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**Simple Keynesian Model**

National Income Determination Four-Sector National Income Model

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**Outline Four-Sector Model Import Function M = f(Y)**

Export Function X = f (Y) Net Exports X - M Aggregate Expenditure Function E = f(Y) Output-Expenditure Approach: Equilibrium National Income Ye

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**Outline Factors affecting Ye Expenditure Multipliers k E**

Tax Multipliers k T Balanced-Budget Multipliers k B Injection-Withdrawal Approach: Equilibrium National Income Ye

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Four-Sector Model With the introduction of the foreign sector (i.e. w/ households C, firms I, government expenditure G) aggregate expenditure E consists of one more component, net exports X- M. E = C + I + G + (X - M) Still, the equilibrium condition is Planned Y = Planned E

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Import Function Imports M is usually assumed to be a function of national income Y. M = M’ M = mY M = M’ + mY M and Y are assumed to be positively correlated. M = M’ + mY is the typical form being used

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**Import Function Autonomous Imports M’**

this is the y-intercept of the import function M’ is an exogenous variable, i.e., independent of the income level Y and is determined by forces outside the simple Keynesian 4-sector model

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**Import Function Marginal Propensity to Import MPM = m**

this is defined as the change in imports per unit change in income Y, i.e., m = M / Y it is the slope of tangent of the import function it is usually assumed to be a constant m = 0 or m is a +ve number MPM is also an exogenous variable

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**Import Function Average Propensity to Import APM**

it is the ratio of total imports to total income, i.e., APM = M / Y it is the slope of ray of the import function APM when Y except M = mY when MPM = APM = m

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**Import Functions M M M Y Y Y M = M’ y-intercept = M’**

slope of tangent = 0 slope of ray as Y M = mY y-intercept = 0 slope of tangent = m slope of ray = m M = M’ + mY y-intercept = M’ slope of tangent = m slope of ray as Y M M M Y Y Y

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**Export Function X = f (Y)**

this is a relationship between the amount of exports X and national income Y it is usually assumed to be an exogenous function X = X’ We always consider the amount of net exports, i.e., X - M Net exports = X - M = X’ - M’ - mY

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Net Exports When net exports is positive, i.e., when X > M, the external sector BOP is in surplus When net exports is negative, i.e., when X < M, the external sector BOP is in deficit When net exports is zero, i.e., when X = M, the external sector BOP is in balance {Trade deficit/surplus v.s. Budget deficit/surplus}

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**Net Exports M, X M = M’ + mY External Deficit X = X’ Y Y1 Y2 Y3**

Surplus How can you determine Ye from this diagram? Y Y1 Y2 Y3

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**Aggregate Expenditure Function**

E = C + I + G + (X - M) C = C’ + cYd T = T’ + tY I = I’ G = G’ X = X’ M = M’ + mY E =

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**Aggregate Expenditure Function**

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**Output-Expenditure Approach**

In equilibrium Y = E Y = ( )Y = Y = k E * E’ k E = E’ =

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**Factors affecting Ye Change in E’ If X’ E’ E Y **

If M’ E’ E Y Change in slope of tangent of E / k E If m c-ct- m E steeper Y

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Import Multiplier k M It is the ratio of change in national income Y to a change in autonomous import M’ Y = M’ -1 1 - c - m + ct

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**Injection-Withdrawal Approach**

S, T, M, I, G, X S = -C’+cT’-T’ + (1-c)Y if T = T’ I+G+X=I’+G’+X’ M= M’+ mY T = T’ Y

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Copyright 2005 © McGraw-Hill Ryerson Ltd.Slide 0.

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