Aggregate Expenditure, GDP, Inflation, and AD-AS: Core Macroeconomics Study Notes

The Measurement of National Income

Nominal and Real GDP

Gross Domestic Product (GDP) measures the total value of goods and services produced in an economy. It can be calculated in nominal or real terms:

• Nominal GDP: Calculated using current prices and quantities for each year.

• Real GDP: Calculated using base-year prices and current quantities, allowing for comparison across years by removing the effects of inflation.

Example Calculation:

• Nominal GDP for 2018: $GDP_{2018} = (20 \times 30) + (60 \times 10) = 600 + 600 = 1200$

• Real GDP for 2019 (using 2017 prices): $GDP_{2019}^{real} = (30 \times 15) + (40 \times 5) = 450 + 200 = 650$

Value-Added Method of GDP

The value-added method sums the value added at each stage of production to avoid double counting:

• Value added = Value of output − Cost of intermediate goods

Example: Farmer sells wheat for $2, baker sells bread for $5, store sells bread for $8. GDP = $2 + 3 + 3 = 8$.

GDP and Standard of Living

• Higher GDP means more goods and services are available.

• GDP per capita reflects average income.

• GDP growth usually means more jobs and production.

Limitations: GDP does not account for environmental quality, unpaid work, income inequality, leisure time, or health and happiness.

The Measurement of Inflation

Consumer Price Index (CPI) and Inflation Rate

The CPI measures the average price level of a basket of goods and services. The inflation rate is the percentage change in the CPI from one year to the next.

Inflation Rate Formula:

$ \text{Inflation rate} = \frac{CPI_t - CPI_{t-1}}{CPI_{t-1}} \times 100 $

Calculating CPI when inflation is known:

$ CPI_t = CPI_{t-1} \times (1 + \text{inflation}) $

Example Table:

Year	CPI	Inflation %
2010	116.5	1.8
2011	119.9	2.9
2012	121.6	1.4
2013	123.1	1.2
2014	125.7	2.1
2015	126.6	0.7
2016	128.4	1.4
2017	130.4	1.6
2018	132.7	1.8
2019	136.0	2.5
2020	137.0	0.7

Adjusting Values for Inflation:

$ \text{Value in new-year dollars} = \text{Old value} \times \frac{CPI_{\text{new year}}}{CPI_{\text{old year}}} $

Example: $30,000 \times \frac{141.6}{85.6} \approx 49,626$

Aggregate Expenditure (AE) Model

Components of Aggregate Expenditure

The AE model explains how total spending determines output and income in the short run. The main components are:

$ AE = C + I + G + NX $

• C: Consumption (household spending)

• I: Investment (business spending on capital and inventories)

• G: Government spending

• NX: Net exports (exports minus imports)

Classification of Spending

Transaction	GDP Category
Nestle buys equipment	Investment (I)
Books added to inventory	Investment (I)
Government buys materials for park	Government (G)
Family buys hamburgers	Consumption (C)
American pays for hotel in Banff	Net Exports (NX)

AE Function and Graph

The AE function is typically written as:

$ AE = \text{Autonomous spending} + zY $

Where z is the marginal propensity to spend out of national income.

• Vertical axis: Aggregate Expenditure (AE)

• Horizontal axis: National Income (Y)

• Slope (z): $z = MPC(1 - t) - m$

• Intercept: Autonomous spending (spending when Y = 0)

Example: $AE = 228 + 0.62Y$

• Intercept = 228 (autonomous spending)

• Slope = 0.62 (marginal propensity to spend)

Equilibrium in the AE Model

Equilibrium occurs where $AE = Y$ (the 45° line on the AE diagram).

• If $AE > Y$: Inventories fall, firms increase production.

• If $AE < Y$: Inventories rise, firms decrease production.

• If $AE = Y$: Economy is in equilibrium.

Marginal Propensity to Consume (MPC) and Save (MPS)

MPC is the fraction of additional income that is spent:

$ MPC = \frac{\Delta C}{\Delta Y} $

MPS is the fraction saved:

$ MPS = 1 - MPC $

Example: If MPC = 0.8, then MPS = 0.2.

Investment (I) in AE

• Includes business equipment, buildings, and inventories (not stocks/bonds).

• Determined by expected rate of return, business expectations, technology, operating costs, capital stock, and interest rates.

• More volatile than consumption due to lumpiness and sensitivity to expectations.

Net Exports (NX) in AE

Imports are endogenous (depend on income), exports are exogenous (determined by foreign factors).

