profit satisficing

1. Introduction – Why Firms Have Different Objectives

In Cambridge AS&A Level Economics (9708) – Topic 7.8 the syllabus asks us to examine a range of firm objectives and the pricing policies that follow from them. The benchmark is profit maximisation. From this point we explore four alternative objectives – survival (break‑even), profit satisficing, sales‑maximising and revenue‑maximising – and three groups of pricing policies: price discrimination, limit/predatory pricing and price leadership. For each objective or policy we give:

• A concise definition.
• The decision rule (the “rule of thumb” the firm follows).
• A diagram suggestion.
• An AO3‑type evaluation (advantages, disadvantages and likely welfare effects).

2. Benchmark: Profit Maximisation

2.1 Definition

The firm chooses the output where marginal revenue (MR) = marginal cost (MC) and where MR is positive. This rule links directly to the syllabus concept of “the margin and decision‑making”. The resulting profit is \(\pi = TR - TC\).

2.2 Decision Rule

\[\text{Choose } Q \text{ such that } MR = MC \text{ and } MR>0\]

2.3 Diagram Suggestion

Standard price‑output diagram showing demand (D), MR, MC and the profit‑maximising output Q_PM where MR = MC. Label the profit area (producer surplus) and note that price > MC in imperfect competition.

2.4 Evaluation (AO3)

Advantages	Disadvantages	Welfare Effects
Generates the highest possible producer surplus for the firm. In perfect competition it leads to an efficient allocation of resources (price = MC).	Can involve high risk (price wars, cost‑cutting). Ignores non‑financial objectives such as employee welfare, product quality or environmental concerns.	In competitive markets total surplus is maximised. In imperfect markets a price above MC creates dead‑weight loss.

3. Alternative Firm Objectives

3.1 Survival (Break‑Even) Objective

• Definition: The firm aims only to cover its total costs, i.e. to achieve \(TR = TC\), so that it can continue operating.
• Decision Rule: Produce the smallest output where \(TR \ge TC\) (profit ≥ 0). This is the “break‑even” rule.
• Diagram Suggestion: Break‑even diagram – the point where the total‑revenue curve meets the total‑cost curve. Label the break‑even output Q_BE and note that at this point the firm is neither making a profit nor a loss.
• Evaluation:

  Pros	Cons	Welfare
  Reduces the risk of loss and bankruptcy; helps preserve employment.	Leaves large profit potential unexploited; may lead to under‑investment and lower long‑run growth.	Consumer surplus may be higher than under profit maximisation if the price is lower, but total surplus is lower because producer surplus is minimal.

3.2 Profit Satisficing

• Definition: The firm sets a “good enough” target profit \(\pi^{*}\) – often for non‑financial reasons such as shareholder expectations, stable employment or corporate social responsibility – and stops seeking higher profit once this target is met.
• Decision Rule: Produce the smallest output \(Q_{S}\) that satisfies \(\pi(Q)=TR(Q)-TC(Q)\ge\pi^{*}\). After reaching the target, other goals (quality, employee welfare, environmental performance) dominate.
• Diagram Suggestion: Profit curve with a horizontal line at \(\pi^{*}\). The intersection gives \(Q_{S}\). Show the profit‑maximising point Q_PM for comparison.
• Evaluation:

  Advantages	Disadvantages	Welfare
  Reduces exposure to risky, aggressive strategies. Allows the firm to devote resources to non‑financial objectives (quality, employee relations, environmental outcomes).	Often results in a lower output than the efficient level, raising price and reducing consumer surplus. Potentially lower total surplus compared with profit maximisation.	Consumer surplus falls relative to the benchmark, but gains in product quality, job security or environmental performance may offset the monetary loss.

