Welcome to Pricing and Revenue Maximisation!
Ever wondered why a new iPhone costs a fortune when it first launches, but a loaf of bread stays roughly the same price? Or why some companies prefer to sell a few items at a high price, while others want to sell millions at a tiny profit? That is exactly what we are exploring today!
Pricing is one of the most critical short-term decisions a management accountant supports. If the price is too high, nobody buys. If it is too low, the company might go bust despite selling out. Let’s dive into how organisations make pricing and revenue-maximising decisions.
1. Understanding Demand and Price Elasticity
Before setting a price, we need to know how customers will react. This is where Price Elasticity of Demand (PED) comes in. It measures how sensitive customer demand is to a change in price.
The PED Formula
To calculate PED, we use this formula:
\( \text{PED} = \frac{\text{% change in quantity demanded}}{\text{% change in price}} \)
Elastic vs. Inelastic: The "Rubber Band" Analogy
Think of demand like a rubber band:
Elastic Demand (\( |\text{PED}| > 1 \)): Demand is very stretchy! A small percentage change in price leads to a large percentage change in the quantity demanded. This typically happens with luxury goods or goods with many close substitutes.
Inelastic Demand (\( |\text{PED}| < 1 \)): Demand is stiff. Even if the price changes significantly, the quantity demanded changes very little. This happens with essential items or products with few substitutes.
Quick Review:
- If demand is Elastic: Lowering the price increases total revenue.
- If demand is Inelastic: Raising the price increases total revenue.
Did you know? Companies try to make demand for their products inelastic through strong branding. If customers are loyal to a specific brand, they keep buying even when prices rise!
Key Takeaway: Knowing PED helps you predict whether a price change will increase total revenue or drive customers straight to competitors.
2. Profit Maximisation vs. Revenue Maximisation
Management accountants must distinguish between two core commercial objectives: maximising total profit and maximising total revenue.
A. Profit Maximisation (\( \text{MR} = \text{MC} \))
Profit is maximised at the output level where Marginal Revenue (MR) equals Marginal Cost (MC).
Step 1: Establish the Demand Equation
\( P = a - bQ \)
Where:
- \( P \) = Selling price per unit
- \( a \) = Price at which demand is zero (the price intercept)
- \( b \) = Slope/gradient of the demand curve (\( \frac{\Delta P}{\Delta Q} \))
- \( Q \) = Quantity demanded
Step 2: Derive the Marginal Revenue Equation
Because the MR line has twice the slope of the demand equation:
\( \text{MR} = a - 2bQ \)
Step 3: Set \( \text{MR} = \text{MC} \) and Solve
Equate \( \text{MR} \) to \( \text{MC} \) (usually variable cost per unit) to find optimal output \( Q \), then substitute \( Q \) back into the demand equation to determine the profit-maximising price \( P \).
B. Revenue-Maximising Decisions (\( \text{MR} = 0 \))
An organisation may pursue revenue maximisation rather than short-term profit maximisation. Total revenue is maximised at the point where Marginal Revenue is zero (\( \text{MR} = 0 \)), which corresponds to unitary price elasticity of demand (\( |\text{PED}| = 1 \)). Beyond this output, making another sale produces negative marginal revenue, causing total sales revenue to fall.
How to calculate the revenue-maximising position:
1. Set \( \text{MR} = 0 \), so \( a - 2bQ = 0 \).
2. Solve for \( Q = \frac{a}{2b} \).
3. Substitute \( Q \) back into \( P = a - bQ \) to find the revenue-maximising price.
Why pursue revenue maximisation instead of profit maximisation?
- Zero or near-zero marginal cost: Digital products, software downloads, and online media often have \( \text{MC} \approx 0 \). Where \( \text{MC} = 0 \), the profit-maximising point and revenue-maximising point coincide!
- Market share and network effects: In early-stage platform markets, gaining users rapidly creates network value that can be monetised later.
- Managerial incentives: Executive bonuses or commercial targets may be tied directly to top-line sales turnover rather than short-term accounting profits.
3. Main Pricing Strategies
In addition to economic models, businesses deploy practical pricing strategies aligned with market conditions and cost structures:
A. Cost-Plus Pricing
- Full Cost-Plus: Adds a profit mark-up to the total absorption cost (variable plus allocated fixed overheads). This ensures fixed costs are covered in the long run.
- Marginal Cost-Plus: Adds a mark-up strictly to marginal (variable) costs. Useful for short-term decisions or utilising spare factory capacity.
B. Market-Based Pricing: Skimming vs. Penetration
1. Price Skimming: Set a high initial price to capture consumer surplus from early adopters who are less price sensitive. Suitable for unique or technologically advanced products (e.g. newly released flagship gaming consoles or smartphones). Prices are lowered later as competitors enter.
2. Penetration Pricing: Set an intentionally low initial price to gain rapid market share and discourage competitors from entering. Once customer loyalty and scale economies are established, the business can gradually adjust prices upward.
C. Product Bundling
Selling complementary products or services together as a bundle at a lower combined price than buying each separately (e.g. meal deals or software suites), stimulating higher overall sales volume.
4. Short-Term Pricing, Special Orders, and Relevant Cash Flows
A key focus of management accounting is short-term pricing for special orders or one-off projects:
- Relevant Costs: The minimum acceptable short-term price must cover all incremental, future cash flows (variable costs, specific fixed costs, and opportunity costs of constrained resources). Sunk costs and allocated general fixed overheads are irrelevant.
- The Conflict Between Marginal Cost Principles and Full Cost Recovery: Pricing at unit variable cost gives zero contribution; pricing above it gives positive contribution. Covering the incremental relevant costs of an order does not necessarily recover general fixed overheads, which must also be covered over the long term.
- Strategic and Qualitative Implications: Management must consider whether a cheap special order will anger existing full-price customers, create customer expectations of permanent discounts, or violate capacity constraints if regular demand rebounds.
Quick Review Quiz (Mental Check)
1. If \( \text{PED} = -0.5 \), is demand elastic or inelastic? (Answer: Inelastic, because \( |\text{PED}| < 1 \))
2. At what point is total sales revenue maximised? (Answer: Where \( \text{MR} = 0 \), or where elasticity is unitary)
3. What is the gradient of the marginal revenue curve compared to the demand curve? (Answer: It is twice as steep; \( 2b \) vs \( b \))
4. What is the absolute minimum short-term selling price for a special order using spare capacity? (Answer: The incremental relevant cash flows of fulfilling the order)
Final Encouragement: Pricing balances economic equations with commercial realism. Keep your relevant cash flows clear and remember: profit is maximised where \( \text{MR} = \text{MC} \), while revenue is maximised where \( \text{MR} = 0 \)!