jb_nc said:
AD = y = GDP = (C + I + (G-T) + (X-M))
Yea well-
C= a + bYD
and YD= Y - NT
and NT= tY
Therefore, C= a + b(Y - tY)
C= a + b(1-t)Y
Now, M equals the Marginal Propensity to Import (m) x Y Therefore, mY
Substituting into AE-
AE= a + b(1-t)Y + I + G + X - mY
= a + I + G + X + b(1-t)Y - mY
= a + I + G + X + [b(1-t) - m]Y
Now, a + I + G + X are components of AUTONOMOUS EXPENDITURE (A)= assumed to be independent of changes in real GDP. C and M are considered to be dependent upon the level of real GDP and deemed INDUCED EXPENDITURE.
Therefore, AE= A + [b(1-t) - m]Y
Now when Eq'm Expenditure occurs, Aggregate Planned Expenditure (AE) equals Real GDP (Y). Therefore, AE=Y
Y= A + [b(1-t) - m]Y
Rearranging-
Y= 1/1- [b(1-t) - m] x A
Therefore, a change in A causes a 'multiplied' change in Y and 1/1- [b(1-t) - m] is the size of the multiplier. As this is the slope of the Aggregate Expenditure Curve, the steeper the curve the larger the multiplier.
Hence, the multiplied effect is larger the greater our MPC (b), the smaller the Marginal Tax Rate (t) and the smaller the MPI (m).
Keynes was a fucking genius!