🔢 Calculating Price Elasticity of Demand
PED formula: $$PED = \frac{\% \Delta Qd}{\% \Delta P} = \frac{\Delta Qd / Qd}{\Delta P / P}$$ The result is always negative (law of demand), but we often use the absolute value.
PED along a linear demand curve
For , the slope is constant (), but PED varies along the curve: $$PED = -b \times \frac{P}{Q}$$ At high prices (low Q), PED is elastic (|PED| > 1). At low prices (high Q), PED is inelastic (|PED| < 1). At the midpoint, PED = −1 (unitary elastic).
Worked example: Given . At P = $15: Q = 100 − 75 = 25. \n (elastic) \n At P = $5: Q = 100 − 25 = 75. \n (inelastic)
Common mistake: Don't confuse SLOPE with ELASTICITY. A steeper demand curve does NOT necessarily mean less elastic — elasticity depends on where you are on the curve (the P/Q ratio).
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📊 Income and Cross Elasticity
Income Elasticity of Demand (YED)
YED formula: $$YED = \frac{\% \Delta Qd}{\% \Delta Y}$$ where Y = income. The sign tells you the type of good: positive = normal good, negative = inferior good.
- YED > 1 = luxury (income-elastic normal good).
- 0 < YED < 1 = necessity (income-inelastic normal good).
- YED < 0 = inferior good (demand falls as income rises).
Cross Elasticity of Demand (XED)
XED formula: $$XED = \frac{\% \Delta Qd(A)}{\% \Delta PB}$$ The sign tells you the relationship between goods A and B.
- XED > 0 = substitutes (price of B rises → demand for A rises).
- XED < 0 = complements (price of B rises → demand for A falls).
- XED ≈ 0 = unrelated goods.
Worked example: Income rises 10%, demand for organic food rises 15%: YED = 15/10 = 1.5 (luxury). \n Price of Pepsi rises 8%, demand for Coca-Cola rises 6%: XED = 6/8 = 0.75 (substitutes).