CA Foundation · Business Economics

Price Determination in Different Markets: formula sheet

Full chapter guide

Key formulas

Perfect competition features: Very many sellers + identical product + free entry/exit + perfect knowledge + perfect mobility of factors → price taker (AR = MR = price); Individual firm cannot influence price. Its demand curve is perfectly elastic (horizontal).
Monopoly features: One seller + no close substitutes + barriers to entry → price maker; The firm is the industry. The demand curve slopes downward.
Monopolistic competition features: Many sellers + differentiated products + free entry/exit → some price control; Selling costs and branding are common. Demand is downward sloping but fairly elastic.
Oligopoly features: Few sellers + interdependence of decisions + entry barriers; Products may be identical (pure oligopoly) or differentiated. Each firm considers rivals' reactions.
Time classification: Market period: supply fixed. Short run: some inputs fixed. Long run: all inputs variable; Demand mainly decides price in the market period. Supply matters more as time lengthens.
Total revenue: TR = P × Q; Price times quantity sold.
Average revenue: AR = TR ÷ Q = P; AR curve is the demand curve facing the firm.
Marginal revenue (discrete): MR = ΔTR ÷ ΔQ = TRn − TRn−1; Use when a table of quantities is given. Valid for one-unit changes in the second form.
Marginal revenue (calculus): MR = dTR/dQ; Use when TR or price is given as a function of Q.
Perfect competition: AR = MR = P; Both are horizontal at the market price.
Linear demand: If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ; MR has the same intercept but double the slope.
AR, MR and elasticity: MR = AR × (e − 1) ÷ e, where e = absolute value of price elasticity; MR > 0 when e > 1, MR = 0 when e = 1, MR < 0 when e < 1.
Firm's demand curve: P = AR = MR (horizontal line at market price); True for a firm under perfect competition because it is a price taker.
Equilibrium condition of the firm: MC = MR (= P), with MC cutting MR from below; Second condition: MC must be rising at the equilibrium output.
Supernormal profit (short run): Profit = (P − AC) × Q; Positive when P > AC.
Normal profit: P = AC; Total revenue equals total cost, including normal return to the entrepreneur.
Short-run shutdown rule: Continue if P ≥ AVC; shut down if P < AVC; Loss is then smaller than total fixed cost if P ≥ AVC.
Long-run equilibrium: P = MR = AR = MC = minimum LAC; Firm earns only normal profit; industry has no incentive for entry or exit.
Profit-maximising condition: MC = MR, and MC cuts MR from below; Applies to a monopolist. The second part is the second-order condition.
Price at equilibrium: Price = AR at the equilibrium output; Find Q from MC = MR, then put Q in the demand equation to get P.
Revenue relations: TR = P × Q; MR = ΔTR ÷ ΔQ; AR = TR ÷ Q; Under monopoly, MR < AR for all units after the first.
Linear demand and MR: If P = a − bQ, then MR = a − 2bQ; MR has the same intercept and twice the slope.
Profit: Profit = (AR − AC) × Q = TR − TC; Abnormal profit if AR > AC; loss if AR < AC.
Monopoly vs perfect competition: Monopoly: P > MR = MC; Perfect competition: P = MR = MC; Use this to compare the two quickly.
Third-degree discrimination rule: Set MR₁ = MR₂ = MC; The market with less elastic demand gets the higher price.
Equilibrium condition: MR = MC, with MC cutting MR from below; Applies in both the short run and the long run. It fixes the profit-maximising output.
Short-run abnormal profit: AR > AC at equilibrium output; profit = (AR − AC) × Q; Profit is the area between the price and AC at that output.
Short-run loss: AR < AC at equilibrium output; loss = (AC − AR) × Q; The firm continues in the short run if AR ≥ AVC.
Long-run equilibrium: MR = MC and AR = AC (normal profit); The AR curve is tangent to the LAC curve at the output where MR = MC.
Excess capacity: Excess capacity = Output at minimum LAC − Actual long-run output; The tangency occurs on the falling part of LAC, so output is below the minimum-cost output.
Price–MC relation: P > MC in equilibrium; Unlike perfect competition, where P = MC.
Profit-maximising rule (all structures): MR = MC, with MC cutting MR from below; Every profit-seeking firm uses this rule. The structure only changes what MR looks like.
Perfect competition: P = AR = MR = MC (equilibrium); Long run also gives P = minimum AC and zero abnormal profit.
Monopoly: P > MR, and at equilibrium P > MC; Price is read from the demand curve (AR) at the MR = MC output.
Monopolistic competition, long run: P = AC, P > MC; Normal profit only, because of free entry. Output is below the minimum-cost level.
Lerner index of market power: L = (P − MC) ÷ P; Zero under perfect competition. Higher values mean more market power.
Terms to remember: Monopsony = 1 buyer; Duopoly = 2 sellers; Oligopoly = few sellers; Oligopsony = few buyers; Most MCQs test these definitions directly.

