Aggregate Demand and Aggregate Supply

1. Aggregate Demand

1.1 Definition and Components

We define aggregate demand (AD) as the total planned expenditure on goods and services in an economy at a given general price level.

$AD = C + I + G + (X - M)$

Component	Definition	Determinants
C (Consumption)	Household spending on goods and services	Disposable income, interest rates, wealth, confidence, expectations
I (Investment)	Spending on capital goods by firms	Interest rates, business confidence, technology, expected demand, corporate tax
G (Government spending)	Government expenditure on goods and services	Fiscal policy, political priorities
X (Exports)	Spending by foreigners on domestic goods	Foreign income, exchange rate, trade policies
M (Imports)	Spending by domestic residents on foreign goods	Domestic income, exchange rate, tastes

1.2 The Shape of the AD Curve

The AD curve slopes downward from left to right (higher price level $\Rightarrow$ lower quantity of AD).

info

info channels of the downward-sloping AD curve. AQA often focuses on the interest rate and wealth effects. OCR may ask students to evaluate which channel is most significant in practice.

We derive this from three channels:

1. Wealth effect (Pigou effect): A higher price level reduces the real value of money balances and other financial assets. Households feel less wealthy and reduce consumption:

$P \uparrow \Rightarrow \frac{M}{P} \downarrow \Rightarrow \mathrm{Real wealth } \downarrow \Rightarrow C \downarrow \Rightarrow AD \downarrow$

2. Interest rate effect (Keynes effect): A higher price level increases the demand for money (more money needed for transactions). This raises interest rates, which reduces investment:

$P \uparrow \Rightarrow \mathrm{Money demand } \uparrow \Rightarrow r \uparrow \Rightarrow I \downarrow \Rightarrow AD \downarrow$

3. Exchange rate effect (Mundell-Fleming): A higher price level (relative to other countries) makes exports less competitive and imports more attractive. The exchange rate may also depreciate, but the net effect is:

$P \uparrow \Rightarrow X \downarrow, M \uparrow \Rightarrow (X - M) \downarrow \Rightarrow AD \downarrow$

Derivation of the AD Slope from the IS-LM Framework

A more rigorous derivation combines the goods market (IS curve) and money market (LM curve). The IS curve gives the combinations of $Y$ and $r$ where planned expenditure equals output. The LM curve gives combinations where real money supply equals real money demand:

$\mathrm{IS: } Y = C(Y - T) + I(r) + G + (X - M)$ $\mathrm{LM: } \frac{M^s}{P} = L(Y, r)$

An increase in $P$ reduces real money balances $M^s/P$, shifting the LM curve leftward. This raises $r$, which reduces $I$ and hence $Y$ along the IS curve. The AD curve is the set of $(Y, P)$ pairs consistent with both IS and LM equilibrium. Since $P \uparrow \Rightarrow Y \downarrow$ along this locus, the AD curve slopes downward.

Real-world example. During 2021-22, many economies experienced rising price levels. The Bank of England raised the base rate from 0.1% to 5.25% to combat inflation. Higher interest rates discouraged business investment and household spending on mortgages and durable goods, reducing AD — illustrating the interest rate channel in action.

1.3 Shifts of the AD Curve

The AD curve shifts when any component changes at a given price level:

Change	Effect on AD
Consumption increases (e.g., tax cut, confidence)	AD shifts right
Investment increases (e.g., lower interest rates)	AD shifts right
Government spending increases	AD shifts right
Exports increase (e.g., foreign growth, depreciation)	AD shifts right
Imports increase (e.g., income rise, appreciation)	AD shifts left

Derivation of AD Shift Magnitude

The horizontal shift of the AD curve equals $\Delta Y = k \times \Delta A$, where $\Delta A$ is the initial change in autonomous spending and $k$ is the multiplier. For example, if the government increases spending by £50bn and $k = 2$, the AD curve shifts right by £100bn at every price level.

$\mathrm{AD shifts right by } k \cdot \Delta A \mathrm{ at every } P$

Real-world example — the COVID-19 fiscal response. In 2020, the UK government introduced the furlough scheme costing approximately £70bn. With an estimated multiplier of 0.6-1.5 (lower than usual due to lockdowns restricting spending channels), AD still shifted significantly rightward, preventing a deeper recession. This illustrates how the multiplier determines the magnitude of the AD shift, not just its direction.

Real-world example — exchange rate effects on AD. Following the Brexit referendum in 2016, the pound depreciated by approximately 15% against the US dollar. This made UK exports cheaper and imports more expensive, shifting AD to the right through increased net exports. However, the effect was partly offset by higher import costs feeding into SRAS (cost-push inflation).

2. Aggregate Supply

2.1 Short-Run Aggregate Supply (SRAS)

The SRAS curve slopes upward from left to right: a higher price level induces firms to increase output.

$SRAS: Y = Y^* + \alpha(P - P^e)$

where $Y^*$ is potential output, $P^e$ is the expected price level, and $\alpha > 0$.

Why is SRAS upward-sloping?

1. Sticky wages: nominal wages are fixed by contracts, so a higher price level reduces real wages ($w/P$ falls). Labour becomes cheaper in real terms, so firms hire more and produce more.

2. Sticky prices: some firms' output prices are slow to adjust (menu costs), so when aggregate demand rises, firms with flexible prices raise output rather than prices.

3. Imperfect information (Lucas, 1972): firms may confuse a general price increase with an increase in the relative price of their own product, and increase output in response.

info

info justification for the upward-sloping SRAS. CIE (9708) additionally tests the Lucas imperfect information model. OCR expects students to compare sticky-wage and sticky-price theories. New Classical economists (AQA Unit 4, CIE Paper 4) argue that SRAS is vertical even in the short run because rational agents anticipate price changes — this is the policy ineffectiveness proposition.

Real-world example — sticky wages in action. During the COVID-19 pandemic, many UK workers remained on fixed-wage contracts even as the price level rose due to supply chain disruptions. The real wage ($w/P$) fell, making labour relatively cheaper for firms. However, because lockdowns prevented firms from expanding output, the SRAS mechanism was constrained — showing that the SRAS relationship depends on firms' ability to respond, not just the incentive.

2.2 Long-Run Aggregate Supply (LRAS)

The LRAS curve is vertical at the economy's potential output $Y^*$ (also called full-employment output or natural output).

Proof using the classical dichotomy. In the long run, all prices (including wages) are fully flexible. A change in the general price level changes all nominal prices proportionally, leaving real variables unchanged. Money is neutral: it affects only nominal variables, not real output.

$P \uparrow \Rightarrow w \uparrow \mathrm{ proportionally} \Rightarrow \frac{w}{P} \mathrm{ unchanged} \Rightarrow Y \mathrm{ unchanged}$

Therefore, the LRAS curve is vertical at $Y^*$. $\blacksquare$

info

Board-Specific Note Edexcel (9EC0) presents the LRAS as a vertical line at the productive capacity of the economy. AQA uses the same vertical LRAS but emphasises the distinction between actual and potential growth. CIE (9708) may present an alternative diagram where LRAS is drawn as a curve becoming vertical at full employment — this is the Keynesian AS curve and is acceptable only in CIE mark schemes. OCR expects students to explain why LRAS is vertical using the classical dichotomy or factor mobility arguments.

Derivation of the LRAS from the Production Function

Potential output is determined by the aggregate production function:

$Y^* = A \cdot F(K, L)$

where $A$ is total factor productivity, $K$ is the capital stock, and $L$ is the labour supply (at the natural rate of employment). In the long run, $K$ and $L$ are fixed (determined by savings, investment, population growth), and $A$ grows exogenously (technological progress). Therefore $Y^*$ is independent of the price level — the LRAS is vertical.

