Lecture 7: Tax Policies and Welfare

Definition of Tax: A tax is a specific payment made to the government on every unit of a good or service transacted in a market.
Primary Purpose: Taxation is most commonly utilized by governments as a mechanism to raise revenue.
The Tax Wedge: The introduction of a tax creates a "wedge" between the price paid by consumers and the price received by producers. The mathematical relationship is expressed as:
- $t = P_D - P_S$
- Where $t$ is the tax per unit.
- $P_D$ is the gross price paid by the consumer.
- $P_S$ is the net price received by the producer.

Tax Imposed on Suppliers:
- If the tax is legally imposed on the seller, the seller requires the price they receive ( $P_S$ ) plus the tax amount ( $t$ ) to supply the same quantity.
- This results in a leftward/upward shift of the supply curve. The new supply curve is denoted as $S + t$ .
- Equilibrium Outcome: The tax reduces the total quantity traded from $Q^*$ to $Q^{**}$ . At this new quantity, the price consumers pay ( $P_D$ ) is higher than the original equilibrium price ( $P^*$ ), and the price producers keep ( $P_S$ ) is lower than $P^*$ .
Tax Imposed on Consumers:
- If the tax is legally imposed on the buyer, at every quantity demanded, buyers are only willing to purchase if the market price they pay is the demand price minus the tax ( $P_D - t$ ).
- This results in a leftward/downward shift of the demand curve.
- Equivalence Principle: The economic outcome in terms of quantity traded and the prices paid/received is identical regardless of whether the tax is legally levied on the buyer or the seller.

Taxation and Efficiency: Any government regulation that causes the quantity traded ( $Q$ ) to differ from the competitive equilibrium quantity ( $Q^*$ ) results in an inefficient outcome.
Deadweight Loss (DWL): Because taxes reduce the quantity traded below the efficient level (Q^{**} < Q^*), they generate a deadweight loss, representing the lost gains from trade.
Welfare Comparison (Before vs. After Tax):
- Consumer Surplus (CS): Reduced. Pre-tax surplus was $A + B + C$ ; post-tax surplus is $A$ . The loss is $-(B + C)$ .
- Producer Surplus (PS): Reduced. Pre-tax surplus was $D + E + F$ ; post-tax surplus is $F$ . The loss is $-(E + D)$ .
- Tax Revenue (TR): The government collects the tax wedge times the quantity traded. Revenue is represented by the areas $B + D$ .
- Deadweight Loss (DWL): The net loss to society is represented by areas $C + E$ .
Tax Incidence: Both sides of the market generally bear a part of the tax burden. This shared burden is characteristic of indirect interventions like taxes and subsidies, distinguishing them from direct interventions like price controls.

The Burden of Taxation: Who pays more of the tax depends on the relative price elasticity of supply and demand.
Elasticity Rule: The tax burden falls more heavily on the side of the market that is less price elastic (more inelastic).
Elastic Demand Case: If demand is highly elastic, consumers are very sensitive to price changes; therefore, sellers will bear the majority of the tax burden to avoid losing too much volume.
Inelastic Demand Case: If demand is price inelastic, consumers are not very sensitive to price changes; therefore, sellers can pass most of the tax on to the consumers in the form of higher prices.
Practice Equations for Welfare Effects of a $1 Tax on Suppliers:
- Case 1: $Q_D = 10 - 4P; Q_S = 2P$
- Case 2: $Q_D = 10 - \frac{1}{4}P; Q_S = 2P$

Definition: A subsidy is a payment from the government to consumers or producers for each unit of a good transacted. It is essentially a negative tax.
Purpose: Subsidies are used to encourage the production or consumption of specific goods.
Subsidy Wedge: $s = P_S - P_D$ . It increases the price suppliers receive relative to what consumers pay.
Market Effects: A subsidy increases the quantity traded beyond the market equilibrium (Q^{**} > Q^*). It shifts the demand curve outward (if given to consumers) or the supply curve outward (if given to producers).
Welfare Analysis of Subsidies:
- Consumer Surplus: Increases (Area $F + E$ ).
- Producer Surplus: Increases (Area $B + C$ ).
- Government Cost: Represents a total expenditure of $B + C + D + E + F$ .
- Efficiency: Because the subsidy encourages trade where the cost of production exceeds the value to the consumer, it creates a deadweight loss (Area $D$ ).
Subsidy Incidence: Similar to tax incidence, the benefit of a subsidy is distributed based on the relative price elasticities of demand and supply, not who receives the payment.

Environmental Policy: New research from the Australia Institute indicates that an EU-style tax on plastic packaging could generate nearly $1.5\,\text{billion}$ per year.
Consumer Subsidies:
- Clean Energy: Solar panel subsidies.
- COVID-19 Economic Recovery: The Australian Government's HomeBuilder Grant ($15,000 to $25,000 for building or renovating homes).
- Regional Tourism: $200 vouchers for holidays in regional areas.
- Midweek Melbourne Money: A program allowing consumers to claim 25% on bills for spending between $40 and $500.
- Social Support: Childcare subsidies and academic scholarships.
Producer Subsidies:
- European Union (EU) agricultural subsidies.
- Pharmaceutical production incentives.
- Industrial Policy: Subsidies to assist developing industries.
- Renewable energy production subsidies.