Question

1. A closed economy is described by the following behavioral functions:

Private Consumption	C = 80 + 0.8YD
Private Investment	I = 180 – 10i
Public Expenditure	G = 200
Rate of Income Tax	t = 0.25
Transfers	TR = 25
Real Demand for Money	L = 0.48Y – 12i
Money Supply (in real terms, P=1)	M/P = 384
Full Employment Income	YP = 1200

a) Find the equilibrium level of income, the interest rate and the public budget balance.

b) The government wants to reach the full employment income using expansionary fiscal policy. Find the new level of public expenditure and the new equilibrium interest rate.

c) Alternatively, starting in the initial equilibrium (in part a), the central bank decides to achieve the full employment income using expansionary monetary policy. Given P=1, what is the real quantity of money needed to achieve this objective and what is the new interest rate in this case.

Answer 1

Given)-  Private consumption       C=80 + 0.8Y_D

Private Investment                      I = 180 – 10i

Public Expenditure                     G = 200

Rate of income Tax                    t = 0.25

Transfers                                     TR = 25

Real Demand for Money	L = 0.48Y – 12i
Money Supply (in real terms, P=1)	M/P = 384
Full Employment Income	YP = 1200

Ans)-

a) Goods Market equilibrium condition (IS Model)

Income = spending

Y = AD

Y = C + I + G

Put C,I and G function

Y = [80 + 0.8Y_D]+ [180 – 10i] + 200

Put disposable income Y_D = Y – tY + TR

Y_D = Y – 0.25Y + 25

Y_D = 0.75Y + 25

Hence,

Y = [80 + 0.8(0.75Y +25)] + 180 -10i +200

Y = 80 + 0.6Y + 20 + 180 -10i +200

Y – 0.6Y = 480 – 10i

0.4Y = 480 -10i

Y = 480/0.4 -10i/0.4

{Y = 1200 – 25i}----------------------------------IS equation

Money Market Equilibrium condition (LM Model)

Money Supply = Money Demand

M/P = L

384 = 0.48Y -12i

12i = 0.48Y -384

i = 0.48Y/12 -384/12

{i = 0.04Y – 32} ----------------------------------------LM equation

Put the value of ‘i’ from LM equation to IS equation

So, Y = 1200 – 25i

Y = 1200 – 25(0.04Y-32)

Y = 1200 – Y + 800

Y + Y = 2000

2y = 2000

[Y = 1,000]---------------------equilibrium level of output (Y)

Put Y = 1000 in LM equation

i = 0.04*1000 – 32

i = 40 -32

[i = 8]-------------------------------equilibrium level of interest rate (i=8%)

Now,

Public Budget balance = Tax – govt. expenditure - Transfers

Public Budget balance = tY – 200 – 25

                                          = 0.25*1000 -225

                                           = 250 – 225

                                           = 25

Hence the equilibrium level of income is Y = 1,000, equilibrium level of interest rate is i=8%, and the public budget balance is 25.

b) Govt. wants to reach full employment income i.e. Y_p = 1200, using expansionary fiscal policy then

From IS model-

We know the Fiscal Policy multiplier    

, b=10(responsiveness of change in Investment due to change in i)

h: 12 (responsiveness of change in speculative money demand due to change in i)

k: 0.48 (responsiveness of change in transaction demand due to change in Y)

c: 0.8 (MPC)

t: 0.25 (tax rate)

So,

Here, dY = Y_P – Y

dY = 1200-1000= 200 i.e. change in Y should be 200 to reach at full employment level.

Now we need to find dY = ?

Hence, to reach at full employment level of income Y_p = 1200, Govt. expenditure must increase by 160.

i.e. New Govt. expenditure level (G*) = 200 +160= 360.

Put Y = 1200 in LM equation to find new interest rate level

[i = 0.04×1200 – 32 = 16%]

c) If central bank wants to achieve full employment income using monetary policy then-

We know the monetary policy multiplier (with p=1)-

Put the values calculated above

Change in Y required i.e. dY = 200

So,

Hence, change in money supply required to reach full employment level is dM=192.

New level of money supply: (M = 384 + 192= 576) i.e. this much amount of money needed.