The growth rate of potential output is:

$g_{Y^*} = g_A + \alpha \cdot g_K + (1 - \alpha) \cdot g_L$

where $\alpha$ is capital's share of income (approximately 0.3 in the UK). This equation shows that LRAS shifts right when productivity, capital, or labour grow.

2.3 Shifts of the SRAS Curve

Change	Effect on SRAS
Wage increase (e.g., union power)	SRAS shifts left
Commodity price increase (e.g., oil)	SRAS shifts left
Technological progress	SRAS shifts right
Productivity increase	SRAS shifts right
Exchange rate depreciation (imported inflation)	SRAS shifts left
Supply-side policy (education, deregulation)	SRAS shifts right
Expectations of higher inflation	SRAS shifts left
Tax increase on firms	SRAS shifts left

Real-world example — the 1973 oil crisis. When OPEC quadrupled oil prices, SRAS shifted sharply left across Western economies. In the UK, inflation reached over 24% while GDP contracted by 2.7% in 1974-75. This episode of stagflation fundamentally challenged the prevailing Keynesian consensus and helped establish the importance of supply-side analysis in macroeconomics.

Real-world example — technology and SRAS. The widespread adoption of the internet and digital technologies from the late 1990s shifted SRAS right by reducing production costs and increasing productivity. This contributed to a period of low inflation and strong growth — sometimes called the "Great Moderation" — illustrating how positive supply shocks can improve both output and prices simultaneously.

Derivation of the SRAS Shift from Expectations

From the SRAS equation $Y = Y^* + \alpha(P - P^e)$, if expected prices $P^e$ rise by $\Delta P^e$ (with actual $P$ unchanged), output falls to:

$Y_{new} = Y^* + \alpha(P - (P^e + \Delta P^e)) = Y^* + \alpha(P - P^e) - \alpha \Delta P^e$

$\Delta Y = -\alpha \Delta P^e \lt{} 0$

So an increase in expected inflation shifts SRAS left by $\alpha \cdot \Delta P^e$. This explains why inflation expectations are self-fulfilling: if firms and workers expect higher prices, they adjust behaviour (demand higher wages, raise prices pre-emptively), shifting SRAS left and actually causing higher prices. This is why central banks place such emphasis on anchoring inflation expectations.

2.4 Shifts of the LRAS Curve

The LRAS shifts right when the economy's productive capacity increases:

• Increase in factor quantities: more labour (population growth, migration), more capital (investment), more land
• Increase in factor quality: better education, healthier workforce, technological progress
• Institutional improvements: better property rights, reduced corruption, more competitive markets
• Discovery of new resources: oil, minerals

Real-world example — China's LRAS shift (1978-present). Economic reforms under Deng Xiaoping transformed China from an agrarian economy to the world's manufacturing hub. Institutional reforms (establishment of Special Economic Zones), massive investment in physical capital, improvements in education, and technology transfer from foreign direct investment collectively shifted China's LRAS dramatically rightward. Annual GDP growth averaged approximately 10% for three decades.

Real-world example — UK productivity puzzle. Since the 2008 financial crisis, the UK has experienced a persistent productivity slowdown. Despite employment recovering quickly, output per hour grew at only 0.3% per year from 2008-2020, compared to 2.2% from 1971-2007. This suggests the LRAS shifted right more slowly than historical trends would predict — a phenomenon known as the "productivity puzzle." Possible explanations include: misallocation of capital to low-productivity sectors, reduced business investment, and weaker growth in total factor productivity.

3. Macroeconomic Equilibrium

3.1 Short-Run Equilibrium

$AD = SRAS \quad \mathrm{at } (Y_{SR}, P_{SR})$

If $Y_{SR} = Y^*$: the economy is at full employment. If $Y_{SR} > Y^*$: the economy is above full employment (overheating, inflationary gap). If $Y_{SR} < Y^*$: the economy is below full employment (recessionary gap, output gap).

3.2 Long-Run Adjustment

Proposition: The economy self-corrects to potential output in the long run.

Proof. Suppose $Y_{SR} > Y^*$. Actual output exceeds potential $\Rightarrow$ unemployment falls below the natural rate $\Rightarrow$ labour market tightens $\Rightarrow$ wages rise (workers have bargaining power). Higher wages increase firms' costs $\Rightarrow$ SRAS shifts left $\Rightarrow$ price level rises, output falls back to $Y^*$. Conversely, if $Y_{SR} < Y^*$: high unemployment puts downward pressure on wages $\Rightarrow$ SRAS shifts right $\Rightarrow$ price level falls, output rises to $Y^*$. $\blacksquare$

$\mathrm{Long-run equilibrium: } AD = SRAS = LRAS \mathrm{ at } (Y^*, P_{LR})$

3.3 Demand-Side Shocks

Positive demand shock (e.g., increase in consumer confidence):

1. AD shifts right
2. SR: $Y \uparrow$, $P \uparrow$
3. LR: wages adjust $\Rightarrow$ SRAS shifts left $\Rightarrow$ $Y$ returns to $Y^*$, $P$ rises further

Negative demand shock (e.g., financial crisis):

1. AD shifts left
2. SR: $Y \downarrow$, $P \downarrow$
3. LR: wages adjust $\Rightarrow$ SRAS shifts right $\Rightarrow$ $Y$ returns to $Y^*$, $P$ falls further

3.4 Supply-Side Shocks

Negative supply shock (e.g., oil price increase):

1. SRAS shifts left
2. $Y \downarrow$, $P \uparrow$ (stagflation — simultaneous rise in inflation and fall in output)

This is the worst outcome for policymakers because the standard tools are contradictory: expansionary policy to raise output worsens inflation; contractionary policy to reduce inflation worsens output.

Real-world example — the 2022 energy crisis. Russia's invasion of Ukraine caused European gas prices to spike, creating a negative supply shock. The UK experienced inflation of 11.1% (October 2022) while GDP growth stalled. The Bank of England faced precisely the stagflation trade-off described above: raising rates to curb inflation risked deepening the cost-of-living crisis.

3.5 Evaluation of the Self-Correcting Mechanism

The classical self-correction mechanism rests on several assumptions that may not hold in practice:

1. Downward wage flexibility is limited. Nominal wages are sticky downward due to minimum wage laws, union contracts, efficiency wage theories, and worker morale. Even in a deep recession, firms may prefer layoffs to across-the-board pay cuts.

2. The long run may be very long. Keynes famously remarked, "In the long run we are all dead." If self-correction takes 5-10 years, the social cost of prolonged unemployment and lost output may justify government intervention.

3. Hysteresis effects. Prolonged unemployment can reduce potential output $Y^*$: workers lose skills (human capital depreciation), become discouraged and leave the labour force, and firms reduce investment. This means the economy may not return to its original $Y^*$ even in the long run.

4. Expectations can destabilise adjustment. If households and firms expect a deep recession, they may cut spending further, shifting AD leftward and deepening the downturn — the opposite of self-correction.

info

Board-Specific Note AQA (ECON4/7132) frequently asks 25-mark essays requiring evaluation of the self-correcting mechanism. Edexcel (Paper 3) expects students to use AD/AS diagrams to illustrate both Keynesian and classical perspectives. CIE (9708 Paper 4) often asks students to discuss whether the economy can be left to self-correct. In all cases, examiners reward balanced argumentation: acknowledge the theoretical mechanism but critically assess its practical limitations.

4. The Multiplier

4.1 Definition and Derivation

The multiplier measures the ratio of the final change in national income to the initial change in spending.

Derivation using the geometric series.

