(1)
(i) Goods market equilibrium occurs when GDP (Y) equals planned aggregate expenditure (PAE = C + I + G).
(ii) Consumption includes an autonomous component (a) and an induced component as function of disposable income (Y - T).
(iii) Investment includes an autonomous component (a) and an induced component as function of GDP (rY).
(iv) Government spending is autonomous.
(v) Total tax includes an autonomous component (f) and an induced component as function of GDP (jY).
(2)
Y = a + b[Y - (f + jY)] + k + rY + G0
Y = a + b[Y - f - jY] + k + rY + G0
Y = a + bY - bf - bjY + k + rY + G0
(1 - b + bj - r)Y = a - bf + k + G0
Y = (a - bf + k + G0) / (1 - b + bj - r)
(3)
Plugging in given values,
Y = [10 - (0.7 x 3) + 25 + 55] / [1 - 0.7 + (0.7 x 0.2) - 0.03]
Y = (90 - 2.1) / (0.27 + 0.14)
Y = 87.9 / 0.41
Y = 214.39
T = 3 + (0.2 x 214.39) = 3 + 42.88 = 45.88
C = 10 + 0.7 x (214.39 - 45.88) = 10 + 0.7 x 168.51 = 10 + 117.96 = 127.96
I = 25 + (0.03 x 214.39) = 25 + 6.43 = 31.43
(4)
Government expenditure multiplier = Y/G0 = 1 / (1 - b + bj - r) = 1 / (1 - 0.7 + 0.7 x 0.2 - 0.03) = 1 / (0.27 + 0.14) = 2.44
It means that as government spending increases (decreases) by 1 unit, GDP (Y) increases (decreases) by 2.44 units.
NOTE: As HOMEWORKLIB Answering Policy, 1st 4 parts have been answered.
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