Question

In an economy which has a national income identity as the following;

Y= C + I + G + NX

Where C = 1400 + 0.8 (Y-T), I = 1000-4000 r, G= 1450

T= 800 + 0.25 Y, NX= 400-0.1 Y-8 00 e

Where e= foreign currency/ domestic currency, and initially set at e = 0.75

The money demand function is Md = 0.60 Y -84000 r, and Money supply is set by the Central Bank at 660. All calculation runs off at the second digit of decimal.

a) Figure the equations and derive the IS and LM curves for the economy

IS :

LM :

b) What is the equilibrium level of GDP and the interest rate?

c) The government increases its expenditures by 450 to 1900. What is show the new equilibrium level of GDP and interest rate. What is the budget multiplier?

d) If there is a recessionary gap of 1200, how much government expenditure should be increased?

e) The Congress decides to cut tax by 200 and increase government spending by 200 instead. What is the new IS curve of a policy mixture of increasing government spending and tax cut.

Based on the new IS curve on budget expansion and tax cut, the Central Bank increase the money supply 8 % to 712.8 . What is the new equilibrium of interest rate and GDP.

Answer 1

a) The IS equation is denoted by Y = C+I+G+NX. We shall use above information to generate IS equation:

The LM relation is shown as:

This is LM relation.

(b) We first sub the expression for i from the LM relation into the IS relation to find equilibirum output Y.

We are provided e = 0.75

We now sub this value for Y into the LM relation to find the corresponding value for r:

(c) When government expenditure increases by 450, the IS equation changes in following way

Initial IS equation :

New IS equation Post Govt expenditure:

Then, new level of GDP and Interest rate would be: Solving IS first for new Y

Now using new Y in the LM equation to find new r:

The budget multiplier would be

In our case, using IS equation we find above relation as

Therefore, the budget multiplier would be 2. This means an increase in government spending by 1$ increases equilibirum level by 2. This means an increase in govt expenditure by 450 increased the equilibrium income by approximately 900.

(d) If there is recessionary gap of 1200, then as per budget multiplier or government multiplier, the government expenditure should increase by 600 (1200/2), so that by multiplier effect it becomes 1200 in the economy.

(e) The Congress decides to cut tax by 200 and increase government spending by 200 instead. Then the new IS curve of a policy mixture of increasing government spending and tax cut would be:

The impact of tax cut would be : (Earlier it was T = 800+0.25Y)

New government expenditure is : G = 1450+200 = 1650

Reconfiguring IS equation to include above changes:(We are using part (a) IS-LM equations.)

We are provided that now Central bank increases money supply by 8% to 712.8. The LM equation would be then

Solving for the new equilibirium interest rate and output. We shall use IS first to derive output value.

We still assume e = 0.75

Solving for the interest rate by using LM equation.

Thus, new equilibirium level of output and interest rate are 6546.03 and 3.82 respectively.