Week 6 - Elasticity, Demand, Supply, and Government Policy Notes

Overview: Demand and supply framework drives consumer and producer decisions; equilibrium shifts affect decisions; economic surplus concepts connect to utility (consumers) and profit (producers).

Consumer vs. Producer objectives:

• Consumers aim to maximize utility (happiness/well-being).

• Producers aim to maximize profit.

Profit definition:

• Profit = Total Revenue − Total Cost.

• Total Revenue (TR) = price × quantity sold: $ext{TR} = P \cdot Q$

• In simple illustration, assume costs are constant to focus on revenue dynamics.

Revenue optimization and price changes:

• A naïve claim: increasing price always raises total revenue.

• Reality: total revenue depends on price elasticity of demand (how quantity demanded responds to price).

Law of demand reminder:

• If price rises, quantity demanded falls; if price falls, quantity demanded rises.

Elasticity as a measure of responsiveness:

• Elasticity captures how responsive buyers/sellers are to price changes (or other factors).

• We focus on magnitude (absolute value) because the sign is typically negative for demand (price ↑ → quantity ↓).

• Major elasticity types: price elasticity of demand, cross elasticity of demand, income elasticity of demand, and elasticity of supply.

Elasticity basics:

• Price elasticity of demand (PED): measures responsiveness of quantity demanded to a price change.

• Formula (definition):
  $E_d = \frac{\%\Delta Q}{\%\Delta P} = \frac{\Delta Q / Q}{\Delta P / P}$

• In practice, we use the percentage change in quantity over the percentage change in price.

• Sign convention: usually negative due to the law of demand, but we focus on magnitude |E_d|.

• Interpretation by magnitude:

• If |E_d| > 1: elastic demand (buyers are very responsive).

• If |E_d| < 1: inelastic demand (buyers are not very responsive).

• If |E_d| = 1: unit elastic.

Midpoint (arc) formula to compute elasticity:

• To avoid base effects, use the midpoint between old and new quantities and prices:

• Percentage change in quantity:
  $\%<br>\Delta Q = \frac{Q<em>2 - Q</em>1}{\frac{Q<em>1 + Q</em>2}{2}}$

• Percentage change in price:
  $\%<br>\Delta P = \frac{P<em>2 - P</em>1}{\frac{P<em>1 + P</em>2}{2}}$

• Then elasticity is:
  $E<em>d = \frac{\frac{Q</em>2 - Q<em>1}{\frac{Q</em>1 + Q<em>2}{2}}}{\frac{P</em>2 - P<em>1}{\frac{P</em>1 + P_2}{2}}}$

• Rationale: midpoint formula yields the same elasticity regardless of which base you start from.

Examples and intuition:

• If price decreases by 15% and quantity demanded increases by 25%: |E_d| = 25% / 15% ≈ 1.67 → elastic.

• If elasticity is greater than one, a price decrease leads to a larger percentage increase in quantity, increasing total revenue.

• If elasticity is less than one, a price increase can raise total revenue because quantity falls by a smaller percentage than price rises.

Elasticity and revenue relationship (summary):

• Elastic demand (|E_d| > 1): lower price → higher total revenue; higher price → lower total revenue.

• Inelastic demand (|E_d| < 1): higher price → higher total revenue; lower price → lower total revenue.

• Unit elastic (|E_d| = 1): price changes have a proportional effect on revenue.

Demand curves and elasticity concepts:

• A perfectly elastic demand curve (horizontal): quantity demanded is extremely sensitive to price; any price increase leads to zero demand. Example: many firms selling identical products (perfect competition, e.g., milk).

• A perfectly inelastic demand curve (vertical): quantity demanded is unresponsive to price changes (e.g., essential medicines).

PED vs. slope:

• Slope measures change in price relative to quantity: (\text{slope} = \Delta P / \Delta Q).

• Elasticity is a percentage-based measure of responsiveness: (E_d = (\%\Delta Q)/(\%\Delta P)).

• Relationship exists, but elasticity is not constant along a curve; slope can be constant on a straight line while elasticity varies on nonlinear curves.

Factors affecting elasticity (why some goods are more or less elastic):

• Availability of substitutes (more substitutes → higher elasticity).

• Time horizon (more elastic in the long run than the short run).

• Proportion of income spent (high-priced items tend to be more elastic).

• Necessity vs luxury and definition (narrowly defined goods tend to be more elastic than broadly defined).

• Other factors include the price of related goods (cross elasticity) and income effects (income elasticity).

Cross elasticity of demand (substitutes and complements):

• Measures how the quantity demanded of one good responds to a price change in another good:

• Definition:
  $E<em>{Q</em>x,P<em>y} = \frac{\%\Delta Q</em>x}{\%\Delta P_y}$

• Sign interpretation:

• Positive: substitutes (price of good Y rises, Q of good X rises).

• Negative: complements (price of good Y rises, Q of good X falls).

• Zero: no relationship.

Income elasticity of demand:

• Measures responsiveness of quantity demanded to changes in income:

• Definition:
  $E_{Q,I} = \frac{\%\Delta Q}{\%\Delta I}$

• Typical signs:

• Positive: normal goods (higher income → higher quantity demanded).

• Negative: inferior goods (higher income → lower quantity demanded).

