Week 6 In-Class Problem

We had to solve the transactions matrix given changes in Theta:


Period 2
Given: G = 20, Y=38.5
T = (Theta) * Y = .2*38.5 = 7.7
YD = Y – T = 38.5 – 7.7 = 30.8
C = (Alpha1) * YD + (Alpha2) * (H-1) = (.6 * 30.8) + (.4 * 0) = 18.5
(ChgHs) = G – T = 20 – 7.7 = 12.3
(ChgHh) = YD – C = 30.8 – 18.5 = 12.3
H = (ChgH) + (H-1) = 0 + 12.3 = 12.3

(Theta) Changes to .3
Period 2:
G = 20
Y = G/(1-(Alpha1)+(Alpha1 * Theta) = 20/(1-.6+[.6*.3]) = 34.5
T = (Theta) * Y = 10.35
YD = (Y-T) = 24.15
C = (Alpha1) * YD + (Alpha2) * (H-1) = 14.5
(ChgHs) = G – T = 9.65
(ChgHh) = YD – C = 9.65
H = (ChgH) + (H-1) = 9.65

Period 3:
G = 20
Y = Y2 + (Alpha2)*H-1 = 34.5+(.4)*(9.65) = 38.36
T = (Theta) * Y = 11.51
YD = (Y-T) = 26.85
C = (Alpha1) * YD + (Alpha2) * (H-1) = 19.97
(ChgHs) = G – T = 8.49
(ChgHh) = YD – C = 6.88
H = (ChgH) + (H-1) = 8.49 + 9.65 = 18.14