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Lecture

the Change Operator.pdf

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Department
Economics
Course
ECON 2000
Professor
Mokhles Hossain
Semester
Fall

Description
“∆” 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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