Elasticity & Total Revenue — Quick Review

Total Revenue & Elasticity

  • TR = P \cdot Q
  • Example: 5 bushels at \$3 each → TR = 5 \times 3 = 15
  • TR is the total spending/revenue received, i.e., price times quantity.

Price Effect vs Output Effect

  • Price effect: changing price alone; Output effect: quantity demanded changes in response to price.
  • If lowering price lowers TR, demand is inelastic on that range; if lowering price raises TR, demand is elastic on that range.
  • Elasticity tells whether TR moves with price:
    • Elastic: TR moves opposite to price change (price up → TR down; price down → TR up).
    • Inelastic: TR moves with price change (price up → TR up; price down → TR down).

Elasticity on the Demand Curve

  • Top half (near high prices): elastic; bottom half (low prices): inelastic.
  • Unit elastic at the midpoint of a linear demand curve.
  • Visual rule: if TR rises when price rises, or falls when price falls, that portion is inelastic; if TR falls when price rises, or rises when price falls, that portion is elastic.

Quick TR and Elasticity Examples

  • Example: price from 10 to 8; quantity from 90 to 100 → TR changes from 10!\times!90 = 900 to 8!\times!100 = 800 (TR falls). In this range, demand is inelastic.
  • Example (elastic): price from 8 to 10; quantity falls a lot (e.g., from 100 to 70) → TR falls as price rises; demand is elastic.
  • Midpoint: unit elastic at the point where TR is maximized on a linear demand curve.

Demand Curve Slope & Revenue Rules (summary)

  • If price ↑ and TR ↑ → inelastic.
  • If price ↓ and TR ↓ → inelastic.
  • If price ↑ and TR ↓ OR price ↓ and TR ↑ → elastic.

Elasticity of Supply

  • Positive relation: as price rises, quantity supplied rises.
  • Elasticity of supply: Es = \dfrac{\%\Delta Qs}{\%\Delta P} > 0
  • Long run generally more elastic than short run.

Short Run vs Long Run

  • Short run: capital fixed; limited adjustments.
  • Long run: capital adjustable; can optimize plant/scale, increasing elasticity.

Harvest/Shocks & Shifts in Supply

  • Good harvest: supply shifts right; price falls; quantity rises; producers generally worse off if demand is inelastic.
  • Poor harvest: supply shifts left; price rises; quantity falls; with inelastic demand (e.g., food), price rise is large and may increase total revenue; overall welfare effects depend on who bears burden.

Tax Incidence & Elasticity (illustrative)

  • A tax creates a price wedge; who bears burden depends on elasticity.
  • If demand is inelastic (consumers less responsive), consumers bear most of the tax; if demand is elastic, producers bear more.
  • Elasticity determines how much quantity falls after tax and how the tax is split between buyers and sellers.

Demand vs Supply Elasticity in Policy Rules (conceptual)

  • Inelastic demand → larger price increases from shifts (e.g., taxes) with smaller quantity changes.
  • Elastic demand → shifts cause larger quantity changes; burden shifts toward producers when supply is elastic, toward consumers when demand is inelastic.

Practice Takeaways

  • Elasticity measures responsiveness: E_p = \dfrac{\%\Delta Q}{\%\Delta P}.
  • Elastic vs inelastic regions on a linear demand curve: top = elastic, bottom = inelastic, midpoint = unit elastic.
  • Long run tends to be more elastic than short run due to adjustable capacity/investment.
  • Tax incidence depends on relative elasticities of demand and supply.