# Microeconomics quantitative analysis (HL only)

> IB Economics Higher Level · IB Diploma Economics HL
> Source: https://www.owlsprep.com/study/ib-economics-hl-u2-microeconomics-quantitative-analysis/

This sub-topic covers all core quantitative calculations required for IB Economics HL Microeconomics, including elasticity, surplus, tax revenue and welfare loss analysis. Mastery of these methods is required for both Paper 1 and Paper 2 exams.

**Prerequisites:** [Basic demand and supply analysis](https://www.owlsprep.com/study/ib-economics-hl-u2-demand-and-supply/); [Core elasticity concepts (SL)](https://www.owlsprep.com/study/ib-economics-hl-u2-elasticity-concepts/)

## Learning objectives

- Calculate elasticities using the HL required midpoint method
- Calculate consumer, producer and total surplus for linear curves
- Calculate government revenue and welfare loss from taxes/subsidies
- Calculate monopoly profit and welfare loss from allocative inefficiency

## Elasticity Calculations: Midpoint Method

**Midpoint (arc) elasticity** — The required HL method for calculating all elasticities. It eliminates bias from the direction of price/quantity change, unlike the simpler point elasticity method used at SL.

*Notation:* E_d = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}

*Example:* Works for PED, PES, XED and YED calculations

Unless a question explicitly tells you to use point elasticity, IB HL examiners expect the midpoint method for all elasticity calculation questions.

**Worked example:** Price of a good increases from \$10 to \$15, and quantity demanded falls from 100 units to 80 units. Calculate PED using the midpoint method.

1. Calculate percentage change in quantity demanded:

   $$\frac{80 - 100}{(100 + 80)/2} = \frac{-20}{90} \approx -0.222$$
2. Calculate percentage change in price:

   $$\frac{15 - 10}{(10 + 15)/2} = \frac{5}{12.5} = 0.4$$
3. Divide to get PED, drop the negative sign:

   $$PED = \left|\frac{-0.222}{0.4}\right| \approx 0.56$$

> **Exam tip:** Always write every step of your calculation, you can get method marks even if you make an arithmetic error.

*Calculator:* allowed

## Consumer and Producer Surplus

**Total Surplus** — Sum of consumer and producer surplus, the standard measure of total welfare in a competitive market. For linear demand and supply, surplus equals the area of a triangle.

*Notation:* \text{Total Surplus} = CS + PS = \frac{1}{2} \times Q^* \times (P_{\text{demand intercept}} - P_{\text{supply intercept}})

*Example:* CS is the area below demand, above equilibrium price

**Worked example:** Given demand $P = 100 - 2Q$ and supply $P = 20 + 2Q$, calculate equilibrium CS and PS.

1. Find equilibrium by setting demand equal to supply:

   $$100 - 2Q = 20 + 2Q \implies 4Q = 80 \implies Q^* = 20$$
2. Find equilibrium price:

   $$P^* = 100 - 2(20) = 60$$
3. Calculate CS (intercept of demand = 100):

   $$CS = \frac{1}{2} \times 20 \times (100 - 60) = 400$$
4. Calculate PS (intercept of supply = 20):

   $$PS = \frac{1}{2} \times 20 \times (60 - 20) = 400$$

*Calculator:* allowed

## Tax Revenue and Welfare Loss

IB HL requires calculation of government revenue from specific (per-unit) and ad valorem (percentage) taxes, plus the deadweight (welfare) loss created by the tax distortion. The same logic applies to subsidy calculations.

**Worked example:** A \$10 per unit specific tax is applied to the market from the previous example: demand $P = 100 - 2Q$, supply $P = 20 + 2Q$, original $Q^* = 20$. Calculate government tax revenue and deadweight loss (DWL).

1. Shift supply up by \$10 for the tax, new supply curve:

   $$P = 20 + 2Q + 10 = 30 + 2Q$$
2. Find new equilibrium quantity:

   $$100 - 2Q = 30 + 2Q \implies Q_{new} = 17.5$$
3. Calculate government tax revenue:

   $$\text{Revenue} = \text{tax per unit} \times Q_{new} = 10 \times 17.5 = 175$$
4. Calculate DWL as area of the triangular deadweight loss:

   $$DWL = \frac{1}{2} \times \text{tax} \times (Q^* - Q_{new}) = \frac{1}{2} \times 10 \times 2.5 = 12.5$$

*Calculator:* allowed

## Monopoly Profit and Welfare Loss

HL requires you to calculate a monopolist's profit at profit-maximizing output, and the welfare loss that results from producing below the allocatively efficient output level.

