Comprehensive Coverage: Lectures 3-7
Comparative statics is the analysis of how equilibrium outcomes change when we vary parameters or assumptions in an economic model. We hold certain factors fixed (like consumer preferences, number of consumers, technology) and examine how changes in other factors affect equilibrium price and quantity.
Comparative statics allows economists to predict how markets respond to changes in underlying conditions, making it a powerful tool for policy analysis and business decision-making.
| Concept | Change in Quantity Demanded | Change in Demand |
|---|---|---|
| Definition | Movement along the demand curve | Shift of the entire demand curve |
| Cause | Change in the price of the good itself | Change in factors other than price (income, preferences, related goods) |
| Visual | Move from one point to another on same curve | Entire curve shifts left or right |
| Example | Coffee price drops from $5 to $3 → buy more coffee | Income increases → demand curve shifts right |
↓ (Demand increases)
Same slope, different intercept → parallel shift
| Type of Shift | Cause | Effect on P | Effect on Q | Graph Movement |
|---|---|---|---|---|
| Demand ↑ | Income ↑, Preferences favor good, Substitute price ↑ | ↑ Increases | ↑ Increases | Curve shifts right |
| Demand ↓ | Income ↓, Preferences against good, Substitute price ↓ | ↓ Decreases | ↓ Decreases | Curve shifts left |
| Supply ↑ | Technology improves, Input costs ↓, More sellers | ↓ Decreases | ↑ Increases | Curve shifts right |
| Supply ↓ | Input costs ↑, Regulations increase, Fewer sellers | ↑ Increases | ↓ Decreases | Curve shifts left |
Shift: Rightward
Result: Both P↑ and Q↑
Example: New study shows coffee prevents disease → demand for coffee increases
Shift: Leftward
Result: Both P↓ and Q↓
Example: Health warning about coffee → demand decreases
Shift: Rightward
Result: P↓ and Q↑
Example: Better farming technology → supply increases
Shift: Leftward
Result: P↑ and Q↓
Example: Frost destroys crops → supply decreases
Measures the responsiveness of quantity demanded to a change in price.
Measures the responsiveness of quantity supplied to a change in price.
| Elasticity Type | Value Range | Interpretation | Example |
|---|---|---|---|
| Perfectly Inelastic | ε = 0 | Quantity doesn't change regardless of price | Life-saving medication |
| Inelastic | 0 < ε < 1 | % change in Q < % change in P | Gasoline, salt |
| Unit Elastic | ε = 1 | % change in Q = % change in P | Theoretical benchmark |
| Elastic | ε > 1 | % change in Q > % change in P | Luxury goods, restaurant meals |
| Perfectly Elastic | ε = ∞ | Any price increase → Q drops to zero | Perfect competition |
Elasticity determines how much quantity responds to price changes. More elastic goods have more substitutes and are more responsive to price changes. This is crucial for understanding tax incidence and market behavior.
Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. It represents the net benefit consumers receive from participating in the market.
Where: wi = willingness to pay, p = market price
CS = Area of triangle above price, below demand curve
Formula: CS = ½ × (Pchoke - P*) × Q*
Scenario: Coffee market
• WTP (choke price): $10
• Market price: $4
• Quantity: 60 units
CS = ½ × ($10 - $4) × 60 = $180
Consumer A:
• WTP: $8
• Price paid: $4
• CSA = $8 - $4 = $4
Consumer B:
• WTP: $6
• Price paid: $4
• CSB = $6 - $4 = $2
Producer surplus is the difference between the price producers receive and their cost of production. It represents the net benefit producers receive from participating in the market.
Where: p = market price, cj = cost of production
PS = Area of triangle below price, above supply curve
Formula: PS = ½ × (P* - Pmin) × Q*
Scenario: Coffee market
• Market price: $4
• Minimum price (cost): $1
• Quantity: 60 units
PS = ½ × ($4 - $1) × 60 = $90
Producer X:
• Price received: $4
• Cost: $2
• PSX = $4 - $2 = $2
Producer Y:
• Price received: $4
• Cost: $3
• PSY = $4 - $3 = $1
Total surplus is the sum of consumer surplus and producer surplus. It represents the total net benefit to society from market transactions.
| Component | Formula | Example Value | Interpretation |
|---|---|---|---|
| Consumer Surplus | ½ × (10 - 4) × 60 | $180 | Benefit to consumers |
| Producer Surplus | ½ × (4 - 1) × 60 | $90 | Benefit to producers |
| Total Surplus | CS + PS | $270 | Total social welfare |
In a competitive market without externalities, the equilibrium maximizes total surplus. Any intervention (like taxes or price controls) typically reduces total surplus, creating deadweight loss.