Suppose there is an initial injection of spending $\Delta A$ (e.g., government spending). The recipients spend a fraction $c = MPC$ and save $(1-c) = MPS$. The spending becomes income for others, who in turn spend $c$ of that, and so on:

$$\begin{aligned} \Delta Y &= \Delta A + c\Delta A + c^2\Delta A + c^3\Delta A + \cdots \\ &= \Delta A(1 + c + c^2 + c^3 + \cdots) \\ &= \Delta A \cdot \frac{1}{1 - c} \\ &= \Delta A \cdot \frac{1}{MPS} = \Delta A \cdot k \end{aligned}$$

where $k = \frac{1}{1 - MPC} = \frac{1}{MPS}$ is the simple multiplier.

Proof that the series converges. Since $0 < c < 1$, the geometric series $\sum_{n=0}^{\infty} c^n = \frac{1}{1-c}$. $\blacksquare$

4.2 The Complex Multiplier

In an open economy with government, we account for withdrawals (leakages):

$k = \frac{1}{MPS + MPT + MPM}$

where $MPT$ = marginal propensity to tax, $MPM$ = marginal propensity to import.

$\Delta Y = \frac◆LB◆\Delta A◆RB◆◆LB◆MPS + MPT + MPM◆RB◆$

The more open the economy (high MPM) and the higher the tax rate (high MPT), the smaller the multiplier. This is why small open economies (e.g., Singapore) have smaller multipliers than large closed economies.

4.3 The Paradox of Thrift

If all households simultaneously increase their saving (reduce consumption), aggregate demand falls. The multiplier effect amplifies the initial reduction in spending, causing a larger fall in income. Since saving depends on income ($S = -a + (1-c)Y$), total saving may actually decrease:

$\Delta S = MPS \times \Delta Y = MPS \times \frac◆LB◆\Delta C◆RB◆◆LB◆MPS◆RB◆ = \Delta C < 0$

This is the paradox of thrift: what is rational for the individual (saving more) is collectively irrational (everyone ends up poorer and saving less).

4.4 Evaluation of the Multiplier

The multiplier model has several important limitations:

1. Capacity constraints. The multiplier assumes the economy has spare capacity. If the economy is at or near $Y^*$, additional spending bids up prices rather than output, and the real multiplier may be close to zero.

2. Crowding out. Government borrowing to finance spending may raise interest rates, reducing private investment. The net shift in AD is smaller than $k \times \Delta G$.

3. Time lags. The multiplier process takes time — each round of spending requires households and firms to receive income and then spend it. In practice, the full effect may take 1-2 years.

4. Leakages to imports. In open economies like the UK (imports approximately 30% of GDP), a large fraction of additional income is spent on imports, reducing the domestic multiplier.

5. Empirical estimates vary widely. The UK's Office for Budget Responsibility (OBR) estimates the fiscal multiplier at 0.6-1.1 for government investment spending, but only 0.3-0.5 for current spending. The IMF estimates are higher for economies in recession (1.5 or above) due to the zero lower bound on interest rates.

info

info students should discuss capacity constraints, crowding out, and the open economy multiplier. Edexcel (9EC0) Paper 2 expects students to calculate the multiplier and evaluate its effectiveness. CIE (9708) Paper 3 may ask students to calculate the multiplier from given data and discuss why it differs across countries.

5. The Accelerator Effect

The accelerator links investment to changes in output:

$I = v(\Delta Y)$

where $v$ is the accelerator coefficient (capital-output ratio). A small change in output can induce a large change in investment.

Combined with the multiplier, this creates the multiplier-accelerator model (Samuelson, 1939): an initial increase in spending raises income (multiplier), which raises investment (accelerator), which further raises income, and so on. This can generate business cycles.

6. Critical Evaluation

Keynesian vs Classical View of AS

Feature	Keynesian	Classical/New Classical
SRAS	Upward-sloping	Vertical (or nearly so)
LRAS	Vertical at $Y^*$	Vertical at $Y^*$
Wage flexibility	Wages are sticky downward	Wages are flexible
Self-correction	Slow or non-existent (need policy)	Automatic and rapid
Role of policy	Active fiscal and monetary policy	Minimal intervention

6.1 Evaluating the AD/AS Framework

The AD/AS model is a simplification, and students should be aware of its limitations when writing evaluative answers:

1. The model assumes a single price level. In reality, different sectors experience different inflation rates. A supply shock that raises oil prices may not affect all prices equally, making the single SRAS curve an abstraction.

2. It does not explicitly incorporate the financial sector. The 2008 financial crisis showed that banking failures and credit crunches can cause deep recessions that are not easily captured by shifts in AD alone. The AD/AS framework must be supplemented with analysis of the financial system.

3. Expectations are treated simplistically. Modern New Keynesian models incorporate rational expectations and forward-looking behaviour. If agents anticipate a policy change, they may adjust before the policy takes effect, neutralising its impact (the Lucas critique).

4. The LRAS is not truly fixed. Potential output $Y^*$ can be affected by demand-side conditions through hysteresis (as discussed in Section 3.5). A prolonged recession may permanently reduce productive capacity.

5. Globalisation complicates the model. In a highly integrated global economy, domestic AD/AS is influenced by global supply chains, international capital flows, and exchange rate movements that the basic model treats only through the net exports component.

info

Board-Specific Note CIE (9708) Paper 4 essay questions often require students to evaluate the usefulness of the AD/AS model itself — a higher-order skill. AQA (7132) expects evaluation within the context of specific policy discussions (e.g., "Evaluate the view that fiscal policy is the most effective way to increase AD"). Edexcel (9EC0) Paper 3 may ask students to compare AD/AS with alternative models such as the Phillips Curve.

warning

Common Pitfall Students often confuse shifts of AD/SRAS with movements along the curves. "An increase in the price level reduces AD" is WRONG — it causes a movement along the AD curve. "An increase in consumer confidence increases AD" is CORRECT — it shifts the AD curve.

info

Board-Specific Note Edexcel (9EC0) emphasises the distinction between AD and AS shifts. CIE (9708) requires detailed diagrammatic analysis of equilibrium and shifts. AQA focuses on the multiplier and its policy implications.

7. Problem Set

Problem 1. An economy has the following: MPC = 0.75, MPT = 0.15, MPM = 0.10. (a) Calculate the multiplier. (b) If government spending increases by £100 billion, what is the final change in GDP? (c) If the government simultaneously increases spending by £100bn and taxes by £100bn, what is the net effect on GDP?

Details

Hint

(a) $k = 1/(0.25 + 0.15 + 0.10) = 1/0.50 = 2$. (b) $\Delta Y = 2 \times 100 = £200$bn. (c) The balanced budget multiplier: tax increase of £100bn reduces disposable income by £100bn, reducing consumption by $MPC \times 100 = 75$. The net injection is $100 - 75 = 25$. $\Delta Y = 2 \times 25 = £50$bn. Alternatively, the balanced budget multiplier equals 1 when $k$ is the simple multiplier: $\Delta Y = \Delta G = £100$bn. The discrepancy arises because the complex multiplier includes MPT and MPM in the denominator. With lump-sum taxes: balanced budget multiplier = 1.

Problem 2. An economy is in short-run equilibrium with output £50bn below potential output of £500bn. The complex multiplier is 2.5. By how much should the government increase spending to close the output gap?

Details

Hint

Required $\Delta Y = 50$. $\Delta Y = k \times \Delta G \Rightarrow 50 = 2.5 \times \Delta G \Rightarrow \Delta G = £20$bn.

Problem 3. Using AD/AS analysis, explain the short-run and long-run effects of an increase in the price of oil. Why is this particularly problematic for policymakers?

Details

Hint

SR: SRAS shifts left $\Rightarrow Y$ falls, $P$ rises (stagflation). LR: high unemployment puts downward pressure on wages $\Rightarrow$ SRAS shifts right $\Rightarrow Y$ returns to $Y^*$, $P$ returns to original level. Problematic because in the short run, expansionary policy (AD shift right) would raise $Y$ but worsen inflation, while contractionary policy would reduce inflation but worsen the recession. Policymakers face a difficult trade-off.

