Comprehensive Study Notes: Elasticity, Total Revenue, and Tax Incidence

Course Logistics and Announcements

Classwork Bonus Points Opportunity:
- Attendance at an upcoming economics-based event (on Thursday) yields 5 bonus points added directly to the classwork grade (not $5\,\%$ total grade, but 5 full points).
- Attendance is officially tracked via QR code registration.
- Target audience: Economics and business majors benefit directly due to topic relevance.
- Grade impact: Missed classwork assignments can be offset. Maintaining a classwork score above $100\,\%$ helps compensate for point losses in other course components.
- Future events may offer additional 5-point bonus opportunities.
Lecture Scope:
- Elasticity is conceptually complex and requires the full lecture duration without early dismissal.

Slope vs. Elasticity on a Linear Demand Curve

Slope Characteristics:
- For a linear (straight-line) demand curve, the slope is constant throughout its entire length.
Elasticity Characteristics:
- Price elasticity of demand ( $PED$ ) is not constant along a linear demand curve.
- Elasticity decreases as movement occurs from left to right (top-left to bottom-right) along the demand curve.
Mathematical and Economic Explanation:
- Top-Left Region of Demand Curve (Elastic):
  - Price is high (e.g., decreasing price by \\$1 on a \\$10 price is a small relative percentage change: $\frac{1}{10} = 10\,\%$ ).
  - Quantity is low (e.g., increasing quantity from 2 to 3 units is a large relative percentage change: $\frac{1}{2} = 50\,\%$ ).
  - Because the percentage change in quantity demanded exceeds the percentage change in price, elasticity is high ( $PED > 1$ ).
- Bottom-Right Region of Demand Curve (Inelastic):
  - Price is low (e.g., decreasing price by \\$1 on a low base price represents a large relative percentage change).
  - Quantity is high (e.g., adding 1 unit to a large existing quantity represents a small relative percentage change).
  - Because the percentage change in quantity demanded is small relative to the percentage change in price, elasticity is low ( $PED < 1$ ).

Price Elasticity of Demand Calculation: World Vaccination Market

Market Scenario:
- Initial Price ( $P_1$ ): \\$20
- New Price ( $P_2$ ): \\$21
- Initial Quantity Demanded ( $Q_1$ ): $10{,}000{,}000$ vaccines ( $10$ \,million)
- New Quantity Demanded ( $Q_2$ ): $9{,}900{,}000$ vaccines ( $9.9$ \,million)
Step-by-Step Midpoint Formula Calculations:
- Percentage Change in Quantity Demanded:
  - Change in Quantity: $9.9 - 10 = -0.1$ \,million vaccines
  - Midpoint Quantity: $\frac{10 + 9.9}{2} = 9.95$ \,million vaccines
  - Formula: $\%\Delta Q_d = \frac{-0.1}{9.95} \times 100 \approx -1.005\,\% \approx -0.01$
- Percentage Change in Price:
  - Change in Price: $\ সম্মানিত21 - \ সম্মানিত20 = \ সম্মানিত1$
  - Midpoint Price: $\frac{20 + 21}{2} = \ সম্মানিত20.5$
  - Formula: $\%\Delta P = \frac{1}{20.5} \times 100 \approx 4.878\,\% \approx 0.05$
- Price Elasticity of Demand ( $PED$ ):
  - Formula (dropping the negative sign for absolute value): $PED = \left|\frac{\%\Delta Q_d}{\%\Delta P}\right| = \frac{0.01}{0.05} = 0.2$
Interpretation:
- $PED = 0.2 < 1$ , indicating that demand for vaccinations is inelastic.
- Vaccinations represent a essential product; significant price changes lead to negligible changes in quantity demanded.

Core Concepts of Elasticity and Product Classifications

Inelastic Demand ( $PED < 1$ ):
- Consumers are highly unresponsive to price changes.
- Economic implication: Represents a necessity (an essential good required for living or functioning that cannot easily be forgone or substituted).
- Examples: Basic food types, gasoline, essential stationery.
Elastic Demand ( $PED > 1$ ):
- Consumers are highly responsive to price changes; a small price increase causes quantity demanded to plummet.
- Economic implication: Represents a luxury (non-essential good that consumers easily forgo if prices rise).
- Examples: Housing, restaurant meals, airline travel.
Unitary Elastic Demand ( $PED = 1$ ):
- The percentage change in quantity demanded exactly equals the percentage change in price.
Comparative Elasticity Analysis:
- Elasticity assessment is comparative; goods can belong to the same general category while differing in relative elasticity.
- Elastic Comparison: Comparing $PED = 2.0$ and $PED = 1.5$ :
  - Both are elastic ( $> 1$ ).
  - $PED = 2.0$ is more elastic than $1.5$
  - $PED = 1.5$ is more inelastic than $2.0$
- Inelastic Comparison: Comparing $PED = 0.4$ and $PED = 0.2$ :
  - Both are inelastic ( $< 1$ ).
  - $PED = 0.2$ is more inelastic (smaller value).
  - $PED = 0.4$ is more elastic (larger value).
- General Rule: Larger numerical coefficients indicate greater elasticity; smaller numerical coefficients indicate greater inelasticity.

