# Global economy quantitative analysis (HL only)

> IB Economics HL · IB Diploma Programme Economics HL
> Source: https://www.owlsprep.com/study/ib-economics-hl-u4-global-economy-quantitative-analysis/

This HL-only sub-topic covers core quantitative calculations for IB Economics global economy, including terms of trade, balance of payments aggregates, and exchange rate changes, all regularly tested on Paper 3. You will learn step-by-step methods for common exam questions.

**Prerequisites:** [Basic balance of payments concepts](https://www.owlsprep.com/study/ib-economics-hl-u4-balance-of-payments/); [Terms of trade fundamentals](https://www.owlsprep.com/study/ib-economics-hl-u4-terms-of-trade/); [Exchange rate systems](https://www.owlsprep.com/study/ib-economics-hl-u4-exchange-rates/)

## Learning objectives

- Calculate terms of trade and percentage changes in ToT
- Calculate balance of payments components and account balances
- Calculate percentage changes in exchange rate values
- Apply core formulas correctly to common HL Paper 3 questions

## Calculating Terms of Trade

**Terms of Trade (ToT)** — The ratio of a country's average export prices to average import prices, with base year ToT always set to 100.

*Notation:* \text{ToT} = \frac{\text{Export Price Index (XPI)}}{\text{Import Price Index (MPI)}} \times 100

*Example:* Base year: XPI = 100, MPI = 100, ToT = 100

Terms of trade can improve (increase) or deteriorate (decrease) over time. Percentage change in ToT is calculated as:

$$\text{Percentage Change} = \frac{\text{New ToT} - \text{Original ToT}}{\text{Original ToT}} \times 100\%$$

**Worked example:** In 2021, a country has an export price index of 110 and import price index of 105. In 2022, export price index rises to 120 and import price index rises to 112. Calculate the percentage change in terms of trade between 2021 and 2022, and state if it improved or deteriorated.

1. Step 1: Calculate 2021 ToT
2. $$\text{ToT}_{2021} = \frac{110}{105} \times 100 \approx 104.76$$
3. Step 2: Calculate 2022 ToT
4. $$\text{ToT}_{2022} = \frac{120}{112} \times 100 \approx 107.14$$
5. Step 3: Calculate percentage change
6. $$\text{Percentage Change} = \frac{107.14 - 104.76}{104.76} \times 100 \approx +2.27\%$$
7. Step 4: Interpret: ToT increased, so terms of trade have improved.

> **Exam tip:** Always multiply the price ratio by 100, as ToT is indexed to base year = 100. Examiners allocate a mark for this step even if the ratio is correct.

## Balance of Payments Calculations

**Balance of Payments Identity** — The sum of all three accounts in the balance of payments must equal zero: Current Account (CA) + Capital Account (KA) + Financial Account (FA) = 0. This identity is used to solve for missing account values.

Common exam questions ask to calculate the balance of the current account, or find the value of a missing account. The current account is made up of four components:

- Balance of trade in goods = Exports of goods - Imports of goods
- Balance of trade in services = Exports of services - Imports of services
- Net primary income = Income received from abroad - Income paid abroad
- Net secondary income = Transfer payments received - Transfer payments paid

**Worked example:** A country has the following transactions: Goods exports = \$350bn, goods imports = \$420bn, services exports = \$180bn, services imports = \$130bn, net primary income = +\$25bn, net secondary income = -\$15bn, capital account balance = +\$10bn. Calculate the current account balance and find the financial account balance.

1. Step 1: Calculate balance of trade in goods
2. $$350 - 420 = -\$70\ \text{bn}$$
3. Step 2: Calculate balance of trade in services
4. $$180 - 130 = +\$50\ \text{bn}$$
5. Step 3: Sum all current account components
6. $$(-70) + 50 + 25 + (-15) = -\$10\ \text{bn}$$
7. Step 4: Use the BoP identity to find financial account balance
8. $$\text{CA} + \text{KA} + \text{FA} = 0 \implies -10 + 10 + \text{FA} = 0 \implies \text{FA} = 0$$
9. Result: Current account deficit of \$10bn, financial account balance = \$0.

> **Exam tip:** Always use the BoP identity to check your calculation: if the sum of accounts is not zero, you made an addition error.

## Calculating Exchange Rate Changes

Exchange rates can be quoted two ways: domestic currency per foreign currency, or foreign currency per domestic currency. You must always convert the quote to get the value of *one unit of the currency you are measuring* before calculating percentage change.

**Worked example:** In 2021, 1 US Dollar (USD) = 1.20 Canadian Dollars (CAD). In 2022, 1 USD = 1.30 CAD. Calculate the percentage change in the value of CAD between 2021 and 2022, and state if CAD appreciated or depreciated.

1. Step 1: Convert the quote to get the value of 1 CAD in USD (the currency we are measuring)
2. 2021: $1 \text{ CAD} = \frac{1}{1.20} \approx 0.8333 \text{ USD}$
3. 2022: $1 \text{ CAD} = \frac{1}{1.30} \approx 0.7692 \text{ USD}$
4. Step 2: Calculate percentage change
5. $$\frac{0.7692 - 0.8333}{0.8333} \times 100 \approx -7.7\%$$
6. Step 3: Interpret: The value of CAD fell against USD, so CAD depreciated by 7.7%.

> **Exam tip:** Double-check which currency the question asks you to calculate: 70% of students get this wrong by calculating change for the wrong currency.

## Common pitfalls

- **Wrong:** Forgetting to multiply the XPI/MPI ratio by 100 when calculating ToT
  - Why it fails: Examiners allocate 1 full mark for this step, so you lose easy marks even if your ratio is correct
  - Correct: Always write the full formula $\text{ToT} = \frac{XPI}{MPI} \times 100$ and include the multiplication step
- **Wrong:** Calculating exchange rate change for the wrong currency
  - Why it fails: Questions often quote exchange rates as domestic per foreign, but ask for change in the domestic currency, leading to inverted calculations
  - Correct: Always convert the quote to get 1 unit of the currency you are measuring before calculating change
- **Wrong:** Mixing up capital and financial account in the BoP identity
  - Why it fails: Many students confuse the small capital account (capital transfers) with the large financial account (investment flows)
  - Correct: Remember: capital account is almost always a small number, financial account offsets most current account imbalances
- **Wrong:** Claiming rising import prices improve the terms of trade
  - Why it fails: Imports are the denominator in the ToT formula, so rising import prices reduce the overall ToT ratio
  - Correct: ToT improves only when export prices rise faster than import prices, leading to a higher index value

## Cheatsheet

| Calculation | Formula | Key Exam Tip |
| --- | --- | --- |
| Terms of Trade | $\frac{\text{XPI}}{\text{MPI}} \times 100$ | Base year = 100, higher = improved |
| Current Account Balance | $(X_g - M_g) + (X_s - M_s) + \text{PI} + \text{SI}$ | Sum all net current transactions |
| BoP Identity | $\text{CA} + \text{KA} + \text{FA} = 0$ | Use for missing account questions |
| Percentage Change | $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$ | Negative = fall, positive = rise in value |

## What's next

Mastering these quantitative calculations is critical for scoring high marks on IB Economics HL Paper 3, which makes up 30% of your final grade. These calculations underpin all analysis of trade policy, exchange rate interventions, and global economic shocks, so building accuracy here will help you with both quantitative and essay questions on the global economy. Practising these calculations repeatedly until you can complete them quickly and correctly is one of the highest-return study activities for IB Economics HL.

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