national income determination using AD and income approach with the multiplier process

National Income Determination – AD & Income‑Approach with the Multiplier Process

This set of notes follows the Cambridge International AS & A Level Economics (9708) syllabus. It covers the circular‑flow model, national‑income accounting (including measurement issues), the AD/AS framework, the multiplier process (simple, tax, import and combined) and exam‑style techniques.

1. The Circular‑Flow Model

1.1 Closed‑economy (two‑sector) diagram

1.2 Open‑economy (five‑sector) diagram

1.3 Flows, Injections and Leakages

Sector	Injections (Inflow)	Leakages (Outflow)
Households	Factor incomes: wages (W), rent (R), interest (i), profit (Π)	Consumption (C), taxes (T), saving (S)
Firms	Revenue = C + I + G + (X‑M)	Factor payments, taxes, investment (I)
Government	Taxes (T) (inflow to gov’t)	Government spending (G), transfers
Financial Institutions	Savings (S) (inflow to banks)	Loans to firms/households (part of I)
Rest of the World	Exports (X)	Imports (M)

Equilibrium condition (open economy) – when total injections equal total leakages:

\[ I + G + X \;=\; S + T + M \]

At this point the circular flow is in a steady state and the level of national income is constant (short‑run equilibrium).

2. National‑Income Accounting

2.1 Measuring national income – from basic to market prices and from gross to net

• Basic (factor‑cost) prices – values of output measured at the cost of the factors of production (no taxes, no subsidies).
• Market prices – add indirect taxes (e.g., VAT) and subtract subsidies; this is the figure used for GDP in the national accounts.
• Gross – includes depreciation (capital consumption allowance).
• Net – subtracts depreciation to give the value of output that can be used for consumption or investment without reducing the capital stock.

2.2 The three main aggregates

Aggregate	Definition	Adjustments required
GDP (Gross Domestic Product)	Value of all final goods and services produced within the domestic territory during a year.	Market‑price, gross‑value (add indirect taxes, subtract subsidies).
GNI (Gross National Income)	GDP + net factor income from abroad (NFIA).	GNI = GDP + (income earned by residents abroad – income earned by non‑residents domestically).
NNI (Net National Income)	GNI – depreciation (capital consumption allowance).	Provides the “real” income available for consumption and investment.

2.3 AD (expenditure) approach

The expenditure approach adds up final demand for domestically produced output:

\[ \boxed{Y \;=\; AD \;=\; C \;+\; I \;+\; G \;+\; (X - M)} \]

• C – consumption expenditure by households.
• I – gross private investment (fixed capital, inventories, residential).
• G – government consumption and investment.
• X‑M – net exports (exports minus imports). Why X‑M? Exports are an injection (they bring foreign income into the economy), whereas imports are a leakage (they represent spending that does not generate domestic income).

2.4 Income (factor‑income) approach

\[ \boxed{Y \;=\; W \;+\; R \;+\; i \;+\; \Pi} \]

• W – wages and salaries.
• R – rent of land.
• i – interest on capital.
• Π – profits of firms.

In equilibrium every dollar spent becomes a dollar earned, so the two approaches give the same figure.

2.5 Example of GDP calculation (market‑price, gross)

Component	Value (£bn)
Consumption (C)	500
Investment (I)	150
Government spending (G)	200
Exports (X)	80
Imports (M)	120
GDP = C + I + G + (X‑M)	810 bn

3. The AD/AS Framework (required for 4.3 of the syllabus)

3.1 Short‑run aggregate supply (SRAS)

• Positively sloped because prices are sticky in the short run while wages and input costs are relatively fixed.
• Shift factors: changes in input costs, expectations of future prices, temporary supply shocks (e.g., oil price rise).

3.2 Long‑run aggregate supply (LRAS)

• Vertical at the economy’s full‑employment (potential) output (Y_p).
• Determined by the quantity and quality of factors of production, technology and institutional environment.
• In the long run price changes do not affect real output.

3.3 Interaction of AD and AS

• AD shift right (e.g., increase in G) → higher output and price level in the short run (movement along SRAS). In the long run the LRAS forces the economy back to Y_p with a higher price level.
• SRAS shift left (e.g., rise in oil price) → lower output and higher price level (stagflation).
• LRAS shift right (e.g., increase in labour force) → higher potential output, no effect on the price level if the economy is at full employment.

3.4 Diagrammatic checklist for exams

1. Draw AD, SRAS and LRAS on the same graph (price level on vertical axis, real GDP on horizontal axis).
2. Label equilibrium points: E₀ (initial), E₁ (short‑run after AD shift), E₂ (long‑run after LRAS adjustment).
3. Show the direction of the shift and state the cause (e.g., “increase in autonomous government spending”).
4. Explain the short‑run impact on output and price level and the long‑run adjustment mechanism.

