CFA Level I · CFA Level I Exam

The Firm and Market Structures: formula sheet

Full chapter guide

Key formulas

Price-taker revenue: MR = AR = P; True for a perfectly competitive firm. Total revenue = P × Q.
Profit-maximizing output: MR = MC (with MC rising), so P = MC; Produce this quantity if the shutdown rule is satisfied.
Economic profit: Profit = (P − ATC) × Q = TR − TC; Positive profit attracts entry. Negative profit drives exit in the long run.
Short-run shutdown rule: Shut down if P < AVC; operate if P ≥ AVC; At P = AVC the firm is indifferent, since either choice loses total fixed cost.
Breakeven point: P = minimum ATC (economic profit = 0); Long-run equilibrium price in perfect competition.
Long-run equilibrium: P = MR = MC = minimum ATC; Zero economic profit and no entry or exit.
Total cost link: ATC = AFC + AVC; Use this to move between average cost measures.
Profit-maximizing rule: Produce the quantity where MR = MC; Then set the price from the demand curve at that quantity. Price is above MR and above MC.
Short-run economic profit: Economic profit = (P − ATC) × Q; Positive if P > ATC, zero if P = ATC, negative if P < ATC.
Long-run equilibrium: P = ATC and MR = MC, so economic profit = 0; Demand is tangent to ATC. Entry or exit drives the firm here.
Excess capacity: Excess capacity = output at minimum ATC − actual long-run output; Actual output sits on the falling part of ATC, so it is below the efficient scale.
Linear demand marginal revenue: If P = a − bQ, then MR = a − 2bQ; MR has the same intercept as demand and twice the slope. Useful for numerical questions.
Nash equilibrium (rule): Each player's strategy is a best response to the other players' strategies; Test it by asking whether any one player gains by deviating alone. If none does, it is a Nash equilibrium. A game can have more than one.
Dominant strategy (rule): Payoff from strategy X ≥ payoff from any other strategy, whatever the rival does; If a player has a dominant strategy, they will play it. Not every game has one.
Cournot with linear demand and constant marginal cost: P = a − bQ; MC = c; n identical firms: each q = (a − c) ÷ [b(n + 1)]; total Q = n(a − c) ÷ [b(n + 1)]; For n = 1 this gives the monopoly output (a − c) ÷ 2b. As n grows, Q approaches the competitive output (a − c) ÷ b. Mainly useful for understanding. Most exam items are conceptual.
Bertrand equilibrium (identical products): P = MC; Holds for identical products, no capacity limits and similar costs. Price competition removes economic profit.
Kinked demand marginal revenue: MR has a vertical gap at the kink; if MC stays within the gap, price and quantity do not change; Above the kink demand is elastic (rivals do not follow a price rise). Below it demand is less elastic (rivals follow a cut).
Stackelberg ordering: Leader output > Cournot output > follower output; The leader moves first and earns more than the follower. Total output is greater than in Cournot, so price is lower.
Total and marginal revenue: TR = P × Q; MR = ΔTR ÷ ΔQ; For a single-price monopolist, MR < P at every positive output.
Linear demand and MR: P = a − bQ → MR = a − 2bQ; MR has the same intercept as demand and twice the slope.
Profit-maximizing rule: MR = MC; then price from demand at that Q; Read price from the demand curve, not from the MR curve.
MR and elasticity: MR = P × (1 − 1 ÷ |E|); MR > 0 only when |E| > 1. A monopolist does not produce where demand is inelastic.
Economic profit: Profit = (P − ATC) × Q; Positive, zero or negative depending on price versus average total cost.
Regulated natural monopoly pricing: Average cost pricing: P = ATC. Marginal cost pricing: P = MC; Average cost pricing gives normal profit with some deadweight loss. Marginal cost pricing is efficient but causes a loss for the firm.
N-firm concentration ratio: CRN = s1 + s2 + … + sN (the N largest market shares); Shares can be of sales or output. Common versions are the 4-firm and 8-firm ratios. Ignores the other firms and the split inside the top N.
Herfindahl-Hirschman Index: HHI = Σ (si)² over all firms in the market; Use shares in whole percentages (HHI up to 10,000) or decimals (up to 1). Say which you use. A monopoly is 10,000 in percentage form; N equal firms give 10,000 ÷ N.
HHI with equal shares: HHI = 1 ÷ N (decimal form) or 10,000 ÷ N (percentage form); Gives the minimum HHI for N firms; any unequal split gives a higher value.
Market structure features: Perfect competition: many firms, identical product, no barriers. Monopolistic competition: many firms, differentiated, low barriers. Oligopoly: few firms, high barriers. Monopoly: one firm, high barriers.; Pricing power: none, some, considerable (interdependent), considerable (possibly regulated).