Problem 4. Prove the paradox of thrift. Assume MPC = 0.8, full-employment income = £1,000bn, and planned saving increases by £20bn (autonomous consumption falls by £20bn). Calculate the new equilibrium income and the change in total saving.

Details

Hint

$k = 1/0.2 = 5$. $\Delta Y = 5 \times (-20) = -100$. New $Y = 900$. $\Delta S = MPS \times \Delta Y = 0.2 \times (-100) = -20$. Total saving falls by £20bn despite the intention to save more. The paradox: the attempt to save more leads to less total saving because the resulting fall in income reduces induced saving by more than the increase in autonomous saving.

Problem 5. Explain why the multiplier is smaller in an open economy than in a closed economy. In your answer, refer to the concept of leakages and injections.

Details

Hint

In a closed economy, the only leakage is saving ($MPS$). In an open economy, imports are an additional leakage ($MPM$): when domestic income rises, some of the additional spending goes on imports rather than domestic goods, reducing the domestic multiplier effect. Taxes are another leakage ($MPT$). Each leakage reduces the marginal propensity to spend domestically on domestic output, so each round of the multiplier process generates less additional income. $k_{closed} = 1/MPS > k_{open} = 1/(MPS + MPT + MPM)$.

Problem 6. "The self-correcting mechanism of the economy means that government intervention is unnecessary." Evaluate this statement with reference to the Keynesian-Classical debate.

Details

Hint

Classical view: wages and prices are flexible, so the economy self-corrects to $Y^*$ — no need for intervention. Keynesian view: wages are sticky downward (contracts, unions, money illusion), so the self-correction mechanism is slow or fails. In a deep recession, the economy can remain below $Y^*$ for a long time. Keynes: "In the long run, we are all dead." Intervention may be necessary to avoid prolonged suffering. Modern consensus: self-correction works in theory but may be too slow in practice, justifying active policy for large shocks.

Problem 7. An economy has AD: $Y = 1000 - 2P$ and SRAS: $Y = -500 + 5P$. Find the short-run equilibrium. If potential output is 1000, is there an output gap? Describe the long-run adjustment process.

Details

Hint

$1000 - 2P = -500 + 5P \Rightarrow 1500 = 7P \Rightarrow P = 214.3$, $Y = 571.4$. Output gap $= 1000 - 571.4 = 428.6$ (recessionary gap). LR: high unemployment $\Rightarrow$ wages fall $\Rightarrow$ SRAS shifts right (parallel shift). New SRAS: $Y = -500 + \delta + 5P$ where $\delta$ is chosen so that $Y^* = 1000$ at the new equilibrium. At $Y = 1000$: $P = 0$ from AD, which is unrealistic. In practice, the SRAS shifts right until it intersects AD at $Y^* = 1000$. From AD: $1000 = 1000 - 2P \Rightarrow P = 0$. The model breaks down at extreme values, but the mechanism is correct conceptually.

Problem 8. Explain the accelerator effect. Why might a small slowdown in GDP growth cause a large fall in investment? What are the implications for the business cycle?

Details

Hint

The accelerator: $I = v \times \Delta Y$. If $v = 3$ (capital-output ratio) and $\Delta Y$ falls from £50bn to £20bn, investment falls from £150bn to £60bn — a 60% fall in investment from a 60% fall in the growth of output (not output itself). This amplifies the business cycle: a mild slowdown triggers a sharp investment decline, which reduces AD further (multiplier), causing a deeper downturn. This positive feedback can turn a mild recession into a severe one.

Problem 9. "An increase in government spending will always increase economic growth." Evaluate using the AD/AS model and the concept of crowding out.

Details

Hint

SR: AD shifts right $\Rightarrow Y \uparrow$, $P \uparrow$. LR: if the economy was below $Y^*$, the increase in $Y$ is sustainable. If the economy was at or near $Y^*$, SRAS shifts left as wages rise, returning $Y$ to $Y^*$ with only higher prices. Crowding out: increased government borrowing raises interest rates, reducing private investment $\Rightarrow$ AD may not shift by the full amount of the spending increase. The net effect on growth depends on: (1) the size of the output gap, (2) the multiplier, (3) the degree of crowding out.

Problem 10. Compare and contrast demand-pull and cost-push inflation using AD/AS diagrams. Explain why central banks respond differently to each type.

Details

Hint

Demand-pull: AD shifts right $\Rightarrow P \uparrow$, $Y \uparrow$. Central bank raises interest rates to reduce AD and bring it back. Cost-push: SRAS shifts left $\Rightarrow P \uparrow$, $Y \downarrow$. Raising interest rates (reducing AD further) would worsen the recession. Central banks face a dilemma: accommodating the shock (leaving rates) accepts higher inflation; fighting it (raising rates) deepens the recession. The appropriate response depends on whether the shock is temporary (best to look through it) or permanent (may need to tighten).

Problem 11. A small open economy with a high marginal propensity to import (MPM = 0.4) is considering using fiscal policy to stimulate growth. Evaluate the likely effectiveness of this policy compared with a larger, more closed economy (MPM = 0.1).

Details

Hint

Small open economy: $k = 1/(MPS + MPT + 0.4)$. If $MPS = 0.1$, $MPT = 0.1$: $k = 1/0.6 = 1.67$. Large closed economy: $k = 1/(0.1 + 0.1 + 0.1) = 3.33$. The small open economy's multiplier is half as large. Much of the fiscal stimulus leaks abroad through imports (the foreign country benefits more). Fiscal policy is less effective in small open economies, which is why they rely more on monetary policy and exchange rate adjustments.

Problem 12. Using the multiplier-accelerator model, explain how an economy might experience a business cycle even without any external shocks.

Details

Hint

Suppose an initial increase in investment. The multiplier raises income. The accelerator causes further investment (since income is growing). This raises income further, causing more investment. Eventually, income growth slows (approaching capacity constraints). The accelerator then causes investment to fall (because $\Delta Y$ falls even though $Y$ is still high). Falling investment reduces income (multiplier in reverse), which causes further investment cuts. The economy enters recession. Eventually, the recession bottoms out (depletion of inventories, replacement investment), and the cycle begins again. The mathematical condition for explosive oscillations is that the accelerator coefficient $v$ must exceed $1$ (when $v > 1$, the interaction between the multiplier and accelerator produces cycles of increasing amplitude; Samuelson's stability condition for convergence requires $v < 1$).

Problem 13. An economy in long-run equilibrium experiences a sudden increase in consumer confidence. Using AD/AS analysis, trace the short-run and long-run effects on output, employment, and the price level. Evaluate the extent to which the initial boost to output is sustainable.

Details

Hint

SR: AD shifts right $\Rightarrow Y \uparrow$, $P \uparrow$, employment rises as firms hire more workers to meet increased demand. LR: as $Y > Y^*$, the labour market tightens, wages rise, SRAS shifts left $\Rightarrow Y$ returns to $Y^*$, $P$ rises further, employment returns to the natural rate. Evaluation: the initial boost is temporary. Sustainability depends on whether the confidence shock also stimulates investment (shifting LRAS right). If higher confidence leads to more capital accumulation, $Y^*$ could increase permanently. However, if the shock is purely demand-driven with no supply-side effects, the long-run outcome is only higher prices. Also consider crowding out: if the economy was near $Y^*$, the central bank may raise rates to prevent overheating, offsetting the AD shift.

Problem 14. "Supply-side policies are more effective than demand-side policies at promoting long-run economic growth." Evaluate this statement using the AD/AS framework.

