Question

The closed economy model with government is considered. We observe following values of autonomous expenditures: Co = 150, Io = 50, Go = 100, To= 50. Marginal propensity to consume equals 0.8, investment sensitivity parameter equals 5 and income tax rate equals 20%. Using this information find IS curve and derive it graphically.

Answer 1

Pago no Co=150..Io -50, Go = 100, To - 50 MPC = 0.8 Anv. Sensitivity = 5, Income tax rate (t)= 20). Consumption_Function : c = 'Cot byd C = 150+ 0.8 (Y-To-ty) where b: MPC=0.8 - Ya: Disposable income - after deducing taxes ca 150+ 0.84 – 0.8T. - 0.8 X0.2 X Y I where t = 20%= 0.9 Now, Investment function : I - I. * Ci where Io : Autonomous Investment 250 - c: garestment sensitivity = 5 ľ : Interest Rate. > I = 504 51 Now IS Equation : Y - C + I +G + NX y = 150 +0.8 Y - 0.8 To - 0.8 X 0.2 xy + 50*5 + 100 Y-150 +0.89 - 0.8X50 - 0.8x0.2X Y +50*51 + 100 [: To -507 Y = 300 + 0.8 Y - 0,8x0.2XY + 51 4 0.8% SO y = 260 t 0.84 – 0.16 Y + 51 Y-0.64 Y = 26051 DELTA My NoteBook 0.36 Y = 2605

Date / – Page no. 2 1 0 .30 0.36 z > Ya entre 200-51] Y-- 100 (260-51] 1 Y= 25 f260-5i | - a Egiuation of . I's curve. * Graphical Derivation : I = 50-51 Tet T = 20% then I = 50-5X = 50-7 sig Now if 16% j a - then I = 50-5x16 = 50-0.8=49.2 Too When i = 20% then AD=14 ct. ItG = 7 ! ! ! ~ 4: 25 [280-51 | It! 9 " 4-25 1260-5X 0.27 4= 25 (260-1 . > 4= 251x2.59 Y = 719.44 1

Page ndes Date / 16 If I'= 16% then I'=49.2 and 4 = 25 (260-5. y'= 25 (260- 0.8 y'= 258 259.2 · 259.2 Y=720 Summary: When i risa faus from Y increases from Y to y an increase in I from i Investment Ala Funcion AS į to i due to I to I? --- - AD'=C+I+9 KAD=C+I+q ---- titt IⓇI tin to *). 49.2 49 I 44 719.44 curve 442Y 720 Is HIS y 719.44 720 Interest Rate falls - Investment increases DELTA My NoteBook → gncome anciens.