IB · ECON HL

Economics HL

Quantitative techniques (HL Paper 3) — Paper 3 HL

Name: ____________________Date: October 2, 2026

1.
An economy has a marginal propensity to consume (MPC) of 0.8, with no other leakages considered. (a) Calculate the simple Keynesian multiplier. (b) Calculate the total change in national income resulting from an initial increase in investment spending of $20 million.
[4 marks]
Marking points
- Uses the multiplier formula k = 1/(1 − MPC).
- Substitutes to obtain k = 1/(1 − 0.8) = 1/0.2 = 5.
- Multiplies the multiplier by the initial spending increase: 5 × $20 million.
- Obtains a total change in national income of $100 million.
Examiner tip: The higher the MPC (the smaller the marginal propensity to save), the larger the multiplier — an MPC close to 1 produces a very large multiplier, since very little income leaks out of the spending cycle at each round.
2.
Marking analysis: A learner attempts the following task: “An economy has a marginal propensity to consume (MPC) of 0.8, with no other leakages considered. (a) Calculate the simple Keynesian multiplier. (b) Calculate the total change in national income resulting from an initial increase in investment spending of $20 million.” Their response addresses only this point: “Uses the multiplier formula k = 1/(1 − MPC).” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Marking points
- Recognises credit for the stated point: Uses the multiplier formula k = 1/(1 − MPC).
- Identifies the missing requirement: Substitutes to obtain k = 1/(1 − 0.8) = 1/0.2 = 5.
- Identifies the missing requirement: Multiplies the multiplier by the initial spending increase: 5 × $20 million.
- Identifies the missing requirement: Obtains a total change in national income of $100 million.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
3.
An economy has a marginal propensity to save (MPS) of 0.25. Calculate the simple Keynesian multiplier for this economy.
[2 marks]
Marking points
- Uses the multiplier formula k = 1/MPS.
- Substitutes to obtain k = 1/0.25 = 4.
Examiner tip: The formula k = 1/MPS is simply a rearrangement of k = 1/(1 − MPC), since MPS = 1 − MPC when there are no other leakages — use whichever form matches the information given in the question.
4.
Marking analysis: A learner attempts the following task: “An economy has a marginal propensity to save (MPS) of 0.25. Calculate the simple Keynesian multiplier for this economy.” Their response addresses only this point: “Uses the multiplier formula k = 1/MPS.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Uses the multiplier formula k = 1/MPS.
- Identifies the missing requirement: Substitutes to obtain k = 1/0.25 = 4.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
5.
A more realistic economy has three leakages from the circular flow of income: a marginal propensity to save (MPS) of 0.2, a marginal propensity to tax (MPT) of 0.1, and a marginal propensity to import (MPM) of 0.1. Calculate the full multiplier for this economy.
[3 marks]
Marking points
- Uses the full multiplier formula k = 1/(MPS + MPT + MPM).
- Substitutes to obtain k = 1/(0.2 + 0.1 + 0.1) = 1/0.4.
- Obtains k = 2.5.
Examiner tip: Every leakage from the circular flow (saving, taxation, and imports) reduces the size of the multiplier, since each one removes some portion of each round of new spending from circulating further within the domestic economy.
6.
Marking analysis: A learner attempts the following task: “A more realistic economy has three leakages from the circular flow of income: a marginal propensity to save (MPS) of 0.2, a marginal propensity to tax (MPT) of 0.1, and a marginal propensity to import (MPM) of 0.1. Calculate the full multiplier for this economy.” Their response addresses only this point: “Uses the full multiplier formula k = 1/(MPS + MPT + MPM).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: Uses the full multiplier formula k = 1/(MPS + MPT + MPM).
- Identifies the missing requirement: Substitutes to obtain k = 1/(0.2 + 0.1 + 0.1) = 1/0.4.
- Identifies the missing requirement: Obtains k = 2.5.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
7.