$ IM = mY $

$ NX = X - mY $

• If the Canadian dollar appreciates, imports (IM) increase.

• NX = 0 when $Y = \frac{X}{m}$

The Multiplier

The multiplier shows how much equilibrium income changes in response to a change in autonomous spending:

$ \text{Multiplier} = \frac{1}{1 - z} $

$ \Delta Y = \text{Multiplier} \times \Delta \text{Spending} $

Example: If $z = 0.60$, multiplier = $2.5$. A $150 million increase in investment raises income by $375 million.

Fiscal Policy and Output Gaps

• Balanced budget: $T = G$

• Deficit: $G > T$

• Surplus: $T > G$

Recessionary gap: Equilibrium GDP below full employment ($AE < Y_{full}$). Fixed by increasing AE (G↑, T↓, I↑, X↑).

Inflationary gap: Equilibrium GDP above full employment ($AE > Y_{full}$). Fixed by decreasing AE (G↓, T↑, I↓, X↓).

Tax changes have a smaller effect than spending changes because part of tax cuts are saved.

Complete AE Function

$ AE = C + I + G + (X - IM) $

Slope: $z = MPC(1 - t) - m$

Multiplier: $\frac{1}{1 - z}$

Equilibrium: $AE = Y$

Aggregate Demand and Aggregate Supply (AD-AS) Model

Aggregate Demand (AD)

AD shows the total demand for goods and services at different price levels:

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

Why AD slopes downward:

• Wealth effect: Lower prices increase real wealth, boosting consumption.

• Interest-rate effect: Lower prices reduce money demand, lowering interest rates and increasing investment.

• International-trade effect: Lower domestic prices make exports more competitive, increasing net exports.

Shifts in Aggregate Demand

AD shifts when spending changes for reasons other than the price level:

• Consumer confidence, wealth, taxes (C)

• Business expectations, technology (I)

• Government spending or taxes (G)

• Foreign income, exchange rates (X − M)

Aggregate Supply (AS)

Short-Run Aggregate Supply (SRAS): Upward sloping because wages and input prices are sticky. Higher prices increase profits and output.

Sticky wages: Wages and some input costs adjust slowly due to contracts, regulations, or expectations.

Shifts in SRAS:

• Input prices (wages, energy, materials)

• Productivity and technology

• Business taxes, subsidies, regulations

• Inflation expectations

Supply shock: Sudden change in production costs or productivity (e.g., oil price spike, natural disaster).

SRAS Shift Table

Cause	SRAS Shift	Result
Input prices fall, productivity rises	Right	Output ↑, Price level ↓
Input prices rise, productivity falls	Left	Output ↓, Price level ↑

Long-Run Aggregate Supply (LRAS) and Potential Output (Y*)

• LRAS is vertical at potential output (Y*), determined by resources, technology, and institutions.

• Short run: Y* fixed; Long run: Y* increases if productive capacity rises (e.g., more labour, better education).

Automatic Stabilizers and Fiscal Policy

Automatic Stabilizers

• Parts of the budget that change automatically with GDP (e.g., taxes, EI, welfare).

• During recession: Taxes ↓, transfers ↑, deficit ↑ (supports AD).

• During boom: Taxes ↑, transfers ↓, deficit ↓ (restrains AD).

• Reduce the size of the multiplier and dampen economic fluctuations.

Discretionary fiscal policy: Deliberate changes in G or T, requiring government action.

Loanable Funds Market

Supply and Demand for Loanable Funds

• Supply: Household saving

• Demand: Business investment

• Interest rate: Adjusts to balance supply and demand

Event	Curve Shift	Interest Rate Effect
Business optimism rises	Demand right	Interest rate rises
Business taxes increase	Demand left	Interest rate falls
Tax-free saving limits rise	Supply right	Interest rate falls

Summary Table: Key Formulas

Concept	Formula (LaTeX)
Nominal GDP	$\sum Q_t \times P_t$
Real GDP	$\sum Q_t \times P_{base}$
Inflation Rate	$\frac{CPI_t - CPI_{t-1}}{CPI_{t-1}} \times 100$
Value Adjustment	$\text{Old value} \times \frac{CPI_{new}}{CPI_{old}}$
AE Slope (z)	$MPC(1 - t) - m$
Multiplier	$\frac{1}{1 - z}$
Change in Income	$\Delta Y = \text{Multiplier} \times \Delta \text{Spending}$
Imports	$IM = mY$
Net Exports	$NX = X - mY$

Additional info: Where slides were fragmented or brief, standard macroeconomic context and definitions were added for completeness and clarity.