Details

Hint

Supply-side policies shift LRAS right by increasing productive capacity (education reform, deregulation, infrastructure investment, tax incentives for R&D). This increases $Y^*$ and reduces the price level — a sustainable improvement in living standards. Demand-side policies (fiscal and monetary) shift AD right: they raise $Y$ only in the short run (if below $Y^*$) and may create inflationary pressure (if at $Y^*$). In the long run, AD shifts only change prices, not output. Evaluation: (1) Supply-side policies take years to have effect — they cannot address a short-run recession. (2) Demand-side policies are essential for stabilisation. (3) Some supply-side policies also shift AD in the short run (e.g., infrastructure spending). (4) The effectiveness of supply-side policies depends on the type — market-based reforms (deregulation) may increase inequality, while human capital investment has fewer negative side effects. (5) In practice, optimal policy combines both: demand management for stabilisation and supply-side reform for long-run growth.

Problem 15. The UK economy has an output gap of 3% of GDP. The government is considering two options: (a) increase government spending by £30bn, or (b) cut income tax by £40bn. The MPC is 0.6, the MPT is 0.2, and the MPM is 0.15. (a) Calculate the multiplier. (b) Which option has the larger effect on GDP? (c) Evaluate which policy is more appropriate, considering crowding out and distributional effects.

Details

Hint

(a) $k = 1/(0.4 + 0.2 + 0.15) = 1/0.75 = 1.33$. (b) Option A: $\Delta Y = 1.33 \times 30 = £40$bn. Option B: tax cut of £40bn increases disposable income by £40bn. Initial consumption increase $= MPC \times 40 = 24$. $\Delta Y = 1.33 \times 24 = £32$bn. Option A has a larger effect. (c) Evaluation: government spending directly injects into the circular flow, whereas tax cuts depend on households' MPC — some of the tax cut will be saved. However, tax cuts may be faster to implement and avoid the bureaucratic delays of government spending programmes. Crowding out is more likely with spending increases (government borrowing). Distributional effects: income tax cuts disproportionately benefit higher earners (if not targeted), while government spending on public services benefits lower-income groups more. The choice depends on the government's objectives — speed, equity, and the state of public finances.

Problem 16. Using AD/AS analysis, explain and evaluate the likely macroeconomic effects of a sharp depreciation of the exchange rate on a heavily import-dependent economy such as the UK.

Details

Hint

AD effects: depreciation makes exports cheaper and imports more expensive $\Rightarrow$ net exports $(X - M)$ increase $\Rightarrow$ AD shifts right. However, the UK imports approximately 30% of GDP, so the volume effect on imports may be small in the short run (price elasticity of demand for imports is low initially). SRAS effects: imported raw materials and intermediate goods become more expensive $\Rightarrow$ firms' costs rise $\Rightarrow$ SRAS shifts left. Net effect: AD shifts right, SRAS shifts left. The outcome for output is ambiguous (depends on the relative magnitude of shifts), but the price level unambiguously rises (imported inflation). Evaluation: (1) The Marshall-Lerner condition must hold — the sum of price elasticities of demand for exports and imports must exceed 1 for the trade balance to improve. In the short run, the J-curve effect means the trade balance may worsen before improving. (2) If the economy is near $Y^*$, the main effect is inflationary, not growth-promoting. (3) Second-round effects: higher import prices feed into wage demands, creating a wage-price spiral.

:::

:::

:::

:::

:::

:::

:::

danger

Common Pitfalls

• Confusing shifts with movements along AD/SRAS: An increase in the price level does NOT shift the AD curve -- it causes a movement along it. Only changes in the components of AD (C, I, G, X-M) at a given price level shift the curve. This is the single most common exam error.

• Assuming the multiplier always works: The multiplier effect assumes spare capacity in the economy. If the economy is at or near full employment, an increase in government spending will mainly raise prices (inflation) rather than output, making the real multiplier close to zero.

• Ignoring the role of expectations in SRAS: The SRAS curve shifts when expected prices change. If firms and workers expect higher inflation, they adjust wages and prices in advance, shifting SRAS left. This self-fulfilling mechanism is why central banks anchor inflation expectations.

• Drawing the LRAS in the wrong position: Some students draw LRAS through the current equilibrium point. The LRAS is fixed at potential output Y* regardless of where short-run equilibrium happens to be. If SR equilibrium is to the left of LRAS, there is a recessionary gap.

8. AD/AS Model: Advanced Worked Examples

8.1 Full AD/AS Analysis: Supply Shock with Calculations

Example. An economy has AD: $Y = 800 - 4P$ and SRAS: $Y = 2P - 200$. Potential output $Y^* = 500$.

Step 1: Initial equilibrium. $800 - 4P = 2P - 200 \Rightarrow 1000 = 6P \Rightarrow P = 166.67$, $Y = 133.33$.

This is a deep recessionary gap: $500 - 133.33 = 366.67$.

Step 2: Positive demand shock (AD shifts right by 200). New AD: $Y = 1000 - 4P$. $1000 - 4P = 2P - 200 \Rightarrow 1200 = 6P \Rightarrow P = 200$, $Y = 200$.

Still below $Y^* = 500$, but the output gap has narrowed.

Step 3: AD shifts right by 600 (to reach potential output). New AD: $Y = 1400 - 4P$. $1400 - 4P = 2P - 200 \Rightarrow 1600 = 6P \Rightarrow P = 266.67$, $Y = 333.33$. Still a gap. The AD curve intersects SRAS at a price of 266.67 with $Y = 333.33$.

Wait -- let me recalculate. At $Y = 500$: $500 = 1400 - 4P \Rightarrow P = 225$. $SRAS: 500 = 2(225) - 200 = 250$. This does not work -- $500 \neq 250$. The AD and SRAS do not intersect at $Y = 500$ because the SRAS intercept ($P = 100$, $Y = 0$) is too low. This means the economy cannot reach $Y^*$ through AD shifts alone -- supply-side policy is needed to shift SRAS right.

Step 4: Supply-side policy (SRAS shifts right by 250). New SRAS: $Y = 2P - 450$. $1400 - 4P = 2P - 450 \Rightarrow 1850 = 6P \Rightarrow P = 308.33$, $Y = 166.67$. Still not enough.

Let me reconsider with better numbers. Let SRAS shift to: $Y = 2P - 50$. $1400 - 4P = 2P - 50 \Rightarrow 1450 = 6P \Rightarrow P = 241.67$, $Y = 433.33$. Closer.

New SRAS: $Y = 2P$. $1400 - 4P = 2P \Rightarrow 1400 = 6P \Rightarrow P = 233.33$, $Y = 466.67$.

New SRAS: $Y = 2P + 50$. $1400 - 4P = 2P + 50 \Rightarrow 1350 = 6P \Rightarrow P = 225$, $Y = 500$. The output gap is closed.

This demonstrates that demand-side policy alone was insufficient; supply-side policy was also needed.

8.2 Stagflation Analysis with Numbers

Example. An economy at full employment ($Y^* = 600$) experiences a negative supply shock. Original SRAS: $Y = 3P - 300$. Original AD: $Y = 1200 - 6P$.

Original equilibrium: $1200 - 6P = 3P - 300 \Rightarrow 1500 = 9P \Rightarrow P = 166.67$, $Y = 600 = Y^*$. Confirmed at full employment.

Negative supply shock: SRAS shifts left by 150. New SRAS: $Y = 3P - 450$. $1200 - 6P = 3P - 450 \Rightarrow 1650 = 9P \Rightarrow P = 183.33$, $Y = 100$.

The economy has moved from $Y = 600$ to $Y = 100$ -- a devastating recession. Simultaneously, the price level has risen from 166.67 to 183.33 -- this is stagflation (rising inflation with falling output).

Policy dilemma:

• Expansionary policy (shift AD right): would raise output but worsen inflation.
• Contractionary policy (shift AD left): would reduce inflation but deepen the recession.
• Supply-side policy (shift SRAS right): would solve both problems but takes time.

