Aggregate Expenditure Model Notes

Aggregate Expenditure Model of the Short Run

Components of Aggregate Expenditure

  • Consumption (C)

  • Planned Investment (IP): Spending by firms on capital goods.

  • Government Purchases (G)

  • Net Exports (NX): Trade balances.

  • Macroeconomic equilibrium occurs where production and consumption intersect.

  • Will cover the multiplier effect, aggregate demand curve, and a numerical example.

Aggregate Expenditure Model

  • A macroeconomic model focusing on the short-run relationship between total spending and real GDP.

  • Assumes a constant price level.

Components of Aggregate Expenditure (AE)

  • AE=C+IP+G+NXAE = C + IP + G + NX

    • AE: Aggregate Expenditure.

    • IP: Planned Investment (planned spending by firms on capital goods).

Planned vs. Actual Investment

  • Example: Restaurant anticipating selling 10 portions of food daily.

  • Difference arises due to unexpected changes in demand.

  • In equilibrium, focus is on planned aggregate expenditure (demand side) and GDP (supply side/production).

Macroeconomic Equilibrium

  • Planned aggregate expenditure = GDP.

  • If Planned Aggregate Expenditure > GDP:

    • Inventories fall.

    • GDP and employment increase (need to produce more).

  • If Planned Aggregate Expenditure < GDP:

    • Inventories rise.

    • GDP and employment decrease (overproduction).

Components of Aggregate Expenditure (2021 Data)

  • Data from 2021, figures in millions of $2012 dollars (real expenditures).

    • Consumption: $1,200,000

    • Investment: $378,000

    • Government Spending: $407,000

    • Net Exports: -$77,000

  • Real consumption has risen steadily since the 1980s.

Determinants of Consumption

  • Current Disposable Income (YD):

    • YD=Y+Transfer−TaxYD = Y + \text{Transfer} - \text{Tax}

    • Y: Overall Income

  • Household Wealth:

    • Household Wealth=Assets−Liabilities\text{Household Wealth} = \text{Assets} - \text{Liabilities}

    • Assets: Properties, stocks, etc.

    • Liabilities: Mortgages, student loans, etc.

    • Positively correlated with consumption (higher wealth leads to higher consumption).

  • Expected Future Income:

    • Higher expected future income leads to higher current consumption.

    • Example: Students investing in education for higher future income.

  • Price Levels:

    • If price of goods rises, real wealth decreases, leading to a decrease in consumption.

    • If price goes down, real wealth increases, leading to increase in consumption.

  • Interest Rate:

    • Focus on real interest rate (nominal interest rate - inflation).

    • If real interest rate increases:

      • Saving goes up.

      • Consumption decreases.

      • More expensive to borrow for firms.

    • If real interest rate decreases:

      • Saving decreases.

      • Consumption increases.

      • Cheaper to borrow for firms.

Consumption Function

  • Includes autonomous consumption (C bar) and disposable income.

  • C=Cˉ+c⋅YDC = \bar{C} + c \cdot YD

    • $\bar{C}$: Autonomous consumption (level of consumption regardless of disposable income).

    • c: Marginal Propensity to Consume (MPC) - fraction of disposable income consumed (typically between 0 and 1).

  • YD=Y+Transfer−TaxesYD = Y + \text{Transfer} - \text{Taxes}

Marginal Propensity to Consume (MPC)

  • MPC=ΔCΔYDMPC = \frac{\Delta C}{\Delta YD}

  • Example: Consumption spending increases by $39.7 billion, disposable income increases by $51.9 billion.

    • MPC=39.751.9=0.76MPC = \frac{39.7}{51.9} = 0.76

    • Interpretation: For every $1 increase in disposable income, consumption increases by $0.76, and $0.24 goes to savings.

Income, Consumption, and Savings at the National Level

  • GDP (Y) components: Y=C+IP+G+NXY = C + IP + G + NX

  • For simplicity, ignoring international trade (NX).

  • Assuming investment equals savings and government spending equals taxes (balanced budget).

