sales maximisation

7.8 – Differing Objectives and Policies of Firms (Cambridge AS & A‑Level)

1. Benchmark: Profit‑maximising Objective (7.8.1)

Most introductory textbooks assume that a firm seeks to maximise profit:

• Objective: \(\displaystyle \max \;\pi = TR - TC\)
• Decision rule: Produce where marginal revenue equals marginal cost (\(MR = MC\)).
• Outcome: The firm chooses the output \(Q_{p}\) and price \(P_{p}\) that give the highest possible profit, subject to market conditions.

This profit‑maximising benchmark is useful because every alternative objective can be compared with it – in terms of output, price, profit and welfare effects.

2. Catalogue of Firm Objectives (7.8.2)

Objective (Syllabus code)	Formal condition	Typical circumstances
Profit maximisation (7.8.2a)	\(MR = MC\)	Well‑established markets; shareholders demand returns.
Sales (revenue) maximisation (7.8.2b)	\(\displaystyle \max_{Q}\;TR(Q)=P(Q)Q\quad\text{s.t.}\quad \pi(Q)\ge\pi_{\min}\)	Market‑share ambitions; managerial utility from volume; entry‑deterrence.
Revenue maximisation (no profit constraint) (7.8.2c)	\(\displaystyle \max_{Q}\;TR(Q)\) (ignoring profit)	State‑owned enterprises; firms with abundant subsidies.
Survival (break‑even) (7.8.2d)	\(\pi = 0 \;\; \Leftrightarrow\;\; TR = TC\)	Firms in recessionary periods; start‑ups with limited cash.
Satisficing (target‑profit) (7.8.2e)	\(\pi \ge \pi_{\min}\) (a pre‑set profit level)	Managerial contracts that reward hitting a profit target rather than maximising.

3. Sales (Revenue) Maximisation in Detail (7.8.2b)

3.1 Definition

A sales‑maximising firm chooses output \(Q\) to maximise total revenue (or total sales) subject to a minimum acceptable profit level:

$$\max_{Q}\; TR(Q)=P(Q)Q \quad\text{s.t.}\quad \pi(Q)=TR(Q)-TC(Q)\ge\pi_{\min }$$

3.2 Decision rule

• Profit floor not binding: The firm behaves like a pure revenue‑maximiser and chooses the quantity where marginal revenue is zero (\(MR=0\)).
• Profit floor binding: The firm expands output until any further unit would push profit below the floor. In the standard linear‑demand/constant‑MC case this yields the rule price = marginal cost (\(P=MC\)).

3.3 Graphical illustration (price‑output diagram)

3.4 Comparison with profit maximisation

Aspect	Profit maximisation (7.8.1)	Sales maximisation (7.8.2b, profit floor binding)
Decision rule	\(MR = MC\)	\(P = MC\)
Typical output	Lower	Higher
Typical price	Higher	Lower
Profit level	Maximum possible	At least \(\pi_{\min}\); usually below the profit‑maximising level
Strategic focus	Shareholder returns	Market share, entry deterrence, managerial utility

3.5 Conditions that make sales maximisation plausible

1. Large fixed costs – Spreading them over a larger output reduces average total cost.
2. Strategic market‑share goals – Dominating a market may provide long‑run pricing power.
3. Managerial utility functions – Managers may derive satisfaction from high sales volume, employment levels or visibility.
4. Access to cheap or abundant capital – The firm can tolerate lower short‑run profits while expanding.
5. Regulatory or contractual arrangements – Minimum‑profit clauses, performance‑related pay based on volume.

4. Link to Growth & Survival of Firms (7.7)

Firms that pursue growth through integration, diversification or cartels often adopt a sales‑maximising objective as a stepping‑stone. By increasing output and market share they can achieve economies of scale, reduce rivals’ market power and improve their bargaining position in any subsequent merger or cartel arrangement. Consequently, understanding sales maximisation is essential when analysing the motives behind firm growth and survival strategies covered in syllabus 7.7.

5. Pricing Policies (7.8.3)

5.1 Price discrimination (7.8.3a)

Charging different prices to different consumers for the same product, where the price differences are not due to cost differences.

Degree	Basis of discrimination	Key condition	Typical example
First‑degree (perfect)	Each consumer pays his/her maximum willingness to pay	Firm can identify and charge each individual consumer	Auctions, personalised pricing in online retail
Second‑degree	Price varies with the quantity purchased or product version	Self‑selection; different marginal rates of substitution	Bulk discounts, “economy vs. premium” software versions
Third‑degree	Different consumer groups are charged different prices	Groups have different price elasticities of demand	Student/elderly discounts, geographic price differences

Numerical illustration (third‑degree): Student market: \(Q_s = 200 - 5P\) Adult market: \(Q_a = 150 - 3P\) Assume constant marginal cost \(MC = £10\). Setting \(MR = MC\) for each segment gives \(P_s = £14\) and \(P_a = £16\). The firm extracts more surplus from the less elastic adult market while still serving the more elastic student market.