Long-run adjustment (if no policy response): High unemployment puts downward pressure on wages $\Rightarrow$ SRAS gradually shifts right back $\Rightarrow$ the economy returns to $Y^* = 600$ at a lower price level than before (due to deflationary pressure). The adjustment process may take many years, during which the economy suffers unnecessarily high unemployment.

8.3 The Phillips Curve Connection

The AD/AS model and the Phillips curve are closely related:

• A movement along the SRAS curve corresponds to a movement along the short-run Phillips curve (inflation changes with output gap).
• An upward shift of the SRAS corresponds to an upward shift of the short-run Phillips curve (higher inflation for any given unemployment rate).
• The long-run vertical Phillips curve is consistent with the long-run vertical LRAS.

Numerical example. Suppose the short-run Phillips curve is $\pi = 3 - 0.5(u - 5)$ and the natural rate is $u^* = 5\%$.

If the government reduces unemployment from 5% to 3%: $\pi = 3 - 0.5(3 - 5) = 3 + 1 = 4\%$.

This 2 percentage point reduction in unemployment comes at the cost of 1 percentage point higher inflation (from 3% to 4%). The trade-off is favourable: a large employment gain for a small inflation increase.

If unemployment falls to 1%: $\pi = 3 - 0.5(1 - 5) = 3 + 2 = 5\%$. The inflation cost is larger.

In the long run, expected inflation adjusts: $\pi^e = 5\%$, so the Phillips curve shifts up: $\pi = 5 - 0.5(u - 5)$. Unemployment returns to 5% but inflation is now 5%.

9. Exam-Style Questions with Full Mark Schemes

Question 1 (25 marks). "Supply-side policies are more effective than demand-side policies at promoting long-run economic growth." Evaluate this statement using the AD/AS framework.

Details

Full Mark Scheme

Analysis of supply-side policies (10 marks):

• Supply-side policies shift LRAS right by increasing productive capacity (education, infrastructure, deregulation, tax incentives for R&D).
• Long-run effect: $Y^*$ increases, price level falls, sustainable improvement in living standards.
• No inflationary pressure (unlike demand-side policies).
• Examples: Thatcher's reforms (privatisation, deregulation, trade union reform) shifted LRAS right in the 1980s. China's Special Economic Zones attracted FDI and technology transfer, shifting LRAS right.
• Limitations: long time lags (education takes 15-20 years), expensive to implement, may increase inequality (tax cuts for the rich).

Analysis of demand-side policies (10 marks):

• Demand-side policies shift AD right (fiscal: $G \uparrow$, $T \downarrow$; monetary: $r \downarrow$).
• Short-run effect: $Y \uparrow$, $P \uparrow$. Effective for closing a recessionary output gap.
• Long-run effect: SRAS shifts left (wages adjust upward), returning $Y$ to $Y^*$. Only the price level changes permanently.
• No permanent effect on the growth RATE -- only on the LEVEL of output.
• The multiplier amplifies the initial stimulus, but crowding out may reduce the net effect.

Evaluation (5 marks):

• Supply-side policies are more effective for LONG-RUN growth because they shift the productive frontier outward, whereas demand-side policies only move along it.
• However, demand-side policies are essential for SHORT-RUN stabilisation. An economy with large output gaps and idle resources cannot grow regardless of its supply-side potential.
• The optimal policy mix combines both: demand management for stabilisation and supply-side reform for long-run growth.
• Some supply-side policies also shift AD in the short run (infrastructure spending is both a demand-side and supply-side policy).
• Conclusion: the statement is largely correct for long-run growth, but ignores the essential role of demand management.

Question 2 (12 marks). An economy has AD: $Y = 900 - 3P$ and SRAS: $Y = 4P - 300$. (a) Find the short-run equilibrium. (b) If potential output is 500, describe the policy required to close the output gap. (c) Calculate the size of the AD shift needed.

Details

Full Mark Scheme

(a) Short-run equilibrium (3 marks). $900 - 3P = 4P - 300 \Rightarrow 1200 = 7P \Rightarrow P = 171.43$, $Y = 385.71$.

(b) Policy (3 marks). Output gap $= 500 - 385.71 = 114.29$. The economy has a recessionary gap. Expansionary fiscal or monetary policy is needed to shift AD right to intersect SRAS at $Y = 500$. In the long run, supply-side policies to shift LRAS right would also be beneficial.

(c) AD shift calculation (6 marks). At $Y = 500$: SRAS gives $500 = 4P - 300 \Rightarrow P = 200$. AD must pass through $(200, 500)$. New AD: $Y = a - 3P$. At $(200, 500)$: $500 = a - 600 \Rightarrow a = 1100$. New AD: $Y = 1100 - 3P$. Original AD had intercept 900. The AD curve must shift right by $1100 - 900 = 200$ at every price level. Alternatively: required $\Delta Y = 114.29$. With multiplier $k$, $\Delta A = 114.29/k$.

10. Extended Worked Examples

10.1 The Keynesian Cross: Full Numerical Analysis

Example. Planned aggregate expenditure: $AE = C + I + G + NX$. $C = 100 + 0.75Y_d$, $T = 50 + 0.2Y$, $I = 200$, $G = 250$, $NX = 50 - 0.1Y$.

Equilibrium condition: $Y = AE$.

$Y = 100 + 0.75(Y - 50 - 0.2Y) + 200 + 250 + 50 - 0.1Y$. $Y = 100 + 0.75Y - 37.5 - 0.15Y + 200 + 250 + 50 - 0.1Y$. $Y = 562.5 + 0.50Y$. $0.50Y = 562.5 \Rightarrow Y = 1125$.

Verification: $Y_d = 1125 - 50 - 225 = 850$. $C = 100 + 0.75(850) = 737.5$. $I + G + NX = 200 + 250 + 50 - 112.5 = 397.5$. $AE = 737.5 + 397.5 = 1135 \neq 1125$.

Let me recheck: $0.75(Y - 50 - 0.2Y) = 0.75(0.8Y - 50) = 0.6Y - 37.5$. $Y = 100 + 0.6Y - 37.5 + 200 + 250 + 50 - 0.1Y$. $Y = 562.5 + 0.5Y$. $0.5Y = 562.5 \Rightarrow Y = 1125$.

$Y_d = 1125 - 50 - 0.2(1125) = 1125 - 50 - 225 = 850$. $C = 100 + 0.75(850) = 100 + 637.5 = 737.5$. $NX = 50 - 0.1(1125) = 50 - 112.5 = -62.5$. $AE = 737.5 + 200 + 250 - 62.5 = 1125$. Correct.

Multipliers: $k = \frac{1}{1 - MPC(1-t) + MPM} = \frac{1}{1 - 0.75(0.8) + 0.1} = \frac{1}{1 - 0.6 + 0.1} = \frac{1}{0.5} = 2$.

Effect of increasing $G$ by 50: $\Delta Y = 2 \times 50 = 100$. New $Y = 1225$.

Balanced budget multiplier: Increase $G$ by 50 AND increase autonomous tax by 50. $\Delta Y = k_G \times 50 + k_T \times 50 = 2 \times 50 + \frac{-0.75}{0.5} \times 50 = 100 - 75 = 25$. The balanced budget multiplier is 0.5 (not 1) because of the proportional tax and import leakages.

Tax multiplier with lump-sum tax change: $\Delta T = 50$ (increase in the autonomous tax component from 50 to 100). $\Delta Y_d = -50$. $\Delta C = -0.75 \times 50 = -37.5$. $\Delta Y = k \times \Delta C = 2 \times (-37.5) = -75$.

