Introduction to Macroeconomics: Math App - Lecture 008

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Department
Economics for Management Studies
Course
MGEA06H3
Professor
Iris Au
Semester
Winter

Description
30 January 2013 CHAPTER 22: ADDING GOVERNMENT AND TRADE TO THE SHORT-RUN MODEL [CONT’D] Effect of a Change in Autonomous AE(AE ) on Y 0 Our extended model (IM = 0, 0nd hold r and E constant) Generic Form Numerical Example C = C 0 C D1 C = 20 + 7/8DI T = T0+ T 1 T = -20 + (2/7)Y TR = TR 0 TR Y 1 TR = 220 – (1/7)Y I = 0 – d(r – ṝ), where r = ṝ I = 100 G G = 250 X = X 0 X (1 – Ē), where E = Ē X = 120 IM = im Y1+ im (2 – Ē) IM = 1/8Y AE = (C 0 C D1) + I +0G + X – 0M Y 1 = (C + C [Y – (T + T Y) + (TR – TR Y)] + I + G + X – IM Y 0 1 0 1 0 1 0 0 1 = (C0+ I 0 G + X +0C TR1– C0T ) 1 0C (1 –1T – TR 1 – IM1] Y 1 We recall that DI = Y – T + TR, we then replace DI with income minus the tax function plus the transfer payment function. Afterwards, we regroup the equation into two parts: those independent of Y (autonomous terms) and those dependent on Y. The autonomous terms will then become the autonomous expenditure (AE ). The terms dependent on Y represent how much aggregated expenditure 0 will change when income changes (C ). Y Y* = (C0+ I0+ G + X +0C TR1) /0(1 – [C (12– T – T1 ) – 1M 1 = AE 0 (1 – C )Y We then isolate for Y. M = Y* / AE 0 = 1 / (1 – C ) Y = 1 / (1 – [C1(1 – T 1 TR )1– IM ] 1 NOTE: Changes in C , T , TR and IM will lead to a change in M. 1 1 1 1 Example #2 In Numerical Form AE = 700 + 3/8Y Y*= 1120 M = 1 / (1 – 3/ 8) = 1.6 A Change in Government Spending, G Suppose G increased by 70 (G increased to 320). What happens to Y? Find the New AE Function AE = (C 0 I 0 G + X +0C TR1– C0T ) 1 0C (1 –1T – TR 1 – IM1] Y 1 When G increased by 70, AE incre0sed by 70 (G affects AE directly as G is a part of the AE equation) 0 AE = (700 + 70) + 3/8Y = 770 + 3/8Y Y = 770 + 3/8Y 5/8Y = 770 Y* = 1232 (Y* increased by 112) Using the Multiplier we will find the Same Change in Y* AE = C + I + G + X + C TR – C T 0 0 0 0 1 0 1 0 CY= C 11 – T –1TR ) –1IM 1 Y* = AE x 1 / (1 – C ) = AE x M = G x M = 70 x 1.6 = 112 0 y 0 New Y* = Initial Y* + Y* = 1120 + 112 = 1232 What happens to the budget? Method 1: Finding the New Values of T, TR, and G New T: T = (2/7) Y – 20 = 2/7(1232) – 20 = 323 (increased by 32) When income goes up, the government collects more taxes from us. New TR: TR = 220 – (1/7) Y = 220 – 1/7(1232) = 44 Income and transfers are inversely related, so if income goes up, the new value of transfers should be lower than the initial one. Budget Balance: Budget balance = T – TR – G = 332 – 44 – 320 = -32 The initial budget deficit was 10. An increase in G leads to a larger budget deficit. Method 2: Calculating the Change in Budget
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