm in the long run has zero profit, the firm exits (NCERT §4.3.3 Case 2, p. 58, Fig. 4.5).
• Graphically, at the profit-maximising q0 (short run) profit equals the area of rectangle EpAB — the gap between price and SAC times output (NCERT §4.3.4, pp. 58-59, Fig. 4.6).
• The short-run supply curve of a firm is the rising part of the SMC curve from and above the minimum AVC, together with zero output for all prices strictly less than minimum AVC (NCERT §4.4.1, pp. 59-60, Fig. 4.8).
• The long-run supply curve of a firm is the rising part of the LRMC curve from and above the minimum LRAC, together with zero output for all prices less than minimum LRAC (NCERT §4.4.2, pp. 60-61, Fig. 4.10).
• The short-run shut-down point is the minimum of AVC where SMC cuts AVC; the long-run shut-down point is the minimum of LRAC (NCERT §4.4.3, p. 61).
• Normal profit is the minimum profit required to keep a firm in business and is part of total cost (an opportunity cost for entrepreneurship); profit over and above normal profit is super-normal profit; the break-even point is the point on the supply curve where the firm earns only normal profit — i.e. where the supply curve cuts LRAC (or SAC in the short run) at its minimum (NCERT §4.4.4, p. 61).
• Technological progress lowers MC at every output, shifts the MC (and hence the supply) curve rightward, so at any given price the firm supplies more (NCERT §4.5.1, p. 62).
• A rise in input prices raises both AC and MC, shifts the supply curve leftward, so at any given price the firm supplies fewer units (NCERT §4.5.2, p. 62).
• A unit tax of Rs t adds Rs t to both LRAC and LRMC at every output, shifting the long-run supply curve leftward (NCERT §4.5.2 box, pp. 62-63, Figs. 4.11 and 4.12).
• The market supply curve is the horizontal summation of individual firms' supply curves at every price; it shifts rightward if the number of firms increases and leftward if it decreases (NCERT §4.6, pp. 63-64, Fig. 4.13).
• Price elasticity of supply eS = (percentage change in quantity supplied) / (percentage change in price) = (ΔQ/Q) × (P/ΔP); it is zero for a vertical supply curve, positive for an upward-sloping curve, and independent of units (NCERT §4.7, pp. 65-66).
• Geometric method: for a straight-line supply curve cutting the price axis (positive part), eS > 1; through the origin, eS = 1; cutting the quantity axis (positive part), eS < 1 (NCERT §4.7 box, p. 66, Fig. 4.14).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 4.1 (p. 55): Total Revenue curve — straight line through origin with slope equal to price p.
• Fig. 4.2 (p. 55): Price Line — horizontal AR/MR/demand curve at height p; perfectly elastic.
• Fig. 4.3 (p. 57): MC curve with output points q1...q6 illustrating why MC must be non-decreasing at the profit-maximising output.
• Fig. 4.4 (p. 57): Short-run case where p < AVC; loss = area of rectangle pEBA, hence firm produces zero.
• Fig. 4.5 (p. 58): Long-run case where p < LRAC; firm exits because shut-down profit (zero) beats negative profit at q1.
• Fig. 4.6 (p. 58): Geometric representation of short-run profit maximisation; profit = area of rectangle EpAB at q0.
• Fig. 4.7 and 4.8 (pp. 59-60): Derivation and shape of the short-run supply curve — rising part of SMC from minimum AVC upward, plus zero output below.
• Fig. 4.9 and 4.10 (pp. 60-61): Long-run supply curve — rising part of LRMC from minimum LRAC upward, plus zero output below.
• Fig. 4.11 and 4.12 (p. 63): Unit tax of Rs t shifts LRAC and LRMC upward by t; supply curve S0 shifts left to S1.
• Fig. 4.13 (p. 64): Market supply curve as horizontal summation of S1 and S2; below p1 supply is zero, between p1 and p2 only firm 1 supplies, above p2 both firms supply.
• Fig. 4.14 (p. 66): Three straight-line supply curves — (a) cuts price axis, eS > 1; (b) through origin, eS = 1; (c) cuts quantity axis, eS < 1.

2.5 Key formulas

2.4 Common confusions / NTA trap points

• For a perfectly competitive firm MR = AR = p, but this equality holds only because the firm is a price-taker; do not assume the same for other market forms.
• p = MC is the profit-maximising condition only when MC is non-decreasing (rising) at that output; an intersection on the falling part of MC is a profit minimum, not a maximum.
• Short-run shut-down condition uses AVC (not AC) — fixed costs are sunk in the short run; in the long run the relevant minimum is LRAC because all costs are variable.
• Normal profit is included in total cost; "zero economic profit" already includes normal profit, so a firm at the break-even point is still in business.
• The market supply curve is obtained by horizontal summation (adding quantities at each price), not vertical summation (which is how individual demands are added for a public good — a frequent NTA trap).
• For a straight-line supply curve, eS depends on which axis it cuts: price axis -> eS > 1, origin -> eS = 1, quantity axis -> eS < 1; the slope alone does not determine elasticity.