Quick revision

Perfect competition: many sellers, identical products, free entry, firms are price takers, price = MR.
Monopolistic competition: many sellers, differentiated products, free entry, downward-sloping demand, non-price competition such as advertising.
Oligopoly: few sellers, high barriers, interdependent decisions, products may be identical or differentiated.
Monopoly: one seller, very high barriers, no close substitutes, MR is below price.
Profit is maximised where MR = MC in every structure.
A firm should shut down in the short run if price is below average variable cost.
In the long run, perfect competition and monopolistic competition both earn zero economic profit because of free entry.
Perfect competition produces at the minimum of long-run average cost; the others typically do not.
A Nash equilibrium is where no player gains by changing strategy while the others hold theirs.
The prisoner's dilemma shows why firms can end up worse off by not cooperating.
HHI = Σ (market share)², using decimal shares consistently, so it ranges from near 0 to 1; a higher HHI means more concentration. If you use whole percentages instead, the scale is 0 to 10,000 and any thresholds change accordingly, so never mix the two.
The N-firm concentration ratio adds the market shares of the N largest firms.

Common mistakes

Using ATC instead of AVC for the shutdown decision Fix: Shutdown depends on P versus AVC in the short run. A loss with P ≥ AVC means keep operating because fixed costs are sunk.
Saying a firm earns zero profit means it makes no money in an accounting sense Fix: Zero economic profit means revenue covers all costs, including the opportunity cost of capital (normal profit).
Saying firms earn positive economic profit in the long run. Fix: Remember that entry is easy. Market power is real, but entry drives economic profit to zero.
Treating the firm as a price taker with a horizontal demand curve. Fix: Differentiation gives a downward-sloping demand curve. Price exceeds MR and MC.
Calling the best joint outcome the Nash equilibrium. Fix: Apply the deviation test. The Nash equilibrium is where no player gains by changing alone, and it may be worse for both than another cell.
Mixing up Cournot and Bertrand. Fix: Cournot firms choose quantity. Bertrand firms choose price, and with identical products the price falls to marginal cost.
Reading the price off the MR curve at the MR = MC output. Fix: After finding Q, always go up to the demand curve for the price. MR is only used to pick the quantity.
Treating MR as equal to price, as in perfect competition. Fix: For a single-price monopolist, MR is below price at every positive output. Only perfect price discrimination makes MR equal to demand.
Adding shares for all firms in the HHI without squaring Fix: HHI always squares each share. The N-firm ratio never squares.
Leaving out small firms in the HHI Fix: Include every firm that is listed. Tiny firms add little but are part of the formula.

Exam tips

Questions often hand you P, ATC and AVC and ask what the firm does. Compare P with ATC first, then AVC.
Watch the time frame. Short-run answers allow profit or loss. Long-run answers settle at zero economic profit.
Do not let an unlisted fixed cost distract you. Fixed cost matters only through ATC and the size of the loss.
Remember the supply curve fact: the short-run firm supply curve is MC above minimum AVC.
With three options and no penalty for wrong answers, eliminate any option claiming long-run economic profit or shutdown when P ≥ AVC.
Long-run questions almost always test zero economic profit and excess capacity together. Remember both.
If an option says the firm produces at minimum ATC with P = MC in the long run, it describes perfect competition. Eliminate it.
For numerical questions, find Q from MR = MC first and then read P from demand. Check what the question asks for: price, quantity or profit.