Explicitly label the import arrow in the circular‑flow diagram; write the full AD equation \(AD = C + I + G + (X-M)\) and highlight the role of \(M = a + mY\).
5 – Government Macro‑intervention
Brief mention of fiscal/monetary effects (Section 8).
Provide a short case‑study of an expansionary fiscal stimulus and calculate the resulting change in imports using the given MPM; discuss policy‑mix (e.g., fiscal expansion + exchange‑rate depreciation).
Insert a balance‑of‑payments table showing how APM feeds the current‑account deficit; explain how exchange‑rate movements shift the import function (changes to \(a\) and/or \(m\)).
7‑11 – A‑Level Extensions
None (core AS material only).
Box “Further Reading / A‑Level Extensions” (Section 11) linking APM/MPM to utility theory, market failure, labour market, multiplier, development and globalisation.
2. Key Concepts for the Circular Flow of Income
Circular flow of income – continuous movement of money between households, firms, government, the financial sector and the foreign sector.
Leakages – withdrawals from the flow (savings, taxes, imports).
Imports – purchases of foreign‑produced goods and services; a leakage because money leaves the domestic economy.
Average Propensity to Import (APM) – proportion of total income spent on imports at a given income level.
Marginal Propensity to Import (MPM) – proportion of an additional unit of income that is spent on imports.
3. The Import Function
In an open economy the total level of imports can be expressed as a function of national income.
3.1 Linear form (most common in Cambridge examinations)
\[
M = a + mY
\]
\(M\) – total imports (value of goods and services purchased from abroad).
\(Y\) – national income (or aggregate expenditure).
\(a\) – autonomous imports: imports that occur even when domestic income is zero (e.g., essential raw materials, capital equipment).
\(m\) – marginal propensity to import (MPM): the slope of the import function; it shows how imports change when income changes by one unit.
3.2 Non‑linear possibilities
The syllabus does not require a linear function, but in reality the import curve may be:
Concave – MPM falls as income rises (luxury imports become a smaller share of income).
Convex – MPM rises as income rises (greater consumer preference for foreign goods at higher income).
When a non‑linear function is used, the MPM is the derivative \(\frac{dM}{dY}\) at the relevant income level.
4. Definitions & Formulas
Propensity
Definition
Formula
Average Propensity to Import (APM)
Share of total income spent on imports at a given income level.
\(\displaystyle \text{APM} = \frac{M}{Y}\)
Marginal Propensity to Import (MPM)
Change in imports resulting from a change in income.
\(\displaystyle \text{MPM} = \frac{\Delta M}{\Delta Y}\) (or \(\frac{dM}{dY}\) for a non‑linear function)
5. Numerical Example – Calculating APM and MPM
Data for a small open economy (values in million $):
National Income (Y)
Total Imports (M)
500
80
600
92
700
104
APM at \(Y = 600\)
\[
\text{APM}_{600}= \frac{92}{600}=0.153\;(15.3\%)
\]
MPM between 500 and 600
\[
\text{MPM}_{500\rightarrow600}= \frac{92-80}{600-500}= \frac{12}{100}=0.12
\]
MPM between 600 and 700
\[
\text{MPM}_{600\rightarrow700}= \frac{104-92}{700-600}= \frac{12}{100}=0.12
\]
Because the change in imports is constant for each $100 million increase in income, the import function is linear with a constant MPM of 0.12. The APM falls as income rises because the autonomous component \(a\) becomes a smaller proportion of total imports.
6. Aggregate‑Demand Equation for an Open Economy
\[
AD = C + I + G + (X - M)
\]
Substituting the import function gives
\[
AD = C + I + G + X - (a + mY)
\]
Re‑arranging: \(\displaystyle AD = (C + I + G + X - a) - mY\). The term \(-mY\) represents the import leakage that grows with income.
In equilibrium, \(Y = AD\); solving for \(Y\) yields the open‑economy multiplier (see Section 7).
7. Relationship to the Keynesian Multiplier
In a closed economy the simple multiplier is \(k = \frac{1}{1-MPC}\). Introducing imports adds an extra leakage:
\[
k_{\text{open}} = \frac{1}{1 - MPC + MPM}
\]
A higher MPM raises total leakages, therefore reduces the multiplier.
If the economy also has a marginal propensity to save (MPS) and a marginal tax rate (t), the full open‑economy multiplier becomes
\[
k = \frac{1}{1 - MPC(1-t) + MPM}
\]
8. Policy Implications
8.1 Fiscal stimulus – a short case study
Assume the government increases spending by \$40 million. The marginal propensities are:
\[
\Delta Y = k \times \Delta G = 1.92 \times 40 \approx \$77\text{ million}
\]
Import increase:
\[
\Delta M = MPM \times \Delta Y = 0.12 \times 77 \approx \$9.2\text{ million}
\]
The stimulus raises income, but the resulting import leakage dampens the overall impact.
8.2 Monetary policy
Lower interest rates raise disposable income (through higher consumption), which in turn raises imports by \(\text{MPM}\times\Delta Y\).
Higher rates have the opposite effect.
8.3 Exchange‑rate movements
A depreciation makes imports more expensive → the import function shifts **upward** (higher intercept \(a\)) and may also reduce the slope \(m\) because the quantity demanded falls.
An appreciation shifts the function **downward** and can increase the slope.
8.4 Trade policy
Tariffs raise the effective price of imports, lowering the MPM (flatter import curve).
Quotas directly limit the quantity imported, reducing both APM and MPM.
Subsidies to domestic producers can have a similar effect.
9. Balance‑of‑Payments Link
Imports appear in the current‑account (CA) component of the balance of payments.
Current‑Account Component
Effect of a Higher APM
Goods (imports)
Increases → CA deficit widens.
Services (imports)
Same logic as goods.
Net income & transfers
Unrelated to APM but part of the overall CA.
Exports (injections)
Unchanged unless policy alters competitiveness.
10. Suggested Diagram for the Lesson
Figure 1 – Circular flow of income for an open economy. The foreign‑sector arrow labelled “Imports (leakage) – APM = \(M/Y\), MPM = \(\Delta M/\Delta Y\)” and the opposite arrow “Exports (injection)”.
11. Further Reading / A‑Level Extensions
Utility & Indifference – consumer choice between domestic and imported goods can be illustrated with indifference curves; a higher MPM implies a steeper budget‑line slope for imported goods.
Market Failure – imports can generate negative externalities (e.g., environmental damage from transport) or positive ones (technology transfer).
Labour Market – import competition may depress wages in import‑competing industries, affecting labour‑market equilibrium.
Multiplier Derivation – show algebraically how the open‑economy multiplier emerges from the AD equation with \(M = a + mY\).
Development & Globalisation – low‑income economies often have low APM because of limited purchasing power; high‑income economies exhibit higher APM but may have lower MPM if they import proportionally less of each extra dollar earned.
12. Key Take‑aways
APM = \(M/Y\) measures the share of total income spent on imports at a given income level.
MPM = \(\Delta M/\Delta Y\) (or \(\frac{dM}{dY}\) for a non‑linear function) measures how imports respond to a change in income; it is the slope of the import function.
Both propensities are **leakages** in the circular‑flow diagram and reduce equilibrium national income.
A higher APM lowers the level of aggregate demand; a higher MPM reduces the size of the Keynesian multiplier.
Understanding APM and MPM is essential for analysing trade policy, balance‑of‑payments outcomes, and the effectiveness of fiscal and monetary policy in an open economy.
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