Objectives and pricing policies of firms
Key terms
Define each term.
Multiple choice
Circle the correct answer.
Which condition is NOT necessary for a firm to practise third-degree price discrimination?
A firm produces where marginal revenue is zero. Which objective is it pursuing?
Worked problems
Show your working.
Three objectives on one demand curve. A firm faces the demand curve P = 100 - Q, so its marginal revenue is MR = 100 - 2Q. Its marginal cost and average cost are both constant at $20. Find the output, price and profit under profit maximisation, revenue maximisation and sales maximisation.
Third-degree price discrimination between two markets. An airline sells seats on a route to business travellers, with demand P = 200 - Q, and to leisure travellers, with demand P = 100 - Q. Marginal cost is constant at $20 per seat. Find the profit-maximising price and number of seats in each market.
Chains of reasoning
The steps are in the wrong order. Write the letters in the order that makes a linked chain.
How predatory pricing works, and why it may fail
- A The smaller rival cannot match the price for long without running out of money, so it exits.
- B A large firm faces a smaller rival in one of its markets.
- C With the rival gone, the large firm raises its price above the original level and recovers its losses.
- D It can fund the losses from profits made in its other markets, or from its larger reserves.
- E The strategy only pays if new firms cannot enter once prices rise, so it depends on high barriers to entry.
- F It cuts its price below average variable cost, knowing it will make a loss on every unit sold in that market.
- G Where entry is easy, the higher price attracts new rivals and the losses are never recovered, which is why genuine predatory pricing is rarer than accusations of it.
Diagrams
Draw a downward-sloping AR curve, its MR curve, and U-shaped MC and AC curves. Mark three outputs: the profit-maximising output where MC = MR, the revenue-maximising output where MR = 0, and the sales-maximising output where AR = AC. Mark the price at each by reading up to the AR curve.
Draw a kinked demand curve with the kink at the current price, relatively elastic above it and relatively inelastic below it. Draw the MR curve with its vertical gap at the output of the kink. Draw two MC curves, both passing through the gap, and show that the profit-maximising price and output are the same for both.
Extended answer
Plan your answer: list the points you would make in each paragraph.
Assess whether price discrimination is always against the interests of consumers. (13 marks)
Answers
Price discrimination: Charging different prices to different consumers for the same good or service, where the difference is not explained by differences in cost.
D. Price discrimination needs market power, separable groups with different elasticities, and no resale. Lower costs are not required: the price differences come from differences in demand, not in cost, which is what distinguishes discrimination from charging more because something costs more to supply.
B. Total revenue stops rising when an extra unit adds nothing to it, which is where MR = 0. Profit maximisation is where MC = MR, and sales maximisation is where AR = AC.
Step 1. Profit maximisation: MC = MR. 100 - 2Q = 20, so Q = 40 and P = 100 - 40 = $60. Profit = (P - AC) x Q = (60 - 20) x 40 = $1,600.
Step 2. Revenue maximisation: MR = 0. 100 - 2Q = 0, so Q = 50 and P = $50. Total revenue = 50 x 50 = $2,500. Profit = (50 - 20) x 50 = $1,500.
Step 3. Sales maximisation: AR = AC. 100 - Q = 20, so Q = 80 and P = $20. Total revenue = $1,600 and profit = 0, which is normal profit only.
Step 4. Compare. Output rises from 40 to 50 to 80 and price falls from $60 to $50 to $20 as the objective changes. Revenue is highest at 50 units, profit at 40, and output at 80. Consumers get the most output at the lowest price under sales maximisation.
Stating the condition first (MC = MR, MR = 0, AR = AC) earns the method mark even if the arithmetic slips. The ranking of outputs in step 4 is worth learning because it holds for any downward-sloping demand curve.
Step 1. Business market. MR = 200 - 2Q. Set MR = MC: 200 - 2Q = 20, so Q = 90 and P = 200 - 90 = $110.
Step 2. Leisure market. MR = 100 - 2Q. Set MR = MC: 100 - 2Q = 20, so Q = 40 and P = 100 - 40 = $60.
Step 3. Compare elasticities at those points. PED = (change in Q / change in P) x (P / Q), and each demand curve has a slope of 1. Business: 110 / 90 = 1.22. Leisure: 60 / 40 = 1.5. Leisure demand is more elastic, so it is charged the lower price.
Step 4. Interpret. The firm charges $110 to the group less able to switch and $60 to the group more able to. Marginal revenue is $20 in both markets, so no seat could be moved from one market to the other to raise profit.
The rule to state is MR1 = MR2 = MC. Candidates who equate the prices, or the elasticities, rather than the marginal revenues have not used the model.
B, F, D, A, C, E, G
- A large firm faces a smaller rival in one of its markets.
- It cuts its price below average variable cost, knowing it will make a loss on every unit sold in that market.
- It can fund the losses from profits made in its other markets, or from its larger reserves.
- The smaller rival cannot match the price for long without running out of money, so it exits.
- With the rival gone, the large firm raises its price above the original level and recovers its losses.
- The strategy only pays if new firms cannot enter once prices rise, so it depends on high barriers to entry.
- Where entry is easy, the higher price attracts new rivals and the losses are never recovered, which is why genuine predatory pricing is rarer than accusations of it.
The last two steps are the evaluation. Contestability is what makes predatory pricing irrational, so it links this topic to market structures.
MR = 0 is where the MR curve crosses the horizontal axis, which is the midpoint of a straight-line demand curve, where PED is exactly 1.
The gap in MR is the explanation for price rigidity. Without it, the model only describes stable prices; with it, the model explains why cost changes do not change the price.
Define and frame: Define price discrimination and the three degrees, and state the three conditions. Identify 'always' as the claim under test, and 'consumers' as a group that is not uniform: those in the high-price and low-price markets are affected differently.
Analysis: the case that it harms consumers: Show third-degree discrimination on a two-market diagram. Consumers with inelastic demand pay more than they would at a single price, and consumer surplus is converted into producer surplus. Under first-degree discrimination all consumer surplus goes to the firm.
Analysis: the case that it benefits some: Consumers in the elastic market pay less and some buy who would not buy at all at a single price, so output and access may rise. A service that could not cover its costs at one price may run only because of discrimination. Profit may fund investment and better products.
Evaluation: Weigh rather than list. The net effect on consumers depends on whether output rises: if discrimination only redistributes surplus, consumers as a whole lose; if it opens new markets, some gain substantially. Equity matters: discounts for students and pensioners transfer from better-off to worse-off groups. The use of the extra profit, reinvested or distributed, decides the long-run effect.
Judgement: Reject 'always'. Price discrimination harms consumers in the inelastic market and benefits those in the elastic market; it is most defensible where it raises output and access, and least where it simply extracts surplus from customers with no alternative. Name the case in the question and say which applies.