Numerical Example (Profit Satisficing)

Demand: \(P = 100 - 2Q\)  Total cost: \(TC = 20Q + 100\)  Target profit: \(\pi^{*}=200\)

Revenue: \(TR = (100-2Q)Q = 100Q - 2Q^{2}\)

Profit function:

\[ \pi = TR - TC = 100Q - 2Q^{2} - (20Q + 100) = 80Q - 2Q^{2} - 100 \]

Set \(\pi = 200\):

\[ -2Q^{2} + 80Q - 300 = 0 \;\Longrightarrow\; Q^{2} - 40Q + 150 = 0 \] \[ Q = \frac{40 \pm \sqrt{40^{2} - 4\cdot150}}{2} = \frac{40 \pm \sqrt{1000}}{2} \]

Economically relevant root:

\[ Q_{S} \approx \frac{40 - 31.62}{2} \approx 4.2 \text{ units} \]

Profit‑maximising output (where MR = MC) is \(Q_{PM}=20\). The satisficing firm accepts a much lower output and a higher price to guarantee the target profit.

3.3 Sales‑Maximising Objective

• Definition: The firm seeks to maximise the quantity sold, even if this means earning a low or zero profit.
• Decision Rule: Produce where \(MR = 0\) (the end of the demand curve) or where price just covers marginal cost while profit is not the primary concern.
• Diagram Suggestion: Demand curve with the sales‑maximising point at the horizontal intercept (maximum feasible Q). Show that price equals the choke price (zero) at that point.
• Evaluation:

  Pros	Cons	Welfare
  Large market share; can generate economies of scale; may deter entry.	Often results in losses or very low profit; may be unsustainable in the long run.	Consumer surplus is maximised (price low), but producer surplus may be negative, risking market exit and possible welfare loss.

3.4 Revenue‑Maximising Objective

• Definition: The firm chooses output to maximise total revenue \(TR\), irrespective of the profit level.
• Decision Rule: Produce where \(MR = 0\) – the peak of the TR curve.
• Diagram Suggestion: Plot TR against Q; the highest point gives the revenue‑maximising output \(Q_{R}\). Show the corresponding price on the demand curve.
• Evaluation:

  Advantages	Disadvantages	Welfare
  High sales volume can increase market power and fund future investment.	Profit may be far below the maximum; if costs are high the firm can incur losses.	Consumer surplus rises (price lower than under profit maximisation) but producer surplus falls; overall welfare depends on the firm’s ability to remain viable.

4. Pricing Policies Required by the Syllabus

4.1 Price Discrimination

4.1.1 First‑Degree (Perfect) Price Discrimination

• Definition: Charging each consumer his/her maximum willingness to pay – i.e. the entire demand curve.
• Conditions: No resale, ability to identify each buyer’s willingness to pay, and complete information.
• Outcome: Producer captures the whole consumer surplus; output equals the efficient (competitive) level.
• Evaluation:

  Pros	Cons	Welfare
  Maximum producer surplus; no dead‑weight loss.	Practically impossible to implement; may be perceived as unfair.	Total surplus unchanged – consumer surplus is transferred to the firm.

4.1.2 Second‑Degree Price Discrimination

• Definition: Different prices for different quantities or versions of a product (e.g., bulk discounts, versioning).
• Conditions: Ability to prevent arbitrage; consumers self‑select according to their own demand elasticity.
• Evaluation:

  Pros	Cons	Welfare
  Captures part of the consumer surplus; can increase output relative to a uniform price.	Requires complex contract design; may be viewed as discriminatory.	Usually reduces dead‑weight loss; total surplus rises compared with single‑price monopoly.

4.1.3 Third‑Degree Price Discrimination

• Definition: Charging different groups (segments) of consumers different prices (e.g., student discounts, geographic pricing).
• Conditions: Segments have different price elasticities; firm can prevent resale between groups.
• Decision Rule: Set price in each segment where \(MR_i = MC\) (the same MC applies to all segments).
• Evaluation:

  Pros	Cons	Welfare
  Higher total profit than uniform pricing; can increase output in the more elastic segment.	May be seen as unfair; requires reliable market segmentation.	Dead‑weight loss is reduced; some consumer surplus is transferred to the firm, but total surplus usually rises.

4.2 Limit Pricing

• Definition: An incumbent sets a price low enough to make market entry unattractive to potential rivals.
• Rationale: Protect market share and preserve long‑run monopoly profits.
• Decision Rule: Choose a price \(P_{L}\) such that the entrant’s expected profit is ≤ 0, i.e. \(P_{L} \le AC_{entrant}\) at the entrant’s likely output.
• Evaluation:

  Advantages	Disadvantages	Welfare
  Maintains monopoly power; deters competition.	Incumbent sacrifices short‑run profit; may breach competition law.	Consumer surplus rises in the short run (lower price) but long‑run welfare may fall if monopoly persists.

