# Taxes and Subsidies

> CIE A-Level Economics · Unit 3: Government Microeconomic Intervention
> Source: https://www.owlsprep.com/study/cie-9708-u3-taxes-and-subsidies/

This sub-topic explains how government taxes and subsidies alter market equilibrium, prices and output. We cover tax types, the division of tax burden, subsidy benefits, and core welfare analysis of these policies.

**Prerequisites:** [Supply, demand and market equilibrium](https://www.owlsprep.com/study/cie-9708-u3-market-equilibrium/); [Price elasticity of demand and supply](https://www.owlsprep.com/study/cie-9708-u3-elasticity/)

## Learning objectives

- Distinguish between specific and ad valorem indirect taxes
- Calculate and explain the incidence of tax between consumers and producers
- Illustrate the impact of taxes and subsidies on market equilibrium
- Evaluate welfare effects of taxes and subsidies in competitive markets

## Types of Indirect Taxes

Indirect taxes are levied on the production or consumption of goods, and are typically passed on to consumers via higher prices. CIE exams focus on two main types of indirect tax for microeconomic analysis, each with a different impact on the market supply curve.

**Indirect Tax** — A tax levied on production/consumption of a good, rather than directly on income or profit. The legal burden can fall on producers or consumers, but the economic incidence depends on elasticities.

*Example:* VAT, cigarette excise duties, alcohol taxes

- **Specific (per-unit) tax**: A fixed absolute tax charged on each unit sold, e.g. \$2 per packet of cigarettes.
- **Ad valorem tax**: A tax charged as a percentage of the good's price, e.g. 20% VAT on most consumer goods.

**Worked example:** Original supply for a good is given by $P = 2 + Q$. Describe the supply curve shift for (a) a \$2 per-unit specific tax, and (b) a 50% ad valorem tax.

1. For a specific tax, every unit costs \$2 more regardless of price, so supply shifts vertically upwards by \$2 (parallel shift):
2. $$P = (2 + 2) + Q = 4 + Q$$
3. For an ad valorem tax, the absolute tax increases with price, so the supply curve pivots inwards (becomes steeper) rather than shifting parallel:
4. $$P = 1.5 \times (2 + Q) = 3 + 1.5Q$$

## Tax Incidence

When a tax is imposed, the total burden is split between consumers (who pay higher prices) and producers (who receive lower revenue per unit). The split depends only on the relative price elasticities of demand and supply, not who the tax is legally imposed on.

**Tax Incidence** — The proportion of the total tax burden that falls on consumers versus producers. The core rule is: the more inelastic your side of the market, the larger your share of the burden.

The formula for the share of tax burden falling on consumers is given by: $\frac{PES}{PED + PES}$, where $PED$ is price elasticity of demand and $PES$ is price elasticity of supply.

**Worked example:** A market has $PED = 0.2$ and $PES = 1.8$. A \$10 per-unit tax is imposed. What share of the tax burden falls on consumers?

1. Substitute values into the consumer share formula:
2. $$\text{Consumer share} = \frac{PES}{PED + PES} = \frac{1.8}{0.2 + 1.8} = 0.9 = 90\%$$
3. The remaining 10% falls on producers. This matches the rule: demand is much more inelastic than supply, so consumers bear almost all the burden.

> **tip**
>
> Always shift the supply curve vertically for a per-unit tax, not horizontally. The vertical distance between the original and new supply curve equals the per-unit tax amount.

## Subsidies: Market Impact and Benefit Sharing

A subsidy is a payment from the government to producers per unit of output, which reduces production costs and shifts the supply curve to the right. Governments use subsidies to increase consumption of merit goods, support vulnerable industries, or reduce prices for low-income households.

**Per-unit Subsidy** — A fixed payment per unit of output to producers, which shifts the supply curve vertically downwards by the full amount of the subsidy, resulting in a parallel shift.

The benefit of a subsidy is split between consumers (lower prices) and producers (higher revenue per unit) following the same elasticity rule as taxes: the more inelastic your curve, the larger your share of the benefit.

**Worked example:** A \$5 per-unit subsidy is given to bread producers. Original equilibrium price is \$8. If $PED = 0.5$ and $PES = 1.5$, what is the new price paid by consumers?