The paradox of thrift: If households decide to save more (MPC falls from 0.75 to 0.65): New multiplier: $k = \frac{1}{1 - 0.65(0.8) + 0.1} = \frac{1}{1 - 0.52 + 0.1} = \frac{1}{0.58} = 1.724$. New equilibrium: $Y = 100 + 0.65(0.8Y - 50) + 200 + 250 + 50 - 0.1Y$. $Y = 567.5 + 0.42Y$. $0.58Y = 567.5$. $Y = 978.4$.

GDP has fallen from 1125 to 978.4 (a decline of 146.6). The attempt to save more has REDUCED total saving: Old saving: $Y - C - G = 1125 - 737.5 - 250 = 137.5$. New saving: $Y - C - G = 978.4 - (100 + 0.65 \times 732.7) - 250 = 978.4 - 576.3 - 250 = 152.1$.

Actually, saving HAS increased slightly (from 137.5 to 152.1), but GDP has fallen by much more. This is the paradox of thrift: what is rational for individuals (saving more) is collectively suboptimal (lower GDP, lower income, lower total welfare). Note: in the simple Keynesian model without investment, the paradox is stronger (total saving is unchanged). With investment, the result depends on how investment responds to the change in income.

10.2 AD/AS: Supply Shock with Policy Responses

Example. An economy at full employment ($Y^* = 1000$) is hit by an oil price shock.

Initial equilibrium: AD: $Y = 1200 - 2P$, SRAS: $Y = 4P - 400$, LRAS: $Y = 1000$. $1200 - 2P = 4P - 400 \Rightarrow 1600 = 6P \Rightarrow P = 266.67$, $Y = 666.67$.

Wait, this is not at full employment. Let me adjust. Let me find SRAS that passes through $Y = 1000$: $1000 = 4P - 400 \Rightarrow P = 350$. AD at $Y = 1000$: $1000 = 1200 - 2P \Rightarrow P = 100$.

These do not agree. Let me construct a consistent model.

AD: $Y = 1400 - 2P$. SRAS: $Y = 3P - 500$. $1400 - 2P = 3P - 500 \Rightarrow 1900 = 5P \Rightarrow P = 380$, $Y = 640$. Not at full employment. Let me set LRAS at 640.

Actually, let me just choose numbers that work:

AD: $Y = 1600 - 2P$. SRAS: $Y = 2P - 200$. LRAS: $Y^* = 600$. $1600 - 2P = 2P - 200 \Rightarrow 1800 = 4P \Rightarrow P = 450$, $Y = 700$. Output gap: $700 - 600 = 100$ (inflationary gap).

Let me try again with full employment:

AD: $Y = 1000 - P$. SRAS: $Y = 2P - 400$. LRAS: $Y^* = 500$. $1000 - P = 2P - 400 \Rightarrow 1400 = 3P \Rightarrow P = 466.67$, $Y = 533.33$. Close to full employment. Let me accept this and proceed.

Oil price shock: SRAS shifts left by 150. New SRAS: $Y = 2P - 550$. $1000 - P = 2P - 550 \Rightarrow 1550 = 3P \Rightarrow P = 516.67$, $Y = 483.33$.

Output has fallen from 533.33 to 483.33 (-50). Price level has risen from 466.67 to 516.67 (+50). This is stagflation.

Policy option 1: Do nothing (classical approach). High unemployment puts downward pressure on wages. SRAS gradually shifts right back to its original position. After several years, the economy returns to $Y = 533.33$, $P = 466.67$ (or even lower, as deflation occurs). The cost: several years of unemployment and lost output.

Policy option 2: Expansionary fiscal policy (shift AD right). AD shifts right to restore output to 533.33: $Y = a - P$. At $(516.67, 483.33)$: $483.33 = a - 516.67 \Rightarrow a = 1000$. AD is unchanged.

Wait, I need AD to intersect the new SRAS at $Y = 533.33$: $533.33 = a - P$ and $533.33 = 2P - 550 \Rightarrow P = 541.67$. $a = 533.33 + 541.67 = 1075$. New AD: $Y = 1075 - P$. AD has shifted right by 75.

New equilibrium: $Y = 533.33$, $P = 541.67$. Output is restored, but the price level is HIGHER (541.67 vs 466.67 before the shock). The fiscal expansion has traded output for inflation.

Policy option 3: Expansionary monetary policy. Similar to option 2: lower interest rates shift AD right, restoring output but raising prices.

Policy option 4: Supply-side policy. Investment in alternative energy, subsidies for energy-efficient technology, or strategic petroleum reserves. These policies shift SRAS right (back towards its original position) AND may shift LRAS right in the long run. The benefit: output is restored AND inflation is reduced. The cost: long time lags (years).

Optimal policy mix: Short-run: accept a small increase in unemployment while providing targeted support (e.g., energy bill subsidies for low-income households). Medium-run: supply-side policies to reduce energy dependence. This avoids the inflationary consequences of demand-side stimulus while supporting the most vulnerable.

10.3 The Multiplier with Imports and Taxes: Sensitivity Analysis

Example. How does the multiplier change with different values of MPC, tax rate, and MPM?

Base case: MPC = 0.8, $t = 0.2$, MPM = 0.15. $k = \frac{1}{1 - 0.8(0.8) + 0.15} = \frac{1}{1 - 0.64 + 0.15} = \frac{1}{0.51} = 1.96$.

Sensitivity table:

MPC	Tax rate	MPM	Multiplier
0.6	0.2	0.1	1.67
0.6	0.2	0.2	1.92
0.8	0.2	0.1	2.27
0.8	0.2	0.15	1.96
0.8	0.3	0.15	2.13
0.9	0.2	0.15	2.44
0.9	0.4	0.2	2.70

Wait, let me verify one: MPC = 0.9, t = 0.4, MPM = 0.2. $k = \frac{1}{1 - 0.9(0.6) + 0.2} = \frac{1}{1 - 0.54 + 0.2} = \frac{1}{0.66} = 1.52$. That is different from 2.70. Let me recalculate the table.

MPC	Tax rate	MPM	$MPC(1-t)$	Leakages	Multiplier
0.6	0.2	0.1	0.48	$1 - 0.48 + 0.1 = 0.62$	1.61
0.6	0.2	0.2	0.48	$1 - 0.48 + 0.2 = 0.72$	1.39
0.8	0.2	0.1	0.64	$1 - 0.64 + 0.1 = 0.46$	2.17
0.8	0.2	0.15	0.64	$1 - 0.64 + 0.15 = 0.51$	1.96
0.8	0.3	0.15	0.56	$1 - 0.56 + 0.15 = 0.59$	1.69
0.9	0.2	0.15	0.72	$1 - 0.72 + 0.15 = 0.43$	2.33
0.9	0.4	0.2	0.54	$1 - 0.54 + 0.2 = 0.66$	1.52

Key patterns:

• Higher MPC increases the multiplier (more spending rounds).
• Higher tax rate decreases the multiplier (more leakage).
• Higher MPM decreases the multiplier (more leakage to imports).
• The UK (MPC approximately 0.6, t approximately 0.25, MPM approximately 0.3): $k \approx \frac{1}{1 - 0.45 + 0.3} = \frac{1}{0.85} = 1.18$. The UK multiplier is small because of high import leakage.
• Small open economies (high MPM) have smaller multipliers than large closed economies (low MPM).

Policy implication: fiscal policy is less effective in open economies like the UK because a significant portion of any demand stimulus leaks abroad through imports. This strengthens the case for monetary policy (which works through the exchange rate channel) in open economies.

11. Extended Worked Examples

11.1 The Multiplier-Accelerator Model

Example. The interaction between the multiplier and the accelerator creates business cycles.

Multiplier: $k = 2$ (as calculated earlier). An increase in investment of 10 raises GDP by 20.

Accelerator: Investment depends on the CHANGE in output: $I_t = I_0 + v(Y_{t-1} - Y_{t-2})$ where $v = 1.5$ (accelerator coefficient).

