relationship between price elasticity of demand and a firm’s revenue: in a normal downward sloping demand curve

Differing Objectives and Policies of Firms

Objective: Relationship between Price Elasticity of Demand and a Firm’s Revenue

In a normal downward‑sloping demand curve, the price elasticity of demand (PED) tells us how much the quantity demanded changes when the price changes.

📈 Analogy: Think of PED like a rubber band. If the band stretches easily (elastic), a small pull (price change) causes a big stretch (quantity change). If the band is stiff (inelastic), a big pull is needed for a small stretch.

Mathematically, PED is expressed as:

\$Ed = \dfrac{\% \Delta Qd}{\% \Delta P}\$

The firm’s revenue is:

\$R = P \times Q\$

When price changes, revenue changes by:

\$\Delta R = \Delta P \times Q + P \times \Delta Q\$

Using PED, we can rewrite the change in revenue as:

\$\dfrac{\Delta R}{R} = \left(1 + \dfrac{1}{E_d}\right) \dfrac{\Delta P}{P}\$

Interpretation:

• Elastic demand (|E_d| > 1): A price cut increases revenue because the drop in price is outweighed by a larger increase in quantity sold.
• Inelastic demand (|E_d| < 1): A price hike increases revenue because the rise in price outweighs the drop in quantity sold.
• : Revenue stays the same no matter what price change occurs.

Example: Smartphone Launch

Imagine a company sells a new smartphone. The initial price is £600, and 10,000 units are sold.

Here, the demand is elastic (quantity rises more than price falls), so cutting the price from £600 to £550 boosts revenue. Raising the price to £650 reduces revenue because the drop in quantity outweighs the price increase.

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