Module 5 – Demand & Supply: Elasticity (Comprehensive Notes)

Price Elasticity of Demand (PED)

• Definition: Responsiveness of $Q_d$ to changes in a good’s own price.
• Formal measure: $E<em>p = \frac{\%\,\Delta Q</em>d}{\%\,\Delta P}$ (always negative → use absolute value).
• Interpretation example:
  • Price of corn ↑ $15\%$, $Q<em>d$ ↓ $3\%$ ⇒ $E</em>p = \frac{-3}{15} = -0.2$.
  • A $1\%$ price rise → $0.2\%$ fall in quantity demanded.
• Unit-free: Uses percentages so currency units (dollars, pesos) or quantity units (tons, cubic feet) cancel.

Sign Convention & Magnitude

• Law of demand ⇒ inverse P–Q relation ⇒ $E_p$ < 0.
• Hence we analyze $|E_p|$:
  • Larger $|E_p|$ ⇒ more elastic.
  • Smaller $|E_p|$ ⇒ more inelastic.

Computing PED Accurately (Midpoint / Arc Method)

• Naïve % change differs by direction; fix via averages.
• Formula: $E<em>p = \frac{\Delta Q}{\Delta P} \times \frac{(P</em>1+P<em>2)/2}{(Q</em>1+Q_2)/2}$.
• Worked numeric example (move 2 → 3 units; price 3 → 2):
  • $\%\,\Delta Q = \frac{1}{2}=50\%$ ; $\%\,\Delta P = \frac{-1}{3}=-33\%$.
  • Midpoint method harmonises to single $E_p$ irrespective of direction.

Applied Policy Example: Tesla EVs in Hong Kong

• Subsidy removal raised price $75{,}000 \rightarrow 130{,}000$.
• Quantity demanded $500 \rightarrow 30$ per month.
• Midpoint calc:
  • $\Delta Q = -470$; $\Delta P = 55{,}000$.
  • Averages: $\bar Q = 265$, $\bar P = 102{,}500$.
  • $E_p = \frac{-470}{55{,}000} \times \frac{102{,}500}{265} = -2.81$.
• Interpretation: 1 % price rise ⇒ 2.81 % drop in demand (highly elastic).

Elasticity Ranges & Classifications

• Elastic: |E_p|>1 – quantity reacts proportionally more than price.
• Unit elastic: $|E_p|=1$ – proportional response.
• Inelastic: |E_p|<1 – quantity reacts proportionally less.

Extreme Cases

• Perfectly Inelastic (vertical D): $E_p=0$.
  • E.g., Daraprim price ↑ 5,000 % yet malaria patients’ usage unchanged.
• Perfectly Elastic (horizontal D): $E_p=\infty$.
  • Any price ↑ triggers demand →0. Commodity markets (corn, gold).
• Unitary Elastic (rectangular hyperbola): $E_p=1$.
  • Example: Cheddar-bay biscuits 15 % price cut → 15 % volume rise.

Elasticity & Government Per-Unit Taxes

• Tax raises price ⇒ lowers quantity.
  • Elastic demand: TR (tax revenue) ↓.
  • Unit elastic: TR unchanged.
  • Inelastic: TR ↑.
• Political takeaway: revenue outcomes hinge on elasticity, not just tax rate.

Total Revenue (TR) Linkage

• $TR = P \times Q$.
• Elastic D: Price ↑ ⇒ TR ↓ ; Price ↓ ⇒ TR ↑ (inverse relation).
• Unit-elastic D: TR unaffected by price changes.
• Inelastic D: Price ↑ ⇒ TR ↑ ; Price ↓ ⇒ TR ↓ (direct relation).
• Graphically:
  • Elastic region (low Q, high P): TR rises at increasing rate as Q expands.
  • Unit elastic: TR max/flat.
  • Inelastic region (high Q, low P): TR falls at increasing rate as Q expands.

Determinants of PED

1. Availability & Closeness of Substitutes

• More & closer substitutes ⇒ higher elasticity.
• Perfect substitutes ⇒ perfectly elastic.
• Example contrasts:
  • Many: Bud Light price ↑ ⇒ consumers switch ⇒ elastic.
  • Few: Niche Japanese sake price ↑ ⇒ inelastic.

2. Budget Share

• Larger share of income ⇒ more elastic.
  • Housing, transportation.
• Small share ⇒ less elastic.
  • Snacks, entertainment.

3. Time Horizon for Adjustment

• Short run: limited ability to alter consumption ⇒ inelastic.
• Long run: consumers can fully adapt ⇒ elastic.
• Illustrative electricity price hike 50 %:
  • SR: turn off lights, sweat.
  • LR: install solar, LED, insulation.
• No fixed calendar length: LR = time needed for full adjustment (product-specific).
• Empirical elasticities:
  • Business air travel: SR 0.4, LR 1.2.
  • Gasoline: SR 0.2, LR 0.5.
  • Fresh tomatoes: SR 4.6 (very elastic).

Cross-Price Elasticity of Demand (CPED)

• Measures responsiveness of demand for good X to price change in good Y.
• Formula: $E<em>{xy} = \frac{\%\,\Delta Q</em>x}{\%\,\Delta P_y}$.
• Interpretation:
  • Substitutes ⇒ E_{xy} > 0.
  • Coffee ↑ ⇒ tea demand ↑.
  • Complements ⇒ E_{xy} < 0.
  • Peanut-butter ↑ ⇒ jelly demand ↓.

Income Elasticity of Demand (YED)

• Formula: $E<em>i = \frac{\%\,\Delta Q</em>d}{\%\,\Delta\,\text{Income}}$.
• Captures demand shift due to income change (price constant).
• Example calculation:
  • Apps purchased rise 6 → 8 per month while income rises $4,000 → $6,000.
  • $\Delta Q = 2$; $\bar Q = 7$; $\Delta I = 2,000$; $\bar I = 5,000$.
  • $E_i = \frac{2}{7} \div \frac{2{,}000}{5{,}000} = 0.2857 / 0.4 = 0.71$.
• Positive YED ⇒ normal goods; negative ⇒ inferior goods; magnitude indicates luxury (>1) vs necessity (<1).

Price Elasticity of Supply (PES)

• Definition: Responsiveness of $Q_s$ to own-price changes.
• Formula: $E<em>s = \frac{\%\,\Delta Q</em>s}{\%\,\Delta P}$.

Extreme Supply Cases

• Perfectly Elastic Supply (horizontal): slightest P↓ ⇒ $Q_s = 0$ (tight-margin industries).
• Perfectly Inelastic Supply (vertical): $Q_s$ fixed regardless of P (e.g., land, fully subsidized goods).

Time & Supply Elasticity

• Market (Immediate) period: no input adjustment possible ⇒ very inelastic.
• Short run: some inputs variable (labor) but capital fixed ⇒ more elastic than market period.
• Long run: all inputs adjustable, entry/exit possible ⇒ most elastic.
• Supply shocks (natural disasters, new mineral finds) shift resource availability; adjustment path traced through these timeframes.
• Firms adapt via:
  • Expansion/contraction of resources & output.
  • Entry/exit of firms.

Recap & Connections

• Elasticity unifies consumer & producer responses, shapes tax incidence, guides pricing, and forecasts revenue.
• Time is a critical axis: both buyers and sellers gain flexibility as horizons lengthen.
• Cross-price & income elasticities enrich analysis by incorporating market interlinkages (substitutes/complements) and macro conditions (income growth).
• Recognizing extreme cases helps benchmark real-world scenarios, though most goods fall in between.