Quick revision

Perfect competition: many sellers, homogeneous product, free entry and exit, price taker.
In perfect competition, AR = MR = price, so the demand curve is horizontal.
Monopoly: single seller, no close substitutes, strong entry barriers, price maker.
For a monopolist, AR slopes downward and MR lies below AR.
A profit-maximising firm produces where MR = MC, with MC cutting MR from below.
Monopolistic competition: many sellers, differentiated products, free entry, some price control.
Oligopoly: few sellers, interdependence, and often heavy advertising or non-price competition.
Kinked demand curve: demand is more elastic above the kink and less elastic below it, so prices stay rigid. Rivals do not follow a price rise but match a price cut.
Price discrimination: same product, different prices to different buyers, with separate markets and different elasticities.
TR is maximum where MR = 0.
In the long run, a perfectly competitive firm earns only normal profit.
Monopolistic competition firms tend to have excess capacity in the long run.

Common mistakes

Thinking a market must be a physical place. Fix: Remember that economics defines a market by contact between buyers and sellers and a common price. Online and phone dealing count.
Confusing monopolistic competition with monopoly. Fix: Monopolistic competition has many sellers with differentiated products. Monopoly has one seller. Count the sellers.
Writing MR = P for a monopolist. Fix: MR = P only when price is constant. For a falling demand curve, MR is less than P.
Doubling the intercept instead of the slope when finding MR. Fix: For P = a − bQ, MR = a − 2bQ. The intercept stays a. The slope b doubles.
Saying the firm sets the price in perfect competition. Fix: Repeat: industry sets price, firm takes it. The firm only chooses output.
Thinking normal profit means zero profit in every sense. Fix: Normal profit is the minimum reward that keeps the entrepreneur in business and is included in cost. Economic (supernormal) profit is zero.
Reading the price from the MR curve instead of the demand curve. Fix: After MC = MR gives Q, always go up to the AR (demand) curve to get P.
Using P = MC for a monopolist. Fix: For monopoly, write MR = MC. Price will be above MC.
Saying the firm earns abnormal profit in the long run. Fix: Free entry removes abnormal profit. Long run means AR = AC and normal profit.
Writing that price equals marginal cost in long-run equilibrium. Fix: Here the AR curve slopes down, so MR is below AR. At MR = MC, price is above MC.

Exam tips

Questions are mostly direct feature-matching, so learn the four structures as a table of seller count, product type, entry and price control.
Watch for 'except' and 'not' in the question. Read all four options before choosing.
The phrase 'price taker' always signals perfect competition. 'Interdependence' always signals oligopoly.
Revise the area and time classifications too. They are short and easy to score on.
If two options both look right, re-read for the exact condition, such as 'differentiated' versus 'identical'.
Memorise the three shapes: horizontal AR = MR for perfect competition, downward AR with lower MR for monopoly, and TR as a hill for monopoly.
For linear demand, use MR = a − 2bQ straight away. It saves a full minute.
Questions often link MR sign to elasticity. Learn: MR > 0 is elastic, MR = 0 is unit elastic, MR < 0 is inelastic.