Question

1. Points = 18. Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 (<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars p> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If we know the parameters of the system, find the numerical value of the equilibrium GDP (Y) as well as the equilibrium levels of C, I, and T (3 points); Parameters' values are as follows: a = 10; b=0.7; f= 3; j=0.2; k= 25;r=0.03. Endogenous Government Expenditure is Go = 55. 4) Find the government-expenditure multiplier and discuss its economic meaning (3 points); 5) Find the non-income tax multiplier and discuss its economic meaning (3 points); 6) Find the extent to which an increase in the income tax rate () will affect the equilibrium income Y* (3 points).

Answer 1

(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 = $\dpi{80} \partial$ Y/$\dpi{80} \partial$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.