“∆” the Change Operator:
Suppose the initial value of the variable Y is 10. If Y increases to 20 then
Change in Y = (20 – 10) = 10.
Define, ∆Y = Change in Y.
Rule # 1
If
Y = X + Z, where Y, X, Z are all variables
Then
∆Y = ∆X + ∆Z
If
Y = X - Z, where Y, X, Z are all variables
∆Y = ∆X - ∆Z
Rule#2
If Y = a + bX, where a and b are constants and Y and X are variables
Then
∆Y = ∆a + b∆X
∆a = 0, if a is a constant and remains as a constant.
Application:
RGDP = Y = Income = Expenditure.
T = Net Taxes
Y-T = Disposable income. Part of the disposable income is used to finance consumption expenditure and
the rest is saved.
Disposable income = Consumption + Households Savings,
(Y-T) = C + PrS, Where, PrS = Households savings = Private sector’s savings. Now apply Rule 1.
∆(Y – T) = ∆C + ∆PrS
Divide the equation by ∆(Y – T) –
, or
( – ) ( – ) ( – )
( – ) ( – )
MPC + MPS = 1
b + s = 1, where b = MPC, s = MPS.
Therefore b = 1-s, or s = 1-b. We assume that b is a constant and it is greater than zero but less than 1.
Why is b a constant? It tells us about households’ preference. Preference does not change
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