An economy's national income data for one year includes: consumption (C) = $300bn, investment (I) = $80bn, government spending (G) = $60bn, exports (X) = $50bn, and imports (M) = $40bn. Calculate GDP using the expenditure approach.
[3 marks]
Marking points
- States the expenditure approach formula: GDP = C + I + G + (X − M).
- Substitutes the given values: 300 + 80 + 60 + (50 − 40).
- Obtains GDP = $450bn.
Examiner tip: Net exports (X − M) can be negative if a country imports more than it exports — always calculate this term as a single combined figure before adding it to the other three components.
8.
Marking analysis: A learner attempts the following task: “An economy's national income data for one year includes: consumption (C) = $300bn, investment (I) = $80bn, government spending (G) = $60bn, exports (X) = $50bn, and imports (M) = $40bn. Calculate GDP using the expenditure approach.” Their response addresses only this point: “States the expenditure approach formula: GDP = C + I + G + (X − M).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: States the expenditure approach formula: GDP = C + I + G + (X − M).
- Identifies the missing requirement: Substitutes the given values: 300 + 80 + 60 + (50 − 40).
- Identifies the missing requirement: Obtains GDP = $450bn.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
9.
An economy's nominal GDP is $500bn, and its GDP deflator for the year is 125 (using a base year value of 100). Calculate the economy's real GDP.
[3 marks]
Marking points
- States the formula: real GDP = (nominal GDP / GDP deflator) × 100.
- Substitutes the given values: (500 / 125) × 100.
- Obtains real GDP = $400bn.
Examiner tip: A GDP deflator above 100 means prices have risen since the base year, so real GDP (adjusted for this price rise) will always be lower than nominal GDP in this case.
10.
Marking analysis: A learner attempts the following task: “An economy's nominal GDP is $500bn, and its GDP deflator for the year is 125 (using a base year value of 100). Calculate the economy's real GDP.” Their response addresses only this point: “States the formula: real GDP = (nominal GDP / GDP deflator) × 100.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: States the formula: real GDP = (nominal GDP / GDP deflator) × 100.
- Identifies the missing requirement: Substitutes the given values: (500 / 125) × 100.
- Identifies the missing requirement: Obtains real GDP = $400bn.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
11.
A country's consumer price index 'basket' of goods cost $250 in Year 1 and $260 in Year 2. Calculate the inflation rate between Year 1 and Year 2.
[2 marks]
Marking points
- Uses the formula: inflation rate = [(new basket cost − old basket cost)/old basket cost] × 100.
- Substitutes to obtain [(260 − 250)/250] × 100 = 4%.
Examiner tip: The CPI inflation calculation is always a percentage change calculation applied specifically to the cost of a fixed basket of goods over time, not to any single price.
12.
Marking analysis: A learner attempts the following task: “A country's consumer price index 'basket' of goods cost $250 in Year 1 and $260 in Year 2. Calculate the inflation rate between Year 1 and Year 2.” Their response addresses only this point: “Uses the formula: inflation rate = [(new basket cost − old basket cost)/old basket cost] × 100.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Uses the formula: inflation rate = [(new basket cost − old basket cost)/old basket cost] × 100.
- Identifies the missing requirement: Substitutes to obtain [(260 − 250)/250] × 100 = 4%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
13.
A country's nominal interest rate is 8%, and its inflation rate is 3%. Use the approximation formula to calculate the real interest rate.
[2 marks]
Marking points
- Uses the approximation formula: real interest rate ≈ nominal interest rate − inflation rate.
- Substitutes to obtain 8% − 3% = 5%.
Examiner tip: The real interest rate reflects the actual increase in purchasing power a saver gains — a high nominal interest rate during a period of even higher inflation can still represent a negative real return.
14.
Marking analysis: A learner attempts the following task: “A country's nominal interest rate is 8%, and its inflation rate is 3%. Use the approximation formula to calculate the real interest rate.” Their response addresses only this point: “Uses the approximation formula: real interest rate ≈ nominal interest rate − inflation rate.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Uses the approximation formula: real interest rate ≈ nominal interest rate − inflation rate.