4.3 Predatory Pricing

• Definition: An incumbent temporarily sets price below cost to drive rivals out of the market.
• Rationale: After competitors exit, the firm raises price to recoup losses and enjoy monopoly profits.
• Decision Rule: Price \(P_{P} < AVC\) for a period sufficient to force exit.
• Evaluation:

  Pros	Cons	Welfare
  Potentially secures long‑run monopoly profits.	Short‑run losses; illegal in many jurisdictions; may fail if rivals have deep pockets.	Short‑run consumer surplus rises, but long‑run welfare falls because of higher monopoly price after exit.

4.4 Price Leadership

• Definition: One dominant firm (the “leader”) sets the market price; other firms (the “followers”) accept it.
• Types:
  • Barometric: Leader signals market conditions; followers adjust accordingly.
  • Dominant‑firm: Leader has a cost advantage and can profitably set the price.
• Evaluation:

  Pros	Cons	Welfare
  Reduces price wars; provides price stability.	Can facilitate tacit collusion; price may stay above the competitive level.	Consumer surplus is lower than in a fully competitive market but may be higher than under a pure monopoly if the leader’s price is moderate.

5. Comparative Summary Table – Objectives & Policies

Objective / Policy	Key Decision Rule	Typical Diagram	Principal Advantages	Principal Disadvantages	Welfare Implications
Profit maximisation	MR = MC (MR > 0)	Price‑output diagram with MR, MC intersecting	Highest producer surplus; efficient in perfect competition	Ignores non‑financial goals; can be risky	Maximises total surplus in competitive markets; creates DWL if price > MC
Survival (break‑even)	Smallest Q with TR ≥ TC	Break‑even diagram (TR = TC)	Reduces risk of loss; preserves jobs	Leaves profit potential unused; may under‑invest	Consumer surplus may rise, but total surplus falls (low producer surplus)
Profit satisficing	Smallest Q with π ≥ π*	Profit curve with horizontal line at π*	Limits risk; frees resources for quality, welfare, environment	Output below efficient level; higher price, lower consumer surplus	Consumer surplus falls; possible gains in non‑monetary welfare
Sales‑maximising	Produce where MR = 0 (max Q)	Demand curve to horizontal axis	Large market share; economies of scale	Often loss‑making; unsustainable long‑run	Consumer surplus maximised; producer surplus may be negative → potential market failure
Revenue‑maximising	Produce where MR = 0 (peak TR)	TR curve peak	High sales volume; can fund investment	Profit may be low or negative	Consumer surplus rises, producer surplus falls; overall welfare depends on viability
First‑degree price discrimination	Charge each consumer his/her willingness to pay	Demand curve = MR = MC	Maximum producer surplus; no DWL	Hard to implement; perceived unfairness	Total surplus unchanged (consumer surplus transferred)
Second‑degree price discrimination	Self‑selection via quantity/quality tiers	Multiple MR curves for each tier	Captures part of CS; can raise output	Complex contracts; possible discrimination concerns	Reduces DWL; total surplus rises vs. uniform pricing
Third‑degree price discrimination	Set Pi where MRi = MC for each segment	Separate MR curves for each market segment	Higher profit than uniform price; can expand output	Requires reliable segmentation; fairness issues	DW​L reduced; some CS transferred, total surplus usually up
Limit pricing	Set PL ≤ AC of potential entrant	Incumbent price below entrant’s break‑even	Deters entry; protects long‑run monopoly	Short‑run profit sacrifice; may breach competition law	Short‑run CS ↑, long‑run welfare ↓ if monopoly persists
Predatory pricing	Set PP < AVC for a period to force exit	Price below cost, then later raise	Potentially secures monopoly profits	Short‑run losses; illegal; uncertain success	Short‑run CS ↑, long‑run welfare ↓ due to higher monopoly price
Price leadership	Leader sets price; followers accept	Leader’s price line with follower reaction curves	Price stability; avoids destructive price wars	Can enable tacit collusion; price may stay above competitive	CS may be lower than perfect competition but higher than pure monopoly if price is moderate