Answer to Question #221077 in Macroeconomics for Chris

Question

Given that in an economy, Given that in an economy, C = 102+0.7Y, I=150-100r, MS =300, Mt = 0.4Y, and Mz=125-200r where, Y= income, C= consumption, I= investment, MS= money supply, Mt= transactional-precautionary money demand, Mz= speculative money demand and r= interest rate. Calculate;
1. The equilibrium level of income and interest rate in this economy.
2. The level of C, I, Mt, and Mz when the economy is in equilibrium.

Now, assuming the economy is open with government (G) participation and external trade which is summarized as follows; export(X)= 100-0.10Y, import(M)=50, G=100, Taxes(T)= 100 and C, I, MS, Mt, and Mz the same as defined in (a) above.
Calculate;
1. The equilibrium income and interest rate in this new economy.
2. The level of C, I, Mt, and Mz when the economy is in equilibrium.
3. Assuming capital is perfectly mobile in this economy, graphically sketch the IS-LM-BOP frame work of this economy. Comment on the balance of payment situation in this economy.

Answer 1

A.

1.

c=102+0.7y

i=150-100R

Ms=300

Mt=0.4y

Mz=15-200r

IS curve is given by;

Y= AD=C+I

y=102+0.7y + 150-100R

Making Y the subject

y=840-333.33r (IS Curve)

Money market

LM is given by;

Md=Ms

Md= Mt+ Mz

Md= 0.4y+125-200r

Md=Ms

0.4y+125-200r=300

Solving for Y

y=437.5+500r (LM Curve)

At equilibrium IS=LM

840-333.33r= 437.5+500r

Solving for r

r^*= 0.48 (equilibrium interest rate)

substituting in y=840-333.33r

y^*= 680(equilibrium income)

2.

c=102+0.7y

but y=680

c=102+0.7x680

c=578

i=150-100r

but r=0.48

i=150-100x0.48

i=102

Mt=0.4y

but y=680

Mt= 0.4x680

Mt=272

Mz=125-200r

M=125-200x0.48

Mz=29

B.

1.

In the open market involving the foreign market

IS= y= c+i+g+t+(x-m)

y=102+0.7y+150+100+(100-0.10y-50)

Solving for y

y=1255-250r (IS Curve)

In the money market

LM is the same as the one we calculated above

LM=437.5 +500r

At equilibrium

IS=LM

1255-250r=437.5 +500r

SOLVING FOR r

r= 1.09 - equiliobrium rate of interest

Substituting r = 1.09 in y=1255-250r

y= 982.5equilibrium income

2.

c=102+0.7y

but y= 982.5

c= 102+0.7x982.5

c=789.75

i=150-100r

but r=1.09

i=150-100x1.09

i=41

Mt=0.4y

but y= 982.5

Mt= 0.4 x 982.5

Mt=393

Mz=125-200r

but r=1.09

Mz=125-200x1.09

Mz=-93

3.

The BOP becomes perfectly horizontal