Extreme Cases of Price Elasticity of Demand

Perfectly Inelastic Demand ( $PED = 0$ ):
- Graphical Representation: Perfectly vertical line parallel to the y-axis (price axis).
- Economic Meaning: Absolute necessity for maintaining life. Quantity demanded remains fixed regardless of price changes.
- Mathematical Derivation: $PED = \frac{0}{\%\Delta P} = 0$
Perfectly Elastic Demand ( $PED = \infty$ or Undefined):
- Graphical Representation: Perfectly horizontal line parallel to the x-axis (quantity axis).
- Economic Meaning: Price is rigidly fixed. Consumers buy infinitely at that exact price, but demand drops to zero at any higher price.
- Examples: High-end haute couture clothing, ultra-exclusive luxury items (e.g., Cartier or Rolex watches).
- Mathematical Derivation: $PED = \frac{\%\Delta Q_d}{0} = \text{undefined} \text{ or } \infty$

Graphical Curve Profiles and The Five PED Cases

Perfectly Inelastic: $PED = 0$ (Vertical line).
Inelastic: $0 < PED < 1$ (Steep curve; e.g., a $20\,\%$ price increase generates a $10\,\%$ quantity decrease, yielding $PED = 0.5$ ).
Unit Elastic: $PED = 1$ (Moderate slope; e.g., a $20\,\%$ price increase generates a $20\,\%$ quantity decrease).
Elastic: $PED > 1$ (Flatter curve; e.g., a $20\,\%$ price increase generates a $40\,\%$ quantity decrease, yielding $PED = 2.0$ ).
Perfectly Elastic: $PED = \infty$ (Horizontal line).

Elasticity and Total Revenue

Total Revenue Definition and Equation:
- Total Revenue ( $TR$ ) is the total value of sales of a good or service.
- Formula: $TR = P \times Q$
- In market equilibrium: $TR = P_e \times Q_e$ (represented graphically as the area of a rectangle under the demand curve bounded by equilibrium price and quantity).
Price Effect vs. Quantity Effect:
- When price changes, two opposing forces dictate the net change in Total Revenue:
  1. Price Effect: Higher price per unit increases revenue generated on each unit sold.
  2. Quantity Effect: Higher price reduces total units sold, decreasing revenue.
- Numerical Equilibrium Comparison:
  - Quantity Effect Area ( $A$ ): $200 \times 0.9 = 180$
  - Price Effect Area ( $C$ ): $0.2 \times 900 = 180$
  - Net Outcome: Area $A = C$ ( $180 = 180$ ). The positive price effect completely offsets the negative quantity effect, keeping total revenue constant. This occurs specifically when demand is unit elastic ( $PED = 1$ ).
Total Revenue Rules Based on Elasticity:
- Elastic Demand ( $PED > 1$ ):
  - Quantity effect is stronger than price effect.
  - Price increase $\rightarrow$ Total Revenue decreases.
  - Price decrease $\rightarrow$ Total Revenue increases.
- Inelastic Demand ( $PED < 1$ ):
  - Price effect is stronger than quantity effect.
  - Price increase $\rightarrow$ Total Revenue increases.
  - Price decrease $\rightarrow$ Total Revenue decreases.
- Unit Elastic Demand ( $PED = 1$ ):
  - Price effect and quantity effect exactly offset each other.
  - Price increase or decrease $\rightarrow$ Total Revenue remains unchanged.
Total Revenue Curve Profile:
- Plotted against quantity, total revenue forms a bell-shaped curve.
- Total revenue increases along the elastic region of the demand curve, reaches its absolute peak at the midpoint where $PED = 1$ (e.g., peak revenue of $25$ in a standard schedule), and decreases along the inelastic region.

Determinants of Price Elasticity

Determinants of Price Elasticity of Demand ( $PED$ ):
1. Availability of Close Substitutes: Presence of close substitutes makes demand more elastic. Lack of substitutes makes demand inelastic.
2. Necessity vs. Luxury: Essential goods are inelastic; luxury goods are elastic.
3. Share of Income Spent on Good: Goods consuming a significant portion of income have more elastic demand; goods consuming a tiny fraction are inelastic.
4. Time Horizon: Demand is more elastic in the long run than in the short run, as consumers require time to adjust habits and locate substitutes.
Price Elasticity of Supply ( $PES$ ):
- Formula: $PES = \frac{\%\Delta Q_s}{\%\Delta P}$
- Always yields a positive coefficient due to the law of supply.
- Example calculation outcome: $PES = 3.53$ (Elastic supply, as $3.53 > 1$ ).
- Classifications ( $PES = 0$ , $<1$ , $=1$ , $>1$ , $=\infty$ ) mirror demand elasticity classifications.
Determinants of Price Elasticity of Supply ( $PES$ ):
1. Availability of Inputs/Resources: Supply is highly elastic if production inputs are readily available at low marginal costs.
2. Time Elapsed Since Price Change: Supply is significantly more elastic in the long run as firms gain time to expand facility capacity and reallocate resource inputs.