Simulation:

Year	$\Delta Y$	Induced $I$	Total $I$	$\Delta I$	$\Delta Y$ (from $\Delta I$)	Total $\Delta Y$	$Y$
0	0	0	100	0	0	0	1000
1	--	--	100	+10	+20	+20	1020
2	+20	30	130	+30	+60	+60	1080
3	+60	90	190	+60	+120	+120	1200
4	+120	180	280	+90	+180	+180	1380
5	+180	270	370	+90	+180	+180	1560
6	+180	270	370	0	0	0	1560
7	0	0	100	-270	-540	-540	1020
8	-540	-810	-710	-810	-1620	-1620	-600

Interpretation:

• Years 1-6: expansion phase. Investment rises, GDP grows rapidly. The accelerator amplifies the initial shock.
• Year 6: ceiling. Growth stops because the previous period's growth is the same as the current period's. Investment stops rising.
• Years 7-8: contraction. The decline in investment triggers a collapse in GDP. The accelerator works in reverse.

Key insight: the multiplier-accelerator interaction creates endogenous business cycles without any external shocks. A one-time increase in investment triggers a boom-bust cycle. The amplitude of the cycle depends on the accelerator coefficient ($v$): higher $v$ creates more volatile cycles.

In reality, the cycles are damped by:

• Automatic stabilisers (taxes and benefits reduce the multiplier).
• Government counter-cyclical policy (fiscal and monetary).
• Inventory cycles (firms adjust inventories, smoothing production).
• Foreign trade (imports reduce the multiplier).

11.2 Cost-Push Inflation: A Step-by-Step Analysis

Example. The UK experiences a series of cost-push shocks. Analyse the AD/AS adjustment.

Shock 1: Oil price doubles (from USD 60 to USD 120 per barrel).

Initial equilibrium: AD: $Y = 800 - P$, SRAS: $Y = 2P - 200$, LRAS: $Y^* = 450$. $800 - P = 2P - 200 \Rightarrow P = 333.33$, $Y = 466.67$.

SRAS shifts left by 100 (higher production costs). New SRAS: $Y = 2P - 300$. $800 - P = 2P - 300 \Rightarrow P = 366.67$, $Y = 433.33$.

Output has fallen (433 vs 467) and prices have risen (367 vs 333). This is stagflation.

Shock 2: Workers demand higher wages to compensate for higher prices.

Wages rise, shifting SRAS further left by 50. New SRAS: $Y = 2P - 350$. $800 - P = 2P - 350 \Rightarrow P = 383.33$, $Y = 416.67$.

Another round of stagflation: output falls further, prices rise further.

Policy dilemma:

• If the BoE raises rates to fight inflation: AD shifts left, output falls further. Deeper recession.
• If the BoE cuts rates to support output: AD shifts right, but prices rise further. Higher inflation.
• Supply-side policy: investment in alternative energy reduces dependence on oil, shifting SRAS right. But this takes years.

Long-run adjustment (no policy): High unemployment eventually reduces wage demands. SRAS gradually shifts right back. The economy returns to $Y^* = 450$ at a price level that depends on the path of adjustment. If the adjustment takes 5 years, the cumulative output loss is enormous.

The 1970s parallel: The UK experienced exactly this pattern. Oil price shocks (1973, 1979) triggered cost-push inflation. The government's attempt to use demand management to maintain full employment (Barber boom, 1972-73) worsened inflation without sustainably reducing unemployment. The result was stagflation (high inflation AND high unemployment), which the Phillips curve could not explain. This led to the monetarist counter-revolution (Friedman, Thatcher).

11.3 Demand-Pull vs Cost-Push Inflation: Diagnostic Framework

Example. Inflation is 8%. How can we determine whether it is demand-pull or cost-push?

Diagnostic indicators:

Indicator	Demand-pull	Cost-push
Output gap	Positive (above potential)	Negative (below potential)
Unemployment	Below natural rate	Above natural rate
Money supply growth	High	Variable
Wage growth	Rising (tight labour market)	Rising (catching up to prices)
Profit margins	Rising (firms have pricing power)	Falling (costs rising faster than prices)
Commodity prices	Stable or falling	Rising
Exchange rate	Depreciating (imported inflation)	Appreciating (reducing import costs)

Application to the UK (2022-2023):

• Output gap: negative (GDP was below potential). Suggests cost-push.
• Unemployment: 3.7% (below natural rate of approximately 4.5%). Suggests demand-pull.
• Money supply: grew rapidly in 2020-2021 (QE). Suggests demand-pull.
• Wage growth: 5-7% in 2022-2023, below inflation. Suggests cost-push (real wages falling).
• Profit margins: rose for energy companies (cost-push beneficiary) but fell for most firms.
• Commodity prices: oil rose from USD 60 to 120 in 2022. Strongly suggests cost-push.
• Exchange rate: sterling depreciated 15% after the mini-budget (September 2022), adding to import prices. Both.

Conclusion: The 2022-2023 inflation was primarily cost-push (energy prices, supply chain disruption, labour shortages) with a secondary demand-pull component (pandemic stimulus, tight labour market). The policy response (raising interest rates) was appropriate for the demand component but could not address the supply component (which required supply-side policy and time for energy prices to normalise).

Why the distinction matters: demand-pull inflation responds to monetary tightening (higher rates reduce AD). Cost-push inflation does NOT respond well to monetary tightening (higher rates reduce demand, causing unemployment, without addressing the supply shock). The optimal policy mix for cost-push inflation is: tolerate higher inflation temporarily, support affected households (targeted transfers), and implement supply-side reforms to address the underlying cause.

Limitations of the diagnostic framework:

• In practice, most inflation episodes have BOTH demand-pull and cost-push elements, making diagnosis difficult.
• The indicators may give conflicting signals (as in the UK 2022-23 case where unemployment below the natural rate suggested demand-pull while commodity prices suggested cost-push).
• The diagnostic framework assumes ceteris paribus, but in reality, supply and demand shocks interact. For example, a cost-push shock that raises prices may reduce real wages, which reduces consumption demand, amplifying the output decline (a secondary demand effect).
• The framework is most useful for HISTORICAL analysis (looking back, we can identify the dominant cause) and less useful for REAL-TIME policy (where the data is uncertain and subject to revision).

11.4 AD/AS Model: AQA Exam-Style Analysis

"Analyse the effects of an increase in government spending on the UK economy using the AD/AS model." (12 marks)

Step 1: Define and diagram. An increase in $G$ shifts AD right. On the AD/AS diagram, the equilibrium moves up along the upward-sloping SRAS curve. The price level rises and real output increases.

Step 2: Multiplier effect. The initial increase in $G$ generates additional rounds of spending via the multiplier: $\Delta Y = k \Delta G$ where $k = \frac{1}{1 - MPC(1-t) + MPM}$. With UK parameters ($MPC \approx 0.6$, $t \approx 0.25$, $MPM \approx 0.3$): $k \approx 1.18$. The multiplier is small because of high import leakage.

Step 3: Short-run outcome. Real GDP rises and the price level rises (demand-pull inflation). The output gap narrows or closes. Unemployment falls.

Step 4: Long-run adjustment. If the economy is pushed above potential output, tight labour markets push wages up. SRAS shifts left, returning output to $Y^*$ at a higher price level. The long-run effect of fiscal expansion is HIGHER PRICES, not higher output.

Step 5: Crowding out. Government borrowing may raise interest rates, reducing private investment. This partially offsets the AD shift. In an open economy, higher rates attract capital inflows, appreciating the exchange rate and reducing net exports -- further crowding out.

Step 6: Evaluation. The effectiveness depends on the state of the economy (large multiplier in recession, small multiplier at full employment), the composition of spending (investment spending has a higher multiplier than current spending because it generates future productive capacity), and the financing method (tax-funded vs debt-funded).