    • Y=C+S+TY = C + S + T

  • Changes in national income: ΔY=ΔC+ΔS+ΔT\Delta Y = \Delta C + \Delta S + \Delta T

  • Assuming taxes do not change (ΔT=0\Delta T = 0): ΔY=ΔC+ΔS\Delta Y = \Delta C + \Delta S

  • Dividing by changes in income: ΔYΔY=ΔCΔY+ΔSΔY\frac{\Delta Y}{\Delta Y} = \frac{\Delta C}{\Delta Y} + \frac{\Delta S}{\Delta Y}

    • 1=c+s1 = c + s

    • c: Marginal propensity to consume.

    • s: Marginal propensity to save.
      Interpreted as the proportion of dollars spent on either consumption or savings.

Example Calculation

  • Year 1: Real GDP = 900, Consumption = 800, Saving = 100

  • Year 2: Real GDP = 1000, Consumption = 860, Saving = 140

    • ΔY=100,ΔC=60,ΔS=40\Delta Y = 100, \Delta C = 60, \Delta S = 40

    • MPC=60100=0.6MPC = \frac{60}{100} = 0.6

    • Marginal propensity to save =40100=0.4= \frac{40}{100} = 0.4

    • A $1 increase in income will lead to a $0.6 increase in consumption and a $0.4 increase in savings.

Planned Investment

  • Factors influencing planned investment:

    • Expectations of future profits (optimistic vs. pessimistic).

    • Real interest rate (high rate discourages borrowing, low rate encourages borrowing).

    • Taxes (corporate taxes can disincentivize investment).

    • Cash flow (cash revenue - cash spending).

Government Purchases

  • Real government spending has risen steadily.

  • Governments may borrow to fund expenditures.

Net Exports

  • Positive net export: Exports > Imports.

  • Negative net export: Imports > Exports.

Macroeconomic Equilibrium (Graphical Representation)

  • Vertical axis: Real Aggregate Expenditure (AE).

  • Horizontal axis: Real National Income (Y) or GDP.

  • Equilibrium: Aggregate Expenditure = Real National Income (along the 45-degree line).

  • Aggregate Expenditure Components: Consumption + Planned Investment + Government Purchases + Net Exports.

Equilibrium and Disequilibrium

  • AE > Y: Inventories fall, economy expands, unemployment falls.

  • AE < Y: Inventories rise, economy enters a recession, unemployment rises.

  • Equilibrium occurs at the intersection of the 45-degree line and the aggregate expenditure function, implying the natural rate of unemployment.

Real GDP and Planned Aggregate Expenditure

  • If Planned Aggregate Expenditure > Real GDP, then Real GDP will increase to meet expenses.

  • If Planned Aggregate Expenditure < Real GDP, there is an overproduction and the GDP will decrease, potentially leading to a recession.

Multiplier Effect

  • Consumption function: C=30+0.8YDC = 30 + 0.8YD (YD = Y, no taxes or transfers).

  • Planned investment (I) = 75.

  • Equilibrium income calculation.

Planned Aggregate Expenditure (PAE)

  • PAE=C+I+G+NXPAE = C + I + G + NX

  • Where G and NX are assumed to be zero for simplicity.

  • PAE=30+0.8Y+75=105+0.8YPAE = 30 + 0.8Y + 75 = 105 + 0.8Y

Equilibrium Calculation

  • In equilibrium, Y = PAE

  • Y=105+0.8Y  ⟹  0.2Y=105  ⟹  Y=525Y = 105 + 0.8Y \implies 0.2Y = 105 \implies Y = 525

General Formula for Equilibrium Calculation

  • PAE=Cˉ+c⋅YD+IˉPAE = \bar{C} + c \cdot YD + \bar{I}

  • Autonomous spending =Cˉ+Iˉ=PAEˉ= \bar{C} + \bar{I} = \bar{PAE}

Equilibrium

  • Y=PAEˉ+c⋅YY = \bar{PAE} + c \cdot Y

Isolating Y:

  • Y(1−c)=PAEˉY(1 - c) = \bar{PAE}

  • Y=PAEˉ1−cY = \frac{\bar{PAE}}{1 - c}

Example: Increase in Business Confidence

  • Investment increases from 75 to 80.