Cross-Price and Income Elasticity of Demand

Cross-Price Elasticity of Demand ( $XED$ ):
- Measures the responsiveness of quantity demanded of Good A to price changes in Good B.
- Formula: $XED = \frac{\%\Delta Q_{d, A}}{\%\Delta P_B}$
- Mathematical Sign Rule: Do NOT drop negative signs for $XED$ .
  - $XED < 0$ (Negative): Goods are complements.
  - $XED > 0$ (Positive): Goods are substitutes.
Income Elasticity of Demand ( $YED$ ):
- Measures the responsiveness of quantity demanded to changes in consumer income.
- Formula: $YED = \frac{\%\Delta Q_d}{\%\Delta Y}$
- Classification Rules:
  - $YED < 0$ (Negative): Inferior Good (demand falls as consumer income rises).
  - $0 \le YED \le 1$ (Positive, less than 1): Normal Good, Income Inelastic (demand rises as income rises, but proportionally less than the income increase).
  - $YED > 1$ (Positive, greater than 1): Normal Good, Income Elastic (demand rises significantly as income rises).

Business Applications: Technology Shifts and Total Revenue

Technology Improvements:
- Technological advancement reduces unit production costs, shifting the supply curve rightward from $S_0$ to $S_1$ and lowering market equilibrium price.
Interaction with Demand Elasticity:
- Inelastic Demand Market:
  - Supply shift rightward causes a major price collapse and a minor quantity increase.
  - Loss from lower price outweighs gain from higher quantity.
  - Result: Total Revenue decreases.
- Elastic Demand Market:
  - Supply shift rightward causes a minor price decrease and a massive quantity expansion.
  - Gain from increased sales volume outweighs loss from price drop.
  - Result: Total Revenue increases.

Government Policy: Tax Incidence and Elasticity

Tax Incidence Definition:
- Tax incidence refers to the manner in which the economic burden of a tax is divided between buyers (consumers) and sellers (producers).
Statutory vs. Economic Tax Incidence:
- Levying a tax legally on consumers shifts the Demand Curve leftward by the exact dollar amount of the tax.
- Levying a tax legally on producers shifts the Supply Curve leftward by the exact dollar amount of the tax.
- Equivalence Principle: Market equilibrium outcomes, total tax revenue, buyer price paid ( $P_C$ ), producer price received ( $P_P$ ), and deadweight loss are 100\% identical regardless of whether the tax is legally assessed on consumers or producers.
Key Tax Metric Formulas:
- Price paid by consumers: $P_C$
- Price received by producers: $P_P$
- Per-Unit Tax Amount: $\text{Per-Unit Tax} = P_C - P_P$
- Total Tax Revenue Collected by Government: $\text{Tax Revenue} = (P_C - P_P) \times Q_{\text{tax}}$
- Consumer Tax Share: $(P_C - P_0) \times Q_{\text{tax}}$ (where $P_0$ is original pre-tax equilibrium price).
- Producer Tax Share: $(P_0 - P_P) \times Q_{\text{tax}}$ .
The Elasticity Rule of Tax Burden:
- The side of the market (buyers or sellers) that is MORE INELASTIC bears the LARGER SHARE of the tax burden.
- Inelastic Demand / Elastic Supply: Consumers bear the majority of the tax burden ( $P_C - P_0 > P_0 - P_P$ ).
- Inelastic Supply / Elastic Demand: Producers bear the majority of the tax burden ( $P_0 - P_P > P_C - P_0$ ).
Deadweight Loss ( $DWL$ ):
- Taxes create a deadweight loss (represented visually as a triangle bounded by $Q_{\text{tax}}$ and $Q_0$ between the demand and supply curves).
- Deadweight loss represents market efficiency lost due to mutually beneficial transactions prevented by the tax.

Questions & Discussion

Question / Dialogue on Inelastic Demand and Goods Assessment:
- Prompt: If price changes substantially (e.g., increases by a large amount) and consumers still purchase the good, what does that indicate?
- Response: It indicates that consumers value the good highly and that the item is a necessity that cannot be easily forgone.
Question / Dialogue on Total Revenue Neutrality:
- Prompt: In a scenario where price increases, sales volume drops, but total monetary inflow remains completely unchanged, what property of the demand curve accounts for this?
- Response: The curve is unit elastic ( $PED = 1$ ), meaning the percentage increase in price perfectly offsets the percentage decrease in quantity.
Question / Dialogue on Identifying Tax Burden Shares:
- Prompt: When examining graphical tax models, how is it determined whether consumers or producers bear the larger tax burden?
- Response: By identifying which curve is steeper (more inelastic) in relative comparison; the market group possessing the more inelastic curve bears the larger rectangle portion of total tax revenue.