Question

3. Now add the foreign sector to the model so that Y = C + I + G + [ X - M ] where the new variables are: X = Xa = 40, and M = Ma + mY = 5 + 0.11Y. The other variables remain the same as in question 2. Solve for the new equilibrium level of national income. Calculate the size of the i) New multiplier ii) Trade balance iii) Budget balance

Please see my previous questions. Thanks!

1.   Assume a private, closed economy where Y = C + I, and C = 10 + 0.9Y and   I = 15. (Values in $ billions.)

1. Solve algebraically for the equilibrium level of national income.
2. Calculate the value of the multiplier.  
3. Solve graphically for the equilibrium income by constructing an accurate

i) The 45 degree graph

ii) savings/investment graph   

2. Now add the government sector to the model so that Y = C + I + G where C = 10 + 0.9[Y – T] , I = 15, G = 25, T = Ta + tY = 5 + 0.10Y.  

   

a)         Solve for the new equilibrium level of national income.

b)         Calculate the size of the

i) new multiplier

                        ii) budget balance

Answer 1

(3)

(i)

Multiplier = 1 / [1 - MPC( x (1 - Tax rate) + MPM]

= 1 / [1 - 0.9 x (1 - 0.1) + 0.11]

= 1 / [1 - (0.9 x 0.9) + 0.11]

= 1 / (1.11 - 0.81)

= 1 / 0.3

= 3.33

(ii)

Y = C + I + G + X - M

Y = 10 + 0.9(Y - 5 - 0.1Y) + 15 + 25 + 40 - 5 - 0.11Y

Y = 85 + 0.9 x (0.9Y - 5) - 0.11Y

Y = 85 + 0.81Y - 4.5 - 0.11Y

0.3Y = 80.5

Y = $268.33 billion

M = 5 + 0.11 x 268.33 = 5 + 29.52 = 34.52

Trade balance = X - M = 40 - 34.52 = $5.48 billion

(iii)

T = 5 + 0.1 x 268.33 = 5 + 26.83 = 31.83

Budget balance = T - G = 31.83 - 25 = $6.83 billion