5.2 Limit pricing (7.8.3b)

• Purpose: Deter entry by setting a price low enough that a potential entrant could not earn a normal profit.
• Condition: Price is set just above the incumbent’s average total cost but below the entrant’s average total cost at the expected output level.
• Result: Short‑run profit sacrifice for long‑run market protection.

5.3 Predatory pricing (7.8.3c)

• Purpose: Drive rivals out of the market by pricing below marginal (or average) cost for a sustained period.
• Legal test (UK/US competition law): The price must be below cost and the firm must have a realistic prospect of recouping the losses later.
• Welfare impact: Consumer surplus rises temporarily but may fall dramatically once the predator raises price after rivals exit.

5.4 Price leadership (7.8.3d)

• Types:
  • Dominant‑firm price leadership – a large firm sets price; others follow.
  • Barometric price leadership – a firm with the most up‑to‑date cost information leads.
  • Collusive price leadership – firms tacitly coordinate to keep price at a mutually beneficial level.
• When it occurs: Oligopolistic markets with relatively homogeneous products and high inter‑dependence.
• Evaluation: Can reduce price competition (beneficial for firms) but may harm consumers if the leader sets a price above the competitive level.

6. Implications of Sales Maximisation for Pricing Policy

• Because the firm produces where \(P = MC\), the equilibrium price is lower than the profit‑maximising price – a “price‑cutting” strategy.
• Higher output raises consumer surplus and total welfare in the short run.
• When combined with a low profit floor, the firm may engage in limit or predatory pricing to secure market share.
• Rivals may be forced to:
  • lower their own prices,
  • improve productivity, or
  • adopt defensive strategies such as capacity expansion or product differentiation.

7. Evaluation – When Is Sales Maximisation “Better”?

1. Consumer welfare – Lower prices and higher output raise consumer surplus, especially where the market is otherwise imperfectly competitive.
2. Long‑run productive efficiency – Spreading large fixed costs can lower average total cost, moving the industry closer to productive efficiency.
3. Strategic benefits – Gaining market share may enable the firm to enjoy economies of scale or later set higher prices (potentially anti‑competitive).
4. Risk of abuse – If sales‑maximisation is used as a cover for predatory or limit pricing, consumer welfare may be harmed in the long run once rivals are driven out.
5. Impact on investment and innovation – Persistent low prices can deter entry and reduce incentives for R&D, possibly slowing technological progress.

8. Policy Considerations for Regulators (7.8.4)

• Distinguish genuine efficiency gains from strategic price‑cutting intended to foreclose the market.
• Monitor profit levels: a sustained profit below a normal return may indicate predatory intent.
• Apply competition‑law tools (market‑share thresholds, cost‑analysis tests, “recoupment” test) to separate benign sales‑maximisation from anti‑competitive conduct.
• Encourage transparency in pricing and cost structures to facilitate effective oversight.

9. Worked Example – Sales vs. Profit Maximisation

Suppose a firm faces the linear demand curve \(P = 30 - 0.02Q\) and has constant marginal cost \(MC = £10\). The firm requires a minimum profit of 10 % of revenue.

1. Profit‑maximising output (7.8.1):
   • Marginal revenue: \(MR = 30 - 0.04Q\).
   • Set \(MR = MC\): \(30 - 0.04Q = 10 \Rightarrow Q_{p}=500\).
   • Price: \(P_{p}=30-0.02(500)=£20\).
   • Profit: \(\pi_{p}= (20-10)\times500 = £5{,}000\).
2. Sales‑maximising output with profit floor \(\pi\ge0.1\,TR\) (7.8.2b):
   • Revenue: \(TR = P Q = (30-0.02Q)Q = 30Q-0.02Q^{2}\).
   • Profit constraint: \(\pi = TR - MC\cdot Q \ge 0.1\,TR\).
   • Substituting \(MC=10\): \[ (30Q-0.02Q^{2}) - 10Q \ge 0.1(30Q-0.02Q^{2}) \] Simplifying gives \(Q \le 750\). The firm chooses the largest feasible quantity, \(Q_{s}=750\).
   • Price: \(P_{s}=30-0.02(750)=£15\).
   • Revenue: \(TR_{s}=£15\times750=£11{,}250\).
   • Profit: \(\pi_{s}=TR_{s}-10\times750 = £1{,}125\) – exactly 10 % of revenue.

Result: The sales‑maximising firm sells 50 % more units at a price 25 % lower, earning a profit far below the profit‑maximising level but just meeting its profit‑floor.

10. Summary

• Sales maximisation is a credible alternative to profit maximisation when firms value market share, managerial utility or strategic positioning (syllabus 7.8.2b).
• Its decision rule (\(P = MC\) subject to a profit floor) leads to higher output and lower price than the profit‑maximising rule (\(MR = MC\)).
• It interacts with other pricing policies – price discrimination, limit pricing, predatory pricing and price leadership – all of which are part of the Cambridge “Differing objectives and policies of firms” syllabus.
• Evaluation must weigh short‑run consumer benefits against possible long‑run anti‑competitive effects; regulators should monitor profit levels and market behaviour to distinguish efficient sales‑maximisation from abuse.