  • New PAE bar = 110 (Cˉ+Iˉ=PAE)(\bar{C} + \bar{I} = PAE)

New Equilibrium GDP

  • Y=PAE1−c=1100.2=550Y = \frac{PAE}{1 - c} = \frac{110}{0.2} = 550

Expenditure Multiplier

  • The investment increased by $5, but equilibrium has increased by $25, illustrating the multiplier effect.

Exploring the Multiplier Effect

  • The multiplier is the change in GDP / the change in investment: 255=5\frac{25}{5} = 5

Intuition Behind the Multiplier Effect

  • $5 added into the economy leads to an increase in GDP by more than $5 dollars.
    *A business buys a computer for $5
    *Computer store receives $5 and spends 0.8 of it = $4
    *Computer part manufacturer receives $4 and spends 0.8 of it = $3.2
    *Mathematical formula to calculate the sum of each of these values:

Adding:
5+4+3.2+2.56+…5 + 4 + 3.2 + 2.56 + …
Factor 5 from the first term (common ratio=0.8\text{common ratio} = 0.8
5(1+0.8+0.82+0.83+…)5(1 + 0.8 + 0.8^2 + 0.8^3+ …)
Using the geometric series:
a1−r\frac{a}{1 - r}
where 'a' is the first term and 'r' is the common ratio:
5∗11−0.8=255* \frac{1}{1 - 0.8} = 25

Multiplier Effect Summary

  • Multiplier effect is present when autonomous expenditure increases.

Multiplier Effect Decreases

  • If we decrease autonomous expenditure, let's say decreasing in investment reduces the GDP by $25

What makes the economy more sensitive to autonomous expenditure

  • Determined by Marginal Propensity to Consume.

  • Larger the marginal propensity to consume, the bigger the multiplier effect.

Mathematical Expression to Calculate a Larger Effect

Multiplier = 11−c\frac{1} {1-c}

If the MPC increases, then (1-MPC) decrease thus a higher value for the multiplier.

Aggregate Demand

  • Price levels play a part in increasing or decreasing a person's real wealth.

  • Price levels play a major roll.

Aggregate Demand Curve

  • Prices are on the vertical axis and Real GDP (Y) on the horizontal axis.

  • Economy wide demand, a downward trending line.

Macroeconomic Equilibrium

*Intersects that planned aggregate expenditure function with the 45 degree line

Price Shift with a new Macroeconomic Equilibrium (PAE to PAE2)

  • Price and GDP increased: Y1 to Y2.
    Price P2 to the aggregate demand has increased and is above the initial price P1.

  • The aggregate Demand curve is a negative correlation.

Story of Correlation:
Price levels increase. so people feel poorer
So your initial real wealth has decreased and as a result the Consumption decreases.

Export decrease = imports increase = Net export FALLS. = GDP fall.

Story #2

If prices increase: Canadian Exports become expensive, foreign imports become cheaper.
GPD FALLS.

Numeral Example: Equilibrium Real GDP

Based on four functions.
C=100+0.8YC = 100 + 0.8Y
PlanInvestment=125Plan Investment = 125
GovernmentExpenditure=125Government Expenditure = 125
Net EXPORT is at negative 30 indicating imports are more that Exports.
What is the Potential GDP in Equilibrium?

IN Equilibrium

Income or GDP (Y) WILL = Aggregate Expenditure AE:

Isolate all GDP(Y):
0.2Y=100+125+125−300.2Y = 100 + 125+ 125 -30\n Solve:
Y=1600Y = 1600
Draw the chart.
Multiplyer Value:
11−MPC=5\frac{1}{1- MPC} = 5
Govt spending increases by 20;
Multiply this and that how you know what impact it would have on a chart.
5 * $20 = $100 the initial GDP will increase by 100.