Externalities occur when the actions of consumers or producers affect third parties who are not directly involved in the market transaction. They represent a market failure where private costs/benefits differ from social costs/benefits.
| Type | Definition | Example | Effect | Solution |
|---|---|---|---|---|
| Negative Externality | Cost imposed on third parties | Factory pollution, secondhand smoke | Overproduction (Qmarket > Qsocial) | Pigouvian tax |
| Positive Externality | Benefit conferred on third parties | Education, vaccination, R&D | Underproduction (Qmarket < Qsocial) | Pigouvian subsidy |
1. Private benefit < Social benefit
2. Market overproduces
3. Creates deadweight loss
4. Tax can correct inefficiency
1. Private benefit < Social benefit
2. Market underproduces
3. Creates deadweight loss
4. Subsidy can correct inefficiency
A tax is an unrequited payment to the government - you are entitled to nothing directly in return. Taxes create a wedge between the price buyers pay and the price sellers receive.
Where: PD = price paid by buyers, PS = price received by sellers, t = tax per unit
1. Revenue Generation
Fund public goods and services
2. Redistribution
Transfer wealth from rich to poor
3. Correct Externalities
Discourage harmful activities
England & Wales (1696)
• Base: 2 shillings per house
• 0-9 windows: no extra charge
• 10-20 windows: +4 shillings
• 20+ windows: +8 shillings
Result: People bricked up windows!
1. Enforceability
Can it be collected effectively?
2. Fairness
Horizontal and vertical equity
3. Minimal Excess Burden
Minimize deadweight loss
| Tax Type | Who Pays Legally | Supply/Demand Shift | Effect on Pbuyers | Effect on Psellers | Effect on Q |
|---|---|---|---|---|---|
| Tax on Sellers | Sellers | Supply shifts up by t | Increases | Decreases | Decreases |
| Tax on Buyers | Buyers | Demand shifts down by t | Increases | Decreases | Decreases |
CRITICAL: It doesn't matter who legally pays the tax (statutory incidence). The economic burden (economic incidence) depends on the relative elasticities of supply and demand. Both scenarios produce identical outcomes!
The side of the market that is MORE INELASTIC bears MORE of the tax burden, regardless of who legally pays the tax.
| Scenario | Demand Elasticity | Supply Elasticity | Who Bears More Burden | Reasoning |
|---|---|---|---|---|
| Inelastic Demand | Low (εD < 1) | High (εS > 1) | Consumers | Consumers can't easily reduce quantity |
| Elastic Demand | High (εD > 1) | Low (εS < 1) | Producers | Consumers easily switch to alternatives |
| Inelastic Supply | High (εD > 1) | Low (εS < 1) | Producers | Producers can't easily adjust quantity |
| Elastic Supply | Low (εD < 1) | High (εS > 1) | Consumers | Producers easily exit market |
Market Characteristics:
• Demand: Inelastic (necessity)
• Supply: Elastic (easy to produce)
Result: Consumers bear most of the tax burden through higher prices
Market Characteristics:
• Demand: Elastic (luxury good)
• Supply: Inelastic (specialized)
Result: Producers bear most of the tax burden through lower revenues
Deadweight loss is the reduction in total surplus that results from a tax. It represents the value of transactions that no longer occur because of the tax - a pure loss to society.
Where: t = tax, Q0 = original quantity, Q1 = new quantity after tax
DWL = Shaded Triangle Area
Represents lost gains from trade
| Tax Size | Effect on Q | DWL | Tax Revenue | Efficiency |
|---|---|---|---|---|
| Small Tax | Small decrease | Small DWL | Moderate revenue | More efficient |
| Large Tax | Large decrease | Large DWL (grows with t²) | May decrease (Laffer curve) | Less efficient |
Deadweight loss grows with the SQUARE of the tax rate. Doubling the tax more than doubles the efficiency loss. This is why economists generally prefer many small taxes over one large tax.
A subsidy is a payment made by the government to a buyer or seller of a good or service. It's the opposite of a tax. Subsidies create a wedge where the price buyers pay is LOWER than the price sellers receive.
