IAI Actuarial Core Principles · Business Economics

Pricing strategies in the financial services sector: formula sheet

Full chapter guide

Key formulas

Cost-plus price: Price = Average total cost per unit × (1 + mark-up %); Mark-up is on cost. Average total cost = (fixed + variable costs) ÷ units.
Mark-up and margin: Margin on price = Mark-up ÷ (1 + Mark-up); A 25% mark-up on cost equals a 20% margin on price. Do not mix them up.
Average total cost: ATC = Total cost ÷ Q = AFC + AVC; Fixed cost per unit falls as volume rises.
Marginal cost: MC = Change in total cost ÷ Change in quantity; For one extra unit, MC is the extra cost of that unit.
Marginal cost pricing floor: Price ≥ MC (short run); Below MC each extra sale reduces profit.
Break-even quantity: Q* = Fixed costs ÷ (Price − Variable cost per unit); Price minus variable cost is the contribution per unit.
Target profit volume: Q = (Fixed costs + Target profit) ÷ (Price − Variable cost per unit); Use when a profit target is given.
Condition for third degree discrimination: MR₁ = MR₂ = MC; Set marginal revenue equal to marginal cost in each segment, with the same MC across segments. This decides the output in each market.
Price and elasticity link: MR = P × (1 − 1/|PED|); Applies for a firm facing a downward sloping demand curve, with |PED| the absolute value of price elasticity at that price. Use it to show why the less elastic segment gets the higher price.
Which segment pays more: Lower |PED| → higher price; higher |PED| → lower price; This holds when MC is the same in both segments and the firm maximises profit.
Perfect (first degree) discrimination: Price for each unit = willingness to pay for that unit; consumer surplus = 0; Output rises to where the demand curve meets MC, so there is no deadweight loss. All surplus moves to the firm.
Price gap not explained by cost: Discrimination component = (P₁ − P₂) − (C₁ − C₂); P is price and C is expected cost to serve each group. A positive result points to discrimination. A result near zero points to risk-based or cost-based pricing.
Profit-maximising rule: MR = MC; Base case for any pricing decision. Strategic pricing departs from it in the short run to gain share or deter entry.
Predatory test (cost-based): Price < average variable cost (AVC); Pricing below AVC is the usual warning sign of predation. Pricing between AVC and ATC is a loss but not clearly predatory.
Loss-leader viability: Loss on lead product < Σ expected profit from cross-sold products; Include the probability that customers actually buy and stay. Discount later profits if the horizon is long.
Bundle gain: Bundle price < Σ stand-alone prices, and bundle revenue ≥ separate revenue; A bundle pays when valuations are negatively correlated or it cuts cost to serve and churn.
Payoff comparison in a price game: Dominant strategy: a choice with the higher payoff whatever the rival does; If both firms have a dominant strategy, the outcome is a Nash equilibrium. It may be worse for both than cooperation.
Price elasticity link: Revenue rises after a price cut if |PED| > 1; Penetration pricing is only attractive on revenue grounds when demand is elastic.
Expected claim cost (pure premium): Pure premium = P(claim) × average claim size; Risk-based pricing sets each risk class's premium from its own expected cost, then adds expenses and profit loading.
Loaded premium: Premium = (Pure premium + fixed expenses) ÷ (1 − variable expense and profit rate); State the loading assumptions. A simple version is Premium = Pure premium × (1 + loading).
Average (pooled) premium: Pooled premium = Σ (weight of group × expected cost of group); Weights are the proportions of each group actually buying cover. If the mix changes, the pooled cost changes.
Risk-based interest rate (single-period): (1 − p) × (1 + r) = 1 + funding rate, when loss given default is 100% and no recovery; p is probability of default, r is the loan rate. With recovery R per ₹1 lent in default: (1 − p)(1 + r) + p × R = 1 + funding rate.
Cross-subsidy: Cross-subsidy for a group = premium charged − expected cost of that group; Positive means the group subsidises others. Negative means it is subsidised.

Quick revision

Pricing objectives can include profit, market share, survival, growth and meeting regulatory or social aims. They can conflict.
Cost-based pricing adds a margin to cost. It ignores demand and rivals, so it can misprice.
Financial products have uncertain costs, because claims or defaults arrive after the sale.
Price discrimination means charging different prices for the same product where cost differences do not explain the gap.
It needs market power, a way to separate customers and limited resale.
Segmentation groups customers by traits such as age, income, channel or risk to set suitable prices.
Competitive pricing depends on rivals' reactions. In an oligopoly, firms are interdependent.
Price wars can hurt all firms. Underpricing risk can lead to losses later in insurance and lending.
Adverse selection: before the deal, the party with less information attracts the riskiest customers.
Moral hazard: after the deal, behaviour changes because risk is covered by someone else.
Risk-based pricing charges higher prices to riskier customers. Screening, deductibles and credit scores help the firm sort them.
Always link the answer to the case given in the question.

Common mistakes

Treating mark-up on cost as margin on price. Fix: Read which base is stated. Convert with margin = mark-up ÷ (1 + mark-up) when needed.
Using marginal cost instead of average total cost in cost-plus pricing. Fix: Cost-plus uses full unit cost. Marginal cost pricing uses only the extra cost.
Calling every price difference price discrimination. Fix: Check whether the gap reflects cost. Higher premiums for higher expected claims are risk-based pricing. Discrimination needs a gap beyond cost.
Mixing up second and third degree. Fix: In second degree, the customer picks the option. In third degree, the firm assigns the group by an observable trait such as age.
Calling any below-cost price predatory. Fix: Predation needs below-cost pricing, the aim of removing rivals, and a plan to recoup losses later. A loss leader aims at cross-sales instead.
Saying skimming works in any market. Fix: State the conditions: few substitutes, strong demand from early buyers and barriers to entry. Otherwise rivals enter and erode prices.
Mixing up adverse selection and moral hazard. Fix: Use timing. Before the contract, hidden type: adverse selection. After the contract, hidden behaviour: moral hazard.
Computing the pooled premium with the original mix after low risks have left. Fix: Recompute the average using only the groups that still buy. State whether the spiral continues.

Exam tips

Always state the pricing objective first. Examiners reward the link between objective and method.
Write each formula before using it and show units in rupees.
For discussion parts, give one strength and one weakness of each method. A common weakness is ignoring demand and competitors.
Use financial services examples: loan pricing, premium loadings, account fees.
Check whether the question says mark-up on cost or margin on price before computing.
Always give a financial services example for each degree. Use no-claim discounts or tiered cover for second degree, and age or channel pricing for third degree.
State the three conditions early in any written answer. Markers look for market power, separation and no resale.
In calculations, write MR = MC for each segment and show the price from the demand curve. Do not stop at quantity.