📐 Consumer Theory

Price elasticity of demand (ε) measures how responsive quantity demanded is to a change in price. It answers: if price rises by 1%, how much does quantity fall?

The formula is: ε = (∂q/∂p) × (p/q). Because demand slopes downward, ε is always negative for demand.

Elastic demand (|ε| > 1): quantity is very sensitive to price. A price increase causes revenue to fall because the quantity drop outweighs the price gain.

Inelastic demand (|ε| < 1): quantity is not very sensitive to price. A price increase causes revenue to rise because the price gain outweighs the quantity drop.

Unit elastic (|ε| = 1): revenue is unchanged for a small price change.

From Equation mode solves for equilibrium P* and Q* first, then computes elasticity at that point — exactly like the lecture worked example.

Solve for P or Q lets you work backwards: given a target elasticity, find the price or quantity where that elasticity holds.

Arc elasticity uses the midpoint formula between two observed data points.

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Curve Shape and Market Power

When demand is steep (inelastic): a supply shift moves price a lot and quantity a little. Sellers have pricing power — they can pass cost increases on to buyers because buyers lack good alternatives.

When demand is flat (elastic): a supply shift moves quantity a lot and price a little. Sellers cannot raise prices without losing most customers — supply changes show up as volume changes, not price changes.

When supply is steep (inelastic): a demand shift moves price a lot and quantity a little. Producers cannot easily expand output, so demand spikes translate directly into higher prices.

When supply is flat (elastic): a demand shift moves quantity a lot and price a little. Producers absorb demand increases by expanding output rather than raising prices.

The unifying principle: the steeper curve determines how much of any shock shows up in price; the flatter curve determines how much shows up in quantity. This is also the foundation of tax incidence — whoever is more inelastic bears more of the tax burden.