Question

Consider the economy of Wiknam. The consumption function is given by C = 250+ 0.6(Y-T). a. Government purchases and taxes are both 100. In the accompanying diagram, graph the IS curve for r ranging from 0 to 8 by dragging and dropping the end points to the correct locations b. The money supply M is 2,875 and the price level Pis 5. In the accompanying diagram, graph the LM curve for r ranging from 0 to 8 by dragging and dropping the end points to the correct locations The investment function is I = 100-20r. The money demand function is M Р =Y-20r.

Answer 1

Firstly, find the IS curve equation.

C=250+0.6(Y-T)

I=100-20r

Given that G=T=100

In goods market equilibrium,

Y=AD

Y=C+I+G

The above equation gives the IS curve.

Put r=0 to 8 and find the corresponding Y and plot them on the x-y axis as shown in figure 1 (blue color) in order to get the IS curve. The table given below shows the value of Y for different values of r.

Figure 1

b) Now, given that M/P=Y-20r

M=2,875

P=5

Find the LM equation

The above equation shows the LM curve

Put r=0 to 8 and find the corresponding Y and plot them as shown in figure 1 (red color) in order to get the LM curve.

c) In order to find the equilibrium interest rate and income, put IS=LM

Put the value of r in IS curve to find income

Y=689.28

Therefore, the equilibrium interest rate is 5.714% and equilibrium income is $689.28

d) Suppose the government purchases are increased from 100 to 150

G=150

Therefore, the new IS curve equation is given above. LM curve remains the same as before. In order to find the equilibrium income and interest rates, put new IS = LM

Put the value of r in the new IS equation in order to get the equilibrium income

Therefore, the new equilibrium interest rate is 7.5% and equilibrium income is $725

e) Now, the money supply has decreased from 2875 to 2500

New LM curve can be found out by:

M/P=Y-20r

The above equation gives the LM curve. IS curve remains the same.

In order to find the equilibrium income and interest rates, put original IS = new LM

975-50r=500+20r

r=6.79

Put the value of r in the new LM curve in order to find the equilibrium income

Y=500+20*6.79

Y=635.71

Therefore, the new equilibrium interest rate is 6.79% and equilibrium income is $635.71

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