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Chapter 10 for final exam studying

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Expenditure Plans and the Circular Flow

Aggregate Planned Expenditure

The aggregate planned expenditure (AE) is the total amount of spending planned in an economy, including consumption, investment, government purchases, exports, and imports. The formula for aggregate planned expenditure is:

  • AE = C + I + G + X - IM

  • C: Planned consumption spending

  • I: Planned business investment spending

  • G: Planned government purchases

  • X: Planned exports

  • IM: Planned imports

In the circular flow model, aggregate spending equals aggregate income (Y), so:

  • AE = Y in equilibrium

Income, Spending, Saving, and Taxes

All income in the economy is either spent, saved, or taxed:

  • Y = C + S + T

  • Where S is savings and T is net taxes

Rearranging the aggregate expenditure equation gives:

  • I + G + X = S + T + IM

  • This shows that injections (I, G, X) must equal leakages (S, T, IM) in equilibrium

Injections and Leakages

Injections are sources of spending that do not originate with consumers, such as government purchases, business investment, and exports. Leakages are uses of income that remove spending from the circular flow, such as savings, taxes, and imports.

  • Injections = I + G + X

  • Leakages = S + T + IM

Equilibrium occurs when injections equal leakages.

Graph showing equilibrium where injections equal leakages

The Bathtub Model

The bathtub model is a metaphor for the circular flow of income. If injections exceed leakages, the 'water level' (real GDP) rises. If leakages exceed injections, the water level falls. Prices are assumed fixed, so all adjustments occur through changes in real GDP.

  • If injections > leakages, real GDP increases

  • If leakages > injections, real GDP decreases

The Consumption Function and Marginal Propensities

Consumption Function

The consumption function shows the relationship between planned consumption (C) and disposable income (YD):

  • C = 0.8YD

  • YD = Y - T, where T is taxes (e.g., T = 100)

  • So, C = 0.8(Y - 100) = 0.8Y - 80

The marginal propensity to consume (MPC) is the fraction of a change in disposable income that is spent on consumption. In this example, MPC = 0.8.

Savings Function and Marginal Propensity to Save

All disposable income is either spent or saved:

  • C + S = YD

  • S = YD - C

  • Given C = 0.8YD, S = 0.2YD

The marginal propensity to save (MPS) is the fraction of a change in disposable income that is saved. Here, MPS = 0.2.

  • MPC + MPS = 1

Autonomous and Induced Spending

Autonomous spending is the part of aggregate planned expenditure that does not depend on real GDP (Y). In the simple AE model, investment (I), government spending (G), and exports (X) are assumed fixed:

  • I = 250

  • G = 150

  • X = 180

Induced spending depends on real GDP. For example:

  • C = 0.8Y - 80

  • IM = 0.3Y (planned imports depend on income)

The marginal propensity to import (MPIM) is the fraction of a change in income spent on imports (0.3 in this example).

The Aggregate Expenditure Model

Aggregate Expenditure Equation

The aggregate expenditure model combines all components:

  • AE = C + I + G + X - IM

  • Given the values above:

Tabular Example of Planned Expenditure

The following table illustrates how aggregate planned expenditure is calculated for different levels of real GDP:

Row

Real GDP (Y)

Consumption (C)

Investment (I)

Government Purchases (G)

Exports (X)

Imports (IM)

Aggregate Planned Expenditure (AE)

A

600

400

250

150

180

180

800

B

800

540

250

150

180

240

1000

C

1000

720

250

150

180

300

1000

D

1200

880

250

150

180

360

1100

E

1400

1040

250

150

180

420

1200

Table of planned expenditure at different levels of real GDP

Graphical Representation of Equilibrium

Equilibrium expenditure occurs where aggregate planned expenditure equals real GDP. This is shown where the AE function crosses the 45º line on a graph. At equilibrium:

  • AE = Y

  • Using the equation:

  • Solving:

At this point, unplanned inventory changes are zero, and the economy is in equilibrium.

Row

Real GDP (Y)

Aggregate Planned Expenditure (AE)

Unplanned Inventory Changes (Y - AE)

A

600

800

-200

B

800

1000

-200

C

1000

1000

0

D

1200

1100

100

E

1400

1200

200

Graph showing aggregate expenditure equilibrium where AE equals Y

Injections, Leakages, and Equilibrium

Equilibrium in the aggregate expenditure model is achieved only when injections equal leakages. If real GDP is below equilibrium, injections exceed leakages, causing GDP to rise. If real GDP is above equilibrium, leakages exceed injections, causing GDP to fall. At equilibrium, there is no tendency for GDP to change.

  • Below equilibrium: AE > Y, GDP rises

  • Above equilibrium: AE < Y, GDP falls

  • At equilibrium: AE = Y, GDP stable

Summary Table: Key Formulas

Concept

Formula

Aggregate Planned Expenditure

Consumption Function

Imports Function

Equilibrium Condition

Equilibrium Solution

MPC + MPS

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