4. The Multiplier Process

4.1 Marginal propensities

Symbol	Name	Definition	Typical range (Cambridge)
c	MPC – marginal propensity to consume	Extra consumption out of an extra unit of disposable income.	0.5 – 0.9
s	MPS – marginal propensity to save	Extra saving out of an extra unit of disposable income.	0 – 0.5 (s = 1‑c)
t	MPT – marginal propensity to tax	Proportion of each extra unit of income taken as tax.	0 – 0.5
m	MPM – marginal propensity to import	Extra imports out of an extra unit of disposable income.	0 – 0.3

4.2 Simple (no‑tax, no‑import, no‑saving) multiplier

Assume a closed two‑sector economy with autonomous consumption a, autonomous investment I and autonomous government spending G. Disposable income equals output (Y) and

\[ C = a + cY \] \[ \begin{aligned} Y &= C + I + G \\ &= a + cY + I + G \\ Y(1-c) &= a + I + G \\ \boxed{Y = \frac{1}{1-c}\;(a + I + G)} \end{aligned} \]

The factor \(\displaystyle k = \frac{1}{1-c}\) is the **simple expenditure multiplier**.

4.3 Multiplier with saving, taxes and imports

Introduce proportional tax rate t, marginal propensity to import m and recognise that part of income is saved (s = 1‑c). Disposable income is \((1-t)Y\); the import function is \(M = m(1-t)Y\).

\[ \begin{aligned} C &= a + c(1-t)Y \\ I &= I_{\text{aut}} \\ G &= G_{\text{aut}} \\ X-M &= X - m(1-t)Y \end{aligned} \] Substituting into the AD identity: \[ Y = a + c(1-t)Y + I_{\text{aut}} + G_{\text{aut}} + X - m(1-t)Y \] Collecting terms in \(Y\): \[ Y\Bigl[1 - c(1-t) + m(1-t)\Bigr] = a + I_{\text{aut}} + G_{\text{aut}} + X \] Because the marginal propensity to import is defined on disposable income, we can write the denominator as \([1 - c(1-t) + m]\). Hence the **combined multiplier** is \[ \boxed{k = \frac{1}{1 - c(1-t) + m}} \]

Special cases (useful for exam questions):

• Tax multiplier (no imports): \(k_t = \dfrac{1}{1 - c(1-t)}\)
• Import multiplier (no taxes): \(k_m = \dfrac{1}{1 - c + m}\)
• Saving multiplier (closed economy, no tax, no import): \(k_s = \dfrac{1}{1 - c}\) (same as the simple multiplier because \(s = 1-c\)).

4.4 The multiplier‑process diagram

• Round 1: ΔG creates income ΔY₁ = ΔG.
• Round 2: Consumption of the new income = c(1‑t)ΔY₁; imports leak m(1‑t)ΔY₁; the net addition = c(1‑t)ΔY₁.
• Round 3: Same process repeats with the reduced amount, giving a geometric series.
• Total change: \(\displaystyle \Delta Y = \Delta G \Bigl[1 + c(1-t) + \bigl(c(1-t)\bigr)^2 + \dots\Bigr] = k \Delta G\).

4.5 Short‑run vs. long‑run operation of the multiplier

• Short‑run: Prices and wages are sticky, so the multiplier works through changes in real output (movement along SRAS). The magnitude of the multiplier depends on the marginal propensities.
• Long‑run: Full‑capacity utilisation is reached; price level adjusts, SRAS shifts left, and the real effect of the initial injection disappears. The multiplier mainly influences the price level (inflation) rather than real GDP.

5. Applying the Multiplier – Worked Example

Government increases spending by £20 bn. Given:

• MPC, \(c = 0.75\)
• Proportional tax rate, \(t = 0.20\)
• MPM, \(m = 0.10\)

Combined multiplier:

\[ k = \frac{1}{1 - c(1-t) + m} = \frac{1}{1 - 0.75(0.8) + 0.10} = \frac{1}{1 - 0.60 + 0.10} = \frac{1}{0.50} = 2.0 \]

Predicted change in equilibrium national income:

\[ \Delta Y = k \times \Delta G = 2.0 \times £20\text{ bn} = £40\text{ bn} \]

Interpretation: The £20 bn injection ultimately raises total output by £40 bn because each round of spending is partially re‑spent, with the size of each round determined by the marginal propensities.

6. Exam‑style Checklist

1. Draw and label the closed‑economy and open‑economy circular‑flow diagrams.
2. State the AD equation \(Y = C + I + G + (X-M)\) and the income‑approach equation \(Y = W + R + i + \Pi\).
3. Explain the four marginal propensities (MPC, MPS, MPT, MPM) and give typical ranges.
4. Identify injections (I, G, X) and leakages (S, T, M); write the equilibrium condition \(I+G+X = S+T+M\).
5. Derive the appropriate multiplier (simple, tax, import or combined) and interpret the denominator \([1 - c(1-t) + m]\).
6. Show a multiplier‑process diagram and explain why the series converges.
7. Apply the multiplier to a fiscal or external‑sector change; calculate \(\Delta Y\) and comment on the short‑run vs. long‑run outcome.
8. In AD/AS questions, draw AD, SRAS and LRAS, indicate the shift, and discuss effects on output and price level in both the short and long run.

7. Suggested Further Reading (Cambridge AS & A Level Economics)

• Chapter 4 – National‑Income Accounting: detailed discussion of basic/market prices, gross/net concepts, and the three aggregates.
• Chapter 5 – Aggregate Demand: components, injections & leakages, and the AD curve.
• Chapter 6 – Aggregate Supply: SRAS and LRAS, determinants of shifts, short‑run vs. long‑run equilibrium.
• Chapter 7 – Fiscal Policy and the Multiplier: derivations, tax and import effects, policy implications.
• Past paper questions on multiplier calculations, circular‑flow diagrams, and AD/AS analysis – use the examiner’s reports for mark‑scheme guidance.