- Identifies the missing requirement: Substitutes to obtain 8% − 3% = 5%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
15.
A country's working-age population is 300 million, its labor force is 200 million, and 184 million of the labor force are currently employed. (a) Calculate the labor force participation rate. (b) Calculate the unemployment rate.
[4 marks]
Marking points
- Uses the formula: participation rate = (labor force / working-age population) × 100.
- Substitutes to obtain (200/300) × 100 ≈ 66.7%.
- Calculates the number unemployed as 200 − 184 = 16 million.
- Uses the formula unemployment rate = (unemployed / labor force) × 100 = (16/200) × 100 = 8%.
Examiner tip: The unemployment rate is always calculated as a percentage of the labor force, not the total population — someone who is not working and not actively seeking work is not counted as unemployed, since they are outside the labor force entirely.
16.
Marking analysis: A learner attempts the following task: “A country's working-age population is 300 million, its labor force is 200 million, and 184 million of the labor force are currently employed. (a) Calculate the labor force participation rate. (b) Calculate the unemployment rate.” Their response addresses only this point: “Uses the formula: participation rate = (labor force / working-age population) × 100.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Marking points
- Recognises credit for the stated point: Uses the formula: participation rate = (labor force / working-age population) × 100.
- Identifies the missing requirement: Substitutes to obtain (200/300) × 100 ≈ 66.7%.
- Identifies the missing requirement: Calculates the number unemployed as 200 − 184 = 16 million.
- Identifies the missing requirement: Uses the formula unemployment rate = (unemployed / labor force) × 100 = (16/200) × 100 = 8%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
17.
A country's current account recorded a deficit of $50 million, and its combined capital and financial account recorded a surplus of $45 million. Calculate the value of net errors and omissions needed for the balance of payments to balance to zero.
[3 marks]
Marking points
- States that, by definition, the balance of payments must sum to zero: current account + capital/financial account + net errors and omissions = 0.
- Substitutes the known values: −50 + 45 + errors and omissions = 0.
- Solves to obtain net errors and omissions = +$5 million.
Examiner tip: 'Net errors and omissions' is a balancing item that exists precisely because real-world balance of payments data is collected imperfectly — it is not a meaningful economic flow on its own, just an accounting correction.
18.
Marking analysis: A learner attempts the following task: “A country's current account recorded a deficit of $50 million, and its combined capital and financial account recorded a surplus of $45 million. Calculate the value of net errors and omissions needed for the balance of payments to balance to zero.” Their response addresses only this point: “States that, by definition, the balance of payments must sum to zero: current account + capital/financial account + net errors and omissions = 0.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: States that, by definition, the balance of payments must sum to zero: current account + capital/financial account + net errors and omissions = 0.
- Identifies the missing requirement: Substitutes the known values: −50 + 45 + errors and omissions = 0.
- Identifies the missing requirement: Solves to obtain net errors and omissions = +$5 million.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
19.
A country's national debt is $800bn, and its GDP is $2,000bn. Calculate the country's debt-to-GDP ratio.
[2 marks]
Marking points
- Uses the formula: debt-to-GDP ratio = (national debt / GDP) × 100.
- Substitutes to obtain (800/2,000) × 100 = 40%.
Examiner tip: The debt-to-GDP ratio, not the raw debt figure alone, is the standard way economists compare the burden of government debt across countries of very different sizes.
20.
Marking analysis: A learner attempts the following task: “A country's national debt is $800bn, and its GDP is $2,000bn. Calculate the country's debt-to-GDP ratio.” Their response addresses only this point: “Uses the formula: debt-to-GDP ratio = (national debt / GDP) × 100.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Uses the formula: debt-to-GDP ratio = (national debt / GDP) × 100.
