Answer to Question #227357 in Macroeconomics for sileshi

Question

Consider a hypothetical economy characterized by the following behavioral equations.

IS                          LM

C=400-200r+0.2Y  Md=Y-1000r

I= 240-400r             Ms=800

G=200                     P=2

a) Show the impact of expansionary monetary policy which is an increase in tax by 50.

b) Show the impact of expansionary fiscal policy which is an increase in nominal money supply by 100.

c) Using balanced budget multiplier show the impact of an increase in government expenditure and tax by 50.

Answer 1

The national income(Y) is the market value of all goods and services produced in the economy in a given period. Real interest rate(r) is the cost of borrowing after taking into account inflation. 

The monetary and fiscal policy is used to stabilize the economy in the short run. In the monetary policy, the central bank changes the money supply and in the fiscal policy, the government changes its expenditure and taxes. 

The IS curve shows the relationship between interest rate and national income when the goods market is in equilibrium. The goods market is in equilibrium when income is equal to aggregate demand.

Aggregate demand shows the aggregate quantity demanded in the economy. It is the sum of consumption, investment and government expenditure.

The goods market is in equilibrium when national income is equal to aggregate demand. 

IS curve equation:

$Y=C+I+G\\Y=400-200r+0.2Y+240-400r+200\\Y-0.2Y=840-600r\\0.8Y=840-600r\\Y=1050-750r$

The LM curve shows the relationship between real interest rate and national income when the money market is in equilibrium. 

LM curve equation:

$Real \space money\space demand=Real\space money\space supply\\M_d=\frac{M_s}{P}\\Y-1000r=400\\Y=400+1000r$

Put the value of Y in IS curve.

$1050-750r=400+1000r\\1750r=650\\r=0.37\\Y=400+1000(0.37)\\=400+370\\=770$

a) When the government increases the taxes by 50, the disposable income of the people decreases which impacted the consumption expenditure in the economy. 

IS curve equation:

$Y=400-200r+0.2(Y-T)+240-400r+200\\Y=840-600r+0.2(Y-50)\\Y-0.2Y=840-600r-10\\0.8Y=830-600r\\Y=103.75-750r$

LM curve equation remains the same:

$Y=400+1000r\\103.75-750r=400+1000r\\1750r=637.5\\r=0.36\\Y=400+1000(0.360\\=400+360\\=760$

The increase in tax by 50 decreases the tax and decreases the national income by 10. 

b) When the nominal money supply increases by 100, the new nominal money supply is 900. The real money supply is 450.

$M_d=\frac{M_s}{P}\\Y-100r=450\\Y=450+1000r$

The IS equation remains the same: Y=1050−750r

$1050-750r=450+1000r\\1750r=600\\r=0.34\\Y=450+1000(0.34)\\=450+340\\=790$

The increase in real money supply causes an increase in income and decrease in real interest rate. 

c) In the balanced budget, the government finances its expenditure by increasing the taxes by the same amount. In this case, the government expenditure increases by 50, which mean a new government expenditure are 250 and taxes are 50.

The IS equation changes while the LM equation remains the same.

IS equation:

$Y=400-200r+0.2(Y-T)+240-400r+250\\Y=890-600r+0.2(Y-50)\\Y-0.2Y=890-600r-10\\0.8Y=880-600r\\Y=1100-750r\\$

LM equation: 

$Y=400+1000r\\1100-750r=400+1000r\\1750r=700\\r=0.4\\Y=400+1000(0.4)\\=400+400\\=800$

The increase in both government expenditure and taxes causes an increase in both real interest rates and national income.