1. Calculate the share of the subsidy benefit passed to consumers:
2. $$\text{Consumer share} = \frac{PES}{PED + PES} = \frac{1.5}{0.5 + 1.5} = 0.75$$
3. Calculate the price reduction for consumers and the new price:
4. $$\text{Price reduction} = 0.75 \times 5 = \$3.75 \\ \text{New consumer price} = 8 - 3.75 = \$4.25$$
5. Producers receive \$4.25 + \$5 = \$9.25 per unit, so they gain \$1.25 per unit, matching their 25% share of the benefit.

## Welfare Analysis

When there is no existing market failure, both taxes and subsidies reduce total social welfare by creating a deadweight loss (DWL). If a tax corrects a negative externality or a subsidy corrects a positive externality, they can increase total welfare instead.

DWL arises because taxes reduce equilibrium output below the socially efficient level, while subsidies increase output above the socially efficient level. DWL is calculated as the area of the welfare triangle between the original and new equilibrium quantity.

**Worked example:** Given demand $P = 20 - Q$ and supply $P = Q$, with no externalities, calculate the deadweight loss from a \$4 per-unit tax.

1. Find the original free market equilibrium:
2. $$20 - Q = Q \implies Q = 10, P = 10$$
3. Find the new equilibrium after the tax, which shifts supply to $P = Q + 4$:
4. $$20 - Q = Q + 4 \implies 2Q = 16 \implies Q = 8$$
5. Calculate DWL as the area of the welfare triangle:
6. $$DWL = \frac{1}{2} \times \text{tax} \times \Delta Q = \frac{1}{2} \times 4 \times (10 - 8) = 4$$

> **note**
>
> Always consider market failure when evaluating welfare effects. A tax on a demerit good with negative externalities will eliminate existing DWL, rather than create new DWL.

## Common pitfalls

- **Wrong:** Shifting the supply curve horizontally instead of vertically for a per-unit tax.
  - Why it fails: A tax increases cost per unit, so the vertical distance between old and new supply equals the tax amount. A horizontal shift changes this distance.
  - Correct: Always shift the supply curve vertically upwards by the full per-unit tax amount.
- **Wrong:** Assuming consumers always bear the full burden of an indirect tax.
  - Why it fails: Burden split depends entirely on elasticities. If supply is perfectly inelastic, producers bear 100% of the burden.
  - Correct: Always use the elasticity rule to calculate burden share, never assume full pass-through to consumers.
- **Wrong:** Drawing a parallel shift for an ad valorem tax.
  - Why it fails: Ad valorem taxes increase in absolute size as price rises, so the shift is larger at higher prices.
  - Correct: Draw an inward pivot (steeper supply curve) for ad valorem taxes.
- **Wrong:** Claiming subsidies never create deadweight loss.
  - Why it fails: Subsidies increase output beyond the socially efficient level when there is no existing market failure, creating a net welfare loss.
  - Correct: Only conclude subsidies increase welfare if they correct a pre-existing market failure like a positive externality.
- **Wrong:** Confusing the price consumers pay with the price producers receive after tax/subsidy.
  - Why it fails: After tax, consumers pay more than producers receive. After subsidy, producers receive more than consumers pay.
  - Correct: Always label both prices on your exam diagram to avoid confusion.

## Cheatsheet

| Concept | Key Rule | Diagram Change |
| --- | --- | --- |
| Specific Tax | Consumer burden = $\frac{PES}{PED+PES}$ | Supply shifts parallel up by tax amount |
| Ad Valorem Tax | Burden shares follow same elasticity rule | Supply pivots inwards (steeper) |
| Per-unit Subsidy | Consumer benefit = $\frac{PES}{PED+PES}$ | Supply shifts parallel down by subsidy amount |
| Tax DWL (no externalities) | DWL = ½ × tax × ΔQ | Welfare triangle between original/new Q |
| Subsidy DWL (no externalities) | DWL = ½ × subsidy × ΔQ | Welfare triangle between original/new Q |

## What's next

Understanding taxes and subsidies is a core requirement for all CIE A-Level Unit 3 exams, and provides the foundation for analyzing all types of government intervention in microeconomics. You will now apply these tools to evaluate policies that correct market failures from externalities, and assess the impact of these policies on equity and efficiency. This knowledge also helps you evaluate the causes and consequences of government failure, a common topic in extended response questions.

- [Policies to correct market failure](https://www.owlsprep.com/study/cie-9708-u3-policies-to-correct-market-failure/)
- [Redistribution of Income](https://www.owlsprep.com/study/cie-9708-u3-redistribution-of-income/)
- [Basic Macroeconomic Concepts](https://www.owlsprep.com/study/cie-9708-u4-overview/)

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