• Magnitude indicates whether a good is a luxury (|E{Q,I}| > 1) or a necessity (|E{Q,I}| < 1).

Elasticity of supply:

• Measures responsiveness of quantity supplied to price changes:

• Definition (sign is positive in standard cases):
  $E<em>s = \frac{\%\Delta Q</em>s}{\%\Delta P}$

• Elastic vs inelastic: similar thresholds as demand (|Es| > 1 elastic; |Es| < 1 inelastic).

Determinants of elasticity of demand recap:

• Substitutes: more substitutes → higher elasticity.

• Time: longer time → higher elasticity.

• Proportion of income: larger outlays → higher elasticity.

• Complements and related goods: price changes in substitutes/complements affect elasticity calculations via cross elasticity.

How elasticity informs business pricing decisions:

• If demand is elastic, lowering price can raise total revenue due to a larger gain in quantity demanded.

• If demand is inelastic, raising price can raise total revenue due to a smaller drop in quantity demanded.

• If demand is unit elastic, price changes have a proportional effect on revenue.

Practical example for revenue impact using elasticity:

• If price has increased by 15% and elasticity is 0.8 (inelastic):

• Percentage change in quantity demanded ≈ 0.8 × 15% = 12% decrease.

• Then revenue change depends on the balance of price rise vs. quantity drop.

Elasticity of demand and market structure (illustration):

• In a market with many firms selling identical products (perfect competition), the demand faced by an individual firm can be highly elastic.

Tax incidence (tax burden and elasticity):

• When a per-unit tax t is applied, there is a wedge between what buyers pay and what sellers receive.

• Graphical intuition (buyers’ price Pd and sellers’ price Ps):

• After-tax buyer price Pd is higher than original P0; seller price Ps is lower than original in a buyers-tax scenario with a tax wedge t = Pd − P_s.

• The tax amount t is the difference between what buyers pay and what sellers receive.

• Burden depends on relative elasticities:

• The more inelastic side bears more of the tax burden.

• Example: If demand is more inelastic than supply, consumers pay most of the tax (larger share of the wedge).

• If supply is more inelastic than demand, producers bear more of the tax burden.

• Numerical example (soft drinks with a 20¢ tax):

• Original equilibrium: price to consumers ~ $1.55, producers receive ~ $1.55, quantity ~ 1.40 L.

• After a 20¢ tax on buyers:

  • Consumers pay ~ $1.70 (price up by 0.15).

  • Producers receive ~ $1.50 (price down by 0.05).

  • New quantity ~ 1.20 L.

  • Tax burden split: consumers bear 0.15/0.20 = 75% and producers bear 0.05/0.20 = 25%.

  • Rationale: demand is relatively more inelastic, so consumers bear more of the burden.

• Tax on sellers yields a similar wedge and a similar decline in quantity; burden shares reallocate according to relative elasticities.

• Key takeaway: tax incidence depends on elasticities of demand and supply, not on whether the tax is imposed on buyers or sellers.

Subsidies (negative taxes):

• Subsidies have the opposite effect of taxes, shifting curves in the opposite direction to encourage the desired activity (e.g., childcare or electric vehicles).

Government interventions beyond taxes:

• Price regulation: price ceiling (maximum legal price) and price floor (minimum legal price).

• Price ceiling consequences: if set below market equilibrium, creates a shortage (quantity demanded > quantity supplied).

• Price floor consequences: if set above market equilibrium, creates a surplus (quantity supplied > quantity demanded); examples include minimum wage policies causing unemployment in labor markets.

• Quantity regulation (quotas) and mandates: limits on imports, emissions caps, or required purchases (insurance mandates, etc.).

• Health insurance and other mandated purchases: examples of quantity regulations and mandates.

How policy analysis combines elasticity with MB-MC (marginal benefit vs. marginal cost) in evaluating outcomes:

• Government uses taxes and regulation to influence the cost-benefit calculation faced by consumers and producers.

• When MB > MC for a policy (taking elasticity into account), the policy tends to be adopted; otherwise not.

Connecting elasticity to real-world relevance:

• Elasticity concepts inform productivity and living standards through policy choices affecting demand and supply (e.g., energy, health, transportation).

• The Canberra productivity roundtable example illustrates using elasticity and regulation to improve economic growth and standard of living via better productivity and efficiency.

Quick recap of how to apply these ideas:

• Identify whether demand is elastic or inelastic for your product using the midpoint elasticity formula.

• Use elasticity to predict how total revenue will respond to price changes.

• When considering taxes or subsidies, assess which side (buyers or sellers) bears more tax burden by comparing elasticities.

• Consider cross elasticity with substitutes and complements to anticipate shifts in demand when related prices change.

• Consider income elasticity to judge how demand for your product responds to income changes (normal vs inferior goods).

• Use price controls and quotas thoughtfully, recognizing their potential to create shortages, surpluses, or market distortions, and connect these outcomes to elasticity and MB–MC analysis.

Final remarks tied to exam readiness:

• Be able to compute elasticity using the midpoint formula and interpret the magnitude and sign.

• Be able to determine effect of a price change on total revenue given the elasticity value.

• Be able to explain tax incidence based on relative elasticities and to illustrate with the buyers-versus-sellers tax scenarios.

• Be able to describe how subsidies, price ceilings, price floors, and quotas affect market outcomes using the elasticity framework.