Where: PD = price paid by buyers, PS = price received by sellers, s = subsidy per unit
| Aspect | Tax | Subsidy |
|---|---|---|
| Price Wedge | PD = PS + t | PD = PS - s |
| Effect on Q | Decreases quantity | Increases quantity |
| Government | Collects revenue | Spends money |
| Efficiency | Creates DWL (usually) | Creates DWL (unless correcting externality) |
| Incidence | More inelastic side bears burden | More elastic side receives more benefit |
Purpose: Support farmers
Effect: Lower food prices, higher farm revenue
Cost: Government spending, potential overproduction
Purpose: Increase enrollment
Effect: Lower tuition, more students
Justification: Positive externality correction
Purpose: Promote clean energy
Effect: Lower cost of solar/wind
Justification: Environmental benefits
| Subsidy Type | Who Receives | Supply/Demand Shift | Effect on Pbuyers | Effect on Psellers | Effect on Q |
|---|---|---|---|---|---|
| Subsidy to Sellers | Sellers | Supply shifts down by s | Decreases | Increases | Increases |
| Subsidy to Buyers | Buyers | Demand shifts up by s | Decreases | Increases | Increases |
CRITICAL: Just like with taxes, it doesn't matter who legally receives the subsidy. Both buyers and sellers benefit regardless of who gets the payment. The distribution of benefits depends on elasticities!
The side of the market that is MORE ELASTIC receives MORE of the subsidy benefit. This is the opposite of tax incidence!
| Scenario | Demand Elasticity | Supply Elasticity | Who Benefits More | Reasoning |
|---|---|---|---|---|
| Elastic Demand | High (εD > 1) | Low (εS < 1) | Consumers | Consumers very responsive to price changes |
| Inelastic Demand | Low (εD < 1) | High (εS > 1) | Producers | Producers can easily expand production |
| Elastic Supply | Low (εD < 1) | High (εS > 1) | Consumers | Producers compete to supply more |
| Inelastic Supply | High (εD > 1) | Low (εS < 1) | Producers | Limited supply → producers capture benefit |
Study Finding:
State funding for higher education
Pass-through rate: 26%
For every $1 of state subsidy:
• Students save $0.26 in tuition
• Universities keep $0.74
Why? Relatively inelastic supply of education
Market Characteristics:
• Demand: Inelastic (food necessity)
• Supply: Elastic (can expand easily)
Result: Consumers (food buyers) receive most of the benefit through lower prices
Subsidies increase both consumer and producer surplus, but create government cost. The net effect depends on whether there's a positive externality being corrected.
| Component | Before Subsidy | After Subsidy | Change |
|---|---|---|---|
| Consumer Surplus | Area A | Area A + B + C | + (B + C) |
| Producer Surplus | Area D | Area D + E + F | + (E + F) |
| Government Cost | 0 | -(B + C + E + F + G) | - (B + C + E + F + G) |
| Total Surplus | A + D | A + B + C + D + E + F - (B + C + E + F + G) | - G (DWL) |
Subsidies create deadweight loss UNLESS they correct a positive externality. If the subsidy equals the external benefit, it can increase total surplus by encouraging the socially optimal quantity.
Positive Externality: Educated citizens benefit society
Market Outcome: Underproduction
Subsidy Effect: Moves Q toward social optimum
Result: Increases total surplus!
No Clear Externality: Questionable environmental benefit
Market Outcome: Already at equilibrium
Subsidy Effect: Overproduction
Result: Creates deadweight loss
| Intervention | Effect on Q | Effect on P | CS Change | PS Change | DWL | Gov Revenue/Cost |
|---|---|---|---|---|---|---|
| No Intervention | Q* | P* | Maximized | Maximized | 0 | 0 |
| Tax | ↓ Decreases | PD↑, PS↓ | ↓ Decreases | ↓ Decreases | Yes (triangle) | + Revenue (t × Q) |
| Subsidy | ↑ Increases | PD↓, PS↑ | ↑ Increases | ↑ Increases | Yes (unless correcting externality) | - Cost (s × Q) |
| Price Floor | ↓ Decreases (surplus) | Above equilibrium | ↓ Decreases | ↑ or ↓ (ambiguous) | Yes | 0 (unless gov buys surplus) |
| Price Ceiling | ↓ Decreases (shortage) | Below equilibrium | ↑ or ↓ (ambiguous) | ↓ Decreases | Yes | 0 |
Taxes: More inelastic side bears more burden
Subsidies: More elastic side receives more benefit
Key: Statutory ≠ Economic incidence
Free Market: Maximizes total surplus (no externalities)
Interventions: Create DWL (usually)
Exception: Correcting externalities
Demand ↑: P↑, Q↑
Supply ↑: P↓, Q↑
Tool: Predict market changes
Negative: Overproduction → Tax
Positive: Underproduction → Subsidy
Goal: Align private and social incentives
CS: Benefit to consumers
PS: Benefit to producers
Total: Measure of social welfare
Elastic: Very responsive to price
Inelastic: Not very responsive
Determines: Incidence and DWL magnitude