**Worked example:** A monopolist faces demand $P = 100 - Q$, has constant marginal cost $MC = 20$ and no fixed costs. Calculate the monopolist's profit and the welfare loss compared to allocative efficiency.

1. For linear demand, marginal revenue (MR) has the same intercept and twice the slope: $MR = 100 - 2Q$. Set $MR = MC$ to find profit-maximizing output:

   $$100 - 2Q = 20 \implies Q_m = 40$$
2. Find monopolist price from the demand curve:

   $$P_m = 100 - 40 = 60$$
3. Calculate total profit:

   $$\pi = TR - TC = (60 \times 40) - (20 \times 40) = 1600$$
4. Allocative efficiency is $P = MC$, so efficient output $Q_e = 80$. Calculate DWL:

   $$DWL = \frac{1}{2} \times (P_m - MC) \times (Q_e - Q_m) = \frac{1}{2} \times 40 \times 40 = 800$$

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Using point elasticity instead of midpoint elasticity when not specified
  - Why it fails: IB HL markers deduct marks for using the wrong method even if the final value is close
  - Correct: Always use the midpoint method for elasticity questions unless told otherwise
- **Wrong:** Omitting the 1/2 factor when calculating area of triangular surplus/DWL
  - Why it fails: This leads to double the correct value and loses full marks for the calculation
  - Correct: Always remember that triangular area for linear curves is $\frac{1}{2} \times \text{base} \times \text{height}$
- **Wrong:** Shifting ad valorem taxes parallel to the original supply curve
  - Why it fails: Specific taxes shift parallel, but ad valorem taxes rotate supply (change slope)
  - Correct: Recalculate the entire supply curve for ad valorem taxes by adding the percentage markup
- **Wrong:** Mixing up demand and supply intercepts for surplus calculations
  - Why it fails: Swapping intercepts gives inverted values for CS and PS
  - Correct: Consumer surplus uses the demand intercept; producer surplus uses the supply intercept
- **Wrong:** Using monopoly profit as the welfare loss for monopoly
  - Why it fails: Profit is a transfer from consumers to monopoly, not a net welfare loss
  - Correct: Welfare loss only counts surplus from units that are not produced at all

## Cheatsheet

| Calculation | Formula | Key Note |
| --- | --- | --- |
| Midpoint PED | $\frac{(Q_2-Q_1)/((Q_1+Q_2)/2)}{(P_2-P_1)/((P_1+P_2)/2)}$ | Drop the negative sign for PED |
| Consumer Surplus (linear) | $\frac{1}{2} Q^* (P_{\text{demand intercept}} - P^*)$ | Area below demand, above price |
| Producer Surplus (linear) | $\frac{1}{2} Q^* (P^* - P_{\text{supply intercept}})$ | Area above supply, below price |
| DWL from tax | $\frac{1}{2} \times \text{tax} \times (Q_{old} - Q_{new})$ | Triangular area of lost surplus |
| Monopoly DWL | $\frac{1}{2} (P_m - MC) (Q_e - Q_m)$ | Only for units not produced |
| Tax Revenue (specific) | $\text{tax per unit} \times Q_{new}$ | Straightforward product calculation |

## What's next

Mastering these quantitative methods is critical for scoring high marks on IB HL Economics exams, as 20-30% of total marks on microeconomics questions come from calculations. These same methods are extended to market failure analysis and game theory quantitative problems later in the unit, so building fluency now will make more advanced topics easier. Practice 1-2 calculation questions per week in the lead-up to exams to avoid making silly arithmetic errors that cost you easy marks.

- [Macroeconomics](https://www.owlsprep.com/study/ib-economics-hl-u3-overview/)
- [Macroeconomic Objectives](https://www.owlsprep.com/study/ib-economics-hl-u3-macroeconomic-objectives/)
- [Aggregate demand](https://www.owlsprep.com/study/ib-economics-hl-u3-aggregate-demand/)

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