Question

III. Suppose the country succeeds in the establishment of a government entity (G). Also, it decides to open its economy to international trade such that the new economy is defined by the following functions:

C = 100 + 0.5Y^d

I = 50

G = 100

NX = 30

TR = 50

TA = 25

1. Find the equilibrium level of income and multiplier in this model.
2. Suppose governments transfers (TR) increases to 100, what is the effect of this change on the equilibrium level of income? What is the new equilibrium level of income?
3. Calculate the budget surplus (BS).
4. Draw a diagram indicating equilibria in both part III (a) and part III(b).
5. Suppose the government decides to impose a proportional income tax (t) instead of lumpsum taxation such that t = 0.2. Using the information provided in part (III), calculate the equilibrium level of income and the multiplier in this model.
6. Calculate the budget surplus in the economy, BS.
7. Suppose that t increases to 0.25. What is the new equilibrium income? The new multiplier?
8. What is the value of the multiplier when t =1? Can you explain why?
9. Draw a diagram indicating equilibria in both part IV(a) and part IV(c).

Answer 1

Yd = Y-TA+TR
Y = C+I+G+NX
Y = 100 + 0.5(Y-25+50) + 50 + 100 + 30
0.5Y = 100+12.5+180
Y = 292.5/0.5 = 585

MPC = 0.5
MPS= 1-MPC = 0.5
Income multiplier = 1/0.5 = 2

TR = 100
Y = 100 + 0.5(Y-25+100) + 50 + 100 + 30
0.5Y = 100+37.5+180
Y = 635, this is the new equilibrium

change in equilibrium level of income = 50

surplus =TA - G - TR, surplus happens when tax receipts are higher than sum of government expenditure and transfers
TR= 25, surplus = 25 - 100 -25 = -100
TR= 100, surplus = 25 - 100 -100 = -175