- Identifies the missing requirement: Substitutes to obtain (800/2,000) × 100 = 40%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
21.
A government spends $500bn and collects $440bn in tax revenue in a given year, with GDP of $2,000bn. (a) Calculate the budget deficit. (b) Express the budget deficit as a percentage of GDP.
[2 marks]
Marking points
- Calculates the budget deficit as spending minus revenue: $500bn − $440bn = $60bn.
- Expresses this as a percentage of GDP: (60/2,000) × 100 = 3%.
Examiner tip: Expressing a budget deficit (or surplus) as a percentage of GDP, rather than as a raw dollar figure, allows meaningful comparison across years and across countries of different economic sizes.
22.
Marking analysis: A learner attempts the following task: “A government spends $500bn and collects $440bn in tax revenue in a given year, with GDP of $2,000bn. (a) Calculate the budget deficit. (b) Express the budget deficit as a percentage of GDP.” Their response addresses only this point: “Calculates the budget deficit as spending minus revenue: $500bn − $440bn = $60bn.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Calculates the budget deficit as spending minus revenue: $500bn − $440bn = $60bn.
- Identifies the missing requirement: Expresses this as a percentage of GDP: (60/2,000) × 100 = 3%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
23.
A country's price elasticity of demand for exports is 0.6, and its price elasticity of demand for imports is 0.5. Using the Marshall-Lerner condition, state whether a currency depreciation would be expected to improve or worsen the country's trade balance, and justify your answer with a calculation.
[3 marks]
Marking points
- Sums the two elasticities: 0.6 + 0.5 = 1.1.
- States the Marshall-Lerner condition: a depreciation improves the trade balance only if the sum of the price elasticities of demand for exports and imports exceeds 1.
- Concludes that since 1.1 > 1, the condition is satisfied, and the depreciation is expected to improve the country's trade balance.
Examiner tip: Always sum the two given elasticities first and compare directly to 1 — this single comparison is the entire Marshall-Lerner test, no further calculation is needed to reach a conclusion.
24.
Marking analysis: A learner attempts the following task: “A country's price elasticity of demand for exports is 0.6, and its price elasticity of demand for imports is 0.5. Using the Marshall-Lerner condition, state whether a currency depreciation would be expected to improve or worsen the country's trade balance, and justify your answer with a calculation.” Their response addresses only this point: “Sums the two elasticities: 0.6 + 0.5 = 1.1.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: Sums the two elasticities: 0.6 + 0.5 = 1.1.
- Identifies the missing requirement: States the Marshall-Lerner condition: a depreciation improves the trade balance only if the sum of the price elasticities of demand for exports and imports exceeds 1.
- Identifies the missing requirement: Concludes that since 1.1 > 1, the condition is satisfied, and the depreciation is expected to improve the country's trade balance.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
25.
A country's export price index is 120, and its import price index is 100 (both relative to the same base year value of 100). Calculate the country's terms of trade index, and state whether its terms of trade have improved or worsened relative to the base year.
[3 marks]
Marking points
- Uses the formula: terms of trade index = (export price index / import price index) × 100.
- Substitutes to obtain (120/100) × 100 = 120.
- States that since this index (120) is above the base year value of 100, the terms of trade have improved: the country can now purchase more imports for the same quantity of exports.
Examiner tip: A terms of trade index above 100 means export prices have risen faster than import prices since the base year — this is described as an 'improvement', even though it can make a country's exports less price-competitive abroad.
26.
Marking analysis: A learner attempts the following task: “A country's export price index is 120, and its import price index is 100 (both relative to the same base year value of 100). Calculate the country's terms of trade index, and state whether its terms of trade have improved or worsened relative to the base year.” Their response addresses only this point: “Uses the formula: terms of trade index = (export price index / import price index) × 100.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: Uses the formula: terms of trade index = (export price index / import price index) × 100.
- Identifies the missing requirement: Substitutes to obtain (120/100) × 100 = 120.
- Identifies the missing requirement: States that since this index (120) is above the base year value of 100, the terms of trade have improved: the country can now purchase more imports for the same quantity of exports.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
27.
Using a Lorenz curve diagram, the area between the line of perfect equality and the actual Lorenz curve is calculated as 15 units, and the total area below the line of perfect equality is 50 units. Calculate the Gini coefficient for this economy.
[2 marks]
Marking points
- Uses the formula: Gini coefficient = (area between the line of equality and the Lorenz curve) / (total area below the line of equality).
- Substitutes to obtain 15/50 = 0.3.
Examiner tip: The Gini coefficient is geometrically derived directly from the Lorenz curve: the further the actual curve bows away from the diagonal line of perfect equality, the larger this ratio (and the Gini coefficient) becomes.
28.
Marking analysis: A learner attempts the following task: “Using a Lorenz curve diagram, the area between the line of perfect equality and the actual Lorenz curve is calculated as 15 units, and the total area below the line of perfect equality is 50 units. Calculate the Gini coefficient for this economy.” Their response addresses only this point: “Uses the formula: Gini coefficient = (area between the line of equality and the Lorenz curve) / (total area below the line of equality).” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: Uses the formula: Gini coefficient = (area between the line of equality and the Lorenz curve) / (total area below the line of equality).
- Identifies the missing requirement: Substitutes to obtain 15/50 = 0.3.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
29.
A country's unemployment rate rises from 5% to 7%. (a) State the change in percentage points. (b) Calculate the percentage change (the relative increase) in the unemployment rate.
[3 marks]
Marking points
- States the change in percentage points as 7 − 5 = 2 percentage points.
- Calculates the percentage change as [(7 − 5)/5] × 100.
- Obtains a percentage change of 40%.
Examiner tip: A 2 percentage point rise and a 40% relative increase describe the exact same change in very different-sounding ways — always read a question carefully to see which measure it is asking for, since using the wrong one is a common error.
30.
Marking analysis: A learner attempts the following task: “A country's unemployment rate rises from 5% to 7%. (a) State the change in percentage points. (b) Calculate the percentage change (the relative increase) in the unemployment rate.” Their response addresses only this point: “States the change in percentage points as 7 − 5 = 2 percentage points.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Marking points
- Recognises credit for the stated point: States the change in percentage points as 7 − 5 = 2 percentage points.
- Identifies the missing requirement: Calculates the percentage change as [(7 − 5)/5] × 100.
- Identifies the missing requirement: Obtains a percentage change of 40%.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
31.
According to the quantity theory of money, MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is real output. If the central bank increases the money supply (M) by 10%, and both the velocity of money (V) and real output (Q) remain constant, predict the approximate percentage change in the price level (P).
[2 marks]
Marking points
- States that since V and Q are held constant, any percentage change in M must be matched by an equal percentage change in P, to keep the equation MV = PQ balanced.
- Predicts that the price level will rise by approximately 10%, matching the percentage increase in the money supply.
Examiner tip: This result is the core monetarist prediction that 'inflation is always and everywhere a monetary phenomenon' — it relies on the simplifying assumption that velocity and real output are unaffected by the change in money supply, which is not always realistic in the short run.
32.
Marking analysis: A learner attempts the following task: “According to the quantity theory of money, MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is real output. If the central bank increases the money supply (M) by 10%, and both the velocity of money (V) and real output (Q) remain constant, predict the approximate percentage change in the price level (P).” Their response addresses only this point: “States that since V and Q are held constant, any percentage change in M must be matched by an equal percentage change in P, to keep the equation MV = PQ balanced.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks]
Marking points
- Recognises credit for the stated point: States that since V and Q are held constant, any percentage change in M must be matched by an equal percentage change in P, to keep the equation MV = PQ balanced.
- Identifies the missing requirement: Predicts that the price level will rise by approximately 10%, matching the percentage increase in the money supply.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.