Question

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   

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.

1. Solve for the new equilibrium level of national income.
2. Calculate the size of the

i)   New multiplier   

            ii) Trade balance  

iii) Budget balance

4. Assume the full employment level of national income (YF ) is at $280 billion. In order to reach YF from the existing equilibrium income level in ( 3 ) above, calculate the required changes, ceteris paribus, in

a)         Government spending ( G )

b)         Autonomous taxes ( Ta )

c)         The tax rate (t)   

Answer 1

(I) Private closed economy

(Part a)

Y = C + I

Y = 10 + 0.9Y + 15

0.1Y = 25

Y = $250 billion

(Part b)

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.9) = 1/0.1 = 10

(Part c)

(i)

PAE = C + I

PAE = 10 + 0.9Y + 15

PAE = 25 + 0.9Y

When Y = 0, PAE = 25 (Vertical intercept)

In following graph, planned aggregate expenditure (PAE) and real GDP (Y) are measured vertically and horizontally respectively. Initial Equilibrium is at point A where 450 line intersects initial aggregate expenditure curve PAE0 (with vertical intercept of 25), with equilibrium GDP Y0 (= 250) and planned aggregate expenditure E0 (= 250).

PAE 450 250 PAEO 25 250 у

(ii)

S = Y - C

S = Y - 10 - 0.9Y

S = 0.1Y - 10

When Y = 0, S = - 10 (Vertical intercept)

In following graph, Saving (S0) and Investment (I0) are shown, where investment is horizontal straight line (being autonomous). Initial Equilibrium is at point A where S0 intersects investment curve I0, with equilibrium GDP Y0 (= 250) and equilibrium saving/investment I0 (= 15).

SI IS А. I 250 Yo у -10

(II) Private economy with government

(Part a)

Y = C + I + G

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

Y = 50 + 0.9(0.9Y - 5)

Y = 50 + 0.81Y - 4.5

0.19Y = 45.5

Y = $239.47 billion

NOTE: As per Chegg's Policy, I've answered 1st 4 parts only. You need